PUZZLE CORNER ALLAN J. GOTTLIEB, '67
Major League Eternity
This being the first issue of a calen tive integer whose square root has a spades and the DA, take a club ruff with East dis dar year, we again offer a "yearly decimal expansion beginning with ten carding a diamond (best), and play the DK. Finally use a club for the coup and all the tricks. problem" in which you are to distinct digits? Now consider cube roots 2) After a diamond discard there is a repeating express small integers in terms of the instead of square roots. Finally consider triple squeeze against West. Discard the S9 on the digits of the new year (1,9,9, and 2) and ith roots for i = 4,5,... ,10. CK, take a heart finesse, the DA, a heart finesse, and the arithmetic operators. The problem is run all the hearts. This will be the position with 1 heart to play: formally stated in the "Problems" sec Speed Department North tion, and the solution to the 1991yearly * 2 problem is in the "Solutions" section. Mark Astolfi wants you to use Major League rules (with no rainouts) and K2 Problems name five ways a baseball game can go 76 on forever. West East Y199Z. Form as many as possible of the * K10 * 7654 integers from 1 to 100 using the digits 1, ¥ - Solutions 9, 9, and 2 exactly once each and the * QJ « 8 * j 10 * - operators +,-,x(multiplication),/ (divi Y1991. The following solution is from David South Brahm, who writes that most of it was worked out sion), and exponentiation. We desire * AQJ by computer, which ran through the 6 possible solutions containing the minimum « 4 number orderings, the 5 possible orders of opera * 5 number of operators; and, among solu tion, and the 7 possible operators (_, +, -, *, /,A, and tions having a given number of opera A-> in each of the 3 positions. * - tors, those using the digits in the order 1 = 1A99! 20=19+lA9 80 = (l+9)*(9-l) On the last heart West cannot discard a spade, so 1, 9, 9, and 2 are preferred. Parenthesis 2 = 1A99 + 1 27 = 19 + 9-1 81=91-9-1 3 = 1+9/9 + 1 28 = 19 + 9M 82 = 91-9*1 s/he discards a minor suit stopper while dummy may be used for grouping; they do not 7 = 9 + 9-11 29 = 19 + 9 + 1 83 = 1-9 + 91 discards C6. Now South cashes the DK and count asoperators. A leading minus 8 = 9-lA19 36 = (l+l)*(9+9) 88= 99-11 whichever minor suit card West has abandoned, sign does count as an operator. 9 = 99/11 38=19 + 19 89 = (l+9)*9-l squeezing West in spades and the other minor. 10 = 19-9*1 63 = 9*(9-l-l) 90 = 11*9-9 3) After a ruff South can set up the spades via a ruffing finesse and draw trumps. The play is: over- JAN 1. Our "first" problem is a comput 11 = 19-9+1 64 = (9-l)'(9-l) 91 = 1^9*91 12 = 11+9/9 70 = 9*9-11 92 = 1A9 + 91 ruff, SA, SQ (ruffing this or the 3rd round of spades er offering from Bob High. Write the 16 = 9 + 9-1-1 71=9*(9-1)-1 97 = 99-1-1 whenever West plays SK), heart finesse, draw first n numbers in alphabetical (dictio 17 = 1*9 + 9-1 72 = 91-19 98 = 1*99-1 trumps and claim. nary) orders as they are spelled out (i.e., 18 = 19-1A9 73 = l+9*(9-l) 99 = 1+99-1 19 = 19*1A9 79 = 9*9-1-1 100 = 1+99*1 A/S 2. Thomas Weiss wants you to find a crossword one, two, three,...one million,...). To puzzle using as few squares as possible but satisfy avoid ambiguity, use no "ands" or A/S 1. We begin with a bridge problem from Don ing: hyphens, so 837,301 would be written Boynton who needs to make 7 Hearts against any (1) All 26 letters of the English alphabet are used at "eight hundred thirty seven thousand defense with anopening lead of the Queen of least once each. Clubs. (2) No proper nouns, abbreviations, contractions, three hundred one". 1,897 is "one thou acronyms, or foreign words are used. North sand eight hundred ninety seven," not (3) All letters are used to form words both horizon * 2 tally and vertically. "eighteen hundred ninety seven." v 32 (4) Radial symmetry about the center is achieved, Define two functions, F(m,n) and G(m,n) « AK2 as is common in American crossword puzzles. as follows: F(m,n) is m th number in the * AK76543 I guess the winner is the following 7x7 solution alphabetical list of the first n numbers; West East from an anonymous reader who stayed at the G(m,w) is the position of the number m * K108 * 76543 Clarion Hotel in Cincinnati. » S v Q1087 in this list. (For given n, F and G are * QJ109 ♦ 876 inverses.) we ask: * QJ1098 * 2 (1) What is F(l,000,1,000,000)? What is South G(1,OOO, 1,000,000)? * AQJ9 (2) What is F(l,000,000, 1,000,000)? v AKJ964 What is G(1,000,000,1,000,000)? * 543 (3) For what numbers n is F(n,n) = G(n,n)=n? List the first dozen. Bart Bramley notes that "this is the famous Vaniva problem, composed in 1928 by the great JAN 2. Robert Bart offers the following player Sidney Lenz for a contest sponsored by Vaniva shaving cream.'' David Gross felt this was a extensions to an old problem from Nob. "nice problem with lots of blind alleys." His solu Yoshigahara. What is the smallest posi- tion is to win the CA (discard D3) and play the CK. East hasa choice of 1) spade discard, 2) diamond SEND PROBLEMS, SOLUTIONS. discard, 3) ruff. Each of these leads to a different AND COMMENTS TO ALLAN J. GOT ending. TLIEB, '67, THE COURANT INSTI 1) After a spade discard play for a trump coup. Play One might object to the use ofa British dictionary TUTE, NEW YORK UNIVERSITY, 251 a low TRUMP on the CK, play the SA and the SQ as representing a foreign language (or using two MERCER ST., NEW YORK, N.Y. 10012, (and a 3rd spade if West does notcover) ruffing out scrabble dictionaries as representing two foreign the SK. Then play the heart double finesse, run the OR TO: [email protected] Continued onPage MIT 42
TEOK0L0CT REVIEW JUT 55 . il>l W' Fti'H's "Cokinel^Powers,; '26;Gt, movedi1 to■\Gaiifdrnia.andtsooh became... ■ inypIvecl-iirUie'motidnnpicturej ; iHl: ■1p'ictiireieciui'pmerit:!;in1'1940; he' wasrcalleajntT.);t.ne:seiyice as capfeih in' th'e'llrrriy. Coips of. Engineers to te'ach;miiitary engjmemig atvQrego nState % J^lll|fc;!^fed ''■;• i -;'■■.'" '.' liianflei;he'established the 3rd. Air-?Fprce Camouflage School' ^.-and served,as'campuflage offi- ■'',. ce'rvfprahe. Army-Air Forces and ' "■■■..; -,as ..ehgineerlinspectm--generar ■i'*"1 ■■ To'r'tiieiWestern-Regipn. He ■^ "i' -',' .'.i'etii;ed;from theVArmyafter ■:; i.:■*■}. ' '■■ .;,-&.: 'service-in itorea. '' !■■' ■'.' ^^r':r'.O\: ^s:'..-,.■ v-o•;;■.. .v ■ :.----;-.- . . -..- Wfeii■hjs'tS}ifesporisjaictep.ted a'position as professor of ■a? , Englisn«at Arizoh'a'State'University,■■Colonel Powers s;Xenrolled|m:a:cp,urse^n beginning Russian. .He also stud- s.v ii;«iWlndlana;yhiversi(.y arfdfVvent pii tb'earn the first Arizona SlafeijUniversijy. ;e^er awarded. ..:'; i.i.e wwju&DfoHonmtyfrjfRussian;tfrcgu-. '■>.;' 1 .'^'lav.yvHvffri'iris and;'with'hisiwife, an English translation1- $>/;''of jfcpppular Russiaiv novel-, and has translated Russian. ;j t.eclmi'eal)articles!,Chpl6nei Powers has,been a-member of ijil^,Sp^i.ety|p|MotipnjRiGture Engineersjanjd^of the lius- i":V^jSn^ifp1riprary^'sJocietyipbbf.pslovc),'an(l'is^ / 'htf:itlv(>r'A'ri5riria..(S!tori|ei!"of;'the-'AnieHcan Association of ; in v-uJoiado and', .■■;'; ■»' ; .'."»;■,■ b pursue a' ', .ALUMNEWS, The Office of PUZZLE CORNER. Continued from Page MIT 55 William E. languages. Eugene Sard has a 9x9 solution but needed an unabridged dictionary for three Roesner words. The following 9x9 from the proposer used only Webster's Students Dictionary and Architect, Ltd. Random House College Dictionary. A Q U Architecture Planning & Continued from pageMTT7 R U N Interior Design K 1 0 the black astronaut who lost his life in the William E. Rooonor AIA '68 Gtallenger explosion. S T O 34 Hancock Ave. Newton Centre, MA 02159 •Stanley Rose, an MIT telethon volun 617-965-4330 teer in New York City for more than 15 ■ I 1 years, has been remarkably effective in F O B enlisting project support from his em A V O ployer. Bankers Trust, notably in provid ing a site and catering the callers' dinner. R E N Presidential Citations honor unusual service to the Institute and the Alumni/ae E N 0 body by its member organizations. This has been a blockbuster year, with citations A/S 3. Our last regular problem is from Nob. Storch going to six alumni/ae groups: Yoshigahara. Choose two digits excluding 0 •The Class of 1950 Student Aid Fund, and 1 and consider the set of numbers that con tain each of the two digits at least once. For Engineers established at the class's 25th Reunion, example, 4 and 8 gives 8848, 4884, 84 and now totals more than $2 million and is infinitely many others. Now consider the small MIT's largest class-supported financial est member of this set that is a multiple of the Engineers New York, NY aid fund. The fund has helped hundreds two original digits. Call this the LYM (least Architects 212-371-4675 Yoshigahara multiple). In our example the Surveyors of students and their families by provid LYM is 48; the LYM of 3 and 5 is 3555. Among Planners Jotlcho, NY ing scholarships and subsidizing loan in the 28 pairs of digits, 4 lead to sets that do not Geologists S16-338-4500 Soil Scientists terest. contain a multiple of the digits and, for these Mundpal Speclellsts Boston, HA •The MIT Club of Cape Cod, founded pairs, the LYM is not defined. For example) all Landscape Architects 617-783-0404 multiples of 2 and 5 end is 0 so are not in the Environmental in 1976, has demonstrated the best that set constructed from 2 and 5. The LYM of 2 and Consultants Providence, Rl clubs can offer their members, through an 4 is 24, which is the smallest of the LYMs. What 401-751-2235 annual directory, quarterly newsletter, is the largest? Apparently considerable searching, guided Ftorham Park, MJ Washington, DC broad range of speakers, and notable ef 201-822-2600 202-765-8433 by some heuristics such as "casting out nines," forts to reach out to all members of the was needed for this problem. Farrel Powsner Robblnsvllle, NJ MIT community in the region. found this question to be a good exercise for 609-259-0840 • In the three short years that it has been teaching problem solving to high school stu dents. Powsner's results were as follows. Manchester, NH in operation, the Young Alumni Steering 603-623-5544 Committee of Boston has done an exem 23-2232 46-4464 Rocky Hill, CT plary job of organizing events tailored to 24-24 (smallest) 47-44744 203-529-7727 the interests of graduates from the past 10 25 - none 48-48 26-2226 49-4,444,444,944 years. 27-2772 56 •none •Since Greg Turner '74 led a revival of 28-2888 57-5775 Richard Dattner the MIT Club of South Texas seven years 29-; 58-none ago, the club has grown steadily and has 34-3444 59-5,555,555,595 established a positive MIT presence in 35-3555 67-76776 Architect, P.C. 36-36 68-6888 Houston. 37-37737 69-6696 •The MIT Club of Boston was honored 38-3888 78-7,888,888 Providing a wide range ol Architectural Serv for its black-tie gala at the Boston Muse 39-3339 79 - 77777,779,779 (largest) ices, Including: Master Planning; Feasibility 45 - none 89-8,888,889,888 Studies; CADD; Construction Documents; In um of Fine Arts to welcome President terior Design; Construction Administration. Charles Vest and Becky Vest. The event Other Respondere Pro|ect Experience: Corporate Headquarters; attracted 450 guests. Office Buildings; Corporate Interiors; Com •The Productivity Commission "Road Responses have also been received from R. puter Facilities; Automated Warehouses; Show," a collaboration of the Alumni/ae Bart, D. Boynton, S. Bragg, B. Bromley, D. Manufacturing Buildings; Distribution Centers; Church N. Cooke J. Cronin, C. Dale, L Daley, J. Sports Facilities; Residential Projects. Association staff, MIT clubs in eight cities, Drumheller, S. Feldman, M. Fountain, J. and the MIT Industrial Liaison Program, Grossman, J. Harmse, W. Hartford, R. High, K. was honored for its success in bringing Kicsel, D. McMahon, A. Ornstein, D. Plass F. the Made in America report of the MIT Powsner, G. Ropes, K. Rosato, J. Rudy, D. Carnegie Hall Studios Savage, A. Tracht, and H. Zaremba, 154 West 57th Street Commission on Industrial Productivity to New York, NY 10019 more than 1,600 attendees coast to coast. Proposer's Solution to Speed Problem Tel.: 212-247-2660 The Road Show attracted national media Fax: 212-562-4857 attention and demonstrated MIT's con One can have a never-ending tie, constant scor Richard Dattner FAIA, '60 ing (without making 3 outs), an infinite series cern for the national agenda to a wide au of foul balls, an infinite series of unsuccessful dience.—Judith Norkin. □ pickoff attempts, or an eternal rundown. MIT 42 JANUARY 1992 entitled "Life as Technology: Representing, Deceased Douglas H. Martin, '50; August 1,1991; Allentown, Intervening, and Molecularizing" to the History The following deaths have been reported to the Penn. of Science Group at the University of California at Alumni/ae Association since the Review last went Dellieware R. Nelson, '51; August 25,1991; Berkeley on October 7 Professor Carl Kaysen to press: ' Cambridge, Mass. was one of three American participants in a semi Stanford A. Guthric, '15 Eugene Yu-Cheng Hsi, '54; July 28,1991; Baltimore, nar on "New Elites in Eastern Europe: Who Will John Homan, 'IS; August 9,1991; Indian Rocks Md. Lead the New Market Economy?" held at Central Beach, Fla. Bryant Gunsenhouser, '56; August 3,1991; European University Center in Prague, in August John H. Holton, '17; September 1,1991; Anderson, Ind. 1991. Kaysen is a coauthor with DACS Colleague Skanealeles, N.Y. Richard Lee Unruh, '56; July 26,1991; Long Beach, George Rathjens and Robert McNamara, former George F. Halfacre, '18; August 9,1991; Palmerton, Calif. U.S. Secretary of Defense, of "Nuclear Weapons Penn. John William Holland, '59; July 9,1991; La Jolla, After the Cold War," published in the current Edward A. Merrill, '22; August 15,1991; Tulsa, Calif. issue of Foreign Affairs. Kaysen has spent the fall Okla. Margaret LA. MacVicar, '65; September 30,1991; term at the Institute for Scientific Interchanges in Charles A. Nicholson, II, '22; July 21,1991; Laguna Cambridge, Mass. Turin, Italy.... Professor Kenneth Keniston has Niguel, Calif. H. Kent Bowden, '68; September 4,1991; Houston, become a member of the NASA Workshop on Robert Prescott, '22; August 1,1991; Wayne, N.J. Tex. Cultural Aspects of SET! (Search for Extra- Thomas F. Richardson, '23; September 5,1991 Percy G. Holton, '69; May 7,1991; Devon, England Terrestrial Intelligence). The workshop explores Robert C. Sprague, '23; September 27.1991; Derek G. Ryan, '69; January 3.1990; Elbirlle, West the "effects on humanity of detection of a signal Williamstown, Mass. Germany from an extraterrestrial civilization." NASA's Edwin D. Wilson, '23; May 21,1991; Everett, Wash. Robert B. Foster, '77; September 12,1991; Chicago, large-scale investigation will begin on Columbus Clarence Edwin Miller, '24; August 7,1991; III. Day, 1992. Hampton, Vir. John Dennett Urmston, 78; August 8,1991; Professor Leo Marx presented a talk entitled Paul E. Pihl, '24; July 18,1991; Charleston, S.C. Bolinas, Calif. "Environmental Degradation and the Ambiguous Maurice Grushky, '25; December 24,1988; Winston Henry Francis, '86; December 31,1989; Social Role of Science and Technology" at the con Charleston, S.C. Sao Paulo, Brazil ference on Social, Cultural, and Political John E McMaster, 76; September?, 1991; Thomas Rolf Petersen, '90; August 1,1991; Dimensions of the Environmental Crisis in the Warcham, Mass. Munich, Germany U.S. and U.S.S.R. in Moscow Professor William Crighton Sessions, '26; August 29,1991; Theodore Postol, '67, SM '72, PhD '76, attended Grosse Pointc Woods, Mich. the International Summer School on Science and Jack B. Peters, '27; September 10,1991; Lenox, Pugh-Roberts World Affairs in Moscow at the end of June. In Mass. August, he spoke on strategic nuclear weapons to Charles St. George Pope, '27; July 7,1991; Associates the National Security Fellows at Harvard Richmond, Vir. A Division of PA Consulting Croup, Inc. University. He was also a discussant at the Naval George Clahane, '28; August 29,1991; Acton, Mass. War College First Annual Force Planning Harry E. Shoemaker, '29; February 16,1991; Mansglng business Management Simulation Conference on "Strategy and Forces for a Temple City, Calif. complexity through Croup Changing Security Environment" in Newport, R.I. Philetus H. Holt, '30; August 30,1991; Summit N.J. computor simulation Edward B. Roberts, '57 Postol's op ed piece, "Whoops! Patriot Missile Willard A. Morairt, '30; July 23,1991; Mt. Vernon, technology. Alexander L. Pugh, 'S3 Sputters" appeared in the San Diego Tribune on Ohio Business Strategy Henry B. Well, '85 July 18 Institute Professor Walter Rosenblith Carlton E. Vanderwarker, '30; August 21,1991; • Quality, productivity, Kenneth Q. Cooper, '72 James M. Lynela, '71 participated in a symposium in Montreal on the Boca Grande, Fla. profits William J. Dalton, '80 early history of the International Brain Research Clement H. Hamblet, '31; August 13,1991; • R&D effectiveness Craig A. Stephens, '78 Organization (IBRO). He had been an officer of • New business plans Newark, Dela. nichard Park, Jr., '81 IBRO in the early 1960s, when IBRO's individual Murray J. Lalone, '31; Closter, N.J. Market Analysis Michael C. Miller, '84 membership amounted to several hundred. Now Alfred Ziegler, '31; September 10,1991; Palmer, • Market ft fleet cycles Thomas W. Mullen, '86 • New product liming IBRO plays the role of a world federation of near Mass. Maurice Glucksman, '85 Todd Stoblem, *75 ly 30,000 neuroscicntists and of the societies in Gerard M. Kincade, '33; June 20,1991; Pittsburgh. Project Management • "What II" manage Kim SMar Relchett, '88 which they are grouped. In June Rosenblith went Penn. ment aid L. Anagnostopoulos, '69 to Beijing as chair of the advisory panel to the Waldron S. MacDonald, '33; August 30,1991; • Delay ft disruption Carl G. Bespolka, '83 Chinese University Development Project to deliv Concord, Mass. claims Sharon A. Els, '88 er an evaluation report to Li Tieying, head of the James H. Burke, '34; September 19,1991; St. Simons • Competitors' bids Thierry Chevaltey, '91 State Education Ministry.... Professor Sherry Mftrit Bsmfofd* *91 Island, Ga. Management Training Turkle announced the arrival of a daughter, Stunner B. Sweetser, '34; August 11,1991; .41 William Unskey Way Rebecca Ellen Willard, in May. Farmington, Conn. Simulation Software: Cambridge, MA 02142 DYNAMO (617)884-8880 Carcn Addis, an STS graduate student, gave Florence J. Driscoll, '35; S. Easton, Mass. birth to a son, Gabriel, on August 15. On hand for John W. Aldrich, '37; August 25.1991; Woodbury, the event was her husband and fellow student, Conn. Antonio Botelho Patricia Bentley, gave birth Charles Frederick Healey, '37; August 1,1991; in May to a daughter, Kathryn Eric Jamesburg, N.J. Zwillineer & Kupferberg presented a paper, "The Bergey's Haskell R. Gordon, '38; September 17,1991; Manual and the Solidification of Bacterial Worcester, Mass. Assorial Taxonomy," at the International Conference for George E. Shea, '38; August 26,1991; Bedford, the History, Philosophy, and Social Study of Mass. Biology, July 10-14 at Northwestern University. Harold H. Butler, '39; May 2,1991; Nutley, N.J. Applied mathematicians He also attended a two-week course on "The Mortimer A. Schultz, '39; June 29,1991; Mashpec, History of Modern Evolutionary Thought" held at Mass. Principals: the Marine Biological Laboratory in Woods Hole Yuen N. Lee, '39; June 21,1991; San Francisco, Calif. Oanlel Zwtltlrtger, '78, PhD and sponsored in part by the Dibncr Institute for Earle D. Benson, '40; August 26,1991; Reading, Michael T. Strauss. '79, PhO '85 the History of Science Steven Rcber, '81, is Mass. the proud father of baby Charlotte, who arrived Augustus Peter Norton, '40; February 22,1991; last spring Jessica Wang married MIT Stafford, Vir. Applied mathematics Economics student Brian Sliker on August 23. George W. Clark, '41; August 9,1991; Topsfield, Business modeling Jessica and Brian met as office-mates in the STS Mass. Mathematical modeling students' office.... Cheng-lin Zhang has been William H. Yocotn, '42; August 10,1991; Process modeling awarded the Sir RunRun Shaw Fellowship. This Bethlehem, Penn. two-year award is funded by the Shaw Warren A. Hurley, '47; August 15,1990; Foundation in Hong Kong, and is earmarked for Hendcrsonville, N.C. support of students from the People's Republic of William Atkinson Schmidt, '48; August 19,1991; China who have "a bent towards science and Mansfield, Mass. management courses."—Phyllis Klein, STS John Elmer Dacey, '49; May 15,1991; Sarasota, Fla. 61 Highland Avenue Program, MIT, Rm. E51-128, Cambridge, MA Frank G. Lane, '49; September 3,1991; Middlebury, Arlington, MA 02174 (617) 646-6565 02139. VI. Kenneth R. Grcider, '50; July, 1990; Davis, Calif. TKCHNOLOGY REVIEW MIT 41 PUZZLE CORNER ALLAN J. GOTTLIEB, '67 Objet Dart This June is my class's 25th reunion F/M 2. John Prussing believes that the K(0,l) is the only solution besides K(1,2), unless and I was asked to write a page of following puzzle, which was actually on there is a bug in my program. K(0,3) obviously "Puzzle Corner" for the book they the 1989 Putnam exam, seems about doesn't work. Each corner square is accessible to only 2 are producing. In preparing for the col right for "Puzzle Corner." squares. Therefore, one of these squares must be umn I reread the introductions from the A dart hits a square dartboard. If any used to enter the corner, and the other to exit it. first seven years of "Puzzle Corner" and two points on the dartboard have the For K(3,4), diagonally opposite corners reach the I must confess that it was fun to escape same probability of being hit, what is same 2 squares; therefore it cannot tour the board. back to those earlier, more carefree the probability that the dart will land This leaves only K(l,4) and K (2,3). The program I wrote found a solution to K(l,2) days. I found some of my old words nearer to the center of the board than it in about 7 seconds on my XT clone. It eliminated touching, some boring, and occasionally does to an edge? K(2,3) in less than that. In fact, K(2,3) can be some were quite surprising. I guess we shown not to work quite easily. Starting at a8, the really do change. If any of you have F/M 3. Our last problem is from my possible first moves are to c5 or d6. Since the two little vignettes of your past life stored NYU colleague, Dennis Shasha, and can are equivalent, choose d6. If the second move is not to g8, g8 will be left with only one accesible away, I recommend that, when no one be found in his book, The Puzzling square, f5. It will be impossible to enter and exit it else is looking, you take some private Adventures of Dr. Ecco. later. Therefore, the second move must be to g8. time with your former self. You are given 20 coins. Some are fake The only possible third move is to f5. If the fourth and some are real. If a coin is real, it move is not to h7, then it will have only one entry square, f4. But if it is to h7, then b7 will have only Problems weighs between 11 and 11.1 grams. If it one entry square, c4. is fake, it weighs between 10.6 and 10.7 With two rapid results from the program, plus a F/M 1. Dave Wachsman sent us a hand grams. You are allowed 15 weighings test of the trivial K(0,l) and K(0,3) to further veri he played (as South) with his wife that on a scale (not a balance). You are to fy program operation, I launched it on K(l,4). It was reported in Truscott's column in determine which coins are real and finished after about 80 hours, having found no solution. the New York Times. which are fake. OCT 2. Gordon Rice wonders how many Pythag North Speed Department orean triangles you can find in which one of the 82 three sides is 1991. A72 Speedy Jim Landau wants to know why The following is from Jerry Grossman, who has secret plans involving this problem: Q75 the Kindom of Metrica chose to use a There are five Pythagorean triangles one of whose KQ942 long, flat piece of wood as their Royal sides is 1991: (10860,1991,11041), (1980,209,1991), Standard of Length. (180180,1991,180191), (1982040,1991,1982041), and West East (16320,1991,16441). The "easiest" way to learn this is by asking a computer algebra package to solve ♦ 973 ♦ 65 Solutions (in integers) x2+y2=19912 and u2+19912=v2. I ¥ J865 ¥10 4 asked Maple and it gave me these answers. Here OCT1. We start with a chess problem (which may ♦ KJ1032 ♦ 984 is how to do it more or less by hand: well be a computer problem) from Victor Barocas. ♦ J ♦ A108 653 Since 1991=11M81, we can look for three kinds It is well known that a knight can tour the chess of solutions: primitive solutions (i.e., no common board, touching each square once and only once, factor to the three sides) in which one side is 1991, South and beginning and ending on the same square. solutions in which one side is 11 (and then multi Consider now the generalized knight K(m,n), m < ♦ AKQJ104 ply all sides by 181 to obtain the desired triangle), n, which moves m spaces along one axis of the ¥ KQ93 and solutions in which one side is 161 (then multi board and n spaces along the other (the normal ♦ A6 ply by 11). knight is K(l,2); also see diagram). For what val The fundamental fact we need to use is that all ♦ 7 ues of m and n can the knight tour the board? primitive triangles are of the form (2mn, m2-n2, nA-n2), where m and n are relatively prime posi Both sides were vulnerable. The bid tive integers. ding: • • Let's start with the solutions in which one side South West North East • • is 11. Clearly 2mn cannot equal 11, nor can m2+n2. 1♦ Pass 2 * Pass So the only possibility here is that m=6 and n=5, giving us the triangle (60,11,61), and hence the 3* Pass 3N.T. Pass K solution to the original problem (60,ll,61)*181= 4 ¥ Pass 4 N.T. Pass (10860,1991,11041). 6 * Pass Pass Pass Next we look for solutions in which one side is • • 181. Again we cannot have 181=2mn, but we can How does Mr. Wachsman bring home • • have 181=m2+n2, with m=10 and n=9 (this is the only way). This gives a triangle (180,19,181), the slam after West leads the dub jack? Moves available to K<2,3) at position e4. yielding the second solution (1980,209,1991). The following solution is from Ken Kiesel: We can also have 181=m2-n2, only by letting Each time the knight moves one space in either SEND PROBLEMS, SOLUTIONS, m=91 and n=90. This gives us the triangle direction, it,moves to a square of the opposite AND COMMENTS TO ALLAN]. GOT (16380,181,16381), and hence our third solution color. Therefore, m + n must be odd, or the knight TLIEB, '67, THE COURANT INSTI (180180,1991,180191). can reach only squares of one color. TUTE, NEW YORK UNIVERSITY, 251 Finally we look for primitive solutions with one A knight on one of the four center squares can MERCER ST., NEW YORK N.Y. 10012, side being 1991. Again, 1991 is not 2mn. A com move a maximum distance of 4,4. Thus, the possi OR TO: [email protected] puter search shows that 1991 cannot equal m2+n2. ble solutions are 0,1 0,3 1,2 1,4 2,3 and 3,4. Continued on Page MET 38 TECHNOLOGY REVIEW MIT 39 Symposium on Kids and Computers" in late Henry D. Addison, '30; October 10,1991; PUZZLE CORNER. September. She delivered the keynote address for Northampton, Mass. the Conference on Cultural Issues in Robert A. Lytle, '30; June 14,1991; Grosse Point, Psychoanalytic Theory in New York in early Mich. Continued from Page MIT 39 October.... Jessica Wang and Bruce Bimber, STS Watson E. Slabaugh, '30; August 31,1991; If 1991=m2-n2=(m+n)(m-n), then cither we graduate students, shared the first Siegel Prize for Mansfield, Ohio have m+n=1991, with m-n=l; or we have their essay on the relationship of science and tech D. Malcolm Fleming, '33; August 12,1991; m+n=181 with m-n=ll. This gives m=996, nology to political events in the U.S. The prize Rockvillc Centre, N.Y. n=995 in the first case; m=96, n=85 in the sec was established in memory of Benjamin M. Siegel, Charles N. Debes, '35; August 31,1991; Rockford, ond. The resulting triangles arc our fourth '38, PhD '40, a pioneer in electron microscopy and 111. and fifth solutions: (1982040,1991,1982041) and (16320,1991,16441). until his death in 1990, professor emeritus of Joseph K. Racs, '35; August 3,1991; Las Vegas, applied engineering and physics at Cornell. Nev. Wang's essay recounted the security problems of Albert J. Del Favero, '36; September 18,1991; OCT 3. That famous riverboat gambler. Bob the scientist E.U. Condon during the loyalty Vista, Calif. High, was inspired by 1989 JUL 5 to ask a investigations of the McCarthy period. Bimber's O. William Muckenhim, '37; September 2,1991; two-part question about shuffling cards. First, essay dealt with the development, philosophy, Toledo, Ohio in a shuffled deck, what is the average and politics of the Office of Technology Robert D. Williams, '37; September 17,1991; Lake (expected) number of cards occupying their Assessment Barbara Masl, '86 (II), SM '88. Helen, Fla. original position? (This is to ask, for n = 52, Wade Roush, and Ken White presented papers Robert R. Chase, '39; January 12,1991; Austin, what is the average number of fixed points of on "Boundaries and Paradigms in Artificial Tex. a permutation of n things.) Second, which is Intelligence Research" at the 4S meeting Joseph W. Harrison, '39; October 14,1991; New more likely in a random shuffle (permutation) November 15 at the Cambridge Center London, N.H. of n things: exactly one fixed point, or exactly none? Marriott.—Phyllis Klein, STS Program, MIT, Rm. Charles A. Lawrence, '39; July 12,1991; Seattle, E51-128, Cambridge, MA 02139. Wash. Gordon Rice has a fine analytic proof, a Edward A. Ruckner, '41; September 12,1991; copy of which can be obtained from Faith Annapolis, Md. Hruby at Technology Review. Curiously, Rice Deceased David G. Edwards, '42; December 29,1990; was in the process of formulating a similar Pacific Grove, Calif. problem when he read OCT 3. The following Anthony P. Batbato, '44; July 17,1991; Kettering, shorter solution is from John Chandler, who The following deaths have been reported to the Ohio believes he might be a 25-year veteran as a reader of "Puzzle Corner." Alumni/ae Association since the Review last went Warren H. Howard, '44; September 29,1991; to press: Sunapce, N.H. Consider any specific card. After a random G. Hobart Stebbins, '17; September 26,1991; Louis H. Roddls, Jr., '44; September 15,1991; izing shuffle, its chance of being in its original Bellevue, Wash. Charleston, S.C. position is simply 1/52. Obviously, the a pos Henry R. Lacey, '18; March 13,1991; Melbourne, Henry F. Lloyd, '46; June 12,1991; St. Augustine, teriori probability of a second card being in Fla. Ha. 'its* original position will depend on the actu Webster W. Frymoyer, '21; October 5,1991; Wilton M. Fraser, '47; February 14,1991; Naples, al position of the first card. Still, there is no Arlington Heights, 111. Fla. preferred treatment of any of the cards, so the Eastman Smith, 72; September 18,1991; C. Gregory Bassett, Jr., '48; September 25,1991; overall expectation of cards remaining in Mountain Home, Ark. Hilton Head Island, S.C. position after the shuffle must be just 52 x Richard H. Frazier, '23; October 24,1991; Aubert L. Mowry, '48; March 16,1991; 1/52 = 1. For n « 52, this is easily proven by Winchester, Mass. Northridge, Calif. enumeration of all the permutations of n George H. Fuller, '25; May 30,1991; Colonia, NJ. Warren W. Houghton, '49; October 20,1991; things. Moreover, it is simple to write down Hyman Katz, '25; January 6,1987; North Quincy, Manchester, Mass. recursion formulas for the count of permuta Mass. Philip A. Lynn, '49; October 29,1991; Reading, tions with a given number of fixed points in Seward S. Merrell, '25; October 5,1991; Saint Mass. terms of the counts for smaller n. For exam Petersburg, Fla. William B. Martz, '50; May 2,1991; Winchester, ple, N(n,l) = N(n-l,0) » n, N(n,2) = N(n-2,0) • W. Alan Williamson, '26; September 19,1991 Mass. n * (n-1) / 2, and so on. The table begins: Marion E. Knowles, '27; September 18,1991; Douglas Porter, '50; June 10,1991; Watertown, n= 012345 6 7 Akron, Ohio Mass. f=0 1 0 1 2 9 44 265 1854 Ralph W. Stober, '27; October 1,1991; Newton Morgan L Foster, '51; January 11,1990; 1 1 0 3 8 45 264 1855 Highlands, Mass. Meadville, Pa. 2 1 0 6 20 135 924 Howard S. Root, '28; September 24,1991; Peler Bishop, '54; September 29,1991; Falmouth, 3 1 0 10 40 315 Harrington Sound, Bermuda Maine 4 1 0 15 70 Francisco Torras, '54; October 3,1991; Fairfield, 5 1 0 21 Conn. 6 1 0 Joseph A. Kissinger, Jr., '55; June 1,1990; La 7 1 Habra, Va. This suggests a further formula: N(n,0) => J. William A. Tyler, '55; February 1,1990; N(n,l) + (-l)n, and that can, in fact, be proved George A. Monroe, Ohio by induction. The answer to the second ques John A. Welsh, '55; September 26,1991; tion is, thus, that exactly one fixed point is Roman & Richardson, Tex. (slightly) more probable if n is odd and exact Herbert Curt Burrowes, Jr., '56; October 1,1991; ly none if n is even. Associates Inc. Concord, Mass. Stanley L Lopata, '56; October 9,1991; Natick, Better Late Than Never Mass. OCT SD. Dan Drucker notes a typo: S should Architecture, Planning, Oeorrjo A. Roman, Charles V. Brown, '58; July 27,1991; Bridge of bc(D-1)/2not(D+l)/Z Interior Doslgn A.I.A. -SS Allan, Stirling, Scotland Marvin H. Cantor, '59; May 16,1991; Rockville, Institutions! Donald W. Mills, '84 Other Responders Md. Commercial Industrial One Gateway Center Irving Levinson, '61; February 26,1991; Silver Responses have also been received from Residential Newton, MA 021SS Spring, Md. Matthew Fountain, Coe Wadelin, Mayer Site Evaluation (617) 332-5427 Frederik O. Jeppesen. '64; April 23,1991; Wantman, Frank Carbin, Winslow Hartford, Land Uso Planning Denmark Master Planning John Woolston, Eric Lund, Jim Landau, Ken Elsie P. Arnold, '65, February 25,1991; Richmond, Programming Rosato, Steven Feldman, Rolph Person, Interior Space Ontario William Waite, Ronnie Haige, Eugene Sard, Planning George T. Onega, 70; March 23,1990; Slidell, La. Max Hailperin, Warren Jasper, Scott Colleges Ronald G. Jackson, 71; June 1,1991; Pytnble, Berhenblit, Avi Omstein, Thomas Lewis, Alan Hospitals New South Wales, Australia Friot. Medical Buildings Daniel R. Siegel, '83; October 20,1991; Wilmette, OHIca Buildings. m. Apartments Proposer's Solution to Speed Problem Condominiums Peter L. Armstrong, '64; August 27,1991; Waban, Mass. Because a plank's constant. MIT 58 FEBRUARY/MARCH 1992 chips. Sieve and Lesli Oaklander have set their .. Margaret O. Meredith, Stephen D. Nelson, and UNESCO in Paris. She is a program specialist wedding date for May 24,1992 at the Boca Raton Albert H. Teich, '64 (VIII), PhD '69, are the edi responsible for the design and execution of Hotel and resort in Florida Edward Wong, SM tors of AAAS Science and Technology Policy UNESCO's programs in nutrition, health, and '91, has a new position as staff engineer at the Yearbook 1991 (AAAS, 1991). According to the home economics education, including the devel Southern California Gas Co.—Fay Wallslrom, book jacket, "The editors have assembled a opment of training and instructional materials for Management of Technology Program, MIT Rm. unique collection of informed discussions of the formal and non-formal education programs. She E56-304, Cambridge, MA 02139. major science and technology policy issues of is also responsible for the supervision and man 1990-91. Topics range from the financial health of agement of country field projects in nutrition, academic science to the state of the art in measur health, and home economics. She is responsible AERONAUTICS AND ing payoffs from research to fraud and miscon for interagency cooperation in nutrition and XVI ASTRONAUTICS duct in science." health and is the representative to the U.N. Administration Committee on Coordination and From Oslo, Norway, Tore Christiansen, SM '82, Subcommittee on Nutrition. She is editor of the reports: "After nine years of working for Det UNESCO Nutrition Education Series The Norske Veritas ship classification society, I have XVIII MATHEMATICS Alumni/ae Association has been notified that returned to student life at Stanford University Elsie P. Arnold, SM '65, of Richmond, Ontario, (oops!) to pursue a PhD in civil engineering (oops From Urbana, III., Douglas B. West, PhD 78, died on February 25,1991. She was employed in again!). My studies will be in the area of construc writes: "I have been promoted to a full professor Canada's Health and Welfare Toxicology tion management, with thesis work on application ship in the Mathematics Department at the Evaluation Division. There was no further infor of communication theory and information engi University of Illinois, effective August 1991."... mation provided. neering to the organization and management of Bob Leonard, SM '57, sends us a clip from the San large multi-functional design teams."... Byron K. Diego Business Journal. The article details the Lichtcnberg, SM 75, ScD '79, writes: "I'm in the takeover of Ticketron by Ticketmaster, the Los final stages of training for my second space flight Angeles-based ticketing firm run by Leonard. The XXI HUMANITIES scheduled for March 1992. Our crew of seven will company's 1991 revenues are projected at more be conducting experiments investigating the than $1 billion, up from $650 million in 1990. Thomas S. Kuhn, professor emeritus of philoso upper atmosphere, the impact of solar energy on Leonard said Ticketmaster was able to take the phy at MIT, has been awarded an honorary the Earth, and natural and artificial auroras."... lead in the ticketing business with superior com degree conferred at a special convocation at the Marc P. Genain, SM 75, is working on the opera puter systems, aggressive marketing, and its University of Chicago last September in celebra tional and ergonomic design of the Channel introduction of telephone sales. Ticketron fol tion of the university's centennial. Kuhn was rec Tunnel control centers. The operations project is lowed a few years later, but Leonard said he ognized for his writings and for "his ground slated to be completed in August 1993 From believes it was too late to stage a comeback breaking contributions to understanding the ways Concord, Mass., Edward B. Bokhour, SM '88, The Mathematical Association of America held in which various scientific views are supported reports: "My spaceflight experiment flew success elections last September and has two MIT alumni and discounted over time."... Jeanne Bamberger, fully aboard STS-48 Discovery this past September. on board. Donald L. Kreider, PhD '59, professor professor of music at MIT, has recently completed I was hardware development manager at Payload of mathematics and computer science at The Mind Behind the Musical Ear: How Children Systems for the MODE experiment, under con Dartmouth College will be the Association's 45th Develop Musical Intelligence (Harvard University tract to M1T-SERC. MODE was structural and president. Kreider will serve a one-year term as Press, 1991). According to the book's jacket. "By fluid dynamics."... From Big Bear Lake, Calif., president elect followed by a two-year term as empasizing the idea that each 'hearing' of musical Creighton Cook, SM '54, sends word that he con president, ending with a one-year term as past- composition is a 'performance,' one among many tinues as an aerospace consultant in the Southern president. Sharon Cutler Ross, '65, has been elect possible hearings, Bamberger suggests that there California area Charles Vehlow, SM '77, ed the Association's second VP. Ross teaches are different ways of constructing meaning and writes: "I have been selected as the Longbow mathematics at DeKalb College in Atlanta, Ga. that the processes of perception and conceptual Apache Program Director at McDonnell Douglas Kreider has been an MAA member for 31 years ization are reciprocal. Helicopter Co. located in Mesa, Ariz."... In the and Ross has been a member for 21. November/December 1991 issue we incorrectly reported that John Kenneth HavUand, PhD '61, NUCLEAR APPLIED BIOLOGICAL retired in 1969. He retired from the University of XXII ENGINEERING Virginia's Department of Mechanical and XX SCIENCES Aerospace Engineering as professor emeritus on Martin Zimmennann, SM '89, sends word: "I am June 1,1991. Jorge L. Sintes, PhD 78, writes: "I am currently currently working as a research associate at the George T. Onega, SM 70, of Slidell, La., died on associate director of Advanced Technology-Oral, Institute of Robotics at the ETH in Zurich, March 23,1990. Upon graduation from MIT he at Colgate Palmolive Co.'s Technology Center in Switzerland, where I am in charge of the design joined the Bell Aerospace Co. as an engineer Piscataway, in New Jersey. I am manager of a for the control system of a combined wheeled and where he spent his entire professional career department in charge of development of new legged robot with insect-like intelligence. Besides, working on engineering applications for the products and technologies for professional use.".. I am heavily involved in teaching students and aerospace and marine fields, rising to the position . Aaron L. Brody, '51, PhD '57, is now the manag working on a new course on 'Designing Smart of director of advanced design. His work at ing director and partner of Rubbright Brody, Inc. Mechatronic Products.' Most important, my wife, Textron Marine Systems (formerly Bell According to a compa Petra, and I are the proud parents of our first Aerospace) involved surface effect ships for the ny news release, "The daughter, Pia Andrea."... From San Jose, Calif., U.S. government The Alumni/ae Association countless honors W. H. D'Ardenne, PhD '64, writes: "I have been has been notifed that Captain Henry F. Lloyd, SM [Brody] has received elected chair of the Nuclear Power Plant '46, USN (ret.), of St. Augustine, Fla., died of a from his peers in the Standards Committee of the American Nuclear heart attack on June 12,1991. There was no fur Institute of Food Society."... Joseph W. Synan, SM '69, NUE '69, is ther information provided. Technologists and founder and president of Leadingwell Associates, Institute of Packaging a leadership and team excellence consulting prac Professionals attest to tice in Houston H. Keith Roe, SM 74, NUE his accomplishments, 74, has added the title of chair to those of presi XVII POLITICAL SCIENCE ability, and integrity. dent, CEO, of Burns & Roe, Inc., in Oradcll, N.J. Brody brings to us over Franklin D. Margiotta, PhD 79, writes that as 20 years of hands-on president and publisher of Brassey's (U.S.), Inc., industry managerial PROGRAM IN SCIENCE, he has "just published President Bush's National experience and more STS TECHNOLOGY & SOCIETY Security Strategy of the U.S. 1991-1992. As a press A.L. Brody than 10 years of con that supports the competition of ideas, Brassey's sulting." The company will conduct market and Professor Leo Marx gave the Lowe Lecture at will soon publish a book developed by another business research, strategic planning, venture and Macalester College in Saint Paul, Minn, in mid- MIT graduate. Representative Los Aspin, PhD 79 acquisition analysis, and opportunity identifica October. The talk was entitled "On the Grace of (XIV), chair of the House Armed Services tion, emphasizing food and food packaging. Nature: The Religious Aspect of Literary Committee, entitled Defense for a New Era: Lessons Brody was technologist on the development of Pastoralism in America."... Professor Eugene of the Persian Gulf War."... Vann H. Van Diepen, microwave food heating and is the inventor of Skolntkoff, '49 (VI), SM '50 (VI), PhD '65 (XVII), SM '83,,reports from Arlington. Va.: "I have been controlled atmosphere food preservation as well reported to the October MIT Faculty meeting on named director of the Office of Weapons as one of the aseptic packaging systems. the study he chaired last year on the subject of Proliferation Policy in the Bureau of Politico- From 1981 to the present, Susan Kathleen Alfano MITs international relationships.... Professor Military Affairs in the U.S. Department of State.". Van Der Vynckt, SM '73, has been woking with Sherry Turkle was a featured speaker at the "MIT TECHNOLOGY REVIEW MIT 37 PUZZLE CORNER ALLAN J. GOTTLIEB, '67 Fiddling with the Roof Mary Lindenberg reports that her furniture. The robots are expensive, so sible contract of 6NT. However, West leads the husband Martin, when inter they bought only seven of them, assum spade 4, which East wins with the ace and returns the spade queen. How can South now make his viewing high school students ing that no more then seven workers contract assuming best defense from this point applying to MIT, always encourages would be needing robots simultaneous onward? them to take advantage of sailing the ly. Each robot can serve any number of North Tech dinghies. Mary usually shows masters (though only one at a time), but A 5 them "Puzzle Corner" and points out an in order to respond to voice commands, ¥ AK8 interesting problem. Martin includes a time-consuming and expensive train * A83 comments in his report if they solve the ing session is needed between each * AJ10754 problem. robot and each master it will serve. To It has been at least a year since I speci avoid waste, the workers want to con West East fied the size of the backlogs for the vari duct as few training sessions as possi * 108743 A AQ9 ous kinds of problems that are printed. ble. Determine what training sessions ¥ 7 ¥ J6542 Let me do so now. When the size of the should be conducted to achieve these « Q10 9 * J652 column was reduced and the number of aims. * Q832 * 6 regular and speed problems per issue halved, the backlog had an instanta APR 3. Liet Van Phan wants you to find South neous doubling (measured in months, angle DAC without using either * KJ62 not letters). I now have nearly 2 years Pythagoras's theorem or trigonometry. ¥ Q1093 worth of speed problems and even more Measured in degrees, angles B and C » K74 for regular problems. However, I have are each 90 and angle D is 75 and CB is * K9 very few of the special (chess, bridge, half as long as DC. computer, go) problems. So if you have Thc following solution is from Jonathan Hardis. any of these special problems, send B William Tripp remarks that the problem is an example of a guard squeeze. them in. If not, I may soon just merge After the ace of spades is played and East leads the special with the regular problems IT the queen, it's easy to count 9 tricks: and print three from the combined list *-K,J each issue instead of the current 1 spe ¥-A,K,Q cial, 2 regular policy. ♦ -A,K *-A, K Problems The problem is to develop three more. South cov ers the queen of spades with his king, and dis cards the diamond 8 (not a club, not the 3!) in APR 1. A wild one from Jorgen Harmse. dummy. South next leads the club 9 from his White is to move and mate in 12. Speed Department hand. If West plays low (best defense). South overtakes with the 10, which becomes the first R Geoff Landis notes that Allen, Beth, and extra trick. If West plays the queen. South over B Chandra built houses with identical takes with the ace and dummy's clubs provide all three extra tricks. planforms, but decided on different roof South next leads the heart 8 from the board. If designs as shown below. The pitch of East plays the jack. South overtakes with the P the roofs are identical. Which has the queen and the 10 of hearts becomes the second p P P P greatest roof surface area and which the extra trick. If East plays low. South plays the 3 least? and the 8 becomes the second extra trick. At this R P P point. West's hand looks like this: 4-10 xx P K B K ♦ -Qxx *-Qxx APR 2. Jerry Grossman needs help South cashes the ace and king of hearts, training his robots. Ten workers in a returns to his hand with the king of certain high-tech office have purchased clubs, and cashes the queen or 10 of a fleet of voice-activated robots to help hearts. West must find three discards for the hearts. (1) If he discards a club, the them with various tasks, such as getting club jack becomes the third extra trick. coffee, delivering mail, and carrying Both (2) If he discards two spades, South's fourth spade becomes the third extra Allen SEND PROBLEMS, SOLUTIONS, trick. (3) He discards at least two dia AND COMMENTS TO ALLAN]. COT- monds. (East protects the diamond jack.) TUEB, '67, THE COURANT INSTI Solutions South plays accordingly: (1) On the fourth heart, TUTE, NEW YORK UNIVERSITY, 251 discard the diamond 3, cross to dummy with the diamond ace, and cash the ace and jack of clubs, MERCER ST.. NEW YORK. N.Y. 10012. N/D 1. We begin with a bridge problem from OR TO: [email protected] Winslow Hartford in which South is in an impos- Continued on Page MIT 45 lUX'STRATIONS: DAVID HRIBV TECHNOLOGY REY1EV MIT 47 ryaircraft; instrumentation andcontrqi; tsi-im'd'Uup'^jni'ng'an asspciatei.pVofgssbr■■ :^imaeiV;inautical ehgineejir&and^ijpr^ehgineejir&and^ijpr jf^ett-leaderf^ld iin theh ihtti''instmrnehtatiqiV:.:;. ^'laboratory. ..■-.-■-'. '„'■'.;.■;.■,;.'' ' '■:'■". ■'■■■■'/' i,' ;Div.Seamans left MIT^tq \jtiirvR&Vias v': chief-ungiri'e'er i'ii;airlVornetsystenis,;.; >'i iillhi{thtl :jft>19(iO/he wenrtoNASA,s;V ^;ii|sbcjat'e:and;the'ivas deputy"admjn-- tetstjWoii'Avitlv all ^program's;, including t^giir;h\i\jK1t|dd^ eturn-,; 3^ |^gftp;MIT^bneflyjn.Uie.jlate;sixties,:;:;.1;^;,.... v pKf3i\yent;backt:o Washington'in 1&6& ;;';;',-■'_ .//■// Ji^secir^tary'pfvthe'Air-Fprvv '»1d^' '^frtf.-'fi ■ ■ ^.gub^eflliently/^iyeda^presiderit^ } . / {iJof,N^tipnal'Academy-ofEngineering.:: !•:•:* t.t'SETO's p^Md Head'of.the EnergyyResource and '•SS ■v'I)eyelopmentAdininistration,.which '■ "'.lhter'becaine the:Departihent of.,': •. •;. EnergjvIn.1977, he'again returned ', '" ' toMIT as the Hen'iy Liiee/professor;. ';■ of:eii\nionmentand'p.ublic'.policy;and ■; sei'vecj'as'itlie' deaii'-prthe^ School of.':.,' mm ^'En'giiieeririg from^ay^rioai: Since:':'\t J '.': ^retiring in 1984, lie has-been asenior.. [ lecturer ih:aerbnaut;icsr. Dr. aiid Mrs; ';: 'Seainans :\vere;marrie*d in 1942;tthey,;;; '■■■: liave■ five'i'Ghildrervand.eleveivVl .,'■v,"vy ^gh''''V;'' '' ' ^$' ^GIFTOF ;CApiTAL:;The Robbff4i.: £# Sl^arnansi; Jn;,Life- Estate F\irid'anc}Hl>e';;- -f- &;-A-poll6, Program ^nd^esMilisKithcj^ It 1 ( iUUi • IN (Of W*1l, 1W1 Si ire w m SsSSBiWRSK imm^ 'fi/.f-SF m ^5 ■"*3 id J &4 ssfr^^flflg^igm™ PUZZLE CORNER Continued from Page MIT 47 boundary equation of a circle in an x-y plane, home, that the bear is white because the man's (x+l)*+(y+l)2=4-(z+l)*, with center P(-1, -1) and home is at the North Pole and the bear is a polar pitching the diamond and spade losers. (2) On radius PA+(4-(z+l)2)"/'. the fourth heart, discard a low club, bear. Sackheim wonders if there is any other cash the spade jack and 6, discarding two low place on earth where a person can go a mile clubs, cash the diamond king, cross to dummy south, then a mile west, then a mile north and with the diamond ace, and take the ace of clubs, be back at the starting point? pitching the diamond loser. (3) On the fourth The answer is clearly yes, there are an infinite heart, discard a low club, play the diamond 4 to number of solutions near the South Pole. Several dummy's diamond ace, pitch the spade 6 on readers pointed out that no bears will be found. dummy's ace of clubs, then lead back the (well The following solution is from Jack Bross: preserved) three of diamonds, finessing East's There are an infinite number of latitudes from jack. which one may go 1 mile south, 1 mile west, 1 mile north, and find oneself back where one N/D 2. Matthew Fountain wants to know how started: alt of them are slightly more than a mile large is the volume that lies within two inches away from the South Pole (accumulating on the of all the corners of a two-inch cube. All the vol circle 1 mile from the pole). The idea is that if ume must lie within two inches of all the cor going one mile south brings you near the pole, ners. west will circle around the pole several times. John Salmon notes that this problem was For any n, we can find a distance so that one solved in his thesis, which I happen to know mile wraps exactly n times around the pole. involves a very sophisticated solution technique Then, north will take us back to where we start for hierarchical N-body problems. Indeed, the ed. The actual values depend on one's assump required formula is actually a numbered equa tion about the curvature of the earth near the The complete shaded area of interest is also pole, but of course the earth is fairly flat at a dis tion (6.8). The solution below is from Eucene bounded by the lines x=0 and y=0. Other key Sard: tance of one mile, so they are well approximated dimensions are PB=OB=1, 0P=2"', and 0A=AB It is convenient to use a rectangular coordinate by 1+1/2idi miles. -0B=(3-(z+l)')>/M. From the law of cosines, system with x-, y-, and z-axes parallel to the angleO= arccos (O+(3-(z+l)*)"/2)/(2(4. Other Responders cube faces, and whose origin is at the center of the Nature Conservancy and the objective is to a safety systems engineer Mark Roberts, SM Lily Kay presented a paper on the technological improve the management of natural resources '90, has been in Washington, D.C., for a year now, roots of early molecular biology at the 1991 4S throughout Central America while promoting sus working at the Congressional Office of meeting. She is spending the spring term at the tainable development projects. PACA is working Technology Assessment. He has found a great Max Planck Institute for Physical Chemistry in in Belize, Guatemala, Honduras, El Salvador, number of TPP alumni/ae at OTA. He is currently Gottingen Professor emeritus Leo Marx gave Nicaragua, and Costa Rica. The project consists of working on a study of defense conversion beating a talk in Sharon, N.H., entitled "Henry Thoreau four technical components: wildland manage missiles into microwave ovens James "Jamie" and the Humanistic Perspective on Environmental ment, environmental education, conservation Winebrake, SM '90, is presently working on a Degradation."... Professor Leon Trilling present information, and strategic planning Gregg F. PhD at the University of Pennsylvania's Center ed a paper on engineering education and interna Martin, SM '88, has mentioned that the College of for Energy and the Environment Paul Chan, tional perspectives at the seventh IEEE Careers Naval Command and Staff is outstanding. There SM '91, has joined the staff of Koencman Capital Conference in Denver last October. are only 200 students—100 Naval officers, 34 Management, Pte, Ltd., which is an international The following are STS graduate student nota Army, 30 Air Force, 25 Marine, and the remainder investment firm based in Singapore. The firm was tions. Bruce Bimber delivered a paper, "The Coast Guard and civilians. The orientation is on started by two MIT alumni. Paul is currently Politics of Expertise and the Separation of joint military operations, strategy, and national working on a data visualization project which he Powers" at the annual American Political Science policy. So far they have analyzed historical mili finds both interesting and challenging.—Rene Association meeting in Washington last tary case studies ranging from antiquity to mod Smith for Richard de Neufville, Technology and September.... Dan Grossman, '82 (VIII), SM '86 ern times Marina Skumanich, SM '88, has Policy Program, MIT, Rm. E40-252, Cambridge, (XVII), and Scth Shulman were the coauthors of joined Battelle's Environmental Policy and Social MA 02139. "Over There: The US. Military's Toxic Reach," in Research Center as a research associate Simon the November 28,1992, issue of Rolling Stone Stokes, SM '88, is working for a patent and corpo David Mindell went to the Galapagos Islands in rate law firm in London. He expects to qualify as PROGRAM IN SCIENCE, November and December as part of the Jason a solicitor in 1992. After Christmas he hopes to STS TECHNOLOGY & SOCIETY Project, an educational program aimed at getting take a part-time course in European law at King's secondary school students interested in science College in London We have heard that Terry Professor Jill Conway gave a talk about and technology. Mindell is control system engi Tumipseed, SM '88, has married a redheaded Australian history entitled "Fatal Shore or Luck neer and navigator for this year's project, having nurse. Country" last December at the Smithsonian developed the undersea robot "Jason Junior" in Jennifer Croissant, SM '89, taught "Women in Institution Professor Deborah Fitzgerald is his work at the Woods Hole Oceanographic Science and Engineering" at Rensselaer High editing a new series. Revisiting Rural America, for Institute.—Phyllis Klein, STS Program, MIT, ES1- School Summer Program. She also completed her The Johns Hopkins University Press Professor 128, Cambridge, MA 02139. qualifying and dissertation exams in the Science Loren Graham delivered the keynote address at and Technology Studies doctoral program at the joint meeting of the Society for the History of Rensselaer.... Jeff Dieffenbach, SM '89, is cur Technology and the History of Science Deceased rently a project manager at IBIS Associates, an Association in Madison, Wise, last November. He engineering consulting firm in Wellesley, Mass. and Professor Eugene Skolnikoff, '49, SM '50 The following deaths have been reported to the He is also working on issues for the Paul Tsongas (VI), PhD '65 (XVH), traveled in early December to Alumni/ae Association since the Review last went for President Campaign Aaron Todd" Moscow to speak to leaders of the Soviet and to press: Curtis, SM '90, is on staff at the Boeing Russian Academies of Science about the restruc L.G. Lee Thomas, '20; November 22,1991; Commercial Airplane Group in Seattle, Wash., as turing of Soviet and Russian science Professor Naples, Fla. TECHNOLOGY REVIEW MIT 45 Warren K. Brimblecom. '21; December 18,1991; N.H. South Yarmouth, Mass. George F. Wollinger, Jr., '37; November 19,1991; Storch Thomas B. Davis, '21; September 20,1991; Laguna Hills, Calif. Memphis, Tex. Murray H. Hayward, '38; November 13,1991; Engineers Irving D. Jakobsen, '21; October 21,1991; Troy, Mich. Bayville, NY. Louis B. Tura, '40; December 28,1991; Chatham, Henry C. Tainlor, "21; August 25,1991; Mission Mass. Marion Loren Wood, '40; October 3,1991; Engineers Now York, NY Viejo, Calif. Architects 212-371-4675 Richard B. Oakes, '22; November 4,1991; Briarcliff, N.Y. Surveyor* Auburndale, Mass. Lawrence E. Beckley, '42; December 30,1991; Planners Jericho, NY William H. Blandy, '23; June 29,1991; Delray Winchester, Mass. Goologl*t» 516-338-4500 Beach, Fla. Donald Stein, '42; October 13,1991; Falls Church, Soil Scientists Laurence Edmund Noble, '23; August 9.1991; Va. Mundpal Specialists Boston, MA Landscape Architects 617-783-0404 Enid, Okla. Marvin N. Stein, '42; November 1,1991; Brcwster, Environmental Clarence j. Odell, '23; November 27,1991; Lee, Mass. Consultants Provldenco, Rl Mass. David J. Crawford, '43; April 15,1991; 401-751-2235 Dunbar L. Shanklin, '23; December 21,1991; Poughkeepsie, N.Y. Delray Beach, Fla. Jonathan H. Sprague Jr., '43; October 2,1991; Florham Pork, HJ Washington, DC Houston, Tex. 201-822-2600 202-785-8433 Frederick B. Stevens, '23; December 17,1991; Akron, Ohio Katherine A. Kulmala, '44; January 5,1992; Robblnsvllle, NJ G. Baer Connard, '25; October 26,1991; Bath, Carlisle, Mass. 609-25941640 Maine Keith W. Cramblel, '45; March 20,1990; Santa Robert B. Hatton, '25; November 26,1991; Ana, Calif. Manchester, NH Andover, Mass. Richard S. Bettes, Jr., '44; August 17,1990; 603-623-5544 Jesse L. Maury, '25; April 4,1991; Arlington, Va. Mountain Lakes, N.J. Rocky Hill, CT William R. Wheeler, '25; November 2,1991; George K. Landon, Jr., '45; November 18,1991 203-529-7727 Southbury, Conn. Edmund L. Czapek, '46; October 31,1991; Quaker Reginald Frank Terrill, '26; November 14,1991; Hill, Conn. Concord, N.H. John M. McMlllin, Jr., '46; July 20,1991; Samuel S. Auchincloss, '27; November 5,1991; Cincinnati, Ohio Design Englcwood, Fla. John M. De Bell, Jr., '47; December 14,1991; Edward R. Coop, '27; December 15,1991; Toms River, N.J. Kumford, R.I. R. Ellsworth Annig, Jr., '48; August 17,1991; West Continuum, Inc. David R. Knox, '27; November 25,1991; Lantana, Yarmouth, Mass. Fla. Roy Oringer, '48; November 16,1991; Quincy, Thomas F. Russell, '27; July 6,1991; Naples, Fla. Mass. Warren Crier Armstrong, '28; October 26,1991; Robert H. Ruth, '49; October 4,1991; Lodi, N.Y. Newark, Del. Paul E. Weamer, '49; December 5,1991; New Product Planning, Design and Development Robert F. Schuler, '28; December 16,1991; Chesterfield, Mo. Newton Centre, Mass. Maurice CM. Grandpierre, '50; September 5, J. Zlndler, '55 Milton H. Clapp, '29; December 1,1991; 1991; Nancy, France H. Koselko, '88 Edgecomb, Maine Frederic D. Grant, '50; November 11,1991; R. Miller, '87 Ruth C. Dean, '29; November 13,1991; Wellesley, Wellesley Hills, Mass. R. von Turkovlch Mass. Yaichi Ayukawa, '52; November 30,1991; Tokyo, A. Zleglor, '87 John J. Jarosh, '30; December 1,1991; Wilmington, Japan Calif. Albert L. McManus, Jr., '52; November 3,1991; 646 Beacon Street Stanley G. Russell, '30; October 16,1991; Framingham, Mass. Boston, MA 02215 Annisquam, Mass. Paul C. Watson, '52; December 25,1991; Davis, Willard W. Selden, '30; November 29,1991; Calif. Telephone: (617) 267-5115 Ludlow, Mass. KJell Loevaas, '53; July 14,1991; Oslo, Norway Teletax: (617) 267-3923 David Nicoll, '31; November 16,1991; La Jolla, Gerald P. Richards, '53; November 18,1991; Calif. Framingham, Mass. Max Kate, '32; January 7,1992; Topsfield, Mass. Roswell I_ Derby, '54; November 7,1991; Richard A. Lobban, '32; December 10,1991; Longmeadow, Mass. Haverford, Pa. Domenic B. Vassallo, '56; November 26,1991; Halsted R. Warrick, '32; August 30,1991; Bethesda, Md. Hendersonvillc, N.C. George W. Walsh, III, '57; October 10,1991; John C. Herbert, '33; October 29,1991; Erie, Pa. Durham, N.C. Eugene Rohman, '33; November 25,1991; West Larry G. Glassmaker, "58; September 29,1991; Feld Hartford, Conn. Palo Verdes Pen, Calif. Frank R. Milliken, '34; December 4,1991; Tucson, Franklin W. Mohney, '61; May 2,1991; New Technologies, Ariz. York, N.Y. John M. Thompson, '34; March 2,1991; Rye, NY. Ralph J. Bahnsen, '65; June 16,1991; Wappingers Inc. W. Olmstead Wright, '34; August 26,1991; Falls, N.Y. Lombard, III. Preston G. Pollock, Jr., '67; November 27,1991; Herbert C Zitzewitz, '34; October 19,1991; Port Cruz Bay, St. John, U.S.V.I. Custom Software Development Republic, Md. Merrill L Andrews, '68; August 23,1991; Network Installation and Support Arthur M. King, '35; August 13,1991; Louisville, Beavercreek, Ohio Information Technology Consulting Ky. John E. Litt, 70; November 1,1991; Mountain John Ayer, Jr., '36; November 13,1991; Denver, View, Calif. Colo. John Chaiken, 71; December 4,1991 Bradley A. Feld, '87, SM '88 D. Elliot Cullaty, '36; June 9,1988; Weston, Mass. William K. Kietrich, 71; September 4,1991; David J. Jllk, '85 William A. Healy, '36; November 26,1991; Houston, Tex. Peggy B. Ng, '89 Concord, N.H. Charles F. Scott, Jr., 73; November 4,1991; Bonnie C. Steele, '91 Merwin Miller, '36; October 4,1991; Berkeley, Boston, Mass. Calif. Carlos Thompson, 74; July 3,1990; Greenville, Samuel Norton Miner, '36; December 8,1991; N.C. 155 Federal Street Lakeville, Conn. Kenneth R. Gobeille, '81; August 31,1991; Boston, MA 02110 Carl M. Peterson, '36; October 3,1991; Pittsburgh, Montreal, Quebec, Canada (617) 451-0055 Pa. Gregory O. Tomlinson, '81; November 8,1991; Edward M. Fischer, '37; October 22,1991; Olathe, Boston, Mass. Kan. Douglas K. Tannatt, "87; October 19,1991; Robert Nedbor, '37; June 18,1991; Plantation, Fla. Philadelphia, Pa. William C. Wold, '37; October 19,1991; Dover, MIT 46 APRIL 1992 PUZZLE CORNER ALLAN J. GOTTLIEB, '67 Coriolis Aloft By the time you read this article I For what values of D do solutions exits? and five-digit numbers beginning with the digit one fall alphabetically under the second digit will be packing for Australia! The Are they unique? Note that AB does (e.g., "eighteen"). International Symposium on Com not represent AxB. Instead it signifies Now we are ready to start answering questions. puter Architecture is being held there juxtaposition, e.g., if A=24 and B=345, (1) What is FUOOO, 1M)? this year. I chaired the program commit AB is 24345. F0002,1M) is "eighteen thousand two," which is the highest number alphabetically in the "eigh tee and am anxious to see if my commit teen thousand" series. Working backwards, M/J 3. Daniel Morgan wants to know tee did a good job in selecting papers. FdOOO, 1M) is "eighteen thousand twenty two" But of course I am even more interested the expected point count for a randomly and FdOOO, 1M) is "eighteen thousand twenty." in seeing the southern cross! As you dealt Bridge hand of 13 cards? High ILandau's full situation also tabulates numbers can probably tell, I have never crossed cards are valued as Ace=4, King=3, with other leading digits. He then proceeds:) What is G(1000, 1M)? The "one thousand" series the equator before. I was planning to Queen=2, and Jack=l. In addition a void falls at the end of the "one" series, which means (no cards in a suit) contributes 3 points, empty a bathtub on the plane to watch Gdxxx, 1M) runs from 549,552 to 550.551. Since the circling water get confused but, alas, a singleton contributes 2, and a double- 1000 falls at the beginning of the "one thousand" the airlines would have none of it (bath ton contributes 1. series, GdOOO, 1M) is 549,552. tubs fit neither under a seat nor in an (2)WhatisF(lM,lM)? Speed Department "Two" sorts highest alphabetically, and can only overhead rack). be followed by "hundred" and "thousand." The last number alphabetically is F(1M, 1M) = two Problems Speedy Jim Landau wants to know the thousand two. smallest possible number of pitches in a What is GUM, 1M)? M/J 1. We begin with a Bridge problem complete baseball game and how many The "one" series goes that Winslow Hartford sent us from the calls does the plate umpire make during one one hundred xxx London Sunday Observer. In the hand this game? one hundred thousand xxx shown, West missed the killing dia one hundred twenty, twenty two, and two mond opener against 7H and instead Solutions one million lead the spade jack. How can South now one thousand xxx Using the answer to d), we find G(1M, 1M) = make the grand slam? JAN 1. Our "first" problem is a computer offering from Bob High. Write the first n numbers in GdOOO, 1M)-1=549,551. alphabetical (dictionary) orders as they are (3) For what n does F(n,n) = G(rt,n) = n? North spelled out (i.e., one, two, three,...one million,...). There are exactly 64 such n. The first 4 such n are: * Q95 To avoid ambiguity, use no "ands" or hyphens, so one 837,301 would be written "eight hundred thirty- two \ 10653 ) seven thousand three hundred one." 1,897 is "one two hundred ' 1 ♦ AQ thousand eight hundred ninety-seven," not "eigh two hundred two '" J872 teen hundred ninety-seven." Define two func Notice the pattern 2, 200, 202. It will repeat itself tions, F(m,n) and G(m,n) as follows: F(m,n) is m below. The next 4 n are: West East th number in the alphabetical list of the first n two thousand two thousand two K6432 numbers; G(m,n) is the position of the number m * J10 8 7 A two thousand two hundred in this list. (For given n, F and G are inverses.) we 4 2 V 9 ask: (1) What is F( 1,000, 1,000,000)? What is two thousand two hundred two (which is KJ974 F(IM.IM) above) 10965 ♦ G(l,000, 1,000,000)? (2) What is F(1,000,000, There will be no new n until we find a suffix for 964 53 1,000,000)? What is G(1,000,000, 1,000,000)? (3) For what numbers n is F(n,n) = G(n,n) = n? List "two" which sorts alphabetically higher than "thousand." The first such is "trillion." The next 8 South the first dozen. Speedy Jim Landau sent us a detailed solution nare: * A to this problem and an extension of it. Interested two trillion ♦ akq;|87 readers should write to Faith Hruby at TR for a two trillion two ♦ 32 copy. A summary of Landau's solution follows: two trillion thousand two hundred two * AKQ 10 Consider the numbers beginning "eight." There are, in alphabetical order JAN 2. Robert Bart offers the following extensions M/J 2. Gordon Rice is thinking of four to an old problem from Nob. Yoshigahara. What number quantity is the smallest positive integer whose square root positive integers eight 1 has a decimal expansion beginning with ten dis 0 TECHNOLOGY REVIEW MIT 55 25 years, he and his associates) discovered! nent of the problem; he turned his attentio^ to Los Angeles smogvHe chairedJan. . X'--^- industry-wide contmift'ee that organized a * concerted natioi^^ack on airjpollution>| Its effpiits res gasolfn,(wcomj Laboratories, where he remained until, he GIFT OF CAPITAL: Charitable Remainder ■ Unitrust to establish theJohn M. Campbell (1925) Undergraduate Student Loan Fund. QUOTE: A charitable remainder gift to MIT is like having your cake and eating.it, too. My wife Marie and I receive a lifetime income that is almost double what we for merly earned from, the same amount of capital and, of course, there is no capital . gains tax. It is also ah excellent way to. return some of the profit that comes from an MIT education and to assist the next generation of technologists. For more information about gifts of capital, write or call Frank H. McGrory or D. HugH Darden'at MIT, 77 Massachusetts Avenue, Room. 4-234; Cambridge,' Massachusetts 02139-4307; (017)253-3827. . ■ I'lmtii: Luiry Hire, SliTling Heights, Michigan ^v 'S —— PUZZLE CORNER — Continued from Page MTT 55 The 2 th root of 143 is 11.95826O7431014 The 3 th root of 939 is 9.792386145009786 The 4 th root of 633 is 5.015923768441686 The 5 th root of 8117 Is 6.051723946894983 The 6 th root of 896 is 3.104926578310817 The 7 th root of 551 is 2.463729851098231 The 8 th root of 558 is 2.204597318658172 The 9 th root of 759 is 2.089425371646355' The 10 th root of 667 is 1.916075348263711 Other Responders Responses have also been received from D. Church, D. Eckhardt S. Feldman, M. Fountain, I. Shalom, Proposer's Solution to Speed Problem 28. One player on the home team hits the first pitch for a home run. Every one else grounds out on the first pitch. The game is called on account of rain after 4 1/2 innings. The home plate umpire makes 1/4 of a call. The ground outs arc called by the first base umpire but the plate umpire participates in the decision to call the game. D ►: PUZZLE CORNER ALLAN J. GOTTLIEB, '67 Dot's Entertainment It has been a year since I reviewed the connect more than two dots if all are in Solutions criteria used to select solutions for a straight line. No line shall be drawn to publication. Let me do so now. a previously connected dot or cross F/M 1. Dave Wachsman sent us a hand he played As responses to problems arrive, they another line. (as South) with his wife that was reported in Truscott's Column in The New York Times. are simply put together in neat piles, The second diagram shows a game in with no regard to their date of arrival or progress where the first player has North postmark. When it is time for me to drawn his first line along a long diago * 82 write the column in which solutions are nal of the field. Is this a winning or a • A72 to appear, I first weed out erroneous losing move? There can be no ties. ♦ Q75 * KQ942 and illegible responses. For difficult problems, this may be enough; the most West East publishable solution becomes obvious. * 973 * 65 Usually, however, many responses still * 1865 ¥ 104 * KJ1032 * 984 remain. I next try to select a solution * J * A108653 that supplies an appropriate amount of detail and that includes a minimal num South ber of characters that are hard to set in * AKQJ104 type. A particularly elegant solution is, v KQ93 * A6 of course, preferred as are contributions Game lost bv first player Game in progress * 7 from correspondents whose solutions have not previ ously appeared. I also JUL 3. Geoffrey Landis has found our Both sides were vulnerable. The bidding: favor solutions that are neatly written, South West North East previous cryptarithmetic problems typed, or sent via e-mail, since these 1 * Pass 2 * Pass (where you are given an arithmetic 3* Pass 3N.T. Pass produce fewer typesetting errors. equation such as XXX + Y = YZZZ and 4» Pass 4N.T. Pass must find which digits to assign to each 6 * Pass Pass Pass Problems letter, in this trivial case X=9, Y=l, Z=0) How docs Mr. Wachsman bring home the slam "rather uninteresting." So he offers a after West leads the club jack? JUL 1. We begin with a bridge problem challenge. Find a cryptarithmetic prob Larry Shiller sent us the following solution. If from Richard Hess, who (I guess) lem with (precisely) two solutions based East lets club K win, declarer draws trumps and always seems to get low point count on two (completely) different keys, i.e., leads to dummy's diamond Q for 12th trick. Oth hands and likes to see how far they can erwise, declarer wins East's return in hand (ruff no letter is assigned the same digit in go. Inspired by the 1991 Jan 1 problem, ing high if a club), draws trumps, cashes diamond both solutions. I would not be surprised A, crosses to dummy with the heart A, and leads Hess asks for the lowest number of high to find that Nob. Yoshigahara has a few the club Q, discarding a diamond from the closed card points that North and South can dozen of these sitting under his socks in hand, squeezing West. have (combined) and still make 7NT his bureau. against best defense. F/M 2. John Prussing believes that the following puzzle, which was actually on the 1989 Putnam Speed Department exam, seems about right for Puz zle Comer. JUL 2. Matthew Fountain suggests we A dart hits a square dartboard. If any two points tackle the "hold that line" problem Pete Chandler wants you to figure out on the dartboard have the same probability of devised by Sid Sackson and appearing each of these eight brain teasers. Continued on Page MFT 46 in his book A Garnet of Games. "Hold That Line" is a game in which two players alternate drawing straight lines between dots on a 4 x 4 dot field. Cycle The player to draw the last line loses. The first diagram shows a game in Cycle which the lines are numbered in the SAND ECNALG Death/Life order they were drawn. Restrictions are Cycle that lines after the first shall only be drawn from the free end of a previously drawn line. All lines must be straight B and start and end at a dot. A line may L GI 0 He's/Himself SEND PROBLEMS, SOLUTIONS, ccccccc MD AND COMMENTS TO ALLAN /. GOT Her cccccc TLIEB. -67, THE COURANT INSTI PhD ccccc TUTE. NEW YORK UNIVERSITY. 251 <*■ cccc MA MERCER ST.. NEWYORK. N.Y. 10012. E OR TO: [email protected] TECHNOLOGY REVIEW MIT 47 in 5.J- ITiW! Alessandro Morclli, '44; November 18,1991; ■ PUZZLE CORNER. Cohassct, Mass. Paoli E.C. Massaglia, '45; January 14,1992; Stuart. Continued from Page MIT 47 Fla. being hit, what is the probability that the dart will land nearer to the center of the board than it Theodore E. Gerber, "46; February 7,1992; Guil- does to an edge. ford. Conn. George Blondin chararactcrizcs the solution Emerson H. Newton, '46; March 14,1992; Arling (4V2 -5)/3 ton, Mass. as "a really neat answer." Blondin writes: For a 2 by 2 square with center at (0,1), equating the Norman f. Gold, '47; March 5,1987; Newton squared distance from the center, x^+O-y)^, to the squared distance from the bottom edge y^ Highlands, Mass. gives a parabola: y=(x2+l)/2 which intersects the lower right diagonal (y=!-x) at Xi, Yi where Thomas K. Hughes, '47; April 10,1991; Dickin Xi= MrT46 JULY 1992 and therapeutic purposes, and the understanding Ray E. Lucey, '25; February 3,1992; Fort Laud- of the health effects of ionizing radiation. erdalc, Fla. XXI HUMANITIES Samuel B. Maddock, '25; 1991; Portsmouth, N.H. Philip S. Mancini, '26; January 29,1992; Beverly Peler C. Perdue, Course XXI associate professor TECHNOLOGY & POLICY, Hills. Fla. and head of the History faculty, has been awarded TPP PROGRAM Donald S. Nelson, '26; January 4,1992; Dallas, the 1992 Levitan Prize in the Humanities. The Texas $20,000 prize was established through a gift from Diana B. Dutton, SM '76, is the author of Worst Francis H. Whitaker, '26; February 9,1992; James A. Levitan, '45 (X), a member of the MIT than the Disease: Pitfalls of Medical Progress (Cam Wayne, Pa. Corporation and a senior partner in the law firm bridge University Press, 1988) Hans Peter Stanley C. Boyle, '27; January 29,1992; Terre of Skadden, Arps, Slate, Meagher, and Flom of Brondmo, SM '87, was featured in an article enti Haute, Ind. New York City. The prize, first awarded in 1990, tled "Ideas Galore, but Where Are the Goods" in Paul E. Parker. '27; August 5,1991; Fair Oaks, supports innovative and creative scholarship in the February 10,1992 issue of Business Week. Calif. the humanities by faculty members in the School Brondmo is co-founder of DIVA in Cambridge, a Alden G. Reed, '27; December 29, 1991; Wood- of Humanities and Social Science. Perdue, a lead Macintosh software developer spun off from the burn, Ore. ing specialist in modern Chinese history, will use MIT Media Lab.... Christoph Hilz, SM '90, is John H. Wever, '27; February 24, 1992 the prize to continue research into the Chinese currently on the staff in the Commission of the Hector E. Hagerdorn, '28; April 10,1991; Madrid, conquest of Central Asia from 1680-1760 EC, DGI-PHARE in Belgium. His thesis for TPP, Spain Irene R. Heim, has been appointed to the Class of International Toxic Waste Trade, has been pub Henry F. Kohlcr, '28; January 21,1992; Alexan 1943 Career Development Chair in linguistics and lished by Van Nostrand Reinhold in New York dria, Va. philosophy. Heim is recognized as one of the most and is being introduced to the market later this William H. Phillips, '28; 1990; Albany, N.Y. prominent and most influential figures in contem month.—Rene Smith for Richard de Neufvillc, Floyd W. Buck, '29; January 15,1992; Hamdcn, porary semantics, an area that is among the most Technology and Policy Program, MIT, Room E40- Conn. technically complex branches of linguistics. As a 252, Cambridge, MA 02139 Harry F. Dickinson, '29; September 20,1991; teacher, Heim is noted for her ability to introduce Rotunda West, Fla. her students to the strands of semantic argument John T. Hallahan, '29; February 25,1992; New and then showing them how these are woven into PROGRAM IN SCIENCE, York, N.Y. the broader picture of the field. In her publica STS TECHNOLOGY & SOCIETY Francis S.F. Leong, '30; 1988; Honolulu, Hawaii tions and colloquium and conference presenta Milton Mezoif, '30; February 25,1992; Provi tion, she has been a force for reshaping the field of Professor Leo Marx was the keynote speaker at a dence, R.I. semantics and is seen as a leading voice affecting March conference on Nature and Arts in the Robert G. Marcus, '31; January 16,1992; Prince the choice of the central questions to be asked and Humanities sponsored by the Maine Alliance for ton, N.J. their answers as well. Arts Education in Portland, Maine. His essay, Doyle L. Northrup, '31; December 15,1991; Satel Douglas J. Forsyth, has been appointed to the "The American Ideology of Space," available as lite Beach, Fla. Class of 1922 Career Development Chair in histo STS Working Paper #8, has been published by the Samuel B. Pritchard, '31; 1991; Saint Petersburg, ry. Forsyth is noted for his research on the politi Museum of Modern Art Professor Merrill Roe Fla. cal economy of 20th century Europe and for his Smith spoke at the Cornell University STS Pro Arthur C. Sugden, '31; 1991; Tuxedo Park, N.Y. innovative teaching. He is the author of the forth gram in March. His topic was "Technology, Charles M. Davis,'32; 1991 coming Monetary and Financial Policy and the Crisis Industrialization, and Social Change in 19th Cen Robert B. Freeman, '32; February 21,1992; Kent- of Liberal Italy, which examines the political econo tury America." He also commented on two papers field, Calif. my and the crisis of parliamentary government in at a March conference on "The Transformation of Rene G. Hochreutiner, '32; November 12,1991; Italy from 1914-22.... Christopher D. Sawyer the New England Landscape" at Old Sturbridge Vaud, Switzerland Laucanno, lecturer in the Program in Writing and Village Professor Sherry Turkle delivered the Herbert J. Pfingslag, '32; June 11,1983 Humanistic Studies, has been awarded a $10,000 keynote address, "Computation and Psychology," Philip W.Snyder,'32; 1990 Translators Fellowship Grant from the National for the Educational Telecommunications Confer Jack F. Andrews, '33; December 29,1991; Endowment for the Arts. The grant will support ence on New Strategies in Distance Learning. The Lawrenceville, N.J. the translation from Spanish of Sobre Los Angeles conference was held in Lexington, Mass., at the James M. Dunlap, '33; December 30,1991; St. (Concerning the Angels), a book of poems by end of February.... Brian O'Donnell gave the Louis, Mo. . Rafael Alberti Catherine V. Chvany, profes Hayes Seminar at St. Joseph's University in Warren G. Webster, '33; March 3,1992; Lexing sor of Russian in the Foreign Languages and Lit Philadelphia in February. His paper was entitled ton, Mass. erature Section at MIT, has received the Distin "Industrialization and Deindustrialization in the Radcliffe G. Edmonds, '34; June 30,1991; Canaan, guished Scholarly Career Award from the Merrimack Valley." N.H. American Assocation of Teachers of Slavic and Edward L. Wemple, '34; February 27,1992; East European Languages. The award, for out Darien, Conn. standing contribution to scholarship, was present Deceased George A. Revell, '35; 1991; Cornwall, Ontario ed at the group's 50th anniversary meeting in San Kenneth B. Galr. '37; January 17,1992; Alamo, Francisco. Chvany, an internationally known The following deaths have been report Calif. expert pn the Russian language and linguistics, is ed to the Alumni/ae Association since James W. Pearce, '37; January 18,1992; Cincinnati, coordinator for MIT's interdisciplinary program Ohio the Review last went to press: in Russian studies. She came to MIT in 1971 and Gerald L. Simard, '37; January 30,1992; Winter- druthers A. Coleman, '16; February 5,1992; Lex was promoted to full professor in 1985. port, Maine ington, Ky. The Association of Alumni and Alumnae has William C. Wulbem, '37; September 17,1990; Elizabeth G. Paltee, 16; March, 1991; Hight- been notified that Osvaldo A. Jaeggli, PhD '80, of Charleston, S.C. stown, N.J. Los Angeles, died on August 20,1990. Jaeggli had Gordon L. Foole, '38; October 24,1991; Colum Richard F. Lyon, '20; 1991; Laguna Hills, Calif. been a professor in the Linguistics Department at bus, N.C. Samuel Schenberg, '20; April 23,1991; Miami, UCLA. There was no further information provided. Marvin M. Kahn, '38; April 27,1990; Sharon, Fla. Mass. Clifton B. Morse, '22; November 4,1990; Carmel J. William Blattenberger, '40; January 26,1992; NUCLEAR Valley, Calif. Lawrcnccville, N.J. Atherlon Hastings, '23; February 8,1992; Flo XXII ENGINEERING James E. Fifield, '40; January 23,1992; Darien, rence, Ala. Conn. Laurence S. McLane, '23; November, 1990; Robert W. Sawdye, SM '78, ScD '85, writes: "I am Kenneth R. Fox, '40; February 22,1992; Rockport, Poway, Calif. in a new postion as principal consultant at Devon- Mass. George B. McReynoIds, '23; 1991; Montecito, rue, Ltd., in Boston. We have new family mem Thomas P. McConville, '40; June, 1990; Santa Calif. bers due soon, twin girls to join 3-year-old son, Maria, Calif. Clifford P. Swaine, '23; February 6,1992; South Alex. Elaine and I are dreaming of a vacation, Karr Parker, Jr., '41; August 3,1991; Buffalo, N.Y. Hamilton, Mass. someday."... Jacquelyn C. Yanch has been William H. Reeder, 3rd, '41; 1991; Warren, N.J. Edward A. Abdun-Nur, '24; October 3,1991; Den appointed to the W. M. Keck Career Development Giulio Ascoli, '42; February 4,1992; Urbana, 111. ver, Colo. Chair in nuclear engineering/Whitaker College. Charles S. Hofmann, '42; January 31,1992; West Carleton Shugg, '24; January 23,1992 Yanch is a Course XXII assistant professor with a Yarmouth, Mass. Hubert D. Barnes, '25; January 2,1992; Milwau secondary appointment at the Whitaker College of Willard D. Nalchajian, '42; February 10,1992; kee, Wis. Health Sciences and Technology. Her research Chelsea, Mass. Leslie B. Bragg, '25; February 24,1992; Skaneate- currently involves investigation of the uses of ion Maynard S. Renner, '42; December 31,1991; Gro- les, NY. izing radiation in medicine for both diagnostic ton. Mass. TECHNOLOGY REVIEW MIT 45 PUZZLE CORNER ALLAN J. GOTTLIEB, '67 Out on a Limerick I must be very brief this issue as I am A/S 3. Our last regular problem is about to leave for Australia and New "Golomb's Gambits" edited by Solomon Zealand. After the "short" flight Golomb in the Johns Hopkins magazine. from New York to Los Angeles, I You are to dissect the figure below into change planes for the hop to Sydney, four congruent pieces. which is your basic 14-hour nonstop endurance test. Wish me luck. Problems A/S 1. Unfortunately, APR 1 was mis printed so that white and black pieces were indistinguishable. As a result we are offering it again (now as A/S 1) but By construction we know that the length of line with the colors indicated as intended. segment BD is a/2 and that angle A is 60 degrees Hence angle a1 is 30 degrees. We apologize for the error. Second, draw chords BE and EC White is to move and mate in 12. m B i Speed Department IF Tom Lydon asks: Two days ago I was 38. Next year I start my 42nd year. How p P p IF old am I, what is my birthday, and what R P if is today's date? P K Solutions By construction, triangle ABE is isosceles with the length of sides AE and AB equal to a. This means B APR I. As indicated this problem was misprinted that angles B and E must equal one another and in April and the corrected version appears above. be 75 degrees each. A/S 2. A real cute one from Jan Davis By drawing parallel (and perpendicular) lines who writes: • APR 2. Arthur Wascrman sent us the following as shown below we can see that we have con solution. The general problem of minimizing the The wife of a man who grew barley structed the figure presented in APR 3 where AF number of training sessions required when there is a/2 in length and the angle in question is 75 Was also the sister of Charlie. are n robots serving n+k users is solved as easily degrees. Her Neighbour grew hay as the n=7, k=3 case. Clearly no robot can be And was married to Ray, trained to less than k+1 users; if a robot has only k potential users and precisely those users do not And one of these girls was named Carly. require the services of a robot then the remaining n users cannot be satisfied. Thus the minimum is The girl who was married to Wayne at least n(k+l). This number is easily seen to be Lived next to the farm that grew grain. adequate. Number the users from 1 to n+k and She liked to eat celery train robot j to user j and also to the k users n+1 to That was grown by Valerie, n+k. If any of the first n users require the services of a robot, they use the correspondingly num And she weighed 80 pounds more than Jane bered robot; if they do not require the use of a robot their robot is freed up to serve one of the k The woman whose husband grew dill users n+1 to n+k. Was never married to Bill Robert High notes that we are assuming that When Jane married Benny when it is time to assign robots to workers, we know in advance all the workers to whom robots And Ray married Jenny, are to be assigned. She went out drinking with Jill. Other Responders APR 3. Our final solution is from Joel Brainard: Norc: Only one couple has rhyming names. Responses have also been received from M. Foun First, draw an equilateral triangle in a circle of tain, K. Rosato, S. Theriault, L. Steffens, R. Whit SEND PROBLEMS, SOLUTIONS, radius "a" and bisect the triangle with another man, A. Cangahuala, W. Hartford, R. Arrison Ir AND COMMENTS TO ALLAN /. COT- radius as shown below. (While it is not necessary E. Sard, G. Stallings, E. SignoreUi, H. Hodara, P. TUEB, '67, THE COURANT INSTI to use the circle, it is a convenient device that Card, S. Root, N. Wickstrand, B. Gunther. TUTE, NE W YORK UNIVERSITY, 251 helps show what is going on.) MERCER ST., NEW YORK N.Y. 10012, Proposer's Solution to Speed Problem OR TO: [email protected] 39,31 December, 1 January. TECHKOLOCYREVIEW SIIT47 MIT LIFE INCOME FUNDS ALBERT J. O'NEILL HOME: Milton, Massachusetts CAREER: The son of a contractor and builder, Mr. O'Neill decided during high school to go into the construction industry. MIT was offering a new course in building engineering and construction, and Mr. O'Neill knew a family that sent four sons there, so the decision to attend MIT was easy. Earning his S.B. in 1932, he worked in govern ment geological surveys for three years, before becoming a construction engineer for private contractors. He spent the war years as a super intendent of construction, specializing in marine installations, for the U.S. Navy, and then joined MIT's building engineering department, which was later absorbed into civil engineering. He taught, conducted research and published in the field of materials—primarily wood, metals and masonry. He later became involved with MIT's Technology and Development Program, a project funded by the U.S. Agency for Inter national Development to help developing coun tries strengthen their engineering capabilities. He retired in 1988. Mr. O'Neill's hobbies are travel, photography, gardening and local senior activities. He and his wife Helen have been married 42 years. GIFT OF CAPITAL: The Albert J. O'Neill (1932) and Helen J. O'Neill Fund in the Maclaurin Pooled Income Fund. QUOTE: When I considered the effect MIT has had on my life, both professional and personal, I had no trouble deciding to make a gift to the Maclaurin Pooled Income Fund. It has been a tax advantage for me and, at the same time/has benefitted MIT. For more information about gifts of capital, write or call Frank H. McGrory or W. Kevin Larkin at MIT, 77 Massachusetts Avenue, Room 4-234, Cambridge, Massachusetts 021394307; (617)253^827. Photo: Richard Howard w- ■ ii PUZZLE CORNER ALLAN J. GOTTLIEB, '67 Roving Riverward Since this is the first issue of a new OCT 2. The following problem is from South academic year, I once more review Robert Sackheim. A is 73 feet from a * the ground rules under which this straight river, and B is on the same side v 7 * 32 department is conducted. of the river but not so far from it. M and * 10 In each issue I present three regular N are the points on the river nearest to On the club. West must discard. If he discards a problems (the first of which is chess, A and B respectively. The length of AB, spade.then you can lead the Q of spades off dummy bridge, go, or computer-related) and MN and BN are whole numbers of feet. for a ruffing finesse against East's king, pinning West's ten. The ace of diamonds provides the entry one "speed" problem. Readers are invit Joan walks from A to B via the river back to the board. So assume that West discards a ed to submit solutions to the regular (i.e., at one point she is at the river), tak diamond. problems, and three issues later, one ing the shortest possible route, and this Now East is squeezed. If he discards a spade, submitted solution is printed for each is also a whole number of feet.How far then ruff a spade and dummy is good. If he dis problem; I also list other readers who does she walk? What is the direct dis cards a diamond, then cash the ace of diamonds, dropping the opponents' remaining cards in that responded. For example, solutions to tance from A to B? suit, and your hand is good. A neat trump squeeze. the problems you see below will appear in the February/March issue and this OCT 3. Richard Hess entitles this one M/J 2. Gordon Rice is thinking of four positive integers issue contains solutions to the problems 'The missing term" and writes: Given 0 TECHNOLOGY REVIEW MIT 55 B M HI Robert W. Barker, '21; January 21,1992; Narbelh, I'a. Mark C Cuibrcath, '30; April 12,1992; Kaymore, Md. PUZZLE CORNER. Richard P. Windisch. '21; May 4,1992; Naples, Fla. Charles D. May, '30; June 13,1992. H.FeltonMetcalf,'22;Mayl2,1992;Newmarkel,N.H. Lloyd E. Montgomery, '30; April 29,1991; Colorado Charles W. Ufford, '22; April 29,1992; Newlo wn. Pa. Springs, Colo. Ed win M. Goldsmith, Jr.,'23; May 4,1991; Wyncote, George D. Love, '31; April 28,1992; Portland, Me. I'a. Carrington Mason, '31; March 12,1992; Houston, Tex. Herbert L Hayden, '23; May 2,1992; Lancaster, Robert Sanders, '31; May 31,1992; Annapolis, Md. Mass. Howard L. Richardson, '31, SM '32; May 1,1992; Max W. Tetlow, '23; May 14,1992; New London, N.H. New Britain, Conn. Jacob Lurie, '24; April 9,1992; Denver, Colo. Allan L. Dunning, SM '32; April 22,1992; Stoning- John E. Black, '25; February 2,1992;Clearwater, Fla. ton. Conn. Homer S. Davis, '25; June 6,1992; Seattle, Wash. j. Richard Rafter, '32; May 18,1992. F. Cushing Foss, '25; May 7,1992; Westford, Vt. Donald C Sanford, '32; April 28,1992; Woodbury, Isaac W. Cleason. '26,SM '27; May 21,1992; Middle- Conn. bury, Vt. HarlandH. Young, Jr., PhD'32; December 31,1991; Albert S. Goleman, MAR '25; November 23,1991; Columbus, Ohio Continued from Page MIT 55 Houston, Tex. Gardner Harvey, '33; February 23,1991; Wilming Naomi C Turner, '26; May 12,1992; Arlington, Mass. ton, Del. (2)(4) (13X39 choose 12) / (52 choose 13) Winfred F. Dunklee, '27; July 25,1991; Hamden, Frederick A. Ladd, Jr., '33; November 12,1991; Lees- E(doubleton pts) = 4 Ptspade doubieton) = (4) Conn. burg, Fla. (13 choose 2)(39 choose 11) / (52 choose 13) Arthur Dunlevy, '27; May 1,1992; North Falmouth, Hugh W. MacDonald, '33; April 29,1992; Green Combining the above, E(distribution pts) = Mass. Brook, N.J. Robert C Wallace, '27; April 21,1992; St. Charles, 111. Meredith E. Morgan, '33; May 3,1992; Kerhonkson, (19)(29)(31)(37)(239) / [ (23)(41)(43)(47)(49) 1 Homer A. Burnell, '28; June 26,1992; Chicago, III. N.Y. =" 1.61748 Harold L. Geiger, '28; April 18,1992; Minneapolis, Charles E Quick, '33; October 26,1990; Traverse So E(pts)=" 11.61748 Minn. City, Mich. Robert High assumes that the proposer "DANIEL Robert Walker Hunn, Jr., '28, MAR '29; January 1, Emst W. Spannhake, '33, SM '35; April 30,1992; MORGAN is your MAIN GOREN LAD," which 1992,Santa Monica, Calif. Akron, Ohio just goes to show what happens when you start Willis G. McCown, '28; May 6,1992; Chicopee Falls, Robert C. Wellwood, '33; May 15,1992; Saline, Mich. hanging out with Nob. Yoshigahara. Mass. Jack Delmonte,SM '34; April 15,1992;GlcndaIe, James Cooper, '29; May 25,1992. Calif. Alfred H. Hayes, '29, SM '30; March 10,1991; Whit Albert M. Grass, '34; May 29,1992; Wollaston, Mass. Better LateThan Never ing, Ind. Louis T. Montant, Jr., '34; 1992. Laurence A. Horan, '29; May 8,1992; North Arthur O. Williams, Jr., '34; May 16,1992; M/J 1. Darold Rorabacher and George Blondin Chatham, Mass. Doylestown, Pa. noticed that numbers ending in one were inad Robert E Jackson. '29; May 3,1992; Marblehead, John L Fuller, PhD'35;June8,1992;Cambridge, vertently omitted. For example, the fourth n Mass. Mass. with F(n,n)=G(n,n)=n is "two hundred one." Annand M. Morgan, SM '29; April 25,1992; Port Chester H. Brown, Jr., '37; September 22,1989; Pitts There are 95, not 64 solutions as previously land, Me. burgh, Pa. claimed. Edward B. Papenfus, SM '29; June 5,1992; Vancou Rolf E. Schneider, '37; January 24,1991; Parkers- ver, BC, Canada. burg, W.V. SD. I really do not normally include comments Leonard C Peskin,'29, SM'31, ScD'36; July 12,1991; F. William Brown, III, '38; May 15,1992; Kensington, on speed problems but quite a ruckus has Wyncote,Pa. Calif. occurred regarding the minimum number of Richard H. Koehrmann, '38; May 3,1992; Alton, III. pitches in a complete baseball game and the num John J. Perkins, '38; November 15,1991; New Bem, ber of calls by the first place umpire. I somehow N.C. cannot resist printing the following from Tony GAZETTE William S. Quigley, Jr., '39; June 6,1992; North Scit- Carpentieri but will try hard to refrain from uate. Mass. speed problem follow-ups in the future MIT ALUMNI JOB LISTINGS George E.B. Hill/ 40; May 7,1992; Kentficid, Calif. "I disagree on the number of pitches/plate Charles S. Butt II, '41; April 16,1992; McLean, Va. umpire calls in a complete game. There are Charles Margnettl, '41; June9,1986; West Roxbury, things that a pitcher can do, such as (I believe) Mass. A bi-weekly bulletin giving em touching his tongue to his pitching hand that John W. Clarke, '42; April 10,1992; Missouri City, ployers the opportunity to reach result in one ball being called. So, each half Tex. inning goes like this: Pitcher licks hand (or other experienced MIT graduates, John Hinchman, '42; May 11,1992; West Cornwall, stuff) 12 times in a row. All calls made by field and MIT graduates the oppor Conn. umpires. He then picks off the three runners, tunity to scan the market. Bernard Brindis, '43; May 29,1992; Boca Raton, Fla. with calls naturally made by field umpires. Well, Tan Chih Lu, SM '44; June 2,1992; Tustin, Calif. this goes on for a bunch of half innings, let's say If you are an employer looking Walter j. Loughlin, '46; May 2,1992. 17. Then a pitcher licks his hand 16 times, and James E Haggett, '47; May 26,1992; Shrewsbury, for talent, or an MIT graduate walks a run home in the bottom of any inning Mass. looking for new directions, con after 8. Pitches: 0, plate umpire calls: 0." tact Bonny Hafner at the ad Victor H. Pomper, '48, SM '50; May 9,1992; Weare, N.H. In addition, Joseph Gurland tells me that our dress below. Roger D. Smith, '48; March 30,1992; New Paltz, N.Y. problem was printed in rec.sport.baseball, a James C Buck, '49, SM '65; August 25,1990; Coron- popular electronic newsgroup. Gurland sent For a subscription to the ado, Calif. copies of several other no-pitch solutions found Gazette clip and mail this ad, Donald P. Germeraad, '50; May 11,1992; Under by newsgroups readers. enclosing a check (made out to wood, Mass. MIT) for $12 for six months or Gerard J. Griesmer, '52; May 29,1990; Aurora, Colo. Other Responders $20 for one year. Howard K. Larson, '52, SM '54; August 5,1991; Saratoga, Calif. Responses have also been received from M. George L. Tuer, Jr., ScD '55; March 5,1991; Aikcn, S.C. Chellino, S. Feldman.M. Fountain, D. Grant, A. Dorothy O. Schlag, '56,1992; Redlands, Calif. Halbcrstadt, M. Handel, R. Hedrick M Herbert, John E. Murray, Jr., '57; 1992; Framingham, Mass. B. Inadomi, R. Loesch, L. Nissim, A. Ornstein, NAME Amarjit Singh, '61; July 11,1991; New Delhi, India. X. Peng, K. Rosato, J. Rosenthal, G. Schwartz, George Piotrowski, '64, SM '65; May 24,1992; Cain- and A. Wasserman. STREET seville, Fla. Dirk Berghager, '62, SM '64; January 29,1984; Cas- Proposer's Solution to Speed Problem cais, Portugal CITY STATE ZIP William J. Day, '67; May 4,1992. 81. Each of the 13 cards has a diamond in the Charles J. Sheehan, SM '67; May 12.1992; Andover, upper left corner and one in the lower right MAIL TO: MIT ALUMNI Mass. corner, for a total of 26. The Jack.Queen, and CAREER SERVICES, RM 12-170. Kathleen S.Sargent, PhD'71; February 18,1991; King have no other diamonds on them. The CAMBRIDGE, MA 02139 Winchester, Mass. Ace throughlO have 1+2+3+4+6+7+8+9+10=55 617-253-4733 Mark E Schaefcr, PhD'77; April 13,1992; Atlanta, Ga. additional diamonds. Albert B. Lester, '82; June 7,1992; Westwood, Mass. Paul J. Ramos. '86; May 24,1992; Seekonk, Mass. MIT 54 OCTOBER 1992 accomplished essayist who has written widely on top cowritten with Allan Prince, a linguistics professor at ing Environmental Thinking, sponsored by the ics in the humanities and social sciences. Rutgers University, concerns the processes of word for MIT Women's Studies Program Professors mation in relation to sound structure. McCarthy will Loren Graham and Kenneth Keniston have writ spend this academic ycaron sabbatical. ten chapters in The Outlook for STS, edited by Sheila NUCLEAR Jasonoff and published by the Department of Sci XXII ENGINEERING ence and Technology Studies at Cornell University. TECHNOLOGY AND ... Professor Emeritus Carl Kaysen has initiated a TPP POLICY PROGRAM project exploring evolving norms that legitimize Robert W. Davis, SM '80, NUE 'BO, writes: "My international intervention in sovereign states. The employer is TRW Space & Technology Group in project is under the auspices of the American Redondo Beach, Calif. I am the advanced system Kent W. Hughes, SM '85, has informed us that his Academy of Arts and Sciences Professor Emeri manager in LightSat Systems. We are working home and all its possessions were destroyed in the tus Leo Man spoke at a conference on American on the leading edge of satellite technology and October 20,1991,firestorm in the Oakland/Beverly Studies in Germany in early June at Bad Munster space systems, with emphasis on the powerful, Hills area (his father's home was also destroyed). They am Stein, Germany Professor Merrltt Roe miniaturized technologies that enable the vastly arc rebuilding and would love to hear from other TFP Smith organized and chaired a session on the Euro increased capabilities of small "LightSats" of the alums.... Steven C. Anderson, SM'87, will be back in pean Roots of the American System at the annual 300-800 lb. class, at low costs for development, the Cambridge area beginning in September. He will be meeting of the Society for the History of Technol fabrication, and costs. This new position is pursuing a PhD at the J FK School of Government at ogy in Uppsala, Sweden, in August Professor responsible for continued growth (through gov Harvard University.... Jessica Stem, SM '88, received Leon Trilling headed a two-week workshop for 60 ernment programs, TRW investments, and a PhD in public policy from Harvard in last June's com middle-school teachers in July. The theme of the acquisitions) and presence in this new market mencement. ... Dava Newman, SM '89, SM '89 (XVI), workshop, held at MIT, was "How Does a City segment. Lead for S380M in sales in 1991. Work PhD '92 (XVD, has been elected to the MIT Corporation Work?"... Professor Sherry Turkle was keynote ing additional S740M in sales for 1992." as one of the "representatives from recent classes." speaker in May at a Tokyo symposium on Mark Melvin, a Course XXII graduate student Congratulations! Da va is the second TPP alum to advanced robotics. The conference, entitled Cybera- from 1984-86, died June3,1992 from complications receive this honor and recognition in leadership in tech nimism: Will Robots Control Human Beings or Live resulting from AIDS. Melvin received a BS from the nology and policy, in the past few years, joining Robin Together in Harmony in the Year 2019?, took place at University of Michigan in 1984. He was active in Wagner, SM '86.... Lee Newman, SM '92, SM '92 (XV), Tokie University.—Phyllis Klein, STS Program, the American Nuclear Society Student Chapter, joined the staff at McKinsey & Co., Inc., in Chicago, III., MIT, Room E51-128, Cambridge, MA 02139 serving as its social chair in 1985. He came to MIT this past September.... Michael "Mick" Rookwood, from Bloomfield Hills, Mich., and his research SM '92, is an environmental consultant with the Eastern focused on fusion reactor design studies. Research Group, Inc.—Richard de Neufville, Technol Deceased ogy and Policy Program, MIT, Room E40-252, Cam bridge, MA 02139. LINGUISTICS The following deaths have been reported to the Alumni/ae Association since the XXIV AND PHILOSOPHY PROGRAM IN SCIENCE, Review last went to press: John J. McCarthy, PhD79,aUniversityof Mas STS TECHNOLOGY & sachusetts professor in the Department of Linguistics, John C Bradley, '07; May 24,1992; Waterbury, has received a Guggenheim Fellowship. He is the direc Conn. tor of the Linguistics Department Graduate Program. Professor Deborah Fitzgerald lectured on sustain Harold C. Wells, '18; January 26,1991. He will be using his grant money to complete research able agriculture in the United States in May. Her George W. Cann, '19; December 30,1991; Conestoga, in theoretical linguistics and finish a book. The book. talk was part of a conference entitled En/Gender Pa. A Fascinating Look at Mathematics !rom mathematics and computers to insights into Fthe workings of the human mind, Mind Tools is a MIND TOOLS reflection of the latest intelligence from the frontiers of mathematical thought. Illuminated by The Five Levels of more than 100 drawings, Mind Tools connects mathe matics to the world around us. Exploring such con Mathematical Reality cepts as digital versus analog processes, logic as a by Rudy Rucker computing tool, and communication as information transmission, Rudy Rucker presents the "mind tools" "A lighthearted romp through contempo for a postmodern age. rary mathematics ....It is shorter and more approachable than G6del, Escher, Paperback, 328 pages including index, $9.95 Bach.... Mind Tools is a delight." - FOR EiSi'MVL ORDER USE TWff COUPON Please send me copies of Mind Tools at $9.95, plus $2.00 shipping Ship to: □ Check enclosed for Total Mue cheeks man to TEnrowr Name Or RF.TEV. US HW»US BINDOKU Address □ Charge my: □ Master Card □ Visa Card Number Cm State Expiration Date ZIP Signature Mail to: Technology Review Books Our Guarantee: If for any reason MITW59 you are not satisfied, return Order by phone today (charges only): (617) 253-8292 (weekdays, 9 am-5 pm est) Cambridge, MA 02139 TECHNOLOGY REVIEW MIT 53 PUZZLE CORNER ALLAN J. GOTTLIEB, '67 Parking Lotto I had an interesting experience yester from Albert Faessler. A primitive suit restriction, they cannot be moved to the East hand, thus they must stay in the South hand. Since day (23 August). My wife Alice had to Pythagorean triple (PPT) is a triple of all 4 honors are necessary, no lower solution exists talk at the National Psoriasis Founda positive integers (a,b,c) such that and the above is a minimum solution. tion in Orlando during the weekend so a2+b2=c2 and a, b, and c have no com the family used the cheap summer air mon factor (this last condition is what JUL 2. Matthew Fountain suggests we tackle the "hold that line" problem devised by Sid Sackson fares for a chance to see Disneyworld. makes the triple "primitive"). The area and appearing in his book A Garnet of Games. Our routing home was Orlando-Miami- of a PPT is ab/Z. Euler found that the "Hold That Line" is a game in which two players NYC (don't ask). Hurricane Andrew smallest area shared by three PPTs is alternate drawing straight lines between dots on a 4 arrived this morning in Miami. Well, yes 13123110. What is the next smallest area x 4 dot field. The player to draw the last line loses. The first diagram shows a game in which the lines terday at Orlando the final word from the shared by three PPTs? are numbered in the order they were drawn. airline was that if you went to Miami, you Restrictions are that lines after the first shall only be were "on your own" and "the Miami air N/D 2. Gordon Rice wants you to find drawn from the free end of a previously drawn line. port is all glass." There was a noticeable (non-equilateral) triangles containing a All lines must be straight and start and end at a dot. A line may connect more than two dots if all are in time warp that occurred at the airport 60-degree angle. How about a 30-degree a straight line. No line shall be drawn to a previous entrance. While we were driving from angle? ly connected dot or cross another line. Orlando, Andrew was reported as due to The second diagram shows a game in progress hit Miami in 14 hours. Once we were N/D 3. Tom Harriman wonders for where the first player has drawn his first line along inside the airport, the only word we could what values of X does the following a long diagonal of the field. Is this a winning or a losing move? There can be no tics. hear is that it would be "soon," and ten "infinite exponential" converge. sions were getting pretty high. We decid ed to chance it, in part because there were no seats available leaving Orlando for anywhere. We were also encouraged by Speed Department the words of a wise pilot, who noted that they would not fly a plane into Miami Speedy Jim Landau sent us a speed unless they were dam sure that the plane problem from Eric Weill. To avoid the 5- Game lost bv first flayer Came in fkocress could get out. Extrapolating (dangerous dollar parking fee at Atlantic City casi Steve Altchuler advocates a "copy your oppo ly?) I concluded that the airline would not nos, it is necessary to place a bet. What nent" strategy. The second diagram shows an easy allow its four o'clock flights to fly in bet should you make to get your free win for the first player. S/he has divided the board in half, and can now mirror whatever move the sec unless it expected they would all get out. parking with the least risk? ond player makes onto the other half of the board. Bottom line: we left Miami at 5:45 in calm Thus, the two halves will always remain identical, weather. But no flights were landing—the Solutions and whenever the second player Is able to make a four o'clock batch was the last move, the first player will be able to make the same Readers may be interested in an JUL 1. We begin with a bridge problem from move on the other half. Richard Hess, who (I guess) always seems to get This strategy means there are many other first impressive compendium of puzzles low point count hands and likes to see how far they moves which guarantee a win for the first player. entitled Index to Mathematical Problems can go. Inspired by the 1991 Jan 1 problem, Hess Using spreadsheet-type notation on a 4x4 board, 1980-1984, edited by Stanley Rabin- asks for the lowest number of high card points that not only is A4-D1 a win, so are: A1-D4, A2-D3, A3- owitz and published by MathPro Press. North and South can have (combined) and still D2,Bl-C4,andCl-B4. make 7NT against best defense. This being the case, "Hold that line" now has all Also, my NYU colleague Dennis Shasha The following solution is from Edward Sheldon: the strategic appeal of tic-tac-toe, unless you ban has just written Codes, Puzzles, and Con South is assumed declarer, and West is on lead. first moves that bisect the board. spiracy, a second Dr. Ecco book. Finally, North/South (NS) must have the ace of every suit our frequent contributor, Nob Yoshiga- in the West hand. Therefore West cannot have 13 JUL 3. Geoffrey Landis has found our previous cards of one suit. If West has 3 or 4 suits, NS must cryptarithmetic problems (where you are given an hara, has written a book including a few have 3 or 4 aces, for 12 or more points. Since at least arithmetic equation such as XXX + Y = YZZZ and problems from "Puzzle Corner." Nob's one solution of less than 12 exists, there is no mini must find which digits to assign to each letter, in book is in Japanese; the only word I can mum solution where West holds more than 2 suits. this trivial case X=9, Y=l, Z=0) "rather uninterest read is "Puzzle" set in big type on the For all minimum solutions. West holds exactly 2 ing." So he offers a challenge. Find a cryptarith suits.. Further, all 13 NS tricks must come from the metic problem with (precisely) two solutions based cover. same 2 suits, to avoid a third NS ace. There are 26 on two (completely) different keys, i.e., no letter is cards in 2 suits; with 13 in the West hand, the other assigned the same digit in both solutions. I would Problems 13 must be played one per trick to win a grand not be surprised to find that Nob Yoshigahara has a slam; therefore they must all be in one hand. few dozen of these sitting under his socks in his Assuming West and South share the hearts and bureau. N/D 1. We begin with a computer-relat spades, with South arbitrarily long in spades, and Bob High sent us some that even "make sense." ed problem that Max Hailperin heard that East holds all the point cards in clubs and dia ONE monds, the following 11-point solution is obvious: ONE SEND PROBLEMS, SOLUTIONS, AND West South ONE ONE COMMENTS TO ALLAN]. COTTUEB, » K A.Q.J->2 • K->2 A ONE ■67. THE COURANT INSTITUTE. This solution is also a minimum. South's aces have ONE NEW YORK UNIVERSITY. 251 MER already been proved necessary, and since the West ONE CER ST.. NEW YORK. N.Y. 10012. OR spade K must be singleton, the spade Q and/or ] TO: [email protected] cannot be moved to the West hand, and by the 2- Continued on Page MIT 46 TECHNOLOGY REVIEW MIT 47 ■ • TT1. Tfr AiWW , HOME:,ConcG^|Massachiisgtls. gX0; , Sc.D. (1051) degrees from MIT^ncivil.engineerr- .;*?'■' :.ing,.pr. Aiclrich.'served'six^ears.bntheMIT [ '■'■. . .'; .•' faculty, teachirig^ourses^jisoirmechanicsand ;£: . foundation engirieeringsln^^j.ihe eo.-founded :;f. the consulting engineeringfiriTi Haley & Aldrich;' ■' ' Inc. Based in Cambridg^; the1 "firm spocializesjn gg^gv^tdtJ il geoscit'nces,';withr3/)Uemployeesandeiglitpffices, ■ locatedprimaiily i"nthe Northeast:.'Dr. Aldrich is : .now chairman emeritus of t.R&3U;ni. . Ss:^-"-1 . Thr6ughoiit'hisx^ireer);Pr. Aldrich has been ; *" active at MIX He^vafpresident otHhe Aluiruii^- Associatioivin 1980r-81.and served on the |Cmipo- ■'ration from'1980 tlfrough 1986; forthree of those years,'he was oii.the Executive Committee. He is vice chairman:of the Boston Campaign Comniit- tee.of the Camp;tign>'for the future. FGAEITAIWT he,Haii;Riar[&M>\fi G ^ ?:y /:/■ /--ft"" " ■ ' Gharit!alj||lR(imffiWEBfiigf JiiToJsneadMl MveanijjMli ny life. Eaenk •rie significant contribution that'strengthens this' ™ world-class institution, while providing us with ,.;; For more information about gifts,o££api write or cairHugh Darden, Frank McGroi^ l^-i -:,^~«r' orKevinLarkinatMIT, . '-"S 77 Massachusetts Avenue, Room 4-234;s«J ;C;imbticJge?Massa|lius^ts02139-43()7^f:;V.. :*.P: ;Ht$|Mfe ■i. ■ toward GAZETTE The following deaths have been reported Robert V. Coleman, '44; January 9,1992; McLean, Va. to the Alumni/ae Association since the Frank J. Huddleston, '45; April 8,1992; Bowie, Md. MIT ALUMNI JOB LISTINGS Review last went to press: Keith Knutzen, '47; October 14,1991; Bronxville, N.Y. James M. Ralston, '16; June 13,1992; Trenton, N J. Richard C.B. Berry, '48, SM '49; August 8,1992; Harvey M. King, MAR '23; July 6,1992; Ft. Walton Danielson,Conn. A bi-weekly bulletin giving em Beach, Fla. Earl D. Hoyt, '48; June 6,1992; Menlo Park, Calif. ployers the opportunity to reach Howard A. Lockhart, '23; June 18,1992; HaverhiU, George G.CK. Mah, PhD '48; May 28,1990; experienced MIT graduates, Mass. Evanston, Ml. and MIT graduates the oppor Arthur R. Stuckcy, '23; July 15,1992; Tucson, Ariz. Manfred G. Wentzel, '48; June 14,1992; Indian Har tunity to scan the market. Hyman J. Verner, '23; June 9,1992; Pikesville, Md. bor Beach, Fla. Neil L. Olken, '24; December 12,1988; Newton Cen Nesblt L. Duncan, '49; June 15,1992; Belmont, Mass. If you are an employer looking tre, Mass. Richard W. Henderson, '50; July 13,1992; Colonia, for talent, or an MIT graduate George A. Whinery, SM '25; July 9,1992; Grand N.J. looking for new directions, con Rapids, Mich. Bernard Edelman, '53; June 28,1992; La Mesa, Calif. Avedis M. Kazazian, '27; January 27,1988; La Howard W. Wong, '53; August 30,1990; Silver tact Bonny Hafner at the ad Canada, Calif. Spring, Md. dress below. Robert G. Loomis,'29, SM '30; August 30,1991; Arthur W. Haines, '54; August 6,1992; Sacramento, Manchester, Conn. Calif. For a subscription to the Michael Anthony, '32; July 13,1992; North Falmouth, William N. Tatmers, PhD '54; July 9,1992; Flushing, Gazette clip and mail this ad, Mass. N.Y. enclosing a check (made out to Robert H. Hansen, '32; May 19,1992; Lakeside, Calif. John R. Segal, PhD '59; January 31,1990; NewYork, MIT) for $12 for six months or Norman M. Johnsen, '34; January, 7,1992; Atlantic N.Y. $20 for one year. Beach, Fla. Immo-Ragnar H. Nordstrom, '60; April 27,1992; Fair Willard F. Bixby, '35, SM '36; July 12,1992; Haven, N.J. Novelty, Ohio Robert Akullian, '70; July 20,1992; San Jose, Calif. J. Lawrence Tobey, '36; June 24,1992; Wenham, Sandra A. Wadsworth, MAR '74; September 15,1991; Mass. NAME Brookline,Mass. William A. Williams, SM '36; February 4,1990 Steven K. McClung, '84; July 11,1992; Atkinson, Herbert P. Gusdane, '37, SM '38; December 1,1991; N.H. STREET Mentor, Ohio Charles J. Palmer, SM '37; July 26,1992; East Sand wich, Mass. Correction: April's Deceased List erroneously CITY STATE ZIP William J. Pattison, '37; June 28,1992; Camden, Maine listed the date ofdeath ofLaurence Edmund Norman E. Weeks, '38; July 8,1992 MAIL TO: MIT ALUMNI Noble, '23, of Enid, Okk.,as August 9,1992. It Donald B. Peck, '39; July 1,1992; Bloomfield,Conn. was actually Mrs. Laurence Edmund Nobte,'23, CAREER SERVICES, RM 12-170, William W. Pomeroy, SM '40; July 14,1992; Alexan CAMBRIDGE, MA 02139 dria, Va. the former Gladys Farmer, who died on that 617-253-4733 Michael B. Bever, SM '42, ScD '44; July 17,1992; Cam date; her late husband was an alumnus ofHar bridge. Mass. vard. Our apologies for the error.—Erf. MIT 16 NOVEMBER/DECEMBER 1992 AACC short course faculty of Introduction to TECHNOLOGY AND Cereal Science and Technology, member of the XVIII MATHEMATICS AACC Cereal Foods World F.ditorial Advisory TPP POLICY PROGRAM Board, president and treasurer of the Institute of Eugene Gath, PhD'89, writes: "1 have been lecturing Food Technologists, part of the VP program of the MIT Professors Joel Clark, SM '75, (XV), ScD '72 in mathematics at the University of Limerick since Calumet Council BSA and chair, vice chair, and (III), David Marks, and Richard de Neuiville. '61. 1990. We are a new technological university in Ire member of the anniversary celebration committee SM '61, PhD '65 (1), traveled to Norway together in land, aspiring to be 'Ireland's MIT! I leach mathe of the AACC Carbohydrate Division. May, along with Frank Field, '78 (XXII), SM '81 matics to scientists and engineers as well as continue The Association of Alumni and Alumnae has (XXII), SM '81 (TPP), PhD '85 (III), as part of an MIT my own research. This year 1 won the Teaching been notified that Kathleen S. Sargent, PhD '71, of team establishing relations with a consortium of Excellence Award (worth~$l,700) at the University Winchester, Mass.,died February 19,1991,asa Norwegian companies and the Norwegian Techni of Limerick. I hope to visit MIT to meet with the few result of an automobile accident. No further infor cal Hockschule At the end of July, Professor de friends there who still haven't graduated!" ... Lance mation was provided. Ncufvillc was the featured speaker at the Mexican Forlnow, I'hD '89, assistant professor of computer Academy of Engineering, speaking on the develop science at the University of Chicago, has been named ment of TPP worldwide and at MIT James a National Science Foundation Presidential Faculty NUCLEAR Durand, SM '78, is now designing simulators for power plant operations at TRAX Corp. in Virginia. Fellow. One of the 30 young scientists and engineers XXII ENGINEERING recognized for excellence in research and teaching, ... Paul M. Hauge, SM '83, has been accepted at Fortnow will receive S500.000 to support his work Harvard Law School beginning September 1993— over the next five years. Fortnow is an expert in com Patrick M. Hogan, SM '89, writes: "1 am currently a Having completed a PhD in economics at Sloan, putational complexity theory—the study of how senior engineer with ABB Impcll Corp. in Lin Mark J. McCabc, SM '86, PhD '92 (XV), is now much computer time and memory are ne«led to colnshire, HI. Presently, I am the project engineer on a employed in the Antitrust Division of the U.S. solvedifferent types of computational problems. In project that involves performing various engineering Department of Justice. There are so many TPPers in his recent research, he has studied methods for veri analyses to support an upcoming dual unit outage Washington, D.C. Friends can contact him at 703- fying long, complex computer programs and has and the associated modification work for the Zion 329-1718 After spending a year and a half in investigated the power of "interactive proofs," a nuclear power plant in Zion, III."... Philip F. Argentina, and running his own company for a technique that uses a trustworthy small computer to Palmedo, SM '58 (X), PhD '61, has been named presi while, Richard Tomlinson, SM '87, has entered the check the results of a much larger, not necessarily dent and CEO of the newly formed Long Island British Foreign Office, working in the Environmen reliable computer. He hopes to build on recent work Research Institute. 1.1 RI was formed when three of tal, Science, and Energy Department. that has shown that the interactive proof technique Long Island's major research institutions joined forces Michael Masslmlno, SM '88, SM '88 (II), ME '90 places a limit on how well computers can estimate to accelerate the flow of technology to industry and to (II), PhD '92 (II), has accepted a position with answers to some extremely difficult problems. contribute to Long Island's economic development. McDonnell Douglas in Houston, Tex. He will be William W. Roberts, Jr., '64, PhD '69, professor Concludinga year of discussions, the University of working on research and operations for the space of applied mathematics at the University of Vir Stony Brook, Associated Universities (the managing station.... David Gold, SM '90 (XVI), SM '90, is ginia's School of Engineering and Applied Science corporation of Brookhaven National Laboratory), and currently the Associate Director of the Manufactur in Charlottesville, Va., has been named Common Cold Spring Harbor Laboratory agreed to create the ing Technology Center Program at the National wealth Professor. As director of the university's URI. The non-profit corporation will focus on bring Institute of Standards and Technology. There are Mathematical-Computational Modeling Labora ing new technologies from the academic sphere to the presently seven centers, each in different states, tory, Roberts' professional work focuses in part on world of commerce. Collectively, the three founding which help small and medium-sized manufactur developing the mathematical equations that institutions employ more than 1,500 PhDorMD ers modernize and become more competitive express events that are observed in nature and in researchers and annually conduct more than S400 mil Ziad Oueslati, SM '90, is working for Citibank in the experimental laboratory. He has developed lion in sponsored research. In its technology transfer Tunis.... Michael R. Berube, '89 (I), SM '92 (XV), algorithms for computer models that allow activities, the Institute will have an active program of SM '92, has started a new job with Chrysler Corp. researchers to study the motion, drag, and stability technology evaluation and will facilitate the applica as an environmental planning specialist working of fibers in steady and turbulent gas flows, the tion of technologies through licensing agreements, on alternative fuels, fuel economy, global warming, dynamics of hypersonic gas flows, and the struc joint ventures, and company start-ups.... Richard R. and electric vehicle issues.... Lola Matysiak, '91 ture and dynamics of galaxies. His olher research Sonstelie, SM '68, has been named president and CEO (I), SM '92, has relocated to Los Alamos, N. Mcx., areas include intelligent-control systems and simu of Puget Sound Power & Light Co. in Bellevue, Wash. where she is working at the Los Alamos National lations, intelligent control, manageability, feed Prior to this May 1992 promotion, Sonstelie was presi Laboratory.—Richard de Neufville, Technology back, computational fluid dynamics, shock waves dent and COO of the company. and Policy Program, MIT, Room E40-252, Cam and nonlinear phenomena, and prototype tech Navy Commander David W. Hearding, SM '77, bridge, MA 02139. nologies for fiber processing operations. Roberts ENE '77, recently received the Legion of Merit. has been at the UVa since 1969. Hearding was cited for "outstanding performance as commanding officer aboard the submarine USS PROGRAM IN SCIENCE, Pargo, homeported in New London, Conn." STS TECHNOLOGY & SOCIETY APPLIED BIOLOGICAL According to a Navy release, "As an extremely competent and resourceful leader, he performed XX SCIENCES his duties in an exemplary and highly professional Professor Merritt Roe Smith became the director manner. His superb leadership abilities were of the Program in Science, Technology, and Soci Charles]. Bates, PhD instrumental in the exceptional performance of the ety on July 1,1992. He succeeded Kenneth Kenis- '57, VP of the technical Pargo, and the remarkable improvement in its ton, who has completed a five-year term as direc group at American material condition and operations readiness. tor. Smith joined the MIT faculty shortly after the Maize Products Co., Under Hearding's expert guidance, the Pargo per founding of STS in 1977. He played a major role in was elected to the board formed superbly and set standards of excellence the development of the doctoral program in the of directors of the during numerous and ever-changing at-sea opera History and Social Study of Science and Technol American Association tions." Hearding is currently assigned with Subma ogy, which he has directed since 1987. Smith has of Cereal Chemists rine Development Squadron 12, Naval Submarine been Metcalfe Professor of Engineering and Lib (AACC). Bates has been Base, New London, Conn. He joined the Navy in eral Arts, co-director of MIT's Context Initiative, with American Maize 1968.... Jacquelyn C. Yanch, the W.M. Keck and immediate past president of the Society for Products Co. for 19 Career Development Assistant Professor in the History of Technology. He is author or editor years. He previously Biomedical Engineering and assistant professor of of three books and numerous articles and reviews. was in the Food Prod nuclear engineering, has received a 525,000 Junior He also edits the Johns Hopkins Press series on ucts Division and Faculty Career Award from the School of Engineer the history of technology and serves on the boards Industrial Detergents ing under a program supported by the GE Founda of trustees of the Hagley Museum and Library, the Division of Procter & tion. The foundation's Faculty for the Future pro Museum of American Textile History, and the C.J. Bates Gamble Co. for 15 gram is designed to increase the number of women Charles Babbage Institute as well as the history years. His work at Procter & Gamble included bak and members of underrepresented minority advisory committees of NASA and the Secretary ery mixes and bulk shortenings and some of his groups on the engineering, science, and business of the Air Force Professor Evelyn Fox Keller, early work led to the Duncan Hines Angel Food faculties in the United States. The foundation has known for her work on gender and science and on Cake Mix. Other career responsibilities have committed $330,000 over three years to MIT. the history of biology, has joined the STS faculty included process and product development for Yanch, a member of the Course XXII faculty and as professor. Keller was most recently on the fac both new and existing products, customer service, Whitaker College since 1989, is involved in three ulty of the University of California at Berkeley. sales and marketing, and most recently, process major projects: the design of neutron beams for Keller began her scholarly career as a natural sci development and plant design and construction for boron-capture therapy for brain cancer victims; entist, with a PhD in physics from Harvard. She high fructose corn syrup. A member of AACC since studies of dose distributions of isotopes injected in went on to work in mathematical biology, and 1972, Bates has served the cereal chemistry profes human joints; and development of data-visualiza became known for her collaborative studies of sion in many capacities including as member of the tion methods for tomography in medical diagnosis. chemotaxis and aggregation. She then turned TECHNOLOGY REVIEW MIT 45