A Homovocalic Survey
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Mathematical Circus & 'Martin Gardner
MARTIN GARDNE MATHEMATICAL ;MATH EMATICAL ASSOCIATION J OF AMERICA MATHEMATICAL CIRCUS & 'MARTIN GARDNER THE MATHEMATICAL ASSOCIATION OF AMERICA Washington, DC 1992 MATHEMATICAL More Puzzles, Games, Paradoxes, and Other Mathematical Entertainments from Scientific American with a Preface by Donald Knuth, A Postscript, from the Author, and a new Bibliography by Mr. Gardner, Thoughts from Readers, and 105 Drawings and Published in the United States of America by The Mathematical Association of America Copyright O 1968,1969,1970,1971,1979,1981,1992by Martin Gardner. All riglhts reserved under International and Pan-American Copyright Conventions. An MAA Spectrum book This book was updated and revised from the 1981 edition published by Vantage Books, New York. Most of this book originally appeared in slightly different form in Scientific American. Library of Congress Catalog Card Number 92-060996 ISBN 0-88385-506-2 Manufactured in the United States of America For Donald E. Knuth, extraordinary mathematician, computer scientist, writer, musician, humorist, recreational math buff, and much more SPECTRUM SERIES Published by THE MATHEMATICAL ASSOCIATION OF AMERICA Committee on Publications ANDREW STERRETT, JR.,Chairman Spectrum Editorial Board ROGER HORN, Chairman SABRA ANDERSON BART BRADEN UNDERWOOD DUDLEY HUGH M. EDGAR JEANNE LADUKE LESTER H. LANGE MARY PARKER MPP.a (@ SPECTRUM Also by Martin Gardner from The Mathematical Association of America 1529 Eighteenth Street, N.W. Washington, D. C. 20036 (202) 387- 5200 Riddles of the Sphinx and Other Mathematical Puzzle Tales Mathematical Carnival Mathematical Magic Show Contents Preface xi .. Introduction Xlll 1. Optical Illusions 3 Answers on page 14 2. Matches 16 Answers on page 27 3. -
Letters in Squares- Word Puzzles in English
UNIVERZA V MARIBORU FILOZOFSKA FAKULTETA ODDELEK ZA ANGLISTIKO IN AMERIKANISTIKO Diplomsko delo LETTERS IN SQUARES- WORD PUZZLES IN ENGLISH Mentorica: Kandidatka: Doc.dr. Katja Plemenitaš Mateja Vinovrški Maribor, 2010 ZAHVALA Hvala vsem, ki ste kakorkoli pomagali, da je ta naloga tukaj! U N I V E R Z A V M A R I B O R U F I L O Z O F S K A F A K U L T E T A Koroška cesta 160 2000 Mariboor IZJAVA O AVTORSTVU Podpisana Mateja Vinovrški, rojena 23. aprila 1980 v Mariboru, študentka Filozofske fakultete Univerze v Mariboru, smer angleški jezik s književnostjo in biologija, izjavljam, da je diplomsko delo z naslovom Črke v kvadratih – besedne uganke v angleščini oz. Letters in squares – Word puzzles in English pri mentorici doc. dr. Katji Plemenitaš, avtorsko delo. V diplomskem delu so uporabljeni viri in literatura korektno navedeni; teksti niso prepisani brez navedbe avtorjev. ABSTRACT Word puzzles and games are an important tool for learning and consolidating language. They appear in various forms and in various media (books, online, board games and newspapers). This diploma thesis presents the history of word puzzles and offers a classification of different types of word puzzles and games. In order to gauge how English language-learning materials in Slovenia utilize word puzzles, an analysis of the number of occurrences and variety of word puzzles in English language study books that are offered in Slovenia is also presented. A survey among Slovenian primary school learners has been made regarding the use of crosswords in the classroom and its results are also presented. -
Howard Bergerson
HOWARD BERGERSON A. ROSS ECKLER Morristown, New Jersey Howard Bergerson was born in Minneapolis on July 29, 1922 to Margaret Jeske, who six years later married Ludvick (or Louie) Bergerson. Howard served in World War 11, and moved in 195 1 to a small house in Sweet Home, Oregon, down the block from a shingle mill where he was employed for over 40 years. In 1967, Howard met Nellie, suffering from multiple sclerosis, with three young children, Gerald age 10, Earl age 8 and Merla age 4. Not wanting to see this family broken up, he married her, exhibiting a nobility of character inexplicable to many (Dave Silverman, Kickshaws editor from 1969 to 1976, wrote me "The poor fellow is the only martyr I know. And I don't even know to what!"). He found Gerald's "disruptive, destructive and criminal" tendencies were too much to deal with, even resorting to hypnosis (with some success) to modify his behavior. By the age of 15 Gerald had left home, to live with relatives. When Merla "fled the coop" in 1982, he had to get a home health aide to watch Nellie while he worked. Nellie died sometime in the 1980s; Howard later married the teenage home health aide, but this apparently did not last long. Howard himself suffered from grand ma1 epilepsy, fortunately well-controlled by medication. When Faith and I visited Howard in the summer of 1979, he was living with Nellie and Merla (the boys by then had left) in straitened circumstances. His somewhat dilapidated house was filled with books which Howard had collected over many years, piled from floor to ceiling (Faith joked that the books in the living room were helping to hold up the roof). -
A College-Level Course in Logology
210 A COLLEGE -LEVEL COURSE IN LOGOLOGY for its site words (I Sl socks, Idi 13 word gam.e In addition used to prepar' PAUL ZASLOW tion, Willa rd J Amhe r st, Mas sachusetts Hay, C. C. Bor and Howard Be The February 1978 issue of Word Ways asked readers for informa Ve rbatim. and I tion on recreational linguistics courses taught in college, secondary The two-ho school, night school 0 r the like. In the spring term of 1978, when I was a junior at the University of Massachusetts, I taught a one-credit ( such as: the v gram is a wore colloquium entitled 11 Recreational Logologyll. In the fall term of 1978, phrase; the lin I taught a three- credit course entitled II An Introduction to Recreational Logology" (Course SW-190) to 15 freshmen and sophomores, 13 of several give-at whom completed it. This met for three hours on Thursday evenings hostile word; f for 13 weeks from September to December, and covered the following and three name topic s: in any position asked wlJ.at corr 1 what is recreational logology? related books, journals, diction aries 2 pangrams, lipograms, ABC language (letter rebuses, as in I A B C D goldfi sh 1 = Abie, see the goldfish, 0 r I F E G I::: effigy) , rebuse s 3 anagrams, palindrome s QUERY 4 word squares, numerical logology (difference words, centrally bal anced beam words, word weights and centers of gravity) While pe 5 word surgery: deletions (beheadments, curtailments, charitable and Schu and stingy wo rds, dismembered words) , inse rtions (hydrations, wick and caudations, hospitable and hostile wo rds , -
A Recreational Linguistics Library
131 A RECREATIONAL LINGUISTICS LIBRARY DAVID MORICE Iowa City, Iowa The following article is adapted from a paper presented to the class "Foundations and Collections Development" in the University of Io\,<ra's School of Library and Information Sciences. The pro fessor, Gerald Hodges, commented on it in part: "It appears to me that you have done the unthinkable - build an enjoyable and entertaining collection for an academic setting... I do feel that your selection process was systematic, and I think you are on solid ground in going with those titles wh ich had mul tiple favorable reviews. Your annotations not only tell me suf ficient information about each title but do indeed justify the selection decision. The use of a variety of sources, including both library and subject specialization, is a real advantage of the process you used... I particularly want to commend you on the four criteria statements you made and upon the decision to exclude certain formats ...Aren 't you glad that you had some what unlimited budgetary possibilities?" SUBJECT AREA Recreational Linguistics, also known as Logology and Wordplay. THE LIBRARY AND ITS USERS The hypothetical site for this project is an English Department Library at a large university. The library has several thousand volumes covering almost all areas and eras of English literature and language. It subscribes to forty literary periodicals, and its media room houses over a hundred films and fi lmstrips. The pri mary users are undergraduate English majors and graduate students in English and in Linguistics. To a lesser extent, users a Iso in clude students in Education, Modern Language, and Comparative Literature, and, on occasion, non-university members of the commu nity. -
COLLOQUY T Is Possible :Onditions Of
149 for example COLLOQUY t is possible :onditions of yth ync Webster's Dictionary defines colloquy as mutual discourse. Read ers are encouraged to submit additions, corrections, and comments about earlier articles appearmg in Word Ways. Comments received at least one month prior to publication of an Issue will appear m that issue. DY, GO, GY, VY, WU, WY, Tributes to the late Dmitri Borgmann continue to arrive. Philip Cohen: February was a fine swan song for Borgmann; it displ ayed his strength s (imagination, indefatigability and range) 19 the Pocket and downplayed what I consider his weaknesses. Whatever nega tive things I've said in the past, I have to agree we've lost e comprehen one of the very greatest. of three-let Harry Partridge: The news about Dmitri Borgmann was dreadful s of the Ox and devastating. You cite Willard Espy as commenting "He was the most dif obviously a difficult man", but one would never know it from his writings, which have always impressed me as uniformly good-hu mored and vivacious ... [a] dense and pregnant style. epared using Darryl Francis: My feelings were echoed by Jeff Grant's words in :ely that the May... Dmitri. .. introduced me to the world of logology [in Language the various nputer might on Vacation]. I can remember the time when I received 6 or 7 letters a day from Dmitri, usually when he was working on a 3ts automa ti prOject that he was particularly enthusiastic a bout. .. Al as! No other individual has so altered my life, except I suppose for my parents, my wife, my kids! The Word Wurcher passed along a n umber of comments on the Borg 's the years mann memorial issue. -
PANGRAMS the Line Religious Will Not ~ in 1875, and Literatt in 1961
90 stone, as PANGRAMS the line religious will not ~ In 1875, and Literatt in 1961. He MAXEY BROOKE who apparel Sweeny, Texas bet, but c 48 letters: The word pangram, though well-known to the logologist for many John P. B years, appears in few dictionaries. Such standard works as the Merriam-Webster Unabridged (both Second and Third Editions) and During th the Oxford English Dictionary omit it, and it is not mentioned in lets called 0 the Encyclopedia Britannica 1 s long section on wordplay. The only a variety dictionaries in which it appears are 6000 Words (1976) and the lish langua third volume of the Supplement to the Oxford English Dictionary letters, by (982). In both, the word is defined as a sentence containing all Pyx crwth 26 letters of the alphabet. It is understood, although not explicit ly specified, that some of these letters may appear more than once. which can t instrument, From the standpoint of the logolog ist, the shorter the pangram In No. 1750 the more meritorious the sentence; the ultimate pangram contains grams. Mos e x act1y 26 1e tte r s . names and The prophet Ezra, who lived about 500 B.C., can be regarded ones, includ as the first pangrammatist. In the book of Ezra, verse 21 of chap Quick zep ter 7 reads In LangE And 1, even 1 Artaxerxes the king, do make a decree to all gives two 2 the treasurers which are beyond the river, that whatsoever Ezra the priest, the scribe of the law of the God of heaven, shall Cwm, fjor require of you, it be done speedily. -
Borgmann: the Man Behind the Legend
195 BORGMANN: THE MAN BEHIND THE LEGEND FAITH W. ECKLER Morristown, New Jersey Dmitri Borgmann has been called the Father of Logology--a term he coined to describe recreational wordplay as distinguished from academic linguistics. His two books, Language on Vacation (1965) and Beyond Language (1967), have become classics in the field. In 1968 Greenwood Press selected him as Word Ways I first editor. Despite this prominence in the field of logology, the man behind the legend has remained tantalizingly obscure. So far as the pres ent editor knows, only one of his logological correspondents ever met Dmitri in person. Several times during the period 1979-81 we had occasion to be in the State of Washington, but Dmitri always discouraged us from paying him a visit. In the summer of 1988 we were once again in the area. and this time we contacted Dmitri's widow, Iris, and offered to visit and, perhaps, ma ke some eva luation of Borgmann I s books and papers. She readily accepted our offer and so, on a scorching hot day, we drove the .400 miles east from the coast, arriving in Dayton about 6 P.M. Dayton is a town whose central business district, a few blocks long. is totally without charm. A.lthough not far from the univers ity town of Walla Walla, and on the edge of the prosperous truck farming area of central Washington, Dayton shows evidence of be ing in a severe economic slump. We were told that unemployment there runs about 20 per cent. When asked why Dmitri chose such an unprepossessing town to move to, Iris replied that after many years in Oak Park (at the edge of Chicago), Dmitri wanted to live someplace where he would never have to see another Black again. -
Dmitri Borgmann, Father of Logology
3 DMITRI BORGMANN, FJ\THER OF LOGOLOGY It has often been Said that an institution is merely the length ened shadow of a man. Logology in generaI, and Word Ways in particular, owes much to Dmitri Borgmann; this issue, consisting entirely of his handiwork (except for this article and Colloquy), is a salute to his long-lasnng devOL ion to the cause of wordplay. DmItri is the one who, in a letter to Howal"d Bergerson in the eady 1960s, wroLe "1 don't believe that the word '10g010gy' has ever appeared In a book devoted to words Ol puzzles. 1 dug il out of the unabridged Oxfold wtlLle seal ching for a sUltable name for my activity." (The OED and tne Century SUlJplelllenL deflne It as the "doctrine of the Logos," a theologlcal concept; the Of\) also defines it as the "SCience of words.") His first book, Langua~,,- on Vacation (Sclibnel's, 19651, is a logological landn,ark-,--definmg the field as the nlampulatLOn of words v1ewed as collections of letters. The bulk of th1S book is devoted to long-established letterplay such as the pallndrollJe, the transpositi.on, the anagram, and the word square, dt-awing exten sively on sources as dlverse as Notes & Quenes and the Nanonal puzzlers' League pubhcation, the Enigma, he exh1b1Led 0. dazzltng variety of special types. Two other wordplay books, Beyond Lan guage (Scl"ibner 's, 1967) and Cunous Crosswords (( Scnbner' s, 1970), so~followed; all are now out of pnn L. Of course, books on wordplay have been pub Iished for many cen tudes, from Taboul-et's Les Digarrures et Touches in tne sixteenth centur y to Bombaugh' s Oddities and CUL-iosiLLes at the end of Lhe n 1nete e r. -
Zadania Redaguje Łukasz BOŻYK M 1540
W następnym numerze: o niemożności. SPIS TREŚCI NUMERU 9 (520) Dlaczego niektóre łamigłówki są tak trudne? Łukasz Grządko str. 1 Testy serii Przemysław Grzegorzewski str. 4 Przerwy w liczbach pierwszych Wojciech Czerwiński str. 8 Wyniki XXXIV Ogólnopolskiego Sejmiku Matematyków, Miesięcznik Delta – matematyka, fizyka, astronomia, informatyka jest wydawany przez Szczyrk, 8–11 VI 2017 str. 10 Uniwersytet Warszawski przy współpracy towarzystw naukowych: Polskiego Towarzystwa Matematycznego, Polskiego Towarzystwa Fizycznego, Polskiego Towarzystwa Astronomicznego Małe Wszechświaty str. 10 i Polskiego Towarzystwa Informatycznego. Komitet Redakcyjny: dr Waldemar Berej, dr Piotr Chrząstowski-Wachtel, Zadania str. 11 dr Krzysztof Ciesielski – wiceprzewodniczący, prof. dr hab. Bożena Czerny, dr Andrzej Dąbrowski, prof. dr hab. Marek Demiański, prof. dr hab. Krzysztof Diks, Rekreacyjna lingwistyka dr Tomasz Greczyło, prof. dr hab. Paweł Idziak, dr hab. Agnieszka Janiuk, z matematyką dr hab. Marcin Kiraga, prof. dr hab. Andrzej Majhofer, prof. dr hab. Zbigniew Marciniak, Andrzej Bartz str. 12 dr hab. Zygmunt Mazur, dr Adam Michalec, prof. dr hab. Michał Nawrocki – przewodniczący, Combinatorial Nullstellensatz dr Zdzisław Pogoda, dr Paweł Preś, prof. dr hab. Wojciech Rytter, prof. dr hab. Paweł Strzelecki. w teorii liczb Redaguje kolegium w składzie: Wiktor Bartol, Michał Bejger, Jacek Dymel str. 14 Szymon Charzyński – z-ca red. nacz., Wojciech Czerwiński, Tomasz Kazana, Migawka informatyczna: Piotr Kaźmierczak, Krystyna Kordos – sekr. red., Marek Kordos – red. nacz., Kamila Łyczek, Ciemna strona Internetu str. 16 Katarzyna Małek, Łukasz Rajkowski, Anna Rudnik, Krzysztof Rudnik, Piotr Zalewski. Adres do korespondencji: Informatyczny kącik Instytut Matematyki UW, Redakcja Delty, ul. Banacha 2, pokój 4020, olimpijski (107): 02-097 Warszawa, e-mail: tel. 22-55-44-402. Palindromiczny podciąg [email protected] Kamil Dębowski str. -
COLLOQUY T Is Possible :Onditions Of
149 for example COLLOQUY t is possible :onditions of yth ync Webster's Dictionary defines colloquy as mutual discourse. Read ers are encouraged to submit additions, corrections, and comments about earlier articles appearmg in Word Ways. Comments received at least one month prior to publication of an Issue will appear m that issue. DY, GO, GY, VY, WU, WY, Tributes to the late Dmitri Borgmann continue to arrive. Philip Cohen: February was a fine swan song for Borgmann; it displ ayed his strength s (imagination, indefatigability and range) 19 the Pocket and downplayed what I consider his weaknesses. Whatever nega tive things I've said in the past, I have to agree we've lost e comprehen one of the very greatest. of three-let Harry Partridge: The news about Dmitri Borgmann was dreadful s of the Ox and devastating. You cite Willard Espy as commenting "He was the most dif obviously a difficult man", but one would never know it from his writings, which have always impressed me as uniformly good-hu mored and vivacious ... [a] dense and pregnant style. epared using Darryl Francis: My feelings were echoed by Jeff Grant's words in :ely that the May... Dmitri. .. introduced me to the world of logology [in Language the various nputer might on Vacation]. I can remember the time when I received 6 or 7 letters a day from Dmitri, usually when he was working on a 3ts automa ti prOject that he was particularly enthusiastic a bout. .. Al as! No other individual has so altered my life, except I suppose for my parents, my wife, my kids! The Word Wurcher passed along a n umber of comments on the Borg 's the years mann memorial issue. -
Best Anagrams and Antigrams
218 I BEST ANAGRAMS AND ANTI GRAMS I I or rea P O. V. MICHAELSEN l Highland Park, New Jersey reI. It There are several criteria available for judging the quality of see an anagram. To begin with, an anagram should be self-explana I tory. The anagram ted THAT'S PRIME NEWS? NO, IT PREYS ON THE WEEK In The newspaper is not The New York Times stn is deficient in this respect; it must be explained that it refers My enc to a New York weekly which regards sensationalism as "prime" news. Unnecess ary words detract from the theme, a s THE GR EAT and c cen THE LATE, GREAT in the anagrams eve THE GREAT THOMAS ALVA EDISON eso The good man, he lit vast areas THE LATE, GREAT DR. MARTIN LUTHER KING I the Think tall -- a "dreamer" greeting truth p The superfluous words most frequently formed from left-over letters t are NOTE, OH, AH, HA, LO, and HA 11. The letter 0 should only be used in a poetic context as an alternative to the standard OH. f Nea In the ultimate anagram, every word relates to the subject. anc A "prime" example is Emmo W. I S April 1948 Enigma anagram ELEVEN + TWO", twelve + one. The perfect anagram is completely transposed I and grammatically correct. It is a rule among veterans of this fie< art that an anagram should never contain more than three letters ern in the same sequence as. in the origina I word (s) (the first anagram above uses NEWS).