David Copperfield's Orient Express Card Trick Author(s): Sidney J. Kolpas Source: The Mathematics Teacher, Vol. 85, No. 7 (OCTOBER 1992), pp. 568-570 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/27967773 . Accessed: 08/12/2014 12:26

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This content downloaded from 155.33.16.124 on Mon, 8 Dec 2014 12:26:36 PM All use subject to JSTOR Terms and Conditions Sidney J. Kolpas

(David CopperfieCd's

Orient Card ^ Express

could Tuesday, 9 April 1991, a major television net see only the backs of the cards and obviously see made themillions of viewers work spotlighted an hour-long evening special fea not the choices by turing illusions of the renowned magician David participating in the privacy of their homes. were three O Copperfield. The program, titled "Mystery on the Participants given the following gen can Orient Express," included a card trick inwhich eral instructions: (1)Moves be only up, down, on moves are viewers could participate. The card trick and its right, or left thematrix, (2) diagonal are of each move is potential use in themathematics classroom the illegal, and (3) the choice entirely focus of this article. up to the participant. Copperfields trick then pro Copperfieldbegan his trickby showingthe audi ceeded according to six sequential steps, with view on ence a close-up on the television screen of four ers starting their chosen card. cards representing four cars on the Orient Express: the shower car, the diner car, the club car, and the THE TRICK was to choose mail car. The audience instructed Step 1:Make fourmoves. Copperfield indicated one of the cards on which to start the trick (fig. 1). that viewers could not then be on the staffcard, so To these four cards were then added an additional itwas removed from thematrix (fig. 2b). five cards tomake feat (ostensibly Copperfields Step 2: Make fivemoves. Copperfield stated that on more difficult) to forma 3 3 matrix of cards since viewers could not have landed on the club the screen 2a). Of course, the could (fig. magician card, itwould be removedfrom thematrix (fig. 2c). Step 3: Make twomoves. Since viewers could not be on themail card, itwas removed from the matrix (fig. 2d). Step 4: Make threemoves. Since viewers could be on neither the baggage card nor the caboose card, those cards were removed (fig. 2e). Step 5: Make threemoves. Copperfield said that sincemany viewers had previously landed on the shower card, he would remove that card from the matrix (fig. 2f). Step 6: Make one move. Copperfield correctly predicted that all viewers participating in the trick were then on the diner card.

SidneyKolpas teachesmathematics at Glendale College, Glendale, CA 91208-2894.He is interestedin mathemat icshistory, rare books,mathematical magic, and theuses of technology.

568 THEMATHEMATICS TEACHER

This content downloaded from 155.33.16.124 on Mon, 8 Dec 2014 12:26:36 PM All use subject to JSTOR Terms and Conditions out which I Readers might want to follow all the steps of the evening I worked the followingproof, classes from basic mathematics trick to verify that they end up on the diner card presented to all my no matter what their choice ofmoves for each of through calculus. Almost every student,without tomathematical understood the the six steps. This trick served as a perfect transi regard level, proof. their formore tion to the climax of the hour-long special: Copper Moreover, itwhetted appetites and them new fieldmade a diner car from the Orient Express mathematical magic gave insight and mathematical vanish while a group of people encircled the car. into, appreciation for, proof. Many ofmy students watched the program?in some instances, instead of doing their homework? THE PROOF as and were intrigued that the trickhad worked. Number thematrix of cards from 1 through 9 a move Most recognized that ithad a mathematical basis shown infigure 3. Notice that upward a move to but were at a loss to prove why itworked. That subtracts 3, a move downward adds 3,

Bar funven Bar fiawer

Diner ngme Diner nfpne

aBoose 9?d aBoose MM (a) (b) The 3x3 matrixof cards The matrix after step 1

(Bar fiozver

(Diner tyjtne Diner nfjme

aBoose aBoose (c) (d) The matrixafter step 2 The matrixafter step 3

(Diner nfpne (Diner ngme (e) (f) The matrix after step 4 The matrix after step 5

Fig. 2

Vol. 85,No. 7? October 1992 569

This content downloaded from 155.33.16.124 on Mon, 8 Dec 2014 12:26:36 PM All use subject to JSTOR Terms and Conditions the left subtracts 1, and a move to the right adds 1; Step5 therefore,each move adds or subtracts an odd Move 1 Move 2 Move 3 number. Moreover, note that the card on which we Location Odd Even Odd start has an even number. Also, keep inmind that? We cannot be on card 2. Remove it.Only cards 1,4, and 5 are left.We are an odd card (1 or 5). an even number plus orminus an odd number results in an odd More cards number and Step 6 an odd number orminus an odd number make plus Move 1 results in an even number. Location Even the feat successive moves must alternate Therefore, We cannot be on cards 1 or 5. Remove them. There appear more between odd and even status. fore,we must be on card 4, the diner card, as Cop difficult perfield predicted! See table 1 for a summary of BAR= 1 SHOWER= 2 BAGGAGE= 3 the proof. Interested readers and their studentsmight DINER = 4 ENGINE = 5 CLUB = 6 want to investigate what happens to the proof when differentnumbering schemes are used for CABOOSE = 7 MAIL = 8 STAFF = 9 the 3 3 matrix. Also, are any othermethods pos sible for the Fig. 3 accomplishing proof? Numberingthe cards from1 through9 This reasoning was satisfying to students and required no more than elementary number theory. Proceed as follows: Start on an even number Mathematical magic tricks such as this one are excellent motivational devices and offer (shower, diner, club, ormail). Remember that each exciting of the nature of can step begins where the previous step ended. ways introducing proof.They also serve as dramatic introductions to new mathe Stepl matics concepts. The interested reader could find Move 1 Move 2 Move 3 Move 4 no better beginning sources onmathematical Location Odd Even Odd Even magic than the outstanding works produced on this fascinating subject byW. W. Rouse Ball We cannot be on card 9. Remove it. cards Only 1,2, (1928),Martin Gardner (1956), Royal Vale Heath 3,4,5,6, 7, and 8 are left.We are on an even card (1953), and William Simon (1964). Creative teach (2,4,6, or 8). ers can findmyriad ways of integrating into the con Step2 mathematics curriculum the exciting tricks tained in these books. Move 1 Move 2 Move 3 Move 4 Move 5 Location Odd Even Odd Even Odd

We cannot be on card 6. Remove it.Only cards 1,2, 3,4,5, 7, and 8 are left.We are on an odd card (1, 3,5, or 7). Step3 Move 1 Move 2 Location Even Odd

We cannot be on card 8. Remove it.Only cards 1,2, 3,4,5, and 7 are left.We are on an odd card (1,3, 5, or 7). Step4 Move 1 Move 2 Move 3 REFERENCES Location Even Odd Even Ball, W. W. Rouse. Mathematical Recreations and London: Macmillan & 1928. We cannot be on cards 3 or 7. Remove them. Only Essays. Co., Gardner, Martin. Mathematics, Magic, and Mystery. cards 1,2,4, and 5 are left.We are on an even card New York: Dover Publications, 1956. (either 2 or 4). For that reason, Copperfield says in Heath, Royal Vale. Math E Magic. New York: Dover 5 that ofus had been on card 2 step many just (the Publications, 1953. 50 ofus are on shower); theoretically, percent card Simon,William. Mathematical Magic. New York: 2 at the end of step 4. Charles Scribner's Sons, 1964. @

570 THEMATHEMATICS TEACHER

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