Sixth Week, March 13. A Trick With Cards.Two magicians, Aaron and Betty, perform the following trick with cards. Betty leaves the room. Aaron lets some member of the audience pull five cards at random from an ordinary deck of 52 cards. He then selects four of the five cards and puts them, face up, left to right in a certain order on the table. He puts the fifth card back in the deck, after showing it to the audience. Betty is then called back into the room. She looks at the four cards in order, and announces the correct value of the fifth card. How do they do it? (I heard of this problem from P. Klarreich.)
Note: I am not giving out solutions to "Problems of the Week". But I am very happy to discuss these problems with you, including any partial or attempted solutions that you might have. I am always interested in hearing about interesting or creative solutions, so let me know if you have any!
See previous Problems of the Week.
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