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Unformatted text preview: Card Trick Problem Set Solutions Michael Allen November 30, 2000 1-4 Lower Bounds With the given procedure, we can establish a lower bound for the size of the deck for which we can perform the card trick for a given number of cards. These results are shown below. hand deck 2 3 3 6 4 15 5 52 6 245 n 2( n- 1)! + ( n- 1) 5-6 Upper Bounds Our procedure, however, is not optimal, and it is theoretically possible to perform the trick with a larger deck. We can set our upper bound at a size which makes maximal use of the information available to us. hand deck 2 3 3 8 4 24 5 124 6 725 n n ! + ( n- 1) 1 7 For the following, assume we have a deck of d cards from which the accomplice chooses a hand of size n . a. The number of ways the accomplice can choose a hand is C ( d, n ). b. The number of different permutations of the n-1 cards the accomplice can show is n !. c. The number of different strategies available to the accomplice and magician are n !...
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