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Unformatted text preview: 8 shuffles. Among the many curious patterns, notice how cards 18 and 35 flip positions after each shuffle. The situation is much different for 54 cards; a similar analysis gives that youll need 52 shuffles in order to return the deck to its initial state. Moreover, each card (other than the top or bottom card) will migrate through each of the other 52 positions of the deck! For the general case, it becomes useful to renumber the deck of n cards from 0 to n1. The equation for the shuffle then becomes p(i) = 2 i ( modulo n1) This gives that the number of shuffles is the order of the residue 2 in the group of units, under multiplication, modulo n1 , from which you can derive the following table for the number of shuffles. n 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 number of shuffles 2 4 3 6 10 12 4 8 18 6 11 20 18 28 5 10 12 36 12 20 14 12 23 21...
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This note was uploaded on 03/01/2010 for the course MATH 301 taught by Professor Albertodelgado during the Spring '10 term at Bradley.
 Spring '10
 AlbertoDelgado
 Combinatorics

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