PROBLEM 8

A perfect shuffle of a deck of cards is a "riffle" shuffle in whichthe deck is divided in two and then the cards interlaced so that the new orderis t1, b1, t2, b2, ... where tn is the nth card in the top half of the originaldeck and bn is the nth card in the bottom half.
If a perfect shuffle is performed repeated on an ordinary deck of 52 cards, howmany shuffles will it take to return the deck to its originalorder?

Send your solutions to David Poole, Department of Mathematics, LEC N127-2 or bye-mail to madgp@blaze.trentu.ca.

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