The Constant Stack

Suppose, in an odd pack, P = ab. We can stack a set of 'b' cards 'a* apart through the pack, so that by dealing out 'a' hands of'b' cards each, all the stacked cards will fall in the same hand.

Taking any card of the stack as a reference card, the position from it of any other card in the stack will be a multiple of'a'; i.e., nQ = xa.

After one shuffle, nt = 2xa or n L = 2xa - P = 2xa - ab = a(2x - b)

In either case, nt is also a multiple of 'a*; i.e., the 'b' cards are still stacked 'a' apart through the pack after one shuffle, and hence after any number of shuffles. The cards will not, however, be in the same order in the stack.

For example, suppose we discard all the diamonds from a full pack, leaving 39 = 3 x 13 cards. We set these up in the order clubs, hearts, spades, clubs, hearts, spades and so on throughout. We now have three separate stacks of thirteen cards, three apart. If after any number of shuffles (with cuts in between, if you like) we deal the cards into three hands, each hand will consist of a full suit.

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