All Questions

Cards Reordering

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Parts

Part 1

The standard procedure for shuffling a deck of cards is to take the pack face downwards in the left hand and then transfer each card one by one to the right hand, putting the second on top of the first, the third under, the fourth above, and so on until all cards are transferred.

If you perform this operation with an even number of cards and keep on repeating the shuffle in the same way, the cards will in due time return to their original order. Try with 4 cards and you will find the order is restored in 3 shuffles. In face, where the number of cards is 2, 4, 8, 16, 32, 64, the number of shuffles to get them back to the original arrangement is 2, 3, 4, 5, 6, 7 respectively.

How many shuffles are necessary in the case of 14 cards?