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Perfect Shuffle (Posted on 2004-05-19) Difficulty: 5 of 5
You have a deck of 52 cards - for convenience, number them 1 through 52. You cut the cards into two equal halves and shuffle them perfectly. That is, the cards were in the order
1,2,3,...,52
and now they are
1,27,2,28,...,26,52. Let's call this a perfect in-shuffle.

If you repeat this in-shuffling process, how many in-shuffles will it take for the deck to return to its initial ordering (taking for granted that the cards will eventually do so)?
________________________

How does the solution change if you have a deck of 64 cards, or 10, or in general, n cards? For odd integer values of n, in-shuffling will take 1,2,3,...,n to 1,(n+3)/2,2,(n+5)/2,...,n,(n+1)/2. For example, when n=5, the first in-shuffle yields 1,4,2,5,3.

No Solution Yet Submitted by SilverKnight    
Rating: 4.2500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Question re(5): Making a sequence (spoilers on the numbers) | Comment 7 of 20 |
(In reply to re(4): Making a sequence (spoilers on the numbers) by Charlie)

But is there a formula? One that can be used to figure it how many shuffles it would take, given n? Writing a program just isn't the same. There has to be some sorta pattern to the numbers.
  Posted by Danny on 2004-05-20 21:39:34

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