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 Perfect Shuffle (Posted on 2004-05-19)
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)?
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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)

 Subject Author Date Cycle Notation Tristan 2005-03-23 00:33:01 recursive observations Ramakanth 2004-07-18 20:24:33 i just wrote it all out. Rachel 2004-07-13 03:28:00 No Subject 081787 2004-06-04 02:54:18 oops, forget previous comment rixar 2004-05-26 11:34:18 forget equations rixar 2004-05-26 08:49:50 for powers of 6 Danny 2004-05-25 14:08:48 re: there's a pattern there. I just know it! Charlie 2004-05-25 11:46:31 re: there's a pattern there. I just know it! Charlie 2004-05-25 11:35:24 there's a pattern there. I just know it! Danny 2004-05-25 10:53:44 re(7): Making a sequence (spoilers on the numbers) SilverKnight 2004-05-21 11:45:53 re(6): Making a sequence (spoilers on the numbers) Charlie 2004-05-21 11:41:11 Solution through code Amitava 2004-05-21 10:11:42 re(5): Making a sequence (spoilers on the numbers) Danny 2004-05-20 21:39:34 re(4): Making a sequence (spoilers on the numbers) Charlie 2004-05-20 09:03:20 A puzzling sequence (VB program used) Penny 2004-05-20 08:54:38 re(3): Making a sequence (spoilers on the numbers) Richard 2004-05-20 00:04:46 re(2): Making a sequence (spoilers on the numbers) Charlie 2004-05-19 21:13:59 re: Making a sequence (spoilers on the numbers) ThoughtProvoker 2004-05-19 15:41:43 Making a sequence (spoilers on the numbers) Charlie 2004-05-19 15:00:18

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