All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > General
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: ( You must be logged in to post comments.)
  Subject Author Date
Cycle NotationTristan2005-03-23 00:33:01
Hints/Tipsrecursive observationsRamakanth2004-07-18 20:24:33
i just wrote it all out.Rachel2004-07-13 03:28:00
No Subject0817872004-06-04 02:54:18
Some Thoughtsoops, forget previous commentrixar2004-05-26 11:34:18
Solutionforget equationsrixar2004-05-26 08:49:50
Some Thoughtsfor powers of 6Danny2004-05-25 14:08:48
re: there's a pattern there. I just know it!Charlie2004-05-25 11:46:31
re: there's a pattern there. I just know it!Charlie2004-05-25 11:35:24
there's a pattern there. I just know it!Danny2004-05-25 10:53:44
re(7): Making a sequence (spoilers on the numbers)SilverKnight2004-05-21 11:45:53
re(6): Making a sequence (spoilers on the numbers)Charlie2004-05-21 11:41:11
Solution through codeAmitava2004-05-21 10:11:42
Questionre(5): Making a sequence (spoilers on the numbers)Danny2004-05-20 21:39:34
re(4): Making a sequence (spoilers on the numbers)Charlie2004-05-20 09:03:20
SolutionA puzzling sequence (VB program used)Penny2004-05-20 08:54:38
re(3): Making a sequence (spoilers on the numbers)Richard2004-05-20 00:04:46
re(2): Making a sequence (spoilers on the numbers)Charlie2004-05-19 21:13:59
re: Making a sequence (spoilers on the numbers)ThoughtProvoker2004-05-19 15:41:43
Some ThoughtsMaking a sequence (spoilers on the numbers)Charlie2004-05-19 15:00:18
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information