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: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts oops, forget previous comment | Comment 16 of 20 |
apologies to charlie and his program. i reviewed my graph of card #2's path through the 52 card deck and found i had made an ERROR of 1 number. i corrected it and came up with 8 SHUFFLES!

confound it, CHARLIE's right again!
  Posted by rixar on 2004-05-26 11:34:18
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 (5)
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