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Originally Posted by mizuchaud Here's a puzzle for everyone.
Try to figure it out in your head before you physically try it.
Just noticed it while shuffling two different colors of chips together.
If you had two stacks of five chips, (total of ten chips), say a red stack on your left and a black stack on your right, how many PERFECT shuffles does it take to retrun the stacks to sorted colors: red on one side and black on the other?
How many shuffles would it take to resort two stacks of six?
Two stacks of seven?
Two stacks of eight?
And the last question: how many shuffles would it take to resort two stacks of four?
Post your answers. Then try it. (For the shuffle-impaired, do it manually.) Then someone post a mathematical reason for it.
(I don't know it, I've just noticed the pattern)
Have fun! If anything, it's great practice for perfect shuffling.    |
I think the rule is:
for 2n chips (shuffling two stacks of n chips each), it takes
* n-1 if n is even
* n+1 if n is odd
I'll check this first, then if I'm write I'll give you the proof.
* EDIT * Nope... trying again.
Depends if n = 2^m for integer m. In that (simplest) case, it takes m+1. I'm working on the other cases.
