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  #9 (permalink)     Top 
Old 10-16-2006, 07:34 PM
mizuchaud's Avatar
mizuchaud mizuchaud is offline
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Re: Chip shuffling puzzle...

Quote:
Originally Posted by jdunford
I think you have to be careful... Let's say you have red on the left and green on the right, after the first shuffle you'll have:
r-g-r-g-r-g-r-g-...
In order to keep the shuffling consistent (with "perfect shuffles"), you'll need to move the top half of this stack to the left (i.e. the left MUST start with a red). Otherwise, you're not shuffling the same way each time. You'll notice that, if you do it "correctly" (or at least the way I did), the top chip will always be the same (and always on the left). If you're starting with red on the left and green on the right, and end up with green on the left, you must have switched your pattern (or kept switching after each shuffle). Using "the top always becomes left", I got the table I posted above.

(Of course, if you shuffle the other way, just switch "left" with "right" in the previous paragraph and you'll get the same result)..
That's an interesting point.
If I start with red on the left and green on the right, I get, from the felt up, g-r-g-r-g-r-g-r-g-r after the first shuffle. I then cut the stack and transfer the top half to the RIGHT. I did this consistently through the sequence and got what I posted (five shuffles for five chip stacks)
If I do it the way you state, which leaves the red on top always, I get what you get, six shuffles.

Is it because of the way the right stack starts as the first chip in the stack sequence? Am I building in a loop by cutting to the right?
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