Re: Brain Teaser????
After 10 shuffles, all chips will return to their original positions. Starting with a single pile, which you will then break into two piles and shuffle together, the position mapping is as follows (1=bottom chip):
1-->2
2-->4
3-->6
4-->8
5-->10
6-->1
7-->3
8-->5
9-->7
10-->9
Follow the path of 1, eg:
1-->2-->4-->8-->5-->10-->9-->7-->3-->6-->1
The other chips are similar.
By some theorem of group theory or other, this will always be the case, no matter how big the piles. That is, eventually you get what you started with.
gm
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