math problem

[kpux]

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If you express the shuffle as a permutation in cycle notation the least common multiple of the cycle lengths is the number of shuffles required. This is basically restating the period thing earlier, but provides a more systematic approach. Now I simply need a quick way to get the cycle lengths and I will be done.

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yeah, we figured out that number of shuffles required is the LCM of all of the cycle lengths.

one problem i thought of with using permutation groups was that if you number the chips, say, 1 2 3 4 5 6 7 8, with 1 2 3 4 being the left stack from bottom to top (and the two stacks are different colors, obviously), then the permutation group answer will tell you how many riffles you need to return to 1 2 3 4 5 6 7 8. but there are other visually identical permutations like 1 3 2 4 5 7 6 8 that maybe occur before the original order occurs again, which would mean that the number of riffles needed is less than what the permutation answer would say. hope that isn't too convoluted.