Wednesday, September 14, 2011
A Bit More Complicated
You have 55 matches arranged in some number of piles of different sizes. You now do the following operation: pick one match from each pile, and form a new pile. You repeat this ad infinitum. What is the steady state? Is it unique?
By steady state I mean the number of piles will remain unchanged or you create an unending loop.
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One possible steady state is 10 piles that have these number of sticks in each pile: 1 2 3 4 5 6 7 8 9 10.
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