K candies
Say I have 'k' candies that I distribute among 'n' people. They all sit in a circle, and those people with two or more candies give one each to their two neighbours. Now there is a new distribution of candies. They go on like this until nobody has two or more candies. Is there a maximum value of k for a given n, such that this cycle will always terminate?
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1 solution
The game stops whenever k<n. For k=n, the game may or may not terminate and for k>n, it is always non-terminating. The latter two cases are easy to see (with specific non-terminating examples for k=n). However, I couldn't figure out how to prove it for the k<n case. I'll be glad if you guys can help out!