Problem

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Tags: combinatorics unsolved, combinatorics



Two concentric circles are divided by $n$ radii into $2n$ parts. Two parts are called neighbors (of each other) if they share either a common side or a common arc. Initially, there are $4n + 1$ frogs inside the parts. At each second, if there are three or more frogs inside one part, then three of the frogs in the part will jump to its neighbors, with one to each neighbor. Prove that in a finite amount of time, for any part either there are frogs in the part or there are frogs in each of its neighbors