# Invariants much?

Imagine a circle divided into $$100$$ sections (this is done by drawing lines through the center). The number $$1$$ is placed in $$51$$ of these sections, and in the rest the number $$0$$ is placed.

In any move, you may add $$1$$ to any two sections that share a side. In how many of these arrangements can you get the same number in every section?

HINT: An invariant is something that remains constant. There is one in particular that will be very useful!

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