Wednesday, April 8, 2015

Circles on a sphere

Given a sphere of radius $R$, we draw 2015 circles with radius $R$ on it, such that there are no three circles that all meet in one point. It's easy to see that there will be $2^{2015}$ regions created on the sphere surface. Prove that we can color each region with black or white so that no two adjacent regions are colored the same and the total area painted black is the same as the total area painted white.

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