Consider the cube whose vertices are the eight points (x, y, z) for which each of x, y, and z is
either 0 or 1. How many ways are there to color its vertices black or white such that, for any vertex,
if all of its neighbors are the same color then it is also that color? Two vertices are neighbors if they
are the two endpoints of some edge of the cube.
Hint: Split the cube. Casework much easier?
Level: 7
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