Can you solve the alien probe riddle? - Dan Finkel
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A larger 4 by 4 by 4 probe were assembled from 64 smaller cubes. If you needed to paint this in 4 different colors instead of 3, could it be done?
To solve this, you’ll want to think about the solution for the 3-color cube. Paint the entire thing red, then look at how many cubes have 0, 1, 2, or 3 faces painted. Then think of how you could use symmetry to paint the other three colors in as well. Note: the 4-color version of this problem CAN be solved!
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