Jane StreetTraderAssistant TraderQuestion #255

If I have a 4x4x4 cube and I paint the outside of the cube, then cut it into 64 1x1x1 cubes: 1) How many of the smaller cubes have at least one side painted? 2) If I pick one of the 64 cubes at random and roll it, what is the probability that the top side is painted?

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