100.A Cube With No Paint Showing
★★★classical probabilityJane Street
A cube is dipped in paint, dried, and cut into 27 unit cubes. One is drawn at random from a bag and rolled onto a table, so five of its faces are visible and one rests hidden against the table. What is the probability that no paint at all is visible?
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Only pieces with at most one painted face can possibly hide all their paint, and for those the painted face has to be the one facing down.
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