No unexpected question. Question: 37^2 = ? Paint a white cube red. Divide it into 27 same small cubes. Pick one small cube randomly and roll. What's the probability of all 5 faces you can see is white?

Question

Anonymous · Accepted Answer

The rolled cube needs to be either the inner cube or one of the six face centres.

answer = (1/27)*(1) + (6/27)*(1/6) = 2/27

bonism · Answer

for the 27 small cubes, the number of "leagal cubes" is 
 - 6, with one face colored red
 - 1, with all faces white

So the probability is 1/27 + (6/27) * (1/6) = 2/27

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