On a cuboidal planet with side length 1, either people live on each of the eight vertices. One day, each of them decides to move to a vertex that is a distance of $\sqrt{2}$ away from him. What is the probability that no two of them occupy the same vertex after this move?
People on a Cube
6
$\begingroup$
combinatorics
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4Is it *eight* people? – 2012-07-18
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0@Ross surely it isn't "eight people live on each of the eight vertices". – 2012-07-18
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0@MarkDominus: that's right, it would be one per vertex. But eight is closer to either. – 2012-07-19