A bug is placed at one corner of a wire frame in the shape of a cube. At the diagonally opposite corner is a piece of sugar.

The bug crawls along the 12 wires of the frame searching for the sugar. At each of the 8 corners the bug randomly chooses one a wire to follow next with the additional rule that it can never cross the same wire twice.

What is the probability that it will dead-end by reaching a corner with no available wires? In the case where it does reach the sugar, what is the expected number of edges the bug traverses?

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