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Bug on a Cube 2 (Posted on 2023-11-27) Difficulty: 3 of 5
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?

No Solution Yet Submitted by Jer    
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re: computer solution | Comment 3 of 5 |
(In reply to computer solution by Charlie)

In going over Larry's solution, I see that my calculation of the expected number of moves for a successful reaching of the sugar was flawed.


I neglected to multiply each value by the probability that the given path would be the one taken.  I assume Larry's computation is correct, though I haven't gone over it yet.

  Posted by Charlie on 2023-11-27 14:00:57
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