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 deadend 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?
(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 20231127 14:00:57 