The teacher in a certain class room allows you to pass a paper with an assignment around, and whomever it ends up on has to do it. The only two rules are you can't pass it to someone who already has had it and you can only pass it to the person to the left, right, forward, or backward.

In a room of 30 students arranged in a 6 by 5 grid, the teacher starts out with the assignment somewhere on the front row of 6 students. At some point someone is stuck holding the assignment because all his neighbors have had it and passed it on to someone else. If this happens after every student in the room has had it, what is the probablity, for each individual, that he or she turns out to be the lucky winner of the assignment?

This is much more difficult than a shortest path problem.  The number of paths seems to be endless.

For a 2x2 grid you get:

.25   .25
.25   .25

for a 3x2 grid you get:

7/30   2/15   7/30
1/5      0       1/5

After that my head gets mushy trying to contemplate all the various valid paths to a dead-end.

Posted by Erik O. on 2004-06-24 13:56:04