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?

(In reply to Simulation with truly random numbers by Charlie)

If not all the students would have had to see the assignment, just that the assignment was trapped by a student being caught with it with no neighbor to pass it to (that is, the unconditional probability given just the way the class is handled), the results would be:

 980  371  400  417  418  919
 208  330  208  224  333  210
 237  233  220  219  232  257
 172  315  223  203  317  176
 735  112  195  197  145  794

1899  789  817
 418  663  432
 494  465  439
 348  632  426
1529  257  392

10000

for probabilities of (again, per 200 rather than per cent):

19  8  8  8  8 19
 4  7  4  4  7  4
 5  5  4  4  5  5
 3  6  4  4  6  3
15  3  4  4  3 15

Posted by Charlie on 2004-06-25 07:25:46