An algorithm should do it. The puzzle is a well-known one. Logical time is divided into three moments.

1. the instant of seeing
2. the time for understanding
3. the moment of concluding

The first prisoner to deduce the color of the disk on his own back will be granted his freedom. The correct deduction appears to depend on the hesitation of the group. "If I had a black disk, then each of the other prisoners would not hesitate to deduce immediately that he was white. Since neither has done so, I must also have a white disk." In fact, this puzzle would make a nice Perl game.