[math-fun] Bob Lord's 100 prisoners
Here is a puzzle I learned about from Bob Lord, a software entrepeneur and puzzle fan who was grievously injured in a 30-foot accidental fall down an abandoned mineshaft outside Jean, Nevada on 27 October 2002. I have a solution but have no idea if it is the best possible. ***** There are 100 prisoners who will be placed into 100 individual jail cells. There is no way for the prisoners to communicate, once inside. Each day, a guard will choose one prisoner, at random, to enter a special room. In this room, there is a light that the prisoner may turn on or off and that will remain as the prisoner left it until the next prisoner enters, the next day. A prisoner may tell the guard that all of the prisoners have been in this room at least once. If he is correct, they will be released. If he is not correct, they will all be killed. The prisoners are allowed to communicate only before they're all locked up. How will the prisoners cooperate to guarantee their release before they all die of old age? The number 100 is not significant. There is no trickery involved; the puzzle revolves entirely around the state of the light switch. Indeed, the light itself is not significant, as long as they can tell whether the switch is in the on or off position. ***** Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/home.htm
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Thane Plambeck