100 prisoners are put into solitary cells. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb from his or her own cell. Every day, the warden picks a prisoner at random, and that prisoner goes to the central living room. While there, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting the claim that all 100 prisoners have been to the living room. If this assertion is false (that is, some prisoners still haven't been to the living room), all 100 prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world can always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.
The prisoners are allowed to get together one night, to discuss a plan. What plan should they agree on, so that eventually, someone will make a correct assertion?
Haven't read any other comments - but surely not simply on the 100th day - so some-one is going to have warn if they have been there more than once ie turn it on. But then how does some-one else say they've been there twice?
What about changing it depending if the day is odd or even - ie it's on on a even day, so that many people visited minus one if on, nope that won't work either. Aaarrgh! Don't want to read answer... but..
Possible options for code in room:
direction of side of bulb - turn it 3.6 degrees only on first visit?
Posted by Dacre
on 2003-08-29 12:25:18