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?
(From http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml)
The prisoners will need to designate a counter among themselves with the first prisoner turning the light on if it is off, or this is their fist time in turning on the lights
The prisoners will start from the default value 0 and each prisoner who turns the light on will increment the value by 1.
Once this value reaches 99 for the last prisoner, he will announce that all 100 prisoners have visited the living room.
Edited on September 19, 2022, 4:09 am
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