Question : There are 100 prisoners in solitary cells. There’s a central living room with one light bulb; this bulb is initially off. No prisoner can see the light bulb from his or her own cell. Everyday, the warden picks a prisoner equally at random, and that prisoner visits the living room. While there, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting that all 100 prisoners have been to the living room by now. If this assertion is false, all 100 prisoners are shot. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world could 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 in the courtyard, to discuss a plan. What plan should they agree on, so that eventually, someone will make a correct assertion?


Answer : ¬†Assuming there’s no ‘cheating’, no passing notes. No writing on the wall. No shouting. So when the prisoners meet they agree the following to set free from the prison:-¬†

  • One prisoner will be selected as the Captain, in charge of counting.
  • When a prisoner (other than the Captain,) enters the room he will turn the light on if and only if the light is off and he has never done so before.
  • When the Captain enters the room if the light is off he will leave it untouched. If the light is on he will turn it off and add one to his count.
  • When the Captain’s count gets to 99 he will assert that all 100 prisoners have entered the room and they will all be released.

 

References :- 100 prisoners and a lightbulb