100 Prisoners and one Light Bulb Problem: description
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. 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?