: Prisoner Puzzle v1.0 : the solution

: Each prisoner except one, which we will call the ring-leader, turns the light on if
: it was off. If it was on already, they leave it on. However, they turn the light on
: exactly once - the first time they take a shower in which the light-switch was off.

: The ring-leader is the only person who does something different. If she finds the
: light on, she increments her counter and turns the light off. If she finds the light off,
: she leaves it in that position.

: In this manner, each other prisoner communicates a single bit of information to
: the ring-leader, i.e. their having had their first shower. If the ring-leader's
: counter ever reaches 'n', then she knows that all 'n' prisoners (including herself)
: have had at least one shower and can make this assertion to the Warden, setting
: them all free.

: Prisoner Puzzle v2.0 : the set-up

: Suppose now that the Warden sets the prisoners an even more difficult task. In order
: to be freed, all of the prisoners must make the assertion that they have all had at
: least one shower. This is a significantly harder problem; one which I don't know of
: a solution for.

: Good luck!