Say there are 100 perfectly intelligent prisoners (who don't have incredibly good memories) who are jailed for life (and also live eternally). The warden decides to play a game with them. There is a room in the prison which has one 3x3 Rubik's Cube and a robot which can solve it. Every day, the warden chooses a prisoner at random, regardless of whether he has entered the room before or not, and leaves him there until he comes out (of his own accord). While inside, he can do anything to the 3x3 Rubik's Cube in there and let the machine solve it but is not allowed to touch anything else or to take anything in / leave with something (That includes making a visible mark on ANYTHING, though you're allowed to turn the cube).
If one prisoner comes up to the warden while in the room and correctly says, "All 100 prisoners have entered this room since the game began," all of the prisioners will be set free. However, if the prisoner is incorrect, all of them will be immediately executed. The prisoners are all confined in their own cells with no way of communication with any other prisoner. However, all the prisoners have one tool each, a permanent marker, which must not leave their cell.
The day before the game begins, the warden lets the prisioners go into the courtyard to formulate an action plan. If the prisoners all want to escape, what will their plan be?