The following version is by Philippe Flajolet and Robert Sedgewick: The director of a prison offers 100 death row prisoners, who are numbered from 1 to 100, a last chance. A room contains a cupboard with 100 drawers. The director randomly puts one prisoner’s number in each closed drawer. The prisoners enter the room, one after another.
Who is the author of the 100 prisoners problem?
The 100 prisoners problem has different renditions in the literature. The following version is by Philippe Flajolet and Robert Sedgewick: The director of a prison offers 100 death row prisoners, who are numbered from 1 to 100, a last chance. A room contains a cupboard with 100 drawers.
Where does Prisoner 2 find his own number?
Prisoner 2 opens drawers 2, 4, and 8 in this order. In the last drawer he finds his own number 2. Prisoner 3 opens drawers 3 and 6, where he finds his own number. Prisoner 4 opens drawers 4, 8, and 2, where he finds his own number.
How are 100 prisoners sentenced to life in prison?
The solution to this problem requires nothing more than a bit of cleverness and some very, very strategic counting. 100 prisoners are sentenced to life in prison in solitary confinement. Upon arrival at the prison, the warden proposes a deal to keep them entertained, certain that the prisoners are too dim-witted and impatient to accomplish it.
What is the problem of the 100 prisoners problem?
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survive.
What happens if 100 prisoners go to the living room?
While in the living room, 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.
Is there a way to save 50% of the prisoners?
I argue that 50% of the prisoners can be saved: regardless of any ordering of the prisoners names in boxes, in any given string of 50 boxes (a string need not be consecutive) there are exactly 50 names which correspond to exactly 50 of the 100 prisoners.
