• 100 Prisoners Riddle -- proposed by Peter Bro Miltersen in 2003

    From henhanna@gmail.com@21:1/5 to All on Fri Jul 1 10:28:52 2022
    Have you ever heard of the 100 Prisoners Riddle? First proposed by the Danish computer scientist Peter Bro Miltersen in 2003, it's a mathematical problem in probability theory and combinatorics that seems completely impossible to solve.
    Here is how the riddle goes: "Say there are 100 prisoners numbered 1 to 100. .................

    ------------- wow... that's amazing , Bro ! how have i managed to not have heard of it until today ?


    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. Each prisoner may open and look into 50 drawers in any order. The drawers are closed again afterwards. If, during this search, every prisoner finds his number in one of the drawers, all prisoners are pardoned. If just one prisoner does not
    find his number, all prisoners die. Before the first prisoner enters the room, the prisoners may discuss strategy — but may not communicate once the first prisoner enters to look in the drawers. What is the prisoners' best strategy?

    If every prisoner selects 50 drawers at random, the probability that a single prisoner finds his number is 50%. Therefore, the probability that all prisoners find their numbers is the product of the single probabilities, which is

    ( 1 / 2 ) ^ 100 ≈ 0.0000000000000000000000000000008,

    a vanishingly small number. The situation appears hopeless.

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