100 Prisoners Problem

hza2002@foxmail.com (按点下班) — Sun, 08 Jan 2023 14:08:24 +0800

The 100 prisoners problem is a counterintuitive problem. It describes a seemingly impossible event: 100 prisoners have a chance to do the same thing, and only when all the prisoners do it can they survive. In fact, there is a reasonable implementation method for this problem to increase its probability by nearly 30 orders of magnitude.

Introduction
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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. The rules state that each prisoner may open only 50 drawers and cannot communicate with other prisoners. Danish computer scientist Peter Bro Miltersen first proposed the problem in 2003. As an upgraded version of this problem, there will be \(2N\) prisoners. Their corresponding \(2N\) number cards are shuffled and placed in \(2N\) drawers. Each prisoner must open at most half of all the drawers and find the corresponding number card for his own number. All prisoners will enter the room separately. The failure of any one prisoner will result in the failure of the entire challenge. What is the maximum probability that the prisoners winning?

Probability on Nand Fun

100 Prisoners Problem

Introduction #

Introduction
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