06-18-2026, 02:36 AM
Summary
The 100 prisoners problem is a famous probability and combinatorics puzzle where 100 prisoners must find their own numbers hidden randomly inside 100 drawers, with each prisoner allowed to open only 50 drawers. If every prisoner succeeds, they survive; if even one fails, they all lose. A random strategy gives an almost zero chance of success, but a clever method based on following permutation cycles greatly improves the odds.
Each prisoner starts by opening the drawer with their own number and then follows the chain of numbers found inside the drawers, which corresponds to tracing cycles in a permutation. The prisoners succeed whenever there is no cycle longer than 50 drawers, giving them a survival probability of about 31%, a surprising result that demonstrates how structure and mathematical strategy can overcome seemingly impossible odds
ARTICLE
The 100 prisoners problem is a famous probability and combinatorics puzzle where 100 prisoners must find their own numbers hidden randomly inside 100 drawers, with each prisoner allowed to open only 50 drawers. If every prisoner succeeds, they survive; if even one fails, they all lose. A random strategy gives an almost zero chance of success, but a clever method based on following permutation cycles greatly improves the odds.
Each prisoner starts by opening the drawer with their own number and then follows the chain of numbers found inside the drawers, which corresponds to tracing cycles in a permutation. The prisoners succeed whenever there is no cycle longer than 50 drawers, giving them a survival probability of about 31%, a surprising result that demonstrates how structure and mathematical strategy can overcome seemingly impossible odds
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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│ KONSTANTINOS MICHAILIDIS │
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