Re: Late Friday Puzzler -- 100 Prisoners

david weaver
Figuring there are 100 prisoners and disregarding the light, it seems like 96 visits can occur each day. So day one is a bad day to claim freedom, even if it starts at midnight.

the chance that an individual is not chosen at least once by the end of day one is 0.99^(96)

Dumping this into a spreadsheet, I figure that (I'm missing something, but) the chance that someone has visited the warden after a certain number of iterations is 1-(0.99^(number of 15 minute sessions))

then, there are a hundred individuals, so after a certain larger number of iterations, the probability that all of the individuals have seen the warden is 1 minus this (per individuals) ^(100)

after 200 separate visits, that would yield a chance of claiming on the 200th that everyone had visited the warden of 1 in 1.8 million. Not good.

After 600 iterations, there's a 78% chance that everyone has been to the room. A drastic difference. Many, of course, have been there multiple times.

I need to factor in the light now.

23 years since probability, I think I'm out of steam to figure out how many times a chosen person should see the light on before they turn it off and claim all have been to the room.

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