Hacker News new | ask | show | jobs
by hollowpython 1420 days ago
OP, if I understood your puzzle, then 99 prisoners can answer correctly. Is that right?
1 comments
tomachello 1419 days ago
No, only one. Think about it this way - if the warden randomly generates their numbers, each prisoner has a 1/100 chance of guessing it right. So best case scenario is exactly one gets it right, which is actually possible.
link
hollowpython 1419 days ago
Ooooh. The prisoners can't hear other prisoners' guesses then. Ok! But in your example, isn't the probability of winning 1-(99/100)*100?

I don't think your "best case scenario" comment is actually true

link
tomachello 1419 days ago
They just need one prisoner to guess correctly - then they all win. Regarding the base case scenario - if each prisoner guesses randomly, each has a 1/100 chance of guessing correctly, and hence they have an expected number of exactly one correct guess. So no deterministic approach can give 2 correct guesses, since no prisoner actually has any real information about their number.
link