100 prisoners (Solution)
I’ll admit, this is not a problem that I solved myself. I did, however, hear the optimal strategy and then worked out the probability that the prisoners survive with that strategy (which still wasn’t trivial!).
Given that fact, and (more imporantly) the fact that this is a famous, well-documented, problem, I’m going to refer you to the solution written up very clearly on wikipedia.
For those of you who quickly want to know whether you’re right or wrong, the prisoners can survive with a shockingly high chance of \(\approx 0.31\)!
Another quick result, is that the answer is very close to:\[1 - (ln(100) - ln(50)) = 1 - ln(2) \approx 0.30685\]