4 ms·
Numbered hats: I'm not sure this is optimal. When the prisoners are together, they assign each person a unique ID from 1 to 100. Once the round starts, each
by evanb 10y ago
Numbered hats: I'm not sure this is optimal.
When the prisoners are together, they assign each person a unique ID from 1 to 100.
Once the round starts, each looks around and adds up the total on everybody else's hat, mod 100. Suppose you see a total of h (mod 100). Then you should make a guess g = h - your ID (mod 100).
With 1000 repeated experiments of 1000 trials each, this saved the prisoners ~ 630±17 ~= 63±2 percent of the time.
- agf 10y agoIf each person just guesses a random number you succeed the same amount of the time. You have a 99% chance of guessing wrong. The chance of 100 people guessing wrong is 0.99 ^ 100. So the chance of at least 1 person guessing right is 1 - 0.99 ^ 100, which is 63.4%.
- evanb 10y agoWell then, I guess my strategy accomplishes nothing!
- twhb 10y agoThere's a strategy that guarantees success. And you're so very close to it. So close, in fact, that I'm going to guess you've heard this before and just don't fully remember the solution.
- deleted 10y ago[deleted]