Puzzle time - prisoners and hats
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wrote on 4 Aug 2020, 14:48 last edited by
@jon-nyc said in Puzzle time - prisoners and hats:
Possibly, but I think there are a lot of puzzles of this type.
Such as these.
Give me some more time. I know there are many "color of your hat" puzzles, but I'm pretty sure I've also seen one involving probabilities in the past. Maybe not exactly that one.
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wrote on 4 Aug 2020, 15:02 last edited by
I think I now remember where I saw the puzzle.
There's a mathematician who publishes such puzzles on a regular basis, Peter Winkler. He has a monthly column in the "Communications of the ACM", of which I'm a subscriber. I believe I saw that puzzle there. If I think about the puzzle more, I may remember parts of the solution, so I guess I better just keep my mouth shut.
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wrote on 4 Aug 2020, 15:37 last edited by
I guess the set of rules would attempt to clump wrong guesses together while right guesses would tend to be alone. The rules would also want to ensure that at least one person guessed.
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wrote on 4 Aug 2020, 15:45 last edited by
If they were that smart they wouldn't be prisoners, now would they?
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wrote on 4 Aug 2020, 15:48 last edited by
Tell that to Stalin and his pogroms against intellectuals.
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I guess the set of rules would attempt to clump wrong guesses together while right guesses would tend to be alone. The rules would also want to ensure that at least one person guessed.
wrote on 4 Aug 2020, 18:35 last edited by@Horace said in Puzzle time - prisoners and hats:
I guess the set of rules would attempt to clump wrong guesses together while right guesses would tend to be alone. The rules would also want to ensure that at least one person guessed.
So, is the answer that simple? Those who see two different colors would not vote. If the other two people are same, guess opposite? This will cause any configuration of colors other than all-same to be a win (one correct vote), while all-same would be a loss (3 wrong votes).
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wrote on 4 Aug 2020, 18:39 last edited by
- Do the prisoners know (or can determine) the order in which they are asked?
- Can the prisoners hear all the answers?
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wrote on 4 Aug 2020, 18:48 last edited by
Oh, I think I now remember the key to the solution. The probability can be raised to 75%.
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wrote on 4 Aug 2020, 18:51 last edited by Horace 8 Apr 2020, 18:52
Yes that is the % of my proposed solution. I got there by figuring that each guess would be 50/50 so the rules would have to clump wrong guesses together and single out right ones. One such set of rules leaves 75% of color combinations yielding one right guess.
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wrote on 4 Aug 2020, 20:36 last edited by
I got the same answer as Horace.
Official answer comes out Saturday but I cant see them improving on 75%.
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wrote on 4 Aug 2020, 20:43 last edited by
It gets interesting if you generalize the number of prisoners and/or the number of colors.
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wrote on 4 Aug 2020, 21:02 last edited by
Oh man, you ruined the bonus round.
