Puzzle time - prisoners and hats

[Horace]

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.

[Mik]

If they were that smart they wouldn't be prisoners, now would they?

[Horace]

Tell that to Stalin and his pogroms against intellectuals.

[Horace]

@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).

[Klaus]

1. Do the prisoners know (or can determine) the order in which they are asked?
2. Can the prisoners hear all the answers?

[Klaus]

Oh, I think I now remember the key to the solution. The probability can be raised to 75%.

[Horace]

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.

[jon-nyc]

I got the same answer as Horace.

Official answer comes out Saturday but I cant see them improving on 75%.

[Klaus]

It gets interesting if you generalize the number of prisoners and/or the number of colors.

https://arxiv.org/abs/cs/0509045

[jon-nyc]

Oh man, you ruined the bonus round.