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71 votes
Accepted

Guessing hat colors. 4 prisoners

This is a bit of a stretch and I'm not sure it'd even work, but...
HugoBDesigner's user avatar
33 votes
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6 prisoners, 2 colors, one mute

It will be Both A and B can see, what C sees, and that's why they both know that From there, the problem reverts to the earlier one:
Bass's user avatar
  • 77.7k
25 votes

Guessing hat colors. 4 prisoners

A simple way would be that Either there is, or there isn’t, but since everybody guessed the same, everyone will be right, or everybody will be wrong. No-one can be wrong by more than one, so whenever ...
Bass's user avatar
  • 77.7k
24 votes

Infinitely many hats

Here is another strategy, which requires looking at just 1 other person's hat:
phenomist's user avatar
  • 13.6k
22 votes
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Numbered hats, Warden and Maths

Sure, it's perfectly doable.
Deusovi's user avatar
  • 147k
21 votes
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3 Numbers on Hats, A = B + C

Answer: First, some observations Alright. Now, let's take a look at different possibilities: Generalizing this, we get the rule above: Do note however that the actual answer is actually slightly ...
votbear's user avatar
  • 4,637
19 votes
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10 prisoners and 10 lists of numbers

The strategy is: Why it works: For example:
athin's user avatar
  • 34.2k
19 votes
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Infinitely many hats

How about this strategy Reasoning
hexomino's user avatar
  • 137k
18 votes

6 prisoners, 2 colors, one mute

I'll try another explanation(with same result): Here are the steps: Next step: So: Who talks?
Tode's user avatar
  • 420
18 votes
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Guess color of your hat cooperatively, goal is all correct or all incorrect

It is possible. All winning strategies:
ralphmerridew's user avatar
17 votes
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Again! 6 prisoners, 2 colors, one mute

Reasoning:
EightAndAHalfTails's user avatar
13 votes

Numbered hats, Warden and Maths

Everybody walks out free and happy.
Evargalo's user avatar
  • 6,290
13 votes
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8 Prisoners wearing hats

Solution: Edit:
Mazement's user avatar
  • 401
13 votes

Sorting kids by hat colours

I think this is a classic (and probably a duplicate): To separate the two groups cleanly
Braegh's user avatar
  • 2,767
11 votes

Numbered hats, Warden and Maths

You're all making this much more complicated than it needs to be. :) Let's take an example:
Trevor Powell's user avatar
11 votes
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A hat puzzle involving wizards

One possibility is It is not possible for the wizards to do better. There are $16$ possible combinations of hat colors. Of these, $7$ of them have at least one wizard with no black hat, so cannot be ...
Julian Rosen's user avatar
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11 votes
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Hat Puzzle with 5 different colours and 3 people

I think they can get all the way to probability of getting all three guesses right. There's probably a possible explanation that utilises Galois fields, modular exponents and discrete logarithms, (...
Bass's user avatar
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11 votes
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Guess simultaneously, color of your hat, no passing allowed

Here is a way to guarantee 500 correct guesses. Edit: The above is optimal, because the expected value of random guessing is 500, and with no extra information given to the logicians about how the ...
Jaap Scherphuis's user avatar
10 votes
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MORE Prisoner Hats!

If the PhDs were allowed to plan a strategy together ahead of time, then the following would work: Unfortunately, the king forbids them from collectively planning. Each couple may come up with a ...
Mike Earnest's user avatar
  • 32.5k
10 votes

Infinitely many hats

So I just wanted to solve an amazing extension of this puzzle that I happen to know of. Suppose that there were more than two colors. In fact, let's suppose that there were an uncountably infinite ...
greenturtle3141's user avatar
9 votes
Accepted

Guessing game with infinity coin flips

A possible strategy is for them to To get the probability of success,
ffao's user avatar
  • 21.8k
9 votes
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Three applicants, six hats

The king has to be nondiscriminatory for each person applied to this job so putting one black on one of them and two red on the others would make the game unfair! So The only way to make this game ...
Oray's user avatar
  • 30.4k
9 votes

6 prisoners, 2 colors, one mute

alternately, for lateral thinking:
Destructible Lemon's user avatar
8 votes

Numbered hats, Warden and Maths

No maths required. Just write any message you want in Morse code, using 1 = dot, 2 = dash, 3 = space. An appropriate message might be something like, "Alice's number is 36473, Bob's number is 758254, ...
Orntt's user avatar
  • 281
8 votes

A hat puzzle involving wizards

Each hat is independently black or white with probability one-half So... Which brings us to...
Ryan Smith's user avatar
8 votes
Accepted

Five Hats and Three Logicians

I claim that: Reasoning:
Dennis Meng's user avatar
  • 1,531
8 votes

A harder version of a Richard Hess logical hat problem

The three hats could be: Before any hints are given One of those is the true case. Bob's clue disproves the alternative; in order to see how the disproof works, let's inhabit that false world for a ...
Tim C's user avatar
  • 2,564
7 votes
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Black-hat/white-hat logicians with a bell and a meal

A strategy: This works as long as This is optimal because:
Deusovi's user avatar
  • 147k
7 votes
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Sheets of paper on foreheads in a quiz show

Call the people A, B, and C.
msh210's user avatar
  • 12.9k
6 votes

MORE Prisoner Hats!

This is just a generalization of the linked question, in which Bass' answer already provides a solution that works with an arbitrary even number of prisoners (which is true for this question, since ...
votbear's user avatar
  • 4,637

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