# Tag Info

Accepted

### Guessing hat colors. 4 prisoners

This is a bit of a stretch and I'm not sure it'd even work, but...
• 1,498
Accepted

### 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:
• 77.7k

### Guessing hat colors. 4 prisoners

A simple way would be that Either there is, or there isnâ€™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 ...
• 77.7k

### Infinitely many hats

Here is another strategy, which requires looking at just 1 other person's hat:
• 13.6k
Accepted

### Numbered hats, Warden and Maths

Sure, it's perfectly doable.
• 147k
Accepted

### 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 ...
• 4,637
Accepted

### 10 prisoners and 10 lists of numbers

The strategy is: Why it works: For example:
• 34.2k
Accepted

• 137k

### 6 prisoners, 2 colors, one mute

I'll try another explanation(with same result): Here are the steps: Next step: So: Who talks?
• 420
Accepted

### Guess color of your hat cooperatively, goal is all correct or all incorrect

It is possible. All winning strategies:
• 4,387
Accepted

Reasoning:
• 1,495

### Numbered hats, Warden and Maths

Everybody walks out free and happy.
• 6,290
Accepted

Solution: Edit:
• 401

### Sorting kids by hat colours

I think this is a classic (and probably a duplicate): To separate the two groups cleanly
• 2,767

### Numbered hats, Warden and Maths

You're all making this much more complicated than it needs to be. :) Let's take an example:
• 5,761
Accepted

### 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 ...
• 14.3k
Accepted

### 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, (...
• 77.7k
Accepted

### 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 ...
• 53.7k
Accepted

### 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 ...
• 32.5k

### 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 ...
• 9,917
Accepted

### Guessing game with infinity coin flips

A possible strategy is for them to To get the probability of success,
• 21.8k
Accepted

### 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 ...
• 30.4k

### 6 prisoners, 2 colors, one mute

alternately, for lateral thinking:
• 2,924

### 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, ...
• 281

### A hat puzzle involving wizards

Each hat is independently black or white with probability one-half So... Which brings us to...
• 531
Accepted

### Five Hats and Three Logicians

I claim that: Reasoning:
• 1,531

### 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 ...
• 2,564
Accepted

### Black-hat/white-hat logicians with a bell and a meal

A strategy: This works as long as This is optimal because:
• 147k
Accepted

### Sheets of paper on foreheads in a quiz show

Call the people A, B, and C.
• 12.9k