# Questions tagged [hat-guessing]

Cooperative games where a team of players must try to guess the color of their hat, but can only see their teammates' hats.

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30k views

### Hats and Aliens

Here's a neat little puzzle taken from a Google interview question: 10 humans are abducted by aliens; each represents 10% of the entire human population. The aliens give each abductee either a ...
9k views

### Guessing hat colors. 4 prisoners

This is a variant about guessing hat colors. You may want to try Hats and alien or Guessing hat colors or Four prisoners wearing black and white hats. Statement 4 prisoners are to be executed. ...
7k views

### 6 prisoners, 2 colors, one mute

Just like the classic 4 prisoners hats riddle, here we have 6 prisoners buried to their necks in the ground. They can only look straight ahead so that A only sees B, C, D, E while B sees C, D, E, and ...
2k views

### Alternating Hat Colors

A prison warden offers his inmates a game for their freedom. He will secretly write a number on each of their foreheads, with no two foreheads having the same number. The inmates get to look around, ...
5k views

### Infinitely many dwarves wearing hats of 2 colours

I have heard of the puzzle with 100 or 10 dwarves wearing a hat of a color, either red or blue, and standing in a straight line, and having to guess the color of their own hat - it's quite easy. The ...
5k views

### N logicians wearing hats of N colors

N logicians are wearing hats which can be of N different colors (each hat has one color; there can be multiple hats with the same color). Each logician can see the colors of all hats except his own. ...
2k views

### Cooperative guessing game: no incorrect guesses

There are 15 players who will play a cooperative game. They begin by closing their eyes. A referee will place either a black hat or a white hat (chosen by fair coin flip) on each player's head. The ...
2k views

### 10 prisoners and 10 lists of numbers [duplicate]

10 prisoners are held captive by a cruel warden. One day he gathers them in the prison hall and tells them about a new game he wants to play: "Tomorrow, I will assign each one of you a random ...
692 views

### 100 Dwarves vs. the Evil Elf

The following is an extension of 100 Dwarves and a tiny room. The text of this puzzles spoils that one in a minor way, so go read that excellent puzzle first! An evil elf puts $100$ dwarves in a ...
952 views

### Hat Guessing Game in Vegas

A team of 10 people are going to play a cooperative game. While their eyes are closed, a pit boss will place either a red or green hat on each of their heads, chosen by fair coin flip. They then all ...
1k views

### Hat-guessing with a spy

After failing to destroy the human race, Aliens have returned to make another attempt. This time they have planned a wicked strategy. They have again abducted $N$ people, but one of these people is ...
5k views

### Infinitely many hats

We are given countably many people numbered $1,2,3,\ldots$ for all $n\in \mathbb{N}$, each wearing a hat that is either black or white. No-one can see the color of their hat, but everyone can see ...
1k views

### 100 Dwarves and a tiny room

I've got this riddle from a friend at work. Say we have 100 dwarves. They all receive little dwarven shirts with numbers between 0-99 (With repetitions), and after that they all enter into a room. (...
1k views

### Numbered hats, Warden and Maths

You are one of 4 prisoners. Tomorrow will be a deciding day: the warden has told you and your cellmates that you can all go free, or all be executed, depending on how you answer tomorrow's challenge. ...
3k views

### Infinite wizards and hats

Each of an infinite number of wizards is independently assigned a black or white hat based on the outcome of an unbiased coin flip. Each wizard can see everyone's hat but his own. At the count of ...
1k views

### A hat puzzle involving wizards

Two wizards, Alice and Bob, each have two hats on their heads. Each hat is independently black or white with probability one-half. When the game starts each wizard will see the hats on the other ...
1k views

### Of men and hats

There's an obvious generalization of this problem: There are a rather large number of prisoners, each of them seeing the color of the hat of all the following sad fellows bot not their; the hats may ...
609 views

### Hat Puzzle with 5 different colours and 3 people

A dad wants to play a game with his 3 children this Christmas. He has a bag with 5 hats; 1 white, 1 yellow, 1 red, 1 blue and 1 black in it. The hats are all equal except their colour. He will place ...
525 views

### One hundred and one hats

You are a prisoner. One day, the Warden summons you and ninety-nine others to see his hat collection. "Bowlers and baseball caps. Stensons and sombreros. One hundred and one headpieces, each unique ...
598 views

### Five Haberdashers

This is yet another hat puzzle, but not one of the usual ones! Key differences/commonalities between other hat puzzles are emphasized. Five friends are going to go on a game show. When the game ...
1k views

### Surviving Captain Nefarious

Captain Nefarious has captured you and two of your friends, Alice and Bob. Being a villain, he has a natural desire to monologue, so he sits you down (guarded, of course by his Largely Incompetent ...
510 views

### Guess simultaneously, color of your hat, no passing allowed

1000 logicians standing in a circle are blindfolded and a hat of either black or white color is placed on each person's head. The blindfolds are then removed and each person can now see everybody's ...
775 views

### Guess another's present

100 clever men receive presents from the president. Each man gets either a red or blue present, and only knows the color of his own gift. Then each man must guess a colour of a gift of some man: he ...
251 views

### Guess another's present 2: Generalised

What if in Guess another's present problem introduce more present's colours? Also i would reduce a number of men to number of colours. So the task basically the following: N clever men receive ...
2k views

### 1000 logicians wearing hats

Pre-game: There are 1000 logicians in a line, each wearing a black or a red hat, completely at random. No one knows the color of their own hat. Each can see the hats on the next 10 people. The ...
1k views

### Hat puzzle - 7 prisoners

There are 7 prisoners buried up to their necks in sand. 6 are on one side of a wall, all facing the wall. They are lined up such that the furthest from the wall can see the 5 prisoners closest to the ...
3k views

### The sadistic executioner (a.k.a the 100 prisoners) [duplicate]

100 prisoners are sent into a room to hear the warden say: "tomorrow I will line you up and put a hat on your head. The hat can be red, green, yellow, …" and he goes on enumerating colors. He then ...
382 views

### Guessing game with infinity coin flips

Evan and Ollie are going to play a game as a team. The two friends placed in separate rooms, and then a coin is flipped infinitely many times*. Evan is told the results of the even numbered flips, ...
429 views

### Four hats and penalty for passing

There are four contestants, each with a red or green hat. They start with a prize pool of one million dollars. They take turns either guessing their hat color or passing. If anyone guesses incorrectly,...
454 views

### N people, N hat colors, and a One-Way Glass

This is a variant of this question, reproduced below: There are $n$ people, who will stand in a circle while a game master places a hat on each of their heads. The hats can each be one of $n$ ...
369 views

### MORE Prisoner Hats!

The king arrests all married couples where both spouses are PhDs in Math, Computer Science, or Logic. He holds each couple separate from the others and tells each couple in turn that all the rounded-...
96 views

### What is my number in circle? [duplicate]

N > 1 people sit in a circle clearly seeing all others. They are going to be blindfolded and, while in this state, hats are put on their heads - one per person, naturally. On each hat there is written ...
1k views

### Five Prisoners wearing hats [duplicate]

I stole this puzzle - but I credited it in the source of this question, so if you really want to cheat you can. No cheating, please. There's a penal colony on an island in the South Pacific. It's ...
402 views

### Minimising information to guess all hats correctly

There is a well known N logicians wearing hats of N colors puzzle: N logicians are wearing hats with numbers from 1 to N (each hat has one number; there can be multiple hats with the same number)...
119 views

### Number hats puzzling [duplicate]

10 people will stand in a circle, and each have a hat placed on their head. The hats will each be labeled with a digit between 0 and 9, with repeats allowed. They will be able to see everyone's hat ...
$n$ villagers wear either black or white hats. The truth is that all the hats are black, but this is not known. They sit in a line, so that each villager can see all the hats in front of them, but not ...