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# 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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5answers
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### 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. ...
6answers
29k 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 ...
1answer
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 ...
4answers
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 ...
2answers
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 ...
13answers
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 ...
7answers
8k 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. ...
4answers
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 ...
5answers
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 ...
1answer
515 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 ...
1answer
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 ...
6answers
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. (...
6answers
766 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 ...
3answers
478 views

### Knowledge about common knowledge (hats puzzle)

$n$ 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 ...