# 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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### 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 ...
548 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 ...
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

### 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 ...
4k 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 ...
6k 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 ...
607 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 $n$ colors (...