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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.

43
votes
6answers
28k 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 ...
14
votes
5answers
4k 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. ...
9
votes
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 ...
15
votes
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 ...
35
votes
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 ...
37
votes
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. ...
6
votes
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 ...
19
votes
4answers
4k 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 ...
16
votes
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 ...
7
votes
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 ...
12
votes
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. (...
8
votes
1answer
497 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 ...
7
votes
6answers
754 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 ...
0
votes
3answers
440 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 ...