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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44 votes
6 answers
33k 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 purple ...
  • 2,168
39 votes
7 answers
11k 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. The ...
  • 2,680
39 votes
13 answers
8k 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 ...
  • 3,634
28 votes
13 answers
6k views

Five hats and four logicians in a circle

I found this question in a book. The solution is correct (and complicated). No tricks involved. Four men were seated around a table. They were blindfolded and a colored hat was placed on each of ...
23 votes
3 answers
4k views

3 Numbers on Hats, A = B + C

This feels like it should be a common puzzle, but I haven't found anything exactly like it searching online, so here goes. Apologies if it's a duplicate. Three logicians, person 1, 2, and 3, along ...
  • 397
21 votes
5 answers
7k 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. ...
21 votes
4 answers
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 ...
  • 618
20 votes
2 answers
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, ...
  • 31.5k
18 votes
5 answers
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 ...
  • 13.9k
15 votes
3 answers
948 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 ...
15 votes
3 answers
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 ...
  • 31.5k
14 votes
2 answers
3k 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 ...
  • 151
13 votes
6 answers
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. (...
13 votes
2 answers
2k views

8 Prisoners wearing hats

A warden lines up these prisoners. He announces, "I see a white hat." He then leaves the room. Every few minutes he comes back in and asks if anybody knows their hat color. Anyone who figured it out ...
13 votes
1 answer
2k 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 ...
  • 3,980
12 votes
9 answers
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. ...
12 votes
8 answers
6k 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 ...
11 votes
11 answers
4k 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 ...
  • 792
11 votes
3 answers
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 ...
  • 5,328
11 votes
1 answer
2k 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 ...
  • 2,067
8 votes
2 answers
790 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 ...
8 votes
1 answer
595 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 ...
8 votes
1 answer
162 views

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

At the 2020 yearly black- and white- hatted logician gathering, the following fun activity is organized. $N$ logicians will sit around a table, each wearing a black or a white hat the color of which ...
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8 votes
8 answers
642 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 ...
  • 31.5k
8 votes
2 answers
457 views

Modifying the puzzle: Cooperative hat-guessing, no mistakes, 3+ colors

Following Guess your hat color, but you don't have to and it's interpretation via Covering codes I tried to create a puzzle with more hat variativity, i.g. 3 types of hats. 4 hats are put on 4 ...
  • 15.9k
8 votes
3 answers
552 views

Guess your hat color, but you don't have to

Here is the puzzle: N hats are put on N logicians, each hat color is selected randomly: black or white. As usual, every logician doesn't see the hat on his own head, but sees the rest. They cannot ...
  • 15.9k
7 votes
3 answers
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 ...
7 votes
3 answers
796 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 ...
7 votes
3 answers
495 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, ...
  • 31.5k
7 votes
6 answers
841 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 ...
  • 15.9k
7 votes
1 answer
458 views

Guess the hat colors - Riddle 1

I have created several riddles with my brother, and one of my favourite ones is this one. It is based on the classic prisoner hat riddle, but it has a twist. TASK: You have to guess which ones are ...
  • 399
7 votes
1 answer
265 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 ...
  • 15.9k
7 votes
1 answer
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 ...
7 votes
2 answers
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 ...
  • 71
6 votes
4 answers
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 ...
  • 295
6 votes
2 answers
616 views

Unseen prisoners figuring out their hats

A warden wants to play a game with his prisoners. He tells them that they have to tell him the color of their own hats if they want to have dinner. note: The warden may be mean, but the prison has a ...
  • 5,474
5 votes
3 answers
690 views

Three applicants, six hats

The king was looking to hire a new scribe. Three bright young lads applied for the job. The king, who was widely known for being very just, made them undergo a test. He took three red and three black ...
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5 votes
4 answers
493 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,...
5 votes
1 answer
236 views

23 people wearing hats with a bell ringing [closed]

24 extremely intelligent people get invited to a really important party. Since it's really important after 9pm (the start time of the party) a guardian will guard the door to enter the party. All of ...
5 votes
2 answers
631 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 (...
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5 votes
1 answer
169 views

Multi-variable hat guessing

Here is a variation of the hat-guessing logicians problem. 100 logicians are given hats. They know that: All the hats are either black or white Each hat may or may not have green stripes on it Each ...
  • 407
4 votes
2 answers
429 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-...
4 votes
3 answers
278 views

Guess the hat colors - Riddle 7

My brother just created this puzzle for me for Halloween, at first I thought it looked simple, but then it turned out to be very challenging (at least for me!) I'll add it to my collection/app soon. I ...
  • 399
4 votes
1 answer
178 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 ...
4 votes
1 answer
202 views

Guess the hat colors - Riddle 2

After the previous riddle I asked was resolved so quickly, I propose you another self-created hat-guessing riddle. This time it is slightly more difficult, good luck! TASK: You have to guess which ...
  • 399
4 votes
1 answer
2k 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 ...
  • 406
3 votes
2 answers
463 views

Sorting kids by hat colours [duplicate]

I have taken a group of students on a school trip. I want to organise them into two groups and so I have given each one a coloured hat. Some hats are red, while others are blue. Each child can see ...
  • 31
3 votes
2 answers
402 views

Ernest does not know the color of his hat

Previously I tried to make a very difficult hat color deduction puzzle: Unseen prisoners figuring out their hats It seems to be too hard for the interested, since I did not get a complete solution. ...
  • 5,474
3 votes
2 answers
474 views

Guess the hat colors - Riddle 3

This time I added a special rule, please let me know what you think about it! CHALLENGE: You have to guess which ones are wearing green hats and which ones are wearing black: SPECIAL RULE: All the ...
  • 399
3 votes
2 answers
427 views

3 hats with numbers, where 2 hats sum to the third

I have outlined a puzzle below, and provided two sources which provide answers. I am disputing that the answer provided in the sources is correct, and I am looking for others to validate or invalidate ...