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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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1 answer
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Guess color of your hat cooperatively, goal is all correct or all incorrect [duplicate]

Let n be an integer. n logicians standing in a circle are blindfolded and a hat of either red or blue is put on each person's head. Blindfolds are then removed; each person can now see the color of ...
Lasting Howling's user avatar
2 votes
0 answers
171 views

Guess Hat Collor [closed]

Five elders are sitting around a large bonfire. They know that Oluf will put a hat of one of four colours (red, green, blue or yellow) on each elder’s head, and after a short time for silent ...
Ali MohammadiNia's user avatar
2 votes
1 answer
376 views

Sheets of paper on foreheads in a quiz show [duplicate]

I have got a puzzle that I wanted to share. In a quiz show, three candidates were shown five slips of paper - three white and two black. Then they were blindfolded and one of the slips of paper was ...
calculatormathematical's user avatar
8 votes
2 answers
582 views

12 logicians each have a number written on their foreheads

12 logicians each have a number written on their foreheads, visible to all but themself. One day, a meta-logician comes by and remarks, "I see all the numbers are distinct natural numbers." ...
Eric's user avatar
  • 6,536
20 votes
6 answers
3k views

A harder version of a Richard Hess logical hat problem

In the July/August 2021 issue of MIT Technology Review, there was a "logical hat" problem by Richard Hess in the Puzzle Corner. I noticed that it could be generalized. Here is the "next ...
Timothy Chow's user avatar
0 votes
3 answers
213 views

Hat guessing without knowing the colors

Generalization of this problem: Guessing hat colors. 4 prisoners Suppose that there are $N$ prisoners, instead of $4$. Show, by finding explicitly the strategy, that if $N$ is even there is a strategy ...
3m0o's user avatar
  • 317
-1 votes
1 answer
171 views

Hat and Earring Guessing Puzzle, with penalty for passing

You are in the final round of a game show with 3,999 other conteseants. Here is the game: The host has blindfolded you at put a red, green or blue hat and red, green or blue earrings (not necessarily ...
3-1-4-One-Five's user avatar
-2 votes
1 answer
410 views

Infinitely many deaf dwarves

A beautiful puzzle, and I know the solution. I read it on an Italian riddle forum. An evil witch kidnaps infinite (countable) dwarves. The witch tells the dwarves that the next day she will put them ...
3m0o's user avatar
  • 317
5 votes
1 answer
295 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 ...
Technical Gaming's user avatar
3 votes
2 answers
498 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 ...
mnbv's user avatar
  • 31
4 votes
2 answers
760 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 ...
Jack Reilly's user avatar
2 votes
2 answers
172 views

Save the poor Gingerbreadmen!

The poor gingerbread men want to survive to Xmas (they don't mind being eaten afterwards). If at least one of them doesn't guess his hat correctly, they will all be cruelly eaten before Xmas. This is ...
Guess Hat's user avatar
  • 449
5 votes
3 answers
318 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 ...
Guess Hat's user avatar
  • 449
2 votes
2 answers
233 views

Guess the hat colors - Riddle 6

And for today, a new original hat guessing puzzle! CHALLENGE: Guess the hats of the 4 prisoners. SPECIAL RULE: One of the prisoners is lying DESCRIPTION: Each one can see the hats that are in front ...
Guess Hat's user avatar
  • 449
3 votes
1 answer
411 views

Ernest does not know the color of his hat (3)

(again a more a difficult one) The (same) premise: An unknown number of people stands on a line playing a hat guessing game they may not move during the game, they can only look straight ahead (each ...
Retudin's user avatar
  • 9,218
2 votes
1 answer
231 views

Ernest does not know the color of his hat (2)

The previous version indeed proved simple; now a medium one (I think) The (same) premise: A number of people stands on a line playing a hat guessing game they may not move during the game, they can ...
Retudin's user avatar
  • 9,218
3 votes
2 answers
452 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. ...
Retudin's user avatar
  • 9,218
6 votes
2 answers
811 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 ...
Retudin's user avatar
  • 9,218
4 votes
1 answer
219 views

Guess the hat colors - Riddle 5

I was impressed with all the answers and interesting reasoning in the previous puzzle (riddle 4). So for today I have another original hat guessing puzzle! Challenge: guess who is wearing the green ...
Guess Hat's user avatar
  • 449
2 votes
7 answers
751 views

Guess the hat colors - Riddle 4

And today's puzzle, a freshly made one that I am thinking of adding to my collection, I hope it's challenging enough! CHALLENGE: Guess the hats of the prisoners. SPECIAL RULE: There are three types of ...
Guess Hat's user avatar
  • 449
3 votes
2 answers
519 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 ...
Guess Hat's user avatar
  • 449
5 votes
1 answer
244 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 ...
Guess Hat's user avatar
  • 449
8 votes
1 answer
687 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 ...
Guess Hat's user avatar
  • 449
0 votes
1 answer
407 views

100 black hats and 99 white hats (Is my solution wrong?)

100 people are sitting in a circle, where every person can see the 99 other people. All of them are wearing hats but they can only see the hats of other people, meaning they can't see their own hat. ...
Puzzlees's user avatar
  • 746
5 votes
1 answer
207 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 ...
Ilak's user avatar
  • 407
8 votes
2 answers
484 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 ...
klm123's user avatar
  • 16.2k
9 votes
1 answer
190 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 ...
Florian F's user avatar
  • 30.2k
8 votes
3 answers
727 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 ...
klm123's user avatar
  • 16.2k
1 vote
1 answer
189 views

Prisoners and their hats [duplicate]

This is a variant some of the existing questions on this exchange, but I can't see this exact problem. Basic example duplicates this question Some prisoners are going to be lined up, all facing ...
dwjohnston's user avatar
  • 2,280
4 votes
1 answer
213 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 ...
user61165's user avatar
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 ...
Dominic van der Zypen's user avatar
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 ...
Bridgeburners's user avatar
7 votes
3 answers
1k 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 ...
Hemant Agarwal's user avatar
8 votes
2 answers
826 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 ...
Ben Franks's user avatar
19 votes
5 answers
2k views

Again! 6 prisoners, 2 colors, one mute

After that last game, the warden didn't like that they escaped. So he made them all play again. Like before, they know there are 6 prisoners, 3 red hats and 3 white hats. They know one prisoner is ...
tyobrien's user avatar
  • 3,663
40 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 ...
tyobrien's user avatar
  • 3,663
2 votes
2 answers
139 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 ...
BananaBuisness's user avatar
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 ...
Max Wang's user avatar
  • 397
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 ...
yotabyte's user avatar
  • 151
4 votes
2 answers
444 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-...
Swiss Frank's user avatar
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. ...
HugoBDesigner's user avatar
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 ...
Untitpoi's user avatar
  • 2,700
7 votes
2 answers
2k 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 ...
rob's user avatar
  • 71
7 votes
3 answers
534 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, ...
Mike Earnest's user avatar
  • 32.4k
5 votes
1 answer
746 views

Five Hats and Three Logicians

Three logicians were seated around a table. They were blindfolded and a colored hat was placed on each of their heads. They were told a true statement The hats on your heads were chosen among 3 ...
Oray's user avatar
  • 30.3k
4 votes
1 answer
447 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)...
klm123's user avatar
  • 16.2k
5 votes
4 answers
519 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,...
Acccumulation's user avatar
12 votes
3 answers
2k 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 ...
Simd's user avatar
  • 7,845
4 votes
3 answers
736 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 ...
vsz's user avatar
  • 1,702
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 ...
Daniel's user avatar
  • 406