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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3
votes
1answer
379 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 ...
3
votes
2answers
446 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 ...
15
votes
3answers
911 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 ...
23
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3answers
3k 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 ...
3
votes
2answers
305 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 ...
28
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13answers
5k 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 ...
2
votes
2answers
153 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 ...
4
votes
3answers
241 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 ...
5
votes
2answers
517 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 ...
1
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2answers
158 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 ...
2
votes
1answer
196 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 ...
3
votes
2answers
366 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. ...
3
votes
1answer
132 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 ...
2
votes
7answers
624 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 ...
3
votes
2answers
435 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 ...
7
votes
1answer
387 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 ...
4
votes
1answer
175 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 ...
0
votes
1answer
230 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. ...
8
votes
2answers
445 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 ...
4
votes
1answer
142 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 ...
8
votes
3answers
524 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 ...
8
votes
1answer
136 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 ...
1
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1answer
156 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 ...
39
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13answers
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
votes
1answer
420 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)...
4
votes
1answer
146 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 ...
12
votes
8answers
5k 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 ...
7
votes
3answers
724 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
2answers
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 ...
8
votes
2answers
764 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 ...
44
votes
6answers
32k 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
votes
2answers
124 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 ...
13
votes
1answer
1k 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 ...
12
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9answers
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. ...
4
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2answers
409 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-...
14
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2answers
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 ...
7
votes
3answers
476 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, ...
20
votes
5answers
6k 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. ...
39
votes
7answers
10k 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 ...
5
votes
4answers
474 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,...
18
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 ...
11
votes
3answers
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 ...
4
votes
1answer
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 ...
2
votes
1answer
1k views

The 100 Hat Riddle [duplicate]

I saw this riddle ealier today on 9GAG (and it's found on multiple news sites), Im not quite sure about the answer, but i'm wondering if someone can solve it. 100 prisoners are lined up by an ...
20
votes
2answers
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, ...
11
votes
11answers
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 ...
8
votes
8answers
633 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 ...
7
votes
1answer
262 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 ...
7
votes
6answers
822 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 ...
7
votes
3answers
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 ...