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Questions tagged [meta-knowledge]

Puzzles where perfect logicians are told different pieces of information, and the reader must figure out something based on their words and actions.

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196 votes
26 answers
96k views

In the 100 blue eyes problem - why is the oracle necessary?

The riddle Randall Munroe (of xkcd fame) has, a bit hidden on his site, a logic puzzle: A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a ...
dwjohnston's user avatar
  • 2,280
49 votes
4 answers
16k views

I don't know the two numbers... but now I do

Two perfect logicians, Summer and Proctor, are told that integers 𝑥 and 𝑦 have been chosen such that 1 < 𝑥 < 𝑦 and 𝑥 + 𝑦 < 100. Summer is given the value 𝑥 + 𝑦 and Proctor is given ...
durron597's user avatar
  • 2,374
16 votes
2 answers
4k views

Product and Sum

My fellow mathematicians Paul and Sam are very fond of mathematical puzzles. One day, I came up with the idea on mathematical puzzles while three of us having lunch together. I: Hey, guys. I am ...
P.-S. Park's user avatar
  • 4,199
23 votes
12 answers
186k views

Four prisoners wearing black and white hats

There are four prisoners. All four prisoners will be freed, if at least one of them correctly guesses the color of the hat on his head. They can't speak to each other, and they can't touch each other. ...
Danny's user avatar
  • 351
12 votes
7 answers
1k views

Blue eyes riddle: what information is gleaned after the first night?

There are good explanations on this site and xkcd of the inductive reasoning leading to the riddle’s solution, but nowhere have I found an answer to the following aspect: Exactly what information is ...
Roland Kuhn's user avatar
10 votes
6 answers
8k views

Who has mud on their forehead?

This is probably my favorite puzzle. It uses logic, but it's not one of those "logic table" puzzles which i dislike immensely. What is this type of puzzle called and are there more like it ...
please delete me's user avatar
75 votes
21 answers
31k views

Are there eighteen or twenty bars in my castle?

Two friends, Mark and Rose, are very famous logicians; they are so clever that they can deduce any logic connection possible in a matter of minutes even from the most vague situation. Unfortunately, ...
Marco Bonelli's user avatar
3 votes
6 answers
1k views

Explaining Cheryl's birthday

Relevant link : Cheryl's birthday I understand the solution. But it feels wrong to me, because Albert cannot possibly make the third statement with the information he has at the moment he makes it. ...
Kalissar's user avatar
  • 271
10 votes
1 answer
1k views

Deducing Two Numbers based on their Difference and Ratio

Yesterday I met the perfect logicians Divvy and Subtra. I told them: I have chosen two positive integers $x$ and $y$ with $2\le x\lt y\le 100$ and with $x$ a divisor of $y$. I will now whisper ...
Abr001am's user avatar
  • 1,004
18 votes
3 answers
11k views

What are the three numbers in this puzzle?

There are three people in a room without any equipment. Each one has a number on his forehead Every person knows the numbers the other two have, Every person knows that his number is either the sum ...
user21233's user avatar
  • 477
13 votes
4 answers
4k views

Guessing hat colors

Red or Black There are 3 children sitting on three chairs. The children can only look forward and all wear one hat. The hats are either black or red. They are a total of 5 hats, 3 are colored red and ...
martijnn2008's user avatar
  • 1,335
12 votes
3 answers
4k views

When is Mr. Hill's birthday?

Jack and Jill are students of Mr. Hill. Mr. Hill's birthday is on $M$ month, $D$ day. Neither student knows when Mr. Hill's birthday is, but both know it is one of the dates below. Mr. Hill told Jack ...
Mox Shah's user avatar
  • 639
10 votes
1 answer
737 views

Two students guessing positive integer

Q. Two students A and B think of a positive integer. They tell the teacher their positive integer, but they don't tell each other their positive integer. The teacher tells both of them two different ...
yigang's user avatar
  • 103
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
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
17 votes
1 answer
1k views

Farm dimensions

Here is a question I was given during an interview a few years ago. There was a farmer who had two daughters. One day he was considering giving his farm to his girls. He took his first daughter, ...
0rtis's user avatar
  • 173
16 votes
6 answers
3k views

Abby and Bobby and three numbers on the blackboard

Abby selects a non-negative integer $A$, and Bobby selects a non-negative integer $B$. They then both tell their number secretly to Summy. Summy writes the numbers $5$, $8$, and $15$ on the ...
Gamow's user avatar
  • 45.6k
12 votes
6 answers
4k views

Find two numbers based on either their product or their sum?

A friend of mine told me the following puzzle and I could not solve it. Sam chooses a positive integer $x$, and Peter chooses another number $y$. They do this secretly, so that Peter does not know Sam'...
user11489's user avatar
  • 137
10 votes
3 answers
2k views

Sum, Product and Difference

I had three mathematician friends at school, and we were hanging out. Out of the blue a question came to my mind, and I decided to ask it to them: "Guys, I have a question for you. Which is actually ...
Oray's user avatar
  • 30.3k
10 votes
7 answers
549 views

3 travelers and 9 diamonds

There are three travelers. They are inside a cave. Deep down in this cave, there are three doors, each door containing at least one diamond, and there are a total of 9 diamonds. Each traveler picks a ...
AtilioA's user avatar
  • 217
9 votes
1 answer
819 views

Product and Sum, Variant 2a

My friends Peter and Sam are excellent mathematicians and always think strictly logical. Yesterday I told them: "I have secretly chosen two integers $x$ and $y$ with $1\le x\le y\le 9$. I have told ...
Gamow's user avatar
  • 45.6k
8 votes
1 answer
685 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
7 votes
1 answer
3k views

Generalization of Sum and Product puzzle

I heard from a clever person that for the problem mentioned before: I don't know the two numbers... but now I do a solution exists even if we change 100 to infinity. So the formulation would be ...
klm123's user avatar
  • 16.2k
7 votes
6 answers
1k views

Five logicians with one or two hats [7,8,9]

There are five logicians seated around a table. They are blindfolded and hats are placed on their heads. After removing the blindfolds, they are told a true statement: Each of you has either one hat ...
ghosts_in_the_code's user avatar
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
  • 9,208
5 votes
3 answers
2k views

Engineers logic test for a job [duplicate]

Two engineers go to a job interview. They are introduced and told they are looking for people with team working skills. Without time to talk or get to know each other, they are guided to two different ...
Evaldor's user avatar
  • 53
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
4 votes
9 answers
878 views

5 logicians with 1 or 2 hats (Part II) [8,9,10]

This is the corrected version of this question. There are 5 logicians seated around a table. They are blindfolded and hats are placed on their heads. After removing the blindfolds, they are told a ...
ghosts_in_the_code's user avatar
3 votes
1 answer
11k views

Black and White Hats Puzzle - Three prisoners

There is a similar question here but with four prisoners. But I am not able to understand the logic. The original question is here. My solution is half way through. Since there are 3 Back Hats (B) and ...
Java Enthusiast's user avatar
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