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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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8 votes
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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
8 votes
1 answer
908 views

A different extension of the sum and product puzzle

How far down the rabbit hole of not knowing can we go? While working on the generalization of I don't know the two numbers... but now I do, I thought of these two extensions. Both have the same ...
Rob Watts's user avatar
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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
7 votes
1 answer
493 views

Where does the math club meet?

A puzzle from John Conway and Pizza Hut. (The competition has ended, so I think it's okay to post the puzzle here.) Our school’s puzzle-club meets in one of the schoolrooms every Friday after ...
Colonel Panic's user avatar
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
2 answers
320 views

Find the ages of mathematician's children

Mathematician: "It was the August of 1997 when they barged into my house..." - Here is his story: Students surprised their mathematics teacher with a cake on his birthday. The teacher was ...
Vepir's user avatar
  • 2,968
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
6 votes
4 answers
462 views

Regain your bearings from the logicians

You have landed on an island of fun-loving logicians (hmmm ...) and don't know how to find your way home. After asking the first person you meet for directions, you are led to a secret, mystical ...
Marconius's user avatar
  • 1,213
6 votes
1 answer
598 views

What is the Unit Digit of the Sum?

I am thinking of 2 integers $x$ and $y$ which follow the following; $$2≤x≤y$$ $$x+y≤47$$ I then write the sum $S = x+y$ and the product $P=xy$ on two separate cards. I pass the sum card to player A ...
Ben Franks's user avatar
6 votes
1 answer
232 views

Lifeless, but Alive

Lifeless, but alive, An aura of death surrounding. Flies and maggots prosper, Unmoving, unyielding. Limbs of crimson, ever grieving. In danger, A stigma. Of whom do I speak? Hints from ...
iiiidk's user avatar
  • 2,900
6 votes
2 answers
812 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
  • 9,278
5 votes
1 answer
324 views

Pingala the Pirate

Pingala the Pirate was well known for many things, most notably the urban legend that he had hidden an enormous haul of riches, but also his poor memory, and his clumsiness. He lost a toe on each foot ...
Darren H's user avatar
  • 357
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
5 votes
1 answer
346 views

I don't want to let my friends down

This is an entry into the Fortnightly Topic Challenge #36 I was supposed to do something, but I can't remember what it was. I know it was supposed to be fun or funny. In a typical effort to hide my ...
Joe-You-Know's user avatar
  • 9,565
5 votes
3 answers
319 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
5 votes
1 answer
297 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
5 votes
1 answer
245 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
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
231 views

Sobot or fauxbot?

Through the bustling hallway, you followed your speed-walking, speed-talking brother, who was hoping to submit an article about the upcoming demonstration to his beloved Logic and Philately Semi-...
C. P. Boyko's user avatar
5 votes
2 answers
306 views

Knight-Knave-Normal Meta-Knowledge

A traveller visited one of the islands described by Raymond Smullyan on which all inhabitants are either knights, who always tell the truth, knaves, who always lie, or normals, who can say anything. ...
fblundun's user avatar
  • 1,536
4 votes
3 answers
740 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
580 views

100 blue-eyed people riddle N=4

The solution of this riddle is usually given with explicit reasoning for two cases: Case where there is only 1 blue-eyed person, Case where there are 2 blue-eyed people. That logic is clear, and I ...
jas's user avatar
  • 51
4 votes
2 answers
766 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
4 votes
1 answer
220 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
4 votes
9 answers
879 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
3 answers
1k views

Blue eyes riddle: a counter-argument to accepted solution

I would like help understanding my flawed logic in my following reasoning: The Blue-eyes Riddle is commonly expressed as A group of people with assorted eye colors live on an island. They are all ...
Acumen Simulator'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
3 votes
3 answers
2k views

"Guess the number" game

two logicians decided to play a lovely well-known game , number-guessing from the least significant informations , the juror proposed to create the challenge : the juror told the logicians two ...
Abr001am's user avatar
  • 1,004
3 votes
2 answers
454 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
  • 9,278
3 votes
2 answers
520 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
3 votes
1 answer
271 views

The two numbers which were overestimated

James: These two cards have two numbers $X$ and $Y$, which are both one-digit numbers and are different. Can you find the sum? Jack: No, that's impossible. Can I get a hint? James: The last digit of $...
Shambhav's user avatar
  • 131
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
3 votes
2 answers
397 views

Product and Sum, Variant 2b

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 $1\le x\le y\le 99$. I have told ...
Gamow's user avatar
  • 45.7k
3 votes
1 answer
39k views

Who will shout first? [duplicate]

There are four guys standing in a line. They need to find out which color their hats are. They can't see their own hat color and only can see to the right. They can't see the person behind the ...
user avatar
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
  • 9,278
2 votes
7 answers
754 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
2 votes
2 answers
235 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
2 votes
2 answers
456 views

Doesn't saying "at least 99 of you have green eyes" give new information?

The Logic Puzzle I have found a catch in the solution of this logic puzzle. Provided that you are not allowed to give the prisoners any new information, the statement "at least 99 of you have ...
Hitarth Vyas's user avatar
2 votes
3 answers
552 views

The Missing House Number

The Visit One day I was visiting my sister in Boston and heard a bunch of kids yelling and playing in the yard ( yahd ). I couldn't see the kids, and hadn't seen my sis for years so I asked her, "...
John S.'s user avatar
  • 2,145
2 votes
1 answer
237 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
  • 9,278
0 votes
3 answers
241 views

Boxed AI, Ethics, and Chivalry, oh my

(Inspired by this somewhat) So, your science lab is on the forefront of super AI. However they may not be on the forefront of good AI. Hence the AI is in a box until they can figure out what to do ...
Destructible Lemon's user avatar
-1 votes
1 answer
173 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
181 views

Variant of blue eyes puzzle [closed]

There are a total of 200 players assigned to either A or B at a certain venue. There are actually 100 of each, but the players don't know that. They don't know which one they are. Of course, there is ...
John's user avatar
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