# 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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### Alice knows a+b, Bob knows a×b. Can we find (a,b)?

There are two distinct positive integers $a,b$ (i.e. $a\neq b$) such that $a < 7$ and $b < 7$. Alice has been told the sum of $a$ and $b$. Bob has been told the product of $a$ and $b$. Both ...
2k views

### Meta Knights and Knaves Puzzle with Hats

I landed on the island of Knights and Knaves. There are only 2 types of people on the island, knights who always tell the truth and knaves who always lie. There are 2 leaders of the entire island, ...
655 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 ...
184k 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. ...
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 ...
2k 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 ...
316 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 ...
95k 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 ...
554 views

### Origin of the "Ages of Three Children" puzzle (Census-taker problem)

There is this puzzle and many variations of it, but it usually comes by as "Ages of Three Children puzzle" (Wikipedia article), the "Census puzzle" (mathsisfun.com, YouTube video), ...
4k views

### A Logician, three students and three initials

A logician decides to test three students named Rich, Ken and Rob. He said: I am thinking of the initials of a full name. First, middle and last. On three separate blank cards I have written those ...
162 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 ...
872 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 ...
2k views

### Mastermind: Win in two

Bob was very lucky in his last game of Mastermind. Alice was the codemaker; Bob was the codebreaker. They played with six colors and a length four code. Bob's first guess wasn't an immediate win. But ...
30k 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, ...
843 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 ...
401 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 ...
727 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 ...
225 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-...
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 ...