# 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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-...
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### 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 ...
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### 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, "...
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### Three people wearing hats

Ms. Doha gave hats with different non-zero single digits (two of which are factors of the third) to Ms. Haha, Ms. Lola and Mr. Hehe. The three of them can't see the digits on their own hat though they ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### A game of multiplication and addition

Carol is playing a game with Alice and Bob. She secretly chooses two integers between 1 and 10 and gives the sum to Alice and the product to Bob. After some time, the following discussion occurs: ...
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### 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 ...
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Seven cards, numbered $1,2,3,4,5,6,7$, are distributed randomly among three people: Rand gets one of them, Deusovi gets three of them, and Gareth gets three of them. All three know what the seven ...
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### 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 ...
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### 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,...
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### Sum of secret numbers is 101

Alice, Bob, and Charlie were given three numbers, respectively. They were said that all the three numbers were positive integers and the sum was 101. Alice: I know we have different numbers. Bob: ...
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### A 3-person hat puzzle (no, not that one) (no, not that one either!)

No, this puzzle isn't a duplicate of any of the well-known hat puzzles we all know. Yes, it does have a valid solution. This puzzle was originally composed by Jack Lance and posted to a friend group ...
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