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 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 $...
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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 ...
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Disaster on Blue-Eyes Island
A particular island has 100 inhabitants. None of them know their own eye colour. They are all perfect logicians. Every night at midnight, a ferry stops on the island, and every islander who has ...
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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2
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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.
...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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), ...
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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 ...
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Another problem with ages
Remember the famous three kids problem with the oldest one who plays the piano? Take a look at the next one:
A priest and a verger were travelling on a train carriage with three more passengers.Then ...
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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 ...
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Three secret numbers and sum
Three students are given one positive integer number each written on a paper. Every student knows only their own number.
Their teacher tells them that the total sum is 16. Later the teacher asks them ...
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Alice, Bob and Charlie know the sum, product and the difference between two numbers
This was sent to me by a friend so I can't source it but here's the full text:
Three Mathematics students, Alice, Bob and Charlie have to find the
values of $x$ and $y$, with $x, y \in \mathbb Z, ...
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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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Communicating Information about Cards
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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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 ...
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