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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Yet Another What am I? Puzzle
1) From my birth I want to rise
But I shall fall, its no surprise
I should display approval from afar
But pedantic snobs is what you are.
2) I could produce a rise in rank
But not if my cachet ...
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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, ...
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Star Puzzle: Determine which circles are True and which circles are False
A circle with number x means:
“This circle is connected (straight line) to x circles with a true statement”
This is valid only if the statement in the circle is True.
If a circle is False, ...
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Liar and the Truth teller with 6 inhabitants
There are two types of people on an island: truth tellers and liars. Truth tellers always tell the truth, while liars always lie. A foreigner meets six of the inhabitants, and asks each of them the ...
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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 ...
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The Twins and the Number of Candies
Yveti and Xerni are twins.
Their mischievous friend, Cubo, one day decides to give them a riddle.
Cubo comes up to them and says, "I have two bags of candies in my bag. The first of you two to guess ...
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Constructing interesting "Don't Know - Don't Know - Now I know!" type puzzles
The professor has a piece of hidden information $C$. Alice is given an envelope containing information $A$, Bob is given information $B$. It is possible to deduce $C$ from $A$ and $B$. The ...
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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 ...
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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 ...
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Cheryl and her annoying birthday
Remember the 1st Singaporean problem that went viral? Try this!
Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them two unknowns: $M$ and $...
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Another sum and product puzzle
The teacher tells Summo and Prodo: "I have picked three positive integers $x\le y\le z$. I have whispered the sum $S=x+y+z$ into Summo's ear, and I have whispered the product $P=xyz$ into Prodo's ear."...
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Who will find the number on their own hat first?
Both $A$ and $B$ have numbered hats on their heads. $A$ and $B$ both cannot see his/her own hat, but they can see other one's hat. $A$ sees number on $B$'s hat as $5$ and $B$ sees $A$'s number as $4$. ...
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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 ...
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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 ...
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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, ...
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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 ...
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The Dot-town suicide
Each resident of Dot-town carries a red or blue dot on his (or her) forehead, but if he ever figures out what color it is he kills himself. Each day the residents gather; one day a stranger comes and ...
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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 ...
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"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 ...
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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.
...
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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'...
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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 ...
user9543
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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 ...
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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 ...
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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 ...
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Determine $X$ and $Y$: sum, difference and ratio
A computer science professor decides to play a game with his three brightest (nearly perfectly intelligent) students. He sits them in a circle with their backs to the center such that they cannot see ...
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1
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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 ...
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Five hats and four logicians in a circle
I found this question in a book. The solution is correct (and complicated). No tricks involved.
Four men were seated around a table. They were blindfolded and a
colored hat was placed on each of ...
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Determine the number $r$ from the statements
Alice and Bob are perfectly logical and super intellegent. Their professor decides to play a game with them, and he tells them:
"I have chosen two numbers (integers) $x$ and $y$ with $2\le y \le x\...
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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 ...
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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, ...
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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 ...
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Three secret numbers (Variant 1 and Variant 2)
The statements of the following two puzzles are almost identical.
The only difference consists in the words printed in boldface.
The two solutions, however, turn out to be totally different.
Variant ...
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answer
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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 ...
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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 ...
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That hat at that head
It seems to me that many mysteries involve hats.
Therefore, a good old hat mystery that I came across a couple of years ago.
Abraham (A), Bingchiang (B), Charly (C) and Derek (D) are sitting in a ...
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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 ...
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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 ...
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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.
...
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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 ...
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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 ...
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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 ...
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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 ...
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