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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7
votes
2answers
181 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 ...
9
votes
1answer
199 views

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 ...
13
votes
4answers
1k views

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 ...
10
votes
2answers
338 views

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, ...
1
vote
2answers
337 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, "...
16
votes
9answers
4k views

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 ...
7
votes
1answer
538 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 ...
5
votes
3answers
1k 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 ...
18
votes
5answers
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 ...
39
votes
13answers
8k views

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 ...
6
votes
1answer
201 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 ...
5
votes
1answer
317 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 ...
25
votes
3answers
2k views

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: ...
22
votes
3answers
2k views

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 ...
17
votes
10answers
1k views

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 ...
7
votes
2answers
1k 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 ...
5
votes
4answers
443 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,...
20
votes
3answers
3k views

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: ...
12
votes
1answer
1k views

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 ...
-1
votes
3answers
214 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 ...
14
votes
2answers
2k views

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 ...
62
votes
15answers
20k 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, ...
19
votes
3answers
2k views

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, ...
25
votes
10answers
5k views

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 ...
16
votes
3answers
9k views

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 ...
8
votes
3answers
484 views

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 ...
17
votes
4answers
876 views

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 ...
6
votes
1answer
444 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 ...
7
votes
1answer
442 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 ...
8
votes
3answers
398 views

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 $...
11
votes
2answers
761 views

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."...
12
votes
3answers
677 views

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 $4$. ...
10
votes
3answers
2k views

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 ...
17
votes
6answers
3k views

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 ...
12
votes
8answers
2k views

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 ...
3
votes
1answer
10k 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 ...
3
votes
3answers
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 ...
3
votes
6answers
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. ...
12
votes
6answers
4k views

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'...
3
votes
1answer
32k 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 ...
12
votes
3answers
4k views

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 ...
2
votes
8answers
577 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 ...
4
votes
6answers
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 ...
14
votes
2answers
1k views

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 ...
9
votes
1answer
564 views

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 ...
28
votes
13answers
5k views

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 ...
20
votes
4answers
9k views

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\...
10
votes
1answer
1k views

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 ...
17
votes
1answer
938 views

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, ...
3
votes
2answers
347 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 ...