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.

Filter by
Sorted by
Tagged with
15
votes
3answers
1k views

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 ...
5
votes
2answers
163 views

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. ...
-2
votes
1answer
144 views

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 ...
4
votes
1answer
449 views

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 ...
3
votes
2answers
263 views

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 ...
4
votes
3answers
232 views

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 ...
1
vote
2answers
153 views

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 ...
3
votes
1answer
373 views

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 ...
2
votes
1answer
194 views

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 ...
3
votes
2answers
358 views

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. ...
5
votes
2answers
499 views

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 ...
3
votes
1answer
129 views

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 ...
2
votes
7answers
614 views

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 ...
3
votes
2answers
410 views

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 ...
4
votes
1answer
171 views

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 ...
7
votes
1answer
372 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 ...
5
votes
1answer
234 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), or as the "Census puzzle" (mathsisfun.com, youtube ...
7
votes
2answers
254 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
243 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
387 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, ...
2
votes
3answers
449 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
553 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 ...
9
votes
7answers
503 views

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 ...
6
votes
1answer
205 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
330 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: ...
23
votes
3answers
3k 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 ...
18
votes
10answers
2k 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
467 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: ...
13
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
225 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 ...
68
votes
19answers
25k 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, ...
24
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
10k 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
493 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 ...
19
votes
4answers
998 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
459 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
467 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
410 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
773 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
697 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 $4$. ...