# 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.

93 questions
Filter by
Sorted by
Tagged with
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 ...
• 2,159
30k 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, ...
• 2,555
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, ...
• 17.8k
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 ...
11k 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 ...
• 477
530 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 ...
• 685
1k 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 ...
• 997
727 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 ...
• 1,702
491 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 ...
• 2,216
433 views

• 9,072
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 ...
• 984
1k 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, ...
• 173
391 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 ...
• 45.4k
794 views

### 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 ...
• 45.4k
815 views

### 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 ...
• 45.4k
4k views

### 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 ...
• 4,169
2k views

### 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 ...
900 views

### 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 ...
• 5,966
3k views

### 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 ...
• 16.1k
184k views

### 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. ...
• 351
8k views

### 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 ...
16k views

### 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 ...
• 2,344
95k views

### 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 ...
• 2,270