A puzzle in which a seemingly impossible situation is presented, or any sort of construction that results in a logical contradiction.

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The following is a probability paradox I've been thinking about. It involves Bayes' rule; if you're not familiar, a good starting example is a urn that has a 50% chance of containing one black ball ...
9k views

How many tries to roll a 6?

Suppose you roll a (fair, 6-sided, perfectly ordinary) die repeatedly until you roll a 6. As is well known, the expected (i.e., long-term average over many trials) number of rolls required is 6. Now ...
13k views

Protagoras's Paradox. An Unsolved Court Case

Many years ago, a Law teacher came across a student who was willing to learn but was unable to pay the fees.The student struck a deal saying, "I will pay your fee the day I win my first case in the ...
9k views

The unexpected hanging paradox is as follows: A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to ...
3k views

A library with less information than one of its books

How can a library contain less information than one of the books in it? The library is intended to be a set of books on shelves. The information content is the least number of bits to describe the ...
3k views

How can the “Boy or Girl” paradox be worded unambiguously?

The first time I encountered the Boy or Girl paradox I was struck by how ambiguous all of the formulations in English are. As Wikipedia notes: Gardner argued that a "failure to specify the ...
2k views

Two many rainbows?

Wish I’d had a camera at the time but a cartoon will have to suffice, representing two actual incomplete rainbows that stop in midair where they meet, lit only by a setting sun. This seemed so ...
1k views

Birthdays celebrated in wrong order

A boy celebrated his birthday with some friends. Strangely, 2 days later, his elder twin celebrated his birthday with the same friends. Now those friends got confused and asked why the order was ...
952 views

Who's the oldest?

A child is born on August 19th 2016 00:12 (local time) on timezone GMT + 1. Another child is born on August 18th 2016 23:48 (local time) on timezone GMT. Which one is the oldest? Note: Not sure I ...
606 views

Epimenides (a Cretan) once wrote a poem, in which he stated that all Cretans are liars. Since he is a Cretan, and therefore a liar, Cretans are veracious. But then again he wouldn't be a liar! This ...
1k views

Who wins in this tic-tac-toe game?

Question sourced from Brilliant.org Jack and Jill are playing Tic-Tac-Toe, with Jack being Os and Jill being Xs. Now, being perfectly logical beings narrow-minded one-move-foresight beings, they move ...
1k views

I exist, but I do not. I change, but I do not

I am a tool but I do not really exist I am always used, even when I am not The people that truly benefit from me are those that have trouble using me I am found everywhere, but I haven't always ...
2k views

A list of 100 statements

I was working my way through some puzzles in Discrete Maths by Rosen, when I came across the following question: The $n^{th}$ statement in a list of 100 statements is : "Exactly $n$ of the ...
786 views

Grelling's Paradox is about certain types of words. An adjective is heterological if it does not describe itself; like 'long', 'German', or 'monosyllabic'. An adjective is autological if it does ...
279 views

At least $N$ false statements

Let $N$ and $M$ be two integers with $M\ge N\ge2$. There is a list of altogether $M$ statements that is divided into three parts: the first part consists only of the first statement; the second part ...
409 views

Do Magicians Really Exist?

Disclaimer: I am not affiliated with the following two users in any way: What I would like to know is: Does the following paradox have a name? What is the fallacy of the argument? If possible, where ...
4k views

Puzzle : O' Barber , Who Art Thou?

I was working my way through some puzzles , when I came across the following question: An ancient Sicilian legend says that the barber in a remote town who can be reached only by traveling a ...
1k views

Where did the extra dime come from? [duplicate]

In a snack bar there were two baskets of pears of different sorts, 60 pears in each. It was proposed to sell pears from the first basket at 4 for 30¢, and pears from the second basket at 6 for 50¢. ...
895 views

A boy and his father [closed]

A young boy is taking a ride with his dad when a truck runs them off the road, killing the father and critically injuring the young boy. He's Medivac'd to the nearest hospital as the child is lying on ...
392 views

It is a logic puzzle left by my discrete math professor. We are learning propositional logic now. Here is the puzzle: Among all the students in our class, at most two students give the 'correct' ...
461 views

Why is my car always in the slowest lane?

Staying in the traffic again this morning, I decided to find a mathematical motivation behind me always being in the slowest lane. Consider the following formalization: there are 4 empty lanes and ...
988 views

Obi-Wan vs Grievous

19 BBY, the Galactic Republic spots General Grievous in Utapau, the Separatists' Council Base; the Jedi Obi-Wan Kenobi is sent there to deal with him. After a long search, Obi-Wan comes face to face ...
262 views

The faster you walk

The faster you walk, the quicker you'll get there, it's true. But be warned, it's not without a price, for the faster you go, the further you'll have to walk before you arrive.
480 views

What happened to the missing £10? [duplicate]

I have come across a puzzle, which makes no sense. Does anyone know the answer to the below? You and two friends go on holiday. When checking out, the total bill comes to £300. You pay the bill ...
1k views

All You Zombies

All You Zombies is a short story by Robert Heinlein, which outlines a rather bizarre time travel paradox. Here is an outline of the paradox with a few key moments missing. Jane is dropped off at an ...
100 views

Help me with these meta questions [closed]

I’ve been thinking about these questions and I wonder what multiple people would write if they can do so in a paragraph or two. Question 1 : What is the answer to this question? Question ...
123 views

The unexpected hanging is described in the Wikipedia article Unexpected hanging paradox. A hanging is said to be a surprise of on the morning that the prisoner is hanged, he cannot deduce that he ...
119 views

In the sentence: "Two guys killing themselves by jumping out of a roof" What is the actual death cause? the roof or themselves?
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Mirror Room Puzzle (Thought Experiment) [closed]

You are in a room with a barrier in the middle. This is not a physical barrier; it is a dividing line of 2 mirror images. When you look across the room, it appears to be a mirror because you see a ...
321 views

A question about Pinocchio's nose [closed]

What happens to Pinocchio's nose if he says to another person "My nose is about to grow"? Does it grow? Does it stay the same? Something else?
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The barber paradox - Who shaves the barber? [closed]

All the men in a village either shave themselves or are shaved by a barber (himself a man from the village). The barber claims to shave only the male villagers who do not shave themselves. So who ...
111 views

God has limitless power. So can he/she create a stone so heavy the no one lift it ? If yes, then god himself/herself can not lift it, so limited power. If no, then there's a limit to what god can ...