Questions tagged [paradox]

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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54
votes
11answers
6k views

Eccentric Millionaire Probability Paradox

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 ...
45
votes
7answers
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 ...
27
votes
13answers
11k 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 ...
25
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8answers
8k views

Unexpected hanging paradox

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 ...
16
votes
3answers
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 ...
15
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10answers
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 ...
14
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10answers
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 ...
11
votes
3answers
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 ...
9
votes
3answers
949 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 ...
9
votes
2answers
589 views

Epimenides paradox

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 ...
7
votes
4answers
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 ...
7
votes
6answers
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 ...
7
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2answers
1k 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 ...
7
votes
1answer
725 views

About Grelling's Paradox

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 ...
6
votes
4answers
274 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 ...
4
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3answers
401 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 ...
4
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2answers
3k 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 ...
3
votes
3answers
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¢. ...
3
votes
3answers
830 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 ...
3
votes
4answers
386 views

What is the 'correct' answer?

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' ...
3
votes
5answers
454 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 ...
1
vote
5answers
946 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 ...
1
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2answers
247 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.
0
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3answers
476 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 ...
0
votes
2answers
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 ...
0
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2answers
98 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 ...
0
votes
1answer
100 views

Is the unexpected hanging paradox really a paradox? [duplicate]

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 ...
-1
votes
1answer
111 views

Death cause Paradox [closed]

In the sentence: "Two guys killing themselves by jumping out of a roof" What is the actual death cause? the roof or themselves?
-2
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6answers
818 views

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 ...
-6
votes
1answer
301 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?
-7
votes
3answers
943 views

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 ...
-7
votes
1answer
96 views

Omnipotence Paradox [closed]

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 ...
-8
votes
6answers
255 views

Average of a Series

The "average" of a series is x. A new data point comes in with the value x + 1. But the new average is less than ...
-9
votes
1answer
199 views

A guy once said he lies. I still think what he really does [closed]

If a guy says "I'm a liar", what could we deduce from it? Is he a liar or not? let us say he isn't a liar, then his statement that he's a liar affirms that he is a liar. Let us say he is a liar ...