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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Sleeping Beauty's evaporating certainty
I thought of a little puzzle while contemplating the Sleeping Beauty problem.
The puzzle: create a variant of the Sleeping Beauty experiment (which involves one fair coin toss) where there is a ...
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Roulette Paradox
I have not seen the following simple paradox anywhere. Maybe most people are so smart that for them it isn't a paradox at all, but I think it is worth identifying.
Is it a "puzzle"? Well, is ...
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Help-paradox: an infinite chess puzzle
In this chess puzzle, the ruleset involves a now-obsolete version of the 3rep draw rule, in which draw is declared upon three consecutive instances of the same series of moves. More precisely, if ...
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Football Pass Rate Paradox [closed]
There are 2 teams - Team A and Team B. Both teams play 2 matches. In both matches, Team A has a higher pass rate than Team B. Can the overall combined pass rate for Team B be higher than that of Team ...
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Explain this incorrect proof that 3=0
Consider the quadratic equation $x^2+x+1=0$.
$x=0$ is not a solution to this equation, so it is safe to divide both sides by $x$.
$x+1+\frac{1}{x}=0$
Rearrange:
$x+1=-\frac{1}{x}$
And substitute into ...
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Is this a solution to the unexpected hanging paradox?
I once wrote an answer to Unexpected hanging paradox that went something like this
"In the context of the unexpected hanging paradox, being hung by surprise is defined to mean he couldn't deduce ...
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a simple paradox [closed]
This is probably the simplest paradox out there and it still confuses me, here it is.
The sentence below is true.
The sentence above is false.
I've known about this one for a few years and it has ...
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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 ...
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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 ...
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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?
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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.
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Average of a Series [closed]
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 ...
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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 ...
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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 ...
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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 ...
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Do Magicians Really Exist?
Disclaimer: I am not affiliated with the following two users in any way:
I heard this from a friend in a version pertaining to Santa Claus.
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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 ...
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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 ...
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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' ...
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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 ...
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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 ...
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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 ...
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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 ...
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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¢. ...
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How can 64 = 65?
Here is a interesting picture with two arrangements of four shapes.
How can they make a different area with the same shapes?
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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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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 and ...
GSS
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 dangerous ...
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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 ...
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Why are all Canadians the same age?
Canada is full of Canadians—about 34 million of them at present. What you may not have known is that all Canadians are the same age.
Don't believe me? I'll prove it to you.
Suppose there are exactly n ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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