What are some of your favorite paradoxes and puzzles?

Catch-22 is always a good one (“That’s some catch, that Catch-22.”) I’m more inclined to muse over word paradoxes than solve them.

My friend is the opposite and hates logic-based paradoxes that are based in the words and not in something more mathematical. One of her favourite jokes is telling people “Happy Christmas” on Halloween. They get so confused. She always has paper on hand to work out the solution. They still walk away confused.

The Monty Hall problem was posted not too long ago (and I answered it there) so I will let someone else take a crack at it this time :) Just remember folks: always switch. Seriously. Your odds increase. We’re not lying.

The Water Temple in The Legend of Zelda: The Ocarina of Time.

Also: Infinity in mathematics. By definition, a set is infinite if it contains the same number of elements as one of its subsets. In other words, something is infinite if its part is as big as its whole.

In time travel, the Grandfather Paradox
Thinking about it makes my eyes spin.

I like this one I cut and pasted from wikipedia since I didn’t want to mess it up:

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

Under this scenario, we can ask the following question: Does the barber shave himself?

@cockswain Why did you specify “male” barber? I guess he does not shave himself as he goes to the female barber.

@Trillian I tried to solve this once by assuming the barber was female, but as the paradox goes, the barber is male. I’m not the author of the paradox, so you can’t hold me accountable for the fact he is male. Also, as it states the town only has one male barber, there is no female barber that shaves the male barber. The barber only shaves those men that do not shave themselves.

@cockswain Ok, I’d like to see the original. If it’s the way you write, it is left open to interpretation. Is he like some duality? Shaving as the barber, being shaved as he customer? Is there an answer?

What original are you talking about? Like I said above I cut and pasted from wikipedia since I didn’t want to mess it up. Further, this is a paradox like the question asks, so there probably isn’t an answer because it’s a paradox because there isn’t an answer because it’s a paradox. Like what happens when an irresistible force strikes an immovable object?

@Trillian @cockswain

Another variation on this paradox is the catalog that lists all catalogs that don’t list themselves. So what catalog lists this one? It doesn’t list itself, therefore it should be listed in itself, but then it would list itself, so it shouldn’t be listed, etc. back and forth forever with no solution.

The set of all sets which do not contain themselves.

“There are things that are true in mathematics (based on basic assumptions).
There are things that are false.
There are things that are true that can never be proved.
There are things that are false that can never be disproved.
And that is a problem, because we cannot ever tell if something is true unless we can prove it.”

@DominicX I have a guided meditation session to go to so I can’t allow this little conundrum of yours to make me gibber and rave at this point. I’ll reserve my brain explosion for a later time. Ciao!

The town maniac kills all and only those persons in town who do not kill themselves. Does he kill himself?

“appended to its own quotation yields a falsehood.” appended to its own quotation yields a falsehood.

That one about the farmer with the grain, the fox, and the duck. I can never remember how it goes. The one about the door that lies and one that tells the truth. That one, too.