Mathematical humour

[jack]

Simont: Is there a set of players each of whom plays a single win-or-lose game against each other player, where every pair of players has a third player who beat both?
Jack: *thinks*
Jack: Yes.
Simont: Not that one.

Comments

[pseudomonas]

Is this explicable to non-mathmos?

[simont]

There's a trivial answer, which is to let the set have fewer than 2 players. Then "every pair" has a third player who beats both, in the vacuous sense that you can't exhibit a pair for which this condition fails.

[jack]

I doubt it[1], but Simon's explanation explains what's _supposed_ to be funny, but I don't know if that can actually make it funny :)

[1] Every so often the perverse urge to post things I know a small minority will get overcomes me.

[pseudomonas]

That's OK, I'll settle for comprehension, even if the aesthetics eludes me.

[(Anonymous)]

Yes.

(Unless that one doesn't count either)

[jack]

:)

I can't remember the exact wording. I think I understood that Simon would realise I could see two trivial answers, but "not that one" was funnier. Though I suppose I could have repeated the joke :)

[khoth.livejournal.com]

I think I can see three answers - two trivial ones, and a third that's not trivial but also probably not what you want.

[jack]

What's the third answer? I can see trivial answers where there's no pair at all, and "genuine" answers (smallest with 7 players, IIRC). But I'm probably blinded by knowing what the question is "supposed" to be, and missing another correct interpretation.

[khoth.livejournal.com]

The one I thought of was when you have an infinite number of players. Label them 1,2,3,... and player x beats y if x>y.

It's arguably still trivial, but it's at least not vacuous like the one or two player solutions.

[simont]

*nods* When I actually mentioned this problem to Jack I did make sure to mention that the set of players had to be finite (but I forgot to mention that it also had to have size at least two, hence the exchange quoted above).

[jack]

ROFL! Yes, good answer.

I couldn't remember if Simon said "finite" or if it was obvious from context it was a number theory question, but I see he says he did specify :)

[sunflowerinrain]

If I look at this exchange and the elucidations as art, they are very beautiful and moving. When I look at the meaning, my brain hurts for a few moments before I get it, and there is no way I'd understand without the explanation.

But after understanding, I go back to admiring the lovely coloured patterns :)