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

[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 :)