Solve This Pzzlr: World Cup

Fair enough, I wasn't deploring the lack of, or advocating for knowledge regarding triangular numbers among the masses -- I was simply observing a (neat?) fact.

I see your point. I think a key difference comes from square numbers working both with integers and reals, in the sense that a 10 by 10 square and a 10 by 10 grid of dots both give 100 for the area or no. of dots. A 10 by 10 triangle grid is going to have 55 dots instead of the 50 sq. unit area of a 10 by 10 right triangle though. Many high school students do at least remember the area of a triangle formula (they say they don't, but if you prod them, many end up remembering it anyway).

I still see triangle numbers and such come up in kids books trying to introduce interesting math or for a visual example of an algebra formula. But there is no emphasis on remembering that since there is enough use for math other than parlor tricks today, and more serious combinatorics efforts are hidden until upper level undergraduate programs or lumped in with basic probability problems. I suppose it is sad for something not to be learned because it is not useful anymore, on the other hand, not so much as long as kids are learning something.

Bravo, Plasmagryphon! A simple explanation, it works with any number of teams, and it's quicker and easier to calculate off the top of one's head.

Ah, I see now. However, I still don't see how they identify a winner unless it's simply who wins the most games and you'll have ties. Seems like a very inefficient way to run a tournament.