Martin Gardner sports question

[grandpascorpion]

A student has just returned home from a track and field event at her school "Springfield High".
Her father pressed her for details.

Girl: "Well, sure enough my boyfriend Johnny won the shotput. That makes it 10 years in a row that our school has won."

Dad: "What about the other events?"

Girl: "Well, um, Middletown High won the whole thing with 22 points. And we tied with Mountain High at 9 points. Just 3 schools today."

Dad: "Too bad, you didn't win. Back in the day, I was quite a high jumper. Which high school won that event?"

Girl: "Jeez Dad, that was definitely one of the events but I wasn't really paying attention. I was just focusing on Johnny. I remember that for each event, the first place finisher receives the most points, the 2nd place finisher receives less points, and the 3rd receives the least. It was the same for each event. [Assume any points awarded are integers]

Can you help Dad with his high jump question?

[axn]

Originally Posted by grandpascorpion

[Assume any points awarded are integers]

Positive integers or any kind of integer will do?

Can two or more athletes from a school compete in the same event?

[grandpascorpion]

To be clear:

f=first place points
s= 2nd place points
t = third place points

f, s, and t are positive integers such that f > s > t

Each school sends exactly one student to each event.

[axn]

Noting the fact that there are 40 pts in total and that and event must offer at least 6 pts in total (3+2+1), we find that there has to be 2, 4 or 5 events.

Lots of trial and error, and we end up with a scoring system of 5,2,1 and 5 events in total. And the winner of high jump is... "Middletown High".
To be fair, the answer can be provided by gut feel because of the huge discrepancies in the scores.

[grandpascorpion]

That's true but breaking down the scores is more interesting I think.