My college operates a high school math contest each year. It involves both an individual competition and a team competition. We’re thinking of starting up a tradition for the team competition where the winners are given a trophy which resides at the winning school each year. So, if Central High School wins, they get the trophy for the year; if they win the next year, they get to keep it; but if Northside High School wins the next year they get the trophy. This is sort of like the Old Oaken Bucket which goes each year to the winner of the IU-Purdue football game — just a fun way to inject some school rivalry, tradition, and bragging rights into the contest.
So, if you were going to do something like this with your math contest, what would the trophy be? And what would you call it?