Super Soccer

Supertown Middle School’s athletic director has instituted a new policy that any pupil who wishes to play in the school soccer program is to be guaranteed to play in a game. The school has built eleven soccer fields to accommodate this. Also, the county’s school soccer league has agreed that games may either be played with the full size (eleven player teams) or in a “short formation” game in which each side plays with a goalie and a two-three-one formation on the field (two strikers, three mid-fielders, and a sweeper). Wednesday Supertown is hosting Specialtown for soccer. Supertown’s athletic director calls Specialtown and says: “We have 202 middle school players who want to play. This is the number of teams we will field.” How many full size teams and how many “short formation” teams will Supertown field? Assume that all the fields will be used.

(Source: Mathematics Teaching in the Middle School, Oct 1995)