Love is the most excellent way

Ben competed in the Latin School math contest today. He competed in the individual and team events. His team came fourth (which earned them medals and a trophy for his school). Individually he placed third - he got a trophy for that.
Last year he was in this contest but his team didn’t place, nor did [...]

Ben asked me if I knew how to do this question yesterday. It’s on his old practice papers for a middle school math competition. He and Steve (the math PhD!) were both having trouble with it.
I was very happy that for once, I actually thought of a better way of doing it than they [...]