Problem: A basketball player has a season free throw average of \(70\%\) halfway through the season, and raises it to \(80\%\) by the end of the season.

Is it necessarily true that it was exactly \(75\%\) at some point? Why or why not? Source

Extension: For which integer triples \((a,b,c)\) can a basketball player go from a free throw average of \(a\) to \(c\) while avoiding a free throw average of \(b\).

Solution