Problem
COM-B1-M04-P012 Who Solved Many Problems
#12
★★☆☆☆ Level 2 of 5
\(25\) students solved \(100\) problems in total. Prove that some student solved at least \(4\) problems.
The average is \(4\).
If everyone solved at most \(3\) problems, the total would be at most \(25\cdot3=75\), less than \(100\). Therefore someone solved at least \(4\) problems.
Simple existence problem via average.