Problem #PRU-78206

Problems Methods Algebraic methods Counting in two ways Pigeonhole principle Pigeonhole principle (other)

Problem

30 pupils in years 7 to 11 took part in the creation of 40 maths problems. Every possible pair of pupils in the same year created the same number of problems. Every possible pair of pupils in different years created a different number of problems. How many pupils created exactly one problem?