Students from 4 different schools come together to form a choir - HSC - SSCE Mathematics Extension 1 - Question 3 - 2024 - Paper 1

According to the pigeonhole principle, if we want at least one school to have at least 20 students, we can distribute students among all schools in the worst-case scenario. If there are n students and k schools, if we want at least one school to have x students, we need to ensure that:

$n = k(x-1) + 1$

Here, k = 4 (schools) and x = 20 (students from one school).

Plugging the values into the formula:

$n = 4(20-1) + 1 = 4(19) + 1 = 76 + 1 = 77$

Thus, the minimum number of students required in the choir must be 77.

Therefore, the minimum size of the choir to ensure that at least 20 students are from one school is 77.