Variation 1 · answer guide

Pigeonhole principle — Classic g(m−1)+1

Question

What is the minimum number of students from schools guaranteeing at least from one school?

This practice question was inspired by Question 3 in the 2024 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: identify the objects and boxes, then show why avoiding a repeated box is impossible.Worst case: with none having .
Finish the calculation, then check that the result meets the question’s conditions.The next student — the th — forces some school to : .
Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Check: can be ; forces a .

Any mark labels are a TestMum study aid, not an official NESA marking allocation.