Variation 2 · answer guide

Pigeonhole principle — Five groups guarantee

Question

Minimum size guaranteeing at least students from one of schools is

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..
Finish the calculation, then check that the result meets the question’s conditions.At one can still have five groups of .
Match the result to the choices and state the correct option.Therefore option B is correct.

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

Verification: Off-by-one: is not the minimal guarantee.

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