Pigeonhole principle — New parameters

Question

Students choose exactly topics from . There are students. Show that at least share the same pair.

This practice question was inspired by Question 12(c) in the 2020 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.Holes: .
Finish the calculation, then check that the result meets the question’s conditions.If each pair has at most students: max .
State the final answer clearly in the form the question requested., so some pair has at least students.

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

Verification: .

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