Pigeonhole principle — Different numbers

Question

12 teams, more than 2 over-age players triggers a penalty, 25 over-age players total. Must a team be penalised?

This practice question was inspired by Question 12(b) in the 2022 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.Max without penalty: .
State the final answer clearly in the form the question requested., so yes.

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

Verification: Compare total to where is the max allowed per team.

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