Pigeonhole principle — A sock guarantee

Question

A drawer contains red, blue and green socks. How many socks guarantee four of one colour?

This practice question was inspired by Question 14(a) in the 2025 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.There are three colour boxes.
Simplify the previous line carefully, keeping exact values where possible.In the worst case take three of each colour: nine socks.
Finish the calculation, then check that the result meets the question’s conditions.The tenth sock creates a group of four.
State the final answer clearly in the form the question requested.Final answer:

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

Verification: Nine do not guarantee four, while ten do.

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