Variation 3 · answer guide

Pigeonhole principle — Two colours pigeonhole

Question

To guarantee at least red marbles when drawing from a bag that only has red and blue, in the worst case you may first take red and all the blue. If there are only two colours and you want of one colour, the minimal guaranteeing monochromatic 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.

Step by step

Set up the solution: identify the objects and boxes, then show why avoiding a repeated box is impossible.Worst case: red and blue ( marbles) with neither colour at .
Finish the calculation, then check that the result meets the question’s conditions.The th forces of one colour: .
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: Same formula with , .

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

← Back to 2024 HSC Extension 1 paper Question 3