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← 2020 HSC Extension 1 paper Question 12(c)

Variation 3 · answer guide

Pigeonhole principle — Minimal guarantee threshold

Question

There are possible triples from topics. How many students guarantee that at least share a triple?

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.

Step by step

  1. Set up the solution: identify the objects and boxes, then show why avoiding a repeated box is impossible.Worst case: per triple gives students.
  2. Finish the calculation, then check that the result meets the question’s conditions.The st student forces some triple to have .
  3. State the final answer clearly in the form the question requested.Answer: students.

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

Verification: General rule: .

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

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