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← 2021 HSC Extension 1 paper Question 10

Variation 3 · answer guide

Pigeonhole principle — Many candidates

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Question

With votes and candidates, the minimal unique winning total is

This practice question was inspired by Question 10 in the 2021 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., so .
  2. Finish the calculation, then check that the result meets the question’s conditions.At , remaining , feasible.
  3. Match the result to the choices and state the correct option.Therefore option C is correct.

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

Verification: At , remaining , impossible.

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

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