Pigeonhole principle — Smaller election

Question

There are votes and candidates. What is the smallest number of votes a unique winner could have received?

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.

Set up the solution: identify the objects and boxes, then show why avoiding a repeated box is impossible.Need , so .
Finish the calculation, then check that the result meets the question’s conditions.At , remaining , feasible.
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: At , remaining , impossible for a unique winner.

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