Practice variation 1 of 3
Pigeonhole principle — Remainders modulo five
Your question
Prove that among any six integers, two have a difference divisible by 5.
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.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?