Track / Stage 3 / 22 of 260 #662 of 2604

Problem 662

AMC 10/12, early questions

Combinatorics Difficulty 3.0 Find the answer UKMT Grey Kangaroo · United Kingdom · 2026

A sports storeroom contains three types of bats: cricket bats, table tennis bats and baseball bats. On Monday, some children each remove two bats chosen at random. What is the smallest number of children who could remove bats to be sure that at least two of them have exactly the same types of bat?

(A) $8$ (B) $7$ (C) $6$ (D) $5$ (E) $4$

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.