Library / UKMT Pink Kangaroo /184 of 220

UKMT Pink Kangaroo, 2025

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Debanshi has a bag of 18 balls, numbered from 1 to 18. What is the smallest number of balls she would have to remove to be sure that at least three of them displayed primes?

(A) $11$ (B) $12$ (C) $13$ (D) $14$ (E) $15$

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

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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