Maths Olympiad Prep

Library / UKMT Grey Kangaroo /177 of 242

UKMT Grey Kangaroo, 2026

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

How many of the four statements below are true? 1. Exactly two of the statements are false. 2. This statement is true. 3. The previous statement is true. 4. The first three statements are false.

(A) 00 (B) 11 (C) 22 (D) 33 (E) 44

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.