Track / Stage 3 / 29 of 260 #669 of 2604

Problem 669

AMC 10/12, early questions

Combinatorics Difficulty 3.0 Find the answer UKMT Junior Mathematical Challenge · United Kingdom · 2026

Five children, Amy, Bob, Cat, Dan and Eve each make a statement about the number of pencils they have in their pencil case. Amy: "I have more than Bob." Bob: "I have more than Cat and more than Dan." Cat: "I have more than Dan." Dan: "I have more than Eve and more than Amy." Eve: "I have more than Amy." What is the largest number of these statements that can be true?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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.