Library / UKMT Junior Kangaroo /228 of 243

UKMT Junior Kangaroo, 2026

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

Nell wants to write the numbers 1, 2, 3, 4 and 5 in the five cells in the diagram so that any number directly below another number is greater than that number and any number directly to the right of another number is greater than that number. In how many ways can she do this?

(A) $3$ (B) $4$ (C) $5$ (D) $6$ (E) $8$

Figure for this problem

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.