Library / UKMT Junior Mathematical Challenge /238 of 274

UKMT Junior Mathematical Challenge, 2026

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

The diagram shows nine squares arranged so that they form two lines, each consisting of five squares. The squares are to be filled with the positive integers from $1$ to $9$ inclusive so that the totals of the five numbers in each line are equal. Three of the numbers have already been placed. What is the sum of the different values which the central number $N$ can take?

(A) $17$ (B) $21$ (C) $22$ (D) $25$ (E) $28$

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.