Library / UKMT Junior Kangaroo /116 of 243

UKMT Junior Kangaroo, 2026

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

Jacques wants to write a positive integer in each box in the diagram so that each integer above the bottom row is the sum of the two integers immediately below it. What is the largest number of odd integers that Jacques can write?

(A) $4$ (B) $5$ (C) $6$ (D) $7$ (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.