Library / UKMT Junior Mathematical Challenge /137 of 274

UKMT Junior Mathematical Challenge, 2015

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

In the figure shown, each line joining two numbers is to be labelled with the sum of the two numbers that are at its end points. How many of these labels are multiples of 3?

(A) $10$ (B) $9$ (C) $8$ (D) $7$ (E) $6$

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.