Library / UKMT Junior Mathematical Challenge /178 of 274

UKMT Junior Mathematical Challenge, 2016

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows five circles placed at the corners of a pentagon. The numbers 1, 2, 3, 4, 5 are placed in the circles shown, one in each, so that the numbers in adjacent circles always differ by more than 1. What is the sum of the numbers in the two circles adjacent to the circle which contains the number 5?

(A) $3$ (B) $4$ (C) $5$ (D) $6$ (E) $7$

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.