Library / UKMT Intermediate Mathematical Challenge /257 of 267

UKMT Intermediate Mathematical Challenge, 2019

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

The diagram shows part of a tessellation of the plane by a quadrilateral. Khelen wants to colour each quadrilateral in the pattern so that no two quadrilaterals that meet (even at a point) have the same colour. What is the smallest number of colours he needs?

(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.