IMC 2019 Q6
6. 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
Intermediate Mathematical Challenge 2019, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 4
At each of the points indicated by a dot, four quadrilaterals meet, so that at least four colours are needed.
The diagram shows that four colours is possible, so the minimum number of colours Khelen needs is four.
Solution © UK Mathematics Trust, from the IMC 2019 solutions. Longer versions with investigations: Solutions and investigations (PDF).