GK 2019 Q21
21. Prab painted each of the eight circles in the diagram red, yellow or blue such that no two circles that are joined directly were painted the same colour. Which two circles must have been painted the same colour?
- A 5 and 8
- B 1 and 6
- C 2 and 7
- D 4 and 5
- E 3 and 6
Grey Kangaroo 2019, Question 21. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 5 and 8
Since no two circles that are joined directly are painted the same colour and circles 2, 5 and 6 are joined to each other, they are all painted different colours. Similarly circles 2, 6 and 8 join to each other and hence are painted different colours. Therefore circles 5 and 8 must have been painted the same colour. It is easy to check that, given any other pair of circles in the diagram, it is possible for them to be coloured differently.
Solution © UK Mathematics Trust, from the GK 2019 solutions.