Problem 26 · 2019 Math Kangaroo
Stretch
Logic & Word Problems
casework
Peter colours each of the eight circles either red, yellow or blue. Two circles that are directly joined by a line are not allowed to be the same colour. Which two circles must Peter definitely colour the same?
Show answer
Answer: A — 5 and 8
Show hints
Hint 1 of 2
With only three colours, look for two circles forced into the same colour by their shared neighbours.
Still stuck? Show hint 2 →
Hint 2 of 2
Find two circles that are both adjacent to the same two differently-coloured circles.
Show solution
Approach: forced colour from a 3-colouring constraint
- Each circle differs in colour from every circle it is joined to.
- Two circles each connected to the same pair of other circles (which take the two remaining colours) are forced to share the one leftover colour.
- Tracing the connections, circles 5 and 8 are forced to be the same colour.
Mark:
· log in to save