Problem 15 · 2023 Math Kangaroo
Hard
Logic & Word Problems
casework
Hanni wants to colour in the circles in the diagram. When two circles are connected by a line they should have different colours. What is the minimum number of colours she needs?
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Answer: B — 3
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Hint 1 of 2
Two circles joined by a line must differ in colour.
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Hint 2 of 2
If three circles are all linked to each other, they need three different colours.
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Approach: find a triangle (forces 3) then show 3 colours suffice
- The diagram contains three circles that are all connected to one another, so they need three distinct colours.
- Trying to colour the whole diagram with just those three colours succeeds.
- So the minimum number of colours is 3.
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