Problem 15 · 2011 Math Kangaroo
Hard
Logic & Word Problems
casework
Each area in the picture should be coloured using one of the colours red (R), green (G), blue (B) or orange (O). Areas which touch must be different colours. Which colour is the area marked X?
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Answer: A — red
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Hint 1 of 2
Adjacent regions must use different colours, so colour the small inner regions first.
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Hint 2 of 2
Check which colours X is forced to avoid, then see which one is left for it.
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Approach: colour the regions in order so neighbours differ, then read off X
- Fill the inner regions with the forced colours so touching areas differ (e.g. R, G, O as marked).
- Region X borders the orange and the inner block but not the red region.
- A consistent colouring lets X be red, so X is red.
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