Problem 17 · 2015 Math Kangaroo
Stretch
Logic & Word Problems
casework
Each of the 9 sides of the triangles in the picture will be coloured blue, green or red. Three of the sides are already coloured (blue and red are shown). Which colour can side x have, if the sides of each triangle must be coloured in three different colours?
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Answer: C — only red
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Hint 1 of 2
Each triangle uses all three colours once, so within one triangle two known sides force the third.
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Hint 2 of 2
Start from the triangle whose two coloured sides are already given and work along the strip toward side x.
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Approach: fill in forced colours triangle by triangle along the strip
- Every triangle shows each of blue, green, red exactly once, so once two of its three sides are coloured the third is forced.
- Beginning at the triangle that already has two coloured sides and moving along the row of triangles, each shared edge passes a forced colour to the next triangle.
- Carrying this through to side x leaves only one possibility: x must be red.
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