Problem 18 · 2015 Math Kangaroo
Medium
Logic & Word Problems
casework
Each side of each triangle in the diagram is painted either blue (blau), green (grün) or red. Four of the sides are already painted, as shown. Which colour can the line marked x have, if each triangle must have all sides in different colours?
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Answer: A — only green
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Hint 1 of 2
Each triangle uses all three colours exactly once, and neighbouring triangles share a side.
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Hint 2 of 2
Start from the known blue sides and force each shared side in turn along the strip until you reach x.
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Approach: propagate the all-different constraint along the strip
- Each triangle must use blue, green and red once.
- Starting from the two given blue sides and using the shared edges, each triangle's remaining colours are forced one after another.
- Following the chain to the side marked x leaves only green possible.
- So x can only be green (A).
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