Problem 18 · 2011 Math Kangaroo
Hard
Logic & Word Problems
casework
The 8 corners of the shape in the picture are to be labelled with the numbers 1, 2, 3 or 4, so that the numbers at the ends of each of the lines shown are different. How often does the number 4 appear on the shape?
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Answer: D — 4
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Hint 1 of 2
Endpoints of every drawn line must get different labels from {1,2,3,4}.
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Hint 2 of 2
This is a colouring; work out how many corners are forced to be 4.
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Approach: treat it as a proper labelling of the figure
- Label the 8 corners with 1, 2, 3 or 4 so that any two corners joined by a line differ.
- Working through the constraints of the drawn lines, the label 4 is forced onto exactly four corners.
- So the number 4 appears 4 times.
Mark:
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