Problem 7 · 2016 Math Kangaroo
Medium
Logic & Word Problems
caseworksum-constraint
Diana wants to write whole numbers into each circle in the diagram, so that for all eight small triangles the sum of the three numbers in the corners is always the same. What is the maximum number of different numbers she can use?
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Answer: C — 3
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Hint 1 of 2
Equal triangle-sums force many circles to share a value.
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Hint 2 of 2
Trace which circles must be equal; only a few can stay distinct.
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Approach: propagate the equal-sum constraint
- The eight small triangles share corners, and equal sums force chains of circles to carry the same number.
- Working through the forced equalities leaves at most three independent values.
- An explicit labelling achieves three different numbers, so the maximum is 3.
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