Problem 17 · 2018 Math Kangaroo
Hard
Algebra & Patterns
sum-constraint
Emily wants to write a number in each empty small triangle. The sum of the numbers in any two triangles that share a side should always be the same. Two of the numbers are already given. What is the sum of all the numbers in the figure?
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Answer: C — 21
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Hint 1 of 2
Equal sums on shared sides force neighbouring triangles to repeat values in a pattern.
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Hint 2 of 2
Use the two given numbers to fill the pattern, then add every triangle's number.
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Approach: propagate the equal-sum rule from the given numbers
- Two triangles sharing a side must give the same total with each neighbour, which forces a repeating pattern of values across the figure.
- Starting from the given 2 and 3, fill every small triangle by that rule.
- Adding all the resulting numbers gives a total of 21.
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