Problem 8 · 2023 Math Kangaroo
Easy
Algebra & Patterns
substitutionsum-constraint
Werner wants to label each side and each corner point of the rhombus shown with exactly one number. He wants the number on each side to be equal to the sum of the numbers at the two corner points of that side. Which number is he going to write in place of the question mark?
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Answer: B — 12
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Hint 1 of 2
Each side label equals the sum of the two corner numbers at its ends; write those four relations.
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Hint 2 of 2
Add opposite sides: the two pairs of opposite sides have the same total, since both use all four corners.
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Approach: opposite sides of the rhombus share the same corner-sum total
- Each side equals the sum of its two corner numbers, and the four corners are split the same way by the two pairs of opposite sides.
- So (top-left side) + (bottom-right side) = (top-right side) + (bottom-left side).
- That gives 8 + 13 = 9 + ?, hence ? = 21 − 9 = 12.
- So the answer is 12 (B).
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