Problem 13 · 2025 Math Kangaroo
Medium
Algebra & Patterns
substitutionsum-constraint
Emma wants to write a number in each circle (see diagram) so that each number equals the sum of the numbers in the two adjacent circles. She has already written two numbers. Which number will she write in the grey circle?
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Answer: D — −3
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Hint 1 of 2
Every circle equals the sum of the two circles touching it, and the 1 and 2 are not next to each other.
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Hint 2 of 2
Start with the empty circle between the 1 and the 2 — it must equal \(1+2\) — then keep applying the rule around the ring.
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Approach: propagate the neighbour-sum rule around the ring
- The top circle sits between the 1 and the 2, so it equals \(1+2=3\).
- Now use 'each circle = sum of its two neighbours' going around: the right circle is \(2-3=-1\), the left circle is \(1-3=-2\), and the grey bottom circle (between them) is \(-1+(-2)=-3\).
- So the grey circle holds −3, which is (D).
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