Problem 23 · 2018 Math Kangaroo
Stretch
Algebra & Patterns
arithmetic-sequencesubstitution
Rita wants to write a number into every square of the diagram shown. Every number should be equal to the sum of the two numbers from the adjacent squares. Squares are adjacent if they share one edge. Two numbers are already given. Which number is she going to write into the square marked with x?
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Answer: B — 7
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Hint 1 of 2
Each square equals the sum of its two neighbours, so going around: next = current − previous.
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Hint 2 of 2
That rule repeats every 6 squares; find x by stepping around the ring.
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Approach: use the period-6 'each equals sum of neighbours' rule
- If each square is the sum of its two neighbours, then next = this − previous, a pattern that repeats every six squares.
- Starting 10, ?, … and forcing the far corner to be 3 fixes the ring as 10, 7, −3, −10, −7, 3, repeating.
- Stepping around to the square marked x lands on the value 7.
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