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UKMT Pink Kangaroo, 2026

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Sanika wants to write the numbers $1, 2, 3, 4, 5, 6$ and $7$ in the boxes in the diagram. She has already written two numbers, as shown. She wants the sum of the numbers in each pair of adjacent boxes to be odd, and to avoid the sum of the numbers in any three consecutive boxes being a multiple of 3. What is the sum of the numbers she will need to write in the shaded boxes?

(A) $5$ (B) $7$ (C) $9$ (D) $11$ (E) $13$

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