Problem 25

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Pink Kangaroo 2023 · Q25 · UK Maths Trust

Problem

Vumos wants to write the integers 1 to 9 in the nine boxes shown so that the sum of the integers in any three adjacent boxes is a multiple of 3. In how many ways can he do this?

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6 \times 6 \times 6 \times 6

6 \times 6 \times 6

2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2

6 \times 5 \times 4 \times 3 \times 2 \times 1

9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1

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Pink Kangaroo (2023)

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