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UKMT Senior Mathematical Challenge, 2023

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

How many lines of three adjacent cells can be chosen from this grid, horizontally, vertically or diagonally, such that the sum of the numbers in the three cells is a multiple of three? The grid is a $4 \times 4$ arrangement: row 1: $1,2,3,4$ ; row 2: $5,6,7,8$ ; row 3: $9,10,11,12$ ; row 4: $13,14,15,16$ .

(A) $30$ (B) $24$ (C) $18$ (D) $12$ (E) $6$

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