Maths Olympiad Prep

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UKMT Pink Kangaroo, 2023

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

Vumos wants to write the integers 11 to 99 in the nine boxes shown so that the sum of the integers in any three adjacent boxes is a multiple of 33. In how many ways can he do this?

(A) 6×6×6×66\times6\times6\times6 (B) 6×6×66\times6\times6 (C) 2×2×2×2×2×2×2×2×22\times2\times2\times2\times2\times2\times2\times2\times2 (D) 6×5×4×3×2×16\times5\times4\times3\times2\times1 (E) 9×8×7×6×5×4×3×2×19\times8\times7\times6\times5\times4\times3\times2\times1

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