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UKMT Maclaurin Olympiad, 2023

Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The digits 1 to 8 are placed into the cells of the grid on the right, making four three-digit numbers when read clockwise. For which values of $k$ from 2 to 6 is it possible to create an arrangement such that all four of the three-digit numbers are multiples of $k$ ?

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