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IMSO 2018 — Math Division — Essay Question 9

IMSO Maths · IMSO 2018 — Math Division — Essay

Question 9

Using digits 1, 2, 3, 4, 5 and 6 to form a six-digit number $\overline{abcdef}$, where different letters represent different digits. If $2\mid\overline{ab}$, $3\mid\overline{abc}$, $4\mid\overline{abcd}$, $5\mid\overline{abcde}$ and $6\mid\overline{abcdef}$, find all possible six-digit numbers $\overline{abcdef}$.