Problem 81

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PROBLEM 81

Note: In this problem a number written as d₁d₂ will denote an integer with 10's digit d₁ and 1's digit d₂.

Find a nine digit positive integer, d₁d₂d₃d₄d₅d₆d₇d₈d₉ with distinct digits, so that 1 divides d₁, 2 divides d₁d₂ , 3 divides d₁d₂d₃ , ... , 8 divides d₁d₂d₃d₄d₅d₆d₇d₈, and 9 divides d₁d₂d₃d₄d₅d₆d₇d₈d₉.

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