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Problem of the Week 1185

Nines

Let N be an integer whose decimal digits from left to right are nondecreasing (e.g., 113445889) and having distinct digits as its two rightmost digits. Let s be the sum of the digits of 9N. Then s is divisible by 9, so s = 9M.

How large can M be?

Source: Felix Lazebnik, Surprises, Math Mag. 87 (2014) 212-221.

© Copyright 2014 Stan Wagon. Reproduced with permission.

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16 July 2014