Mock AIME 1 Pre 2005 Problems/Problem 1

Problem

Let denote the sum of all of the three digit positive integers with three distinct digits. Compute the remainder when is divided by .

Solution

We find the sum of all possible hundreds digits, then tens digits, then units digits. Every one of may appear as the hundreds digit, and there are choices for the tens and units digits. Thus the sum of the hundreds places is .

To finish later.

See also

Mock AIME 1 Pre 2005 (Problems, Source)
Preceded by First question	Followed by Problem 2
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