2006 AIME I Problems/Problem 6
Revision as of 21:24, 4 July 2006 by Joml88 (talk | contribs) (2006 AIME I Problem 6 moved to 2006 AIME I Problems/Problem 6)
Problem
Let be the set of real numbers that can be represented as repeating decimals of the form
where
are distinct digits. Find the sum of the elements of
Solution
Numbers of the form can be written as
. There are
numbers total. Each digit will appear in each place value
times, and the sum of the digits, 0 through 9, is 45. So the sum of all the numbers is
.