Difference between revisions of "2006 AIME I Problems/Problem 6"
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== See also == | == See also == | ||
| + | * [[2006 AIME I Problems/Problem 5 | Previous problem]] | ||
| + | * [[2006 AIME I Problems/Problem 7 | Next problem]] | ||
* [[2006 AIME I Problems]] | * [[2006 AIME I Problems]] | ||
[[Category:Intermediate Combinatorics Problems]] | [[Category:Intermediate Combinatorics Problems]] | ||
[[Category:Intermediate Number Theory Problems]] | [[Category:Intermediate Number Theory Problems]] | ||
Revision as of 19:41, 11 March 2007
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 
such numbers. 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 
.
