1999 AIME Problems/Problem 5
Problem
For any positive integer , let be the sum of the digits of , and let be For example, How many values do not exceed 1999?
Solution
For most values of , will equal . For those that don't, the difference must be bumping the number up a ten, a hundred, etc. If we take as an example,
And in general, the values of will then be in the form of . From 7 to 1999, there are solutions; including and there are a total of solutions.
See also
1999 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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All AIME Problems and Solutions |