2003 AMC 10B Problems/Problem 13
Problem
Let denote the sum of the digits of the positive integer
. For example,
and
. For how many two-digit values of
is
?
Solution
We can divide into two cases so that
The first is where
is a one-digit number, and the second is where it is a two=digit number.
For to be a one-digit number,
's digits must add up to be
This can be done in three ways
and
For to be a two-digit number,
's digits must add up to be
since the sum cannot exceed
This can be done in seven ways
and
Add the number of ways together
See Also
2003 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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All AMC 10 Problems and Solutions |