Difference between revisions of "2003 AMC 10B Problems/Problem 13"
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Revision as of 12:10, 4 July 2013
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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