2003 AMC 12B Problems/Problem 8
(Redirected from 2003 AMC 10B Problems/Problem 13)
- The following problem is from both the 2003 AMC 12B #8 and 2003 AMC 10B #13, so both problems redirect to this page.
Problem
Let denote the sum of the digits of the positive integer . For example, and . For how many two-digit values of is ?
Solution
Let . Since , we have . Thus if , then or . The 3 values of for which are 12, 21, and 30, and the 7 values of for which are 39, 48, 57, 66, 75, 84, and 93. There are = values in all.
~Andrew_Lu/Mismatchedcubing
See Also
2003 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
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 12 Problems and Solutions |
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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