2017 AMC 10B Problems/Problem 17
Contents
[hide]Problem
Call a positive integer if it is a one-digit number or its digits, when read from left to right, form either a strictly increasing or a strictly decreasing sequence. For example, , , and are monotonous, but , , and are not. How many monotonous positive integers are there?
Solution
The number of one-digit numbers that work is , and the number of two-digit integers that work is . We use similar logic for three-digit integers, four digit integers, etc. Summing, we have , and we need to subtract another 1 for the 0 case, so the answer is .
Legit Solution
The number of one-digit numbers that work is , and the number of two-digit integers that work is . We use similar logic for three-digit integers, four digit integers, etc. Summing, we have , and we need to subtract another 1 for the 0 case, so the answer is .
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.