2017 AMC 10B Problems/Problem 16
Contents
Problem
How many of the base-ten numerals for the positive integers less than or equal to contain the digit ?
Solution 1
We can use complementary counting. There are positive integers in total to consider, and there are one-digit integers, two digit integers without a zero, three digit integers without a zero, and four-digit integers starting with a 1 without a zero. Therefore, the answer is .
Solution 2
First, we notice there are no one-digit numbers that contain a zero. There are two-digit integers and three-digit integers containing at least one zero. Next, we consider the four-digit integers beginning with one. There are of these four-digit integers with one zero, with two zeros, and with three zeros . Finally, we consider the numbers to which all contain at least one zero. Adding all of these together we get .
~vsinghminhas
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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