2004 AMC 10B Problems/Problem 2
Contents
Problem
How many two-digit positive integers have at least one as a digit?
Solution
Ten numbers have
as the tens digit. Nine numbers
have it as the ones digit. Number
is in both sets.
Thus the result is
.
Solution 2
We use complementary counting. The complement of having at least one as a digit is having no
s as a digit.
We have digits to choose from for the first digit, and
digits for the second. This gives a total of
two-digit numbers.
But since we cannot have a as a digit, we have
first digits and
second digits to choose from.
Thus there are two-digit numbers without a
as a digit.
(The total number of two-digit numbers)
(The number of two-digit numbers without a
)
.
See also
2004 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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.