Problem:
How many of the base-ten numerals for the positive integers less than or equal to contain the digit ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
It will be easier to count the complementary set. There are one-digit numerals that do not contain the digit two-digit numerals that do not contain the digit three-digit numerals that do not contain the digit , and four-digit numerals starting with that do not contain the digit , a total of . All four-digit numerals between and , inclusive, contain the digit . Therefore numerals in the required range do contain the digit .
The problems on this page are the property of the MAA's American Mathematics Competitions