2009 AMC 8 Problem 22
Attempt Problem 22 of the 2009 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
How many whole numbers between and do not contain the digit
Answer: D
Small hint:
Count by number of digits, or pad numbers with leading zeroes.
Big hint:
For three padded digits, each position has choices if digit is forbidden, but exclude
Solution:
We can case on the number of digits.
There are one digit numbers excluding
There are two digit numbers that lack the digit
There are three digit numbers that do not include
This yields a total of numbers that do not contain the digit
Thus, D is the correct answer.
Problem 22 in other years
- 1985 AMC 8
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