2002 AMC 8 Problem 19

Attempt Problem 19 of the 2002 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 2002 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

19.

How many whole numbers between 9999 and 999999 contain exactly one 0?0?
7272
9090
144144
162162
180180
Answer: D
Concepts:digitscasework
Small hint:
The number is a three-digit number.
Big hint:
The single 00 can be in the tens place or the ones place, but not the hundreds place.
Solution:
Note that the 00 digit can either be the tens or the units digit. This gives us 22 options for this.
There are 99 options for each of the other digits for a total of 2⋅9⋅9=162 2 \cdot 9 \cdot 9 = 162 numbers.
Thus, D is the correct answer.
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