AMC8 2002

AMC8 2002 · Q19

AMC8 2002 · Q19. It mainly tests Basic counting (rules of product/sum), Base representation.

How many whole numbers between 99 and 999 contain exactly one 0?

99和999之间有多少个整数恰好包含一个0？

(A) 72 72

(B) 90 90

(D) 162 162

(E) 180 180

Answer

Correct choice: (D)

正确答案：（D）

Solution

Numbers with exactly one zero have the form a0b or ab0, where the blanks are not zeros. There are (9 · 1 · 9) + (9 · 9 · 1) = 81 + 81 = 162 such numbers.

恰好一个0的数形式为a0b或ab0，其中空白处不为零。有(9 · 1 · 9) + (9 · 9 · 1) = 81 + 81 = 162个数。

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