AMC10 2002 B

AMC10 2002 B · Q3

AMC10 2002 B · Q3. It mainly tests Averages (mean), Patterns & sequences (misc).

The arithmetic mean of the nine numbers in the set $\{9,99,999,9999,\dots ,999999999\}$ is a 9-digit number $M$, all of whose digits are distinct. The number $M$ does not contain the digit

集合 $\{9,99,999,9999,\dots ,999999999\}$ 中九个数的算术平均数是一个 9 位数 $M$，其所有数字均不同。数 $M$ 不包含数字

(A) 0 0

(B) 2 2

(D) 6 6

(E) 8 8

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) The number $M$ is equal to $\frac{1}{9}(9+99+999+\ldots+999,999,999)=1+11+111+\ldots+111,111,111=123,456,789.$ The number $M$ does not contain the digit $0$.

（A）数 $M$ 等于 $\frac{1}{9}(9+99+999+\ldots+999,999,999)=1+11+111+\ldots+111,111,111=123,456,789.$ 数 $M$ 不包含数字 $0$。

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