2002 AMC 12B Problems/Problem 1

Problem

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

$\mathrm{(A)}\ 0 \qquad\mathrm{(B)}\ 2 \qquad\mathrm{(C)}\ 4 \qquad\mathrm{(D)}\ 6 \qquad\mathrm{(E)}\ 8$

Solution

The average of the nine numbers is $M=\frac{9 + 99 + \cdots + 999999999}{9} = 1 + 11 + \cdots + 111111111 = 123456789$

which does not have the digit $0 \Rightarrow \mathrm{(A)}$ .

2002 AMC 12B (Problems • Answer Key • Resources)
Preceded by First question	Followed by Problem 2
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2002 AMC 12B Problems/Problem 1

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