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For each number from 0 to 99, Andrew wrote down the product of its digits. What is the mean of the numbers andrew wrote down?

 
 Oct 11, 2021
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assuming single digit numbers are written without the leading zero

the mean is:

\(\frac{1+2+\cdots+9+1\cdot1+1\cdot2+\cdots1\cdot9+2\cdot1+2\cdot2+\cdots2\cdot9+\cdots\cdots9\cdot1+9\cdot2+\cdots9\cdot9}{100} \\=\frac{45+1(45)+2(45)+\cdots+9(45)}{100} \\=\frac{45\cdot46}{100} \\=\boxed{20.7}\)

 
 Oct 11, 2021

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