99999

Algebra Level 3

There is a function defined in the following way: f ( n ) = 0.99.....99 f\left( n \right) = 0.99.....99 so that the number of 9s in the number f ( n ) f\left( n \right) is n n .

If that is the case, how many number 9s has the following number r = f ( 1000 ) × f ( 1000 ) r = f\left( 1000 \right) \times f\left( 1000 \right) ?


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1999 2001 999 99999 1000 2000 1001

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