How many zeroes can be found in the square of 999,999,999,999,999,999,999,999,999,999?

The answer is 29.

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This one again can be solved by induction.

$\begin {matrix} 9^2 & = 81 \\ 99^2& = 9801 \\ 999^2 & = 998001 \\ 9999^2 & = 99980001 \\ 99999^2 & = 9999800001 \end {matrix}$

It can be seen that the number of zeros in a square of a $n$ -digit string of $9$ is $n-1$ . Therefore, the answer is $30-1 = \boxed{29}$ .