Observe the following pattern and the missing digits. - Vidyadip

Question

Observe the following pattern and the missing digits.

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Answer

According to the first three pattern, if the first and the last digits of a given number is 1 and having $n$ zeroes between it, then the square of that given number gives out the number whose first and last digits is 1, the middle digit is 2 and between the digits 1 and 2 and the digits 2 and 1, n zeroes exist.
In the number $100001^2$, there are four zeroes between first and last digits. So, the missing digits in $1 \ldots \ldots \ldots$ $2 \ldots \ldots \ldots 1$, are four zeroes lie between 1 and 2 and also four zeroes lie between 2 and 1 .
Hence, the required number is 10000200001.
In the number $10000001^2$, there are six zeroes between first and last digits.
So, the required number is 100000020000001.

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