Consider the ^@600^@-digit integer ^@234234234 ..... 234.^@ | Math Question and Answer

Answer:

$522$

Step by Step Explanation:

Observe that the given number has $234$ repeated $200$ times.
The sum of the repeating digits $=2 + 3 + 4 = 9$
$\implies$ The sum of digits of the given number $= 9 \times 200 = 1800$
After crossing out the first $m$ digits and the last $n$ digits, the sum of the remaining digits is $234$ .
$\implies$ the sum of first $m$ and last $n$ digits is $1800 - 234 = 1566$
Observe that $1566 = 174 \times 9$ . Thus, we have to cross out $174$ blocks of $3$ digits $2, 3, \text{ and } 4$ either from the front or the back. Thus, $m + n = 174 \times 3 = 522$ .
Hence, the value of $m + n$ is $522$ .

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