Consider the 600600-digit integer
234234234.....234.234234234.....234.
The first mm and the last nn digits of the above integer are crossed out so that the sum of the remaining digits is 234234. Find the value of m+nm+n.


Answer:

522522

Step by Step Explanation:
  1. Observe that the given number has 234234 repeated 200200 times.
    The sum of the repeating digits =2+3+4=9=2+3+4=9
    The sum of digits of the given number =9×200=1800=9×200=1800
  2. After crossing out the first mm digits and the last nn digits, the sum of the remaining digits is 234234.
    the sum of first mm and last nn digits is 1800234=15661800234=1566
  3. Observe that 1566=174×91566=174×9. Thus, we have to cross out 174174 blocks of 33 digits 2,3, and 42,3, and 4 either from the front or the back. Thus, m+n=174×3=522m+n=174×3=522.
  4. Hence, the value of m+nm+n is 522522.

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