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Concatenation sum (Posted on 2019-05-15) Difficulty: 3 of 5
The number 123456789 is concatenated 1729 times to form a number A

Similarly, the number 987654321 is concatenated 1729 times to form another number B

If A+B=C, find the sum of digits of C

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 2.0000 (1 votes)

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Solution Explanation to Puzzle Answer Comment 4 of 4 |
(In reply to Puzzle Answer by K Sengupta)

• If 123456789 is added to its digital reversal  the sum would be 1,111,111,110

                                                                                                                   --------------------- 
                                                                                                                         9   1s

•  If 123456789 is concatenated twice and added to its digit reversal, the sum would be:  1,111,111,111,111,111,110
                    ------------------------------------------
                               18        1s

• If 123456789 is concatenated 3 times and added to its digit reversal, the sum would be: 1,111,111,111,111,111,111,111 111,110
                   --------------------------------------------------------------
                           27     1s

Since there will be carries starting from (1+9), (2+8), (3+7), ......., (7+3), (8, 2), and (9+1) for each concatenation, it follows that:
-> When 123456789 is concatenated N times and added to its digit reversal,  the 
result would be:
11...................1110
      9*N      1s

so that, 
The sum of the digits is: 9*N 

Since,   9*1729 = 15,561, then substituting N = 1729, 
we have the required result as 15,561.

Edited on June 16, 2022, 2:48 am
  Posted by K Sengupta on 2022-06-16 02:45:17

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