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
(In reply to
Puzzle Answer by K Sengupta)
• If 123456789 is added to its digital reversal the sum would be 1,111,111,110
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9 1s
• If 123456789 is concatenated twice and added to its digit reversal, the sum would be: 1,111,111,111,111,111,110
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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
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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
Explanation to Puzzle Answer
