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How can I Find a number N which sum of digits of N = 100 and sum of digits of 2*N = 110 ?
By abba5, history, 8 years ago, In English

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8 years ago, hide # |
 
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What about 90,90,90,90,90,90,90,90,90,90,442.

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8 years ago, hide # |
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Since the maximum sum of digits of a k-digit decimal number representation is 9k, the minimum number of digits of the decimal representation of N and 2N should be 13 digits and 14 digits, respectively.

UPDATE: It turns out that it is sufficient to concatenate two instances of the number M = 1,994,999 whose sum of digits is 50, and whose double 2 M = 3,989,998 has sum of digits equal to 55. The concatenation leads to doubling the sum of digits as the most significant digit in M is less than 5, and no carry operation is performed between the two instances when M is doubled.

Therefore, the 14-digit decimal number N = 19,949,991,994,999 is a possible solution of the problem.

The following is the simple DP-based solution that generated such number.

https://ideone.com/LuMF89

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