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bonanova

Fun with digital sums

Question

Inspired by FUZZY's recent puzzle

Suppose abcd is the normal decimal representation of a number: abcd = (1000a)+(100b)+(10c)+c.
The digital sum of a number is defined as a+b+c+d.

Are there numbers for which the product of its digital sum and its reversal is the original number?

For example, the digital sum of 12345 is 15.
Its reversal is 51. 15x51 is 765, 12345 is not equal ti 765,
So 12345 is
not a solution.

Hint: 81 is a solution, as is 1.

Are there others?

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yes there are still 2 more solution.

Spoiler

 

1458 = 18 * 81

and 1729 = 19 * 91

No more solution, because for numbers bigger than that (addition of digits) * (reverse of addition of digits)  will too small for the numbers.

 

 

Edited by jasen

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