Or, let the answer (n) be a two digit number with the first digit represented by a and the second digit represented by b
n = 10a + b
We are told that the sum of the digits multiplied by 8 is the same as the original number
n = 8(a + b)
Therefore,
10a + b = 8(a + b)
10a + b = 8a + 8b
2a = 7b
We know a and b are single digit integers, so the number of solutions to this equation is limited:
Specifically b must be an even number for a to remain an integer
Furthermore b must be <= 2 for a to remain a single digit integer
Consequently b = 2 and a = 7
Therefore the answer is 72
I just can't be arsed to extend the solution to more than two digits, in fact, on reflection, I don't really know why I put this much effort into it
