## Sum Digital Sum And Product

#### Problem

The number 49 is unusual in that 49 + (4+9) = 36 + 13 = 49. In other words, if we add the product and sum of the digits we get the number itself.

Find all 2-digit solutions.

#### Solution

Let the number, N = 10`a`+`b` = `ab` + `a`+`b`.

9`a` = `ab`, 9`a` `ab` = 0, `a`(9 `b`) = 0 `a` = 0 or `b` = 9.

But as N is a 2-digit number, `a` 0.

Hence the 2-digit solutions are: 19, 29, 39, ..., 99.

What about 3-digit solutions?

Problem ID: 171 (May 2004) Difficulty: 1 Star