N is a positive base ten integer having at least 2-digits but at most 4-digits, which is obtained by multiplying the sum of its digits with the product of its digits. It is known that N cannot contain any leading zero.

Determine all possible value(s) of N.

Apparently I was misled by the phrase "is obtained by" which suggested to me that values of N were derived by formula from each of a set of numbers between 10 and 9999. Adding two lines of code to my program shows that, given the interpretation of Charlie (and perhaps others) there are just two values for N which meet these criteria: 135 (= 9 * 15), and 144 (= 9 * 16). That doesn't seem much of a challenge. Why not just say ('is equal to" the formula product)? Generally, to say that something is "obtained" does NOT mean that you start with it. Of course to find all possible solutions you would still need to consider all products of the formula (or perhaps use some heuristics to reduce the cases to be considered). To return to my original comment, why the spec "it is known that N cannot contain any leading zero" which suggests that there might be a non-leading zero, since you need no inspection to know that any product containing zero as a factor will be zero?