[Karliss]

I was going to give the same example. Even simpler example would be dividing 5/2 = x. If all you know is whole numbers there is no solution, but if you introduce fractions you get a solution and a new tool which has many practical applications.

The original problem statement might not mention something, but that might be due to not knowing the solution and insight about fundamental relationship between the numbers that it represents. Unless you are filling a school test where you are expected a specific answer (even when it's wrong in more general case) the "children story" part of a math problem shouldn't be mistaken for what it actually represents. The more general solution might not be applicable in all cases due to real world limitations, but in some it may. You can't (don't want to) split one of 5 officers in half, but having half an apple or sack of grain is not a problem. If Euler knew the solution maybe he would have chosen something else than officers and ranks to describe the problem.