FizzBuzz comes from a game for six to eight year olds, who also don't understand modulus. That's part of the reason it is such a great problem: they fact that you realize "Hey, this is a whole lot easier with modulus" demonstrates that you can reason abstractly. You certainly don't need a mod operator to make it work -- if you're capable of writing a function, you can write
divides_evenly_by_3(int number) using facts that every fourth grader knows.
If you prefer, you can substitute a similar problem which doesn't require even fourth grade math. Here's one: write a program which calculates the sum of all numbers between 1 and 1,000 whose digits sum up to 7. Or write a program which takes this post as input and tells me what the 3rd most common letter used was.