You don't actually need mod to do fizzbuzz, even if that's the most obvious way for people who know what mod is. But without any "real" math at all you can do

You don't actually need mod to do fizzbuzz, even if that's the most obvious way for people who know what mod is. But without any "real" math at all you can do it with, eg, two counters and some if statements. Or if you recognise that there's a repeating pattern you can work out that pattern manually and just write code to emit it over and over.