The problem is that the sensitivity to the number growth is supposed to be exponential. So if you need 100 samples for "within 10% of the value", then 10 samples should give you almost completely random behavior.

In reality, it depends on your actual distribution, but the OP from this thread here is unreasonably conservative for something described as a "rule of thumb". Almost always, if you have at least 10 of every category, you can already discover every interesting thing that a rule of thumb will allow. And you probably could go with less. But if you want precision, you can't get it with rules of thumb.