You can’t divide by zero; the answer is undefined. Some questions have no answer, and spotting that is a skill too.

Undefined is not the same as unknown. Asking how many times nothing goes into something is not a hard question with a hidden answer, it is a question that does not mean anything, and no amount of cleverness will produce a number. Recognising that shape saves a great deal of wasted effort. Plenty of arguments outside maths are the same: badly formed rather than unresolved.

If something will not resolve no matter how you approach it, check whether the question is well put. Ask what would count as an answer. If you cannot say, the next move is rewriting the question rather than attacking it harder.