> Or even: 1. Test 2. Implement IMO, this last popular approach gets things completely backwards. It assumes there is no need to think about the problem before hand

I think you misunderstand this approach.

The point of writing the tests is to think about the desired behaviour of the system/module you are implementing, before your mind gets lost in all the complexities which necessarily happens during the implementation.

When you write code, and hit a wall, it’s super easy to get hyper-focused on solving that one problem, and while doing so: lose the big picture.

Writing tests first can be a way to avoid this, by thinking of the tests as a specification you think you should adhere to later, without having to worry about how you get there.

For some problems, this works really well. For others, it might not. Just don’t dismiss the idea completely :)