If you know you got it wrong and you don't know why, what's the alternative to working backwards?
Sir, the topic of this thread is "back in my days the road to school went through a forest full of bears, an active volcano, a drug cartel turf, and a warzone", not "how to teach effectively". Of course you won't learn anything without the answers because how are you supposed to know if you should adjust your thinking or not. If you can correct your own scribbles without answers, then it means that you're practicing things you already know, which isn't what most people consider "learning".
But that ought to be the last resort. Many of my textbooks had answers for only some questions, answers to the others were only in the teacher's manual.