Go easy - remember, your professor is the one that assigns your grade. A good professor won't let personal feelings affect that one way or the other, but not all professors are that good. Keep in mind that it is unlikely that they intentionally gave you a problem that has no solution or that, if they did, it was because they wanted you to learn this very lesson. Mostly likely it was a simple transcription error or honest mistake when developing the problem.Oh boy I'm gonna let my professor have it. Thank you guys, I've been losing my mind trying to solve this. It means alot that you put in all this effort
The best thing is simply to write up your "solution" to the problem claiming that no solution exists and then proving that your claim is correct.