Should I admit that I can't find a solution to a math problem?
I don't know why you think there are any options other than both.  Of course you shouldn't just say "I'm having difficulties, full stop" without talking about what you have tried.  Of course you shouldn't just say "this is what I did" without also talking about where you're stuck.

You sound like you're worried about making the best impression on this professor.  The best impression you can make here is showing that you have the maturity to deal with doing research: to work hard on a problem, be aware of both what you've accomplished and what you haven't, and be able to ask for help where you need it.

There are bunch of things that could be happening:


You went off in the wrong direction, or missed something, and the professor will be able to help get you back on the right track.
The problem is actually harder than the professor thought, and explaining why you're stuck will make that clear to them.
The problem is harder than you thought, and the professor expected you to need some help.


In all of those cases, the absolute best thing to do is honestly present the work you've done.  The less you worry about framing things to make you look good, the better you actually end up looking.