The difficulty is "proving" it, especially under the rules. Supposedly, it has been "proven" impossible.
Now, I know about the Seven Bridges of Königsberg. That's obviously impossible, and easily proven to be so, but how do you prove that the angle can't be trisected?
I mean... hmmm... I presume they measure the trisected angle with a protractor, but, how do they know the protractor is accurate, and that the compass drew a perfect arch, and that the ruler is a perfect straight edge. Not to mention that a pencil cannot be sharpened to an infinitesimal point (and in any case, we can't see infinitesimal), that human eyes and hands cannot place the pencil, ruler, or compass in the exact spot......