I agree with the main argument but would like to note "crank" in not an all or nothing description. Sometimes the problem as publicized doesn't exactly match the precise problem. For example you can trisect an arbitrary angle if allowed an infinite number of steps. Sometimes the problem is in breaking the abstraction layer. For example one of my kids thought you could make arbitrarily slow motion videos by taking slow motion videos of slow motion videos. And that brings up the issue of how to handle a crank. I loved that my son thought through the video issue and didn't want to inhibit future thinking. We ran some experiments taking video of the tv and it was fun. Sometimes people won't accept counter arguments and evidence (sometimes that person is me) and there's a time to move on. Still, in my experience few people are true die hard cranks and most people respond well if given the right direction.