I'm curious why my comment has been voted down. Was "suitably embarrassed" an offensive way to phrase it, or do people disagree with the distinction I made in the last sentence? I think it's pretty valuable to have a sense, even if you can't solve something, of whether the solution is likely to be simple or not.
I think the problem people have with this approach is that they don't want to be defined by their performance on one very specific problem. Most people, myself included, want to be seen as the sum of many accomplishments, not just one superficial one in an interview.
This topic as a whole seems to be very contentious, and stuff is getting downvoted seemingly randomly. Even comments that are interesting and that nobody could surely be objecting to.