That is the thing that makes me want to beat my supervisor to death. Thank you, I hadn't defined it before.

Oh, and then when I use the right approach, telling me it's too difficult for me and that I should try something else facile that I've already proved doesn't work.

Hahaha. That's like every day at work. I either get sullenly suggested several wrong approaches from $student, or several (probably right) ones from various geeks. Sometimes, the hard part is stringing everything together and understanding what it is you have to do first before people leap gaily in to 'advise'.

/me buys in pile of O'Reilly books that don't talk back

Gah, yes, I know exactly what you mean.

To be fair, sometimes that's a fair approach. To someone who really doesn't know, or who has thought of only some possibilities and not looked further afield, a selection of suggested starting points would be useful.

Or even, someone is bringing themselves up to speed by thinking things through aloud from the start, hoping to get up to speed with where you are and maybe be able to help -- but uses a self-satisfied tone of voice that sounds as if what they said is the last word.

But either way, it's intensely aggravating when someone's opinion discounts all your thoughts and implies you're stupid for not having decided yet. I remember once playing dominos with dad in the pub with Dad, and there were a couple of kibitzers, old gentlemen who at least some of who have played the game for thirty years (and have an incredibly good intuition what to play next). I was hesitating over a move, it was near the end of the round, there were only a couple of dominos I could play, and I was trying to work out all the possibilities for the next play or two and ensure I had the smallest/no chance of giving away a big score. One kibitzer sees me stuck and points to a domino, saying "you could play this one". On which I feel really stupid, as there's no indication if that takes into account everything I'm thinking, or is simply a plausible play. And I can't ask, as Dad's sitting right there. Only later did I admit that the comment was really unhelpful, even if it had been helpful in spirit. (What was especially annoying is that it is quite possible he was utterly right, but even if so I'll never learn anything by randomly having right answers exposed to me if I've no way to approach them myself.)

Though I much prefer the problems where the hard part is working out how to approach the problem.

"The eldest plays the piano."

Or maybe they're parrots. If you're talking a mathematician and want to sound like you're making a valuable contribution, you can reasonably safely say something like "Perhaps you could use induction?" or "Why not use proof by contradiction?" Whatever they're doing, there's almost always _something_ to be gained by considering the induction, even if you already have, even if it cant' work :) (I don't think that actually has anything to do with your point, I just thought it was funny.)

Just occasionally, the hard part can be working out which is the correct basic approach (that is, the one that will result in a solution that is fifty times faster than any other approach can produce, or requires fewest resources, or is the only one that will actually work, in extreme cases). But only occasionally, and in such cases the people who try pointing out numerous starting points to you are very unlikely to suggest the correct solution, because they probably haven't understood the problem - or why it matters what starting point you use....