"Without it you can't accurately assess the difficulty of a problem, even seemingly simple ones like this."

And with a background, you'd recognize hard problems?

Sure, very well-known NP-complete problems you'll recognize, but there are plenty of other problems that are equivalent to them, which you might stumble upon without even realizing it (I recently wrote a post about one such problem: http://www.loopycode.com/a-surprisingly-hard-problem-post-co...).