I have tutored some high school students in programming/algorithms, and I find it is definitely better to explain "NP-hard" after they take a crack at the probl

I have tutored some high school students in programming/algorithms, and I find it is definitely better to explain "NP-hard" after they take a crack at the problem. Classically educated CS students tend to see the true difficulty of the problem at hand, which typically results in their not being able to see potential solutions, and many times abandoning the problem completely. However, students without that level of "training" tend to come up with more novel solutions. I am always anxious to see what they come up with. Overall, classic education just seems to put people into boxes. Even PhD candidates don't seem to deviate much from standard techniques. I just wish I had done something like IOI in my past; I feel it's much more effective at opening up your mind.