Say he gives you a list of 300 students who can't go together in rooms. You say, good, I will take the remaining 100 students, and give them rooms. It even has unique solution :)
Any NP-Complete problem will have cases that are trivial. The complexity of the problems is how they grow in the worst case.
Correction: every natural NP-complete problem will have easy cases. You can construct problems for which there is no easy case, which is a shame since I thought at one point you could use this trait to seperate P and NP
Interesting. How do you need to define "easy" for this to work? Can you give an example of a problem without an easy solution? Has this class of problem been studied?