Solving the Knapsack problem is pretty easy, it's probably the textbook example for explaining branch-and-bound algorithms. What you probably had in mind is tha

Solving the Knapsack problem is pretty easy, it's probably the textbook example for explaining branch-and-bound algorithms. What you probably had in mind is that it's NP-complete, meaning that we don't know any polynomial-time algorithms and most experts think that none can be found, although nobody has been able to prove that (this is the famous P=NP? problem).