One important addendum: complexity classes always consider how hard a problem is depending on the input size. Sorting is in P (usually O(n*log(n)), so one of the easiest problems overall) but given a few trillion inputs, it would be pretty much impossible to solve on consumer hardware. On the other hand, problems like 3-sat, the knapsack problem or travelling salesman are all NP-hard but with small enough inputs (up to a few dozen or so), they are easy to solve, even with pen and paper and are even regularly included in puzzle books.