P versus NP problem
Suppose someone wants to build two towers, by stacking rocks of different mass. One wants to make sure that each of the towers has exactly the same mass. That means one will have to put the rocks into two piles that have the same mass. If one guesses a division of the rocks that one thinks will work, it would be easy for one to check if one was right.  (To check the answer, one can divide the rocks into two piles, then use a balance to see if they have the same mass.) Because it is easy to check this problem, called 'Partition' by computer scientists—easier than to solve it outright, as we will see—it is not a P problem.