Doing something others think impossible, and doing it with finesse, cleverness, or brilliance implies the solution has hack value.
Picking a lock has hack value. Smashing a lock does not.
Proving Fermat's last theorem by linking together most of modern mathematics has hack value. Solving the four color map problem by exhaustively trying all possibilities does not. Writing a program to solve the four-color map problem exhaustively, however, does have hack value (as generating all the possibilities is itself potentially difficult).