Computer generates a number, player tries to guess it and computer answers
Enhancements:
You guess a thing/animal etc. Computer asks questions, you answer yes/no, until runs out of questions.
Enhancements:
3 cannibals and 3 missionaries, or sheep, dog and hay: program searches through all possibilities, rejects invalid moves, finds all possible solution
Generate labyrinth with one entrance, one exit, and one possible path (or path to center). Every cell needs be connected to path, many dead ends possible, but no "closed islands".
Enhancements:
like these generators