I'm looking for straightforward puzzle types where it is difficult to determine ahead of time whether or not there will be an solution to the puzzle (and therefore one must either try to solve it, or develop a deep intuition through practice.)
To clarify: I am not looking for NP complete problems. In fact, I need to be able to compute, for any given puzzle example, whether or not a puzzle is tractable ahead of time. I will then be tracking the amount of time it takes for a player to either solve the puzzle, or decide that it's unsolvable.
One example is Euler path puzzles (e.g. 'don't lift the pencil') where most varieties of the puzzle are straightforwardly solvable, and others are impossible. If you don't know graph theory, you actually have to work it out before deciding whether it's solvable or unsolvable.
I was wondering what other puzzles have this characteristic -- simple ruleset, engaging, but difficult to know ahead of time whether it is solvable.
Other examples include:
- Flow Free (https://codepen.io/dom111/full/mwJwmM/)