Tangentially, in fact-checking this comment I learned that during Pontiac's War an Ojibwe war party took a fort on the Straits of Michilimackinac from the British (recently ceded by the French the end of the Seven Years' War) by holding a ball game outside its walls as a ruse. Classic stuff.

Unironically, the Three Fires did burn for a thousand years at Michilimackinac.

Which would also mean that any scenario with randomness as a deciding factor for whether a solution is valid or not would have to be on the right side of the chart, since if a solution can be validated or invalidated by dice rolls there can't be exactly one valid solution.

Looking back at the doors example, I think there's also a distinction that needs be made about whether "perfect info" includes random outcomes. For the record I'm thinking of the "info" in question being the definition of the scenario, which wouldn't include future randomness.

Something I find interesting here for GM-based play is that perfect info might be more conducive to generative play, since players can come up with any kind of solution and be sure whether it works based on info they have. Whereas imperfect info can lead to players being gunshy.

So on the multiple solution side we have two types of scenario without a single perfect solution, which differ in whether the solver is given all info needed to verify a potential solution. As for names, I think "dilemma" might actually be a better name for top right, and "problem" for bottom right.

This implies a different kind of thinking, since a riddle requires you to play a bit of theory of mind to figure out what the asker would consider a valid solution. This is especially important in a gaming context, because it means an imperfect info scenario plays in part in the GM's imagination.

Because that's where the puzzle/riddle distinction comes from, right? If someone asks you a riddle, you know you found the answer when they say you have, but if someone hands you, like, a sudoku, you can solve it and verify your solution without any external input.

I think a key element here is that (at least in GM-party play) the limited info scenarios require the GM to verify that a solution works since the solvers don't have all the info, whereas with the perfect info scenarios the info the solvers get is identical to the info to check the solution.