Propositional Parlor Puzzle

Summary

April 21, 2025 Propositional Parlor Puzzle I've recently been playing Blue Prince, which is a great time if you are a fan of puzzle games like Return of the Obra Dinn or Outer Wilds and also a fan of roguelike games like Slay the Spire. One of the game's rooms, the Parlor, features a logic puzzle that is different on each run. In this post we'll be doing some modelling and analysis of these puzzles. Some people might consider that a spoiler! In the parlor, there are three boxes, a blue box, a white box, and a black box. Each box makes some set of statements. We are also given the following rules: There will always be at least one box that makes only true statements. There will always be at least one box that makes only false statements. There is a prize in exactly one box. Here's one example of such a puzzle: Blue: You are in the parlor White: This box is empty Black: The blue box is true The blue box is making an obviously true statement—the box game always takes place in the Parlor. The black box thus is also making a true statement, since blue is true. Since we know by the rules that there must be at least one box making false statements, it can only be white, and so we can deduce that white is not empty and has the prize. The puzzles get a bit trickier than this sometimes. Consider: Blue: the gems are in a box with a true statement White: the gems are in a box with a false statement Black: The white box is true There are actually two consistent interpretations here: both Blue: true White: false Black: false and Blue: false White: true Black: true are valid. The trick is that the game is not to determine which boxes are telling the truth, but where the prize is, and in this case, either interpretation gives that the prize is in the blue box. Let's make a tool that solves these puzzles automatically! This might be useful, if, say, you were making this game and writing a lot of them and wanted some kind of mechanical assurance as part of a test suite that you hadn'...