The Blue Prince billiard room puzzle will give you keys as a reward, but only if you can solve the math problems that use colored segments on a dartboard instead of the usual symbols. Thankfully ...

The Billiards Room has a dartboard in the back-right corner when you enter. Interacting with it allows you to choose a number — if you look at the board, you’ll see math signs on the chalkboar ...

which can help you get through locked doors. Here’s how to solve the Billiard Room dart puzzle in Blue Prince. Every time you draft the Billiard Room, you’ll be able to access the darts puzzle.