Blue Prince dartboard puzzle: how it works and how to solve it

As you explore the mysterious mansion in Blue Prince, you’re going to find the dartboard puzzle pretty quickly and pretty often. Located in the billiards room, the dartboard contains a math puzzle that isn’t easy to solve unless you’ve worked out the rules.

You’ll want to get good at the Blue Prince dartboard puzzle since it’ll come up just about every time you play. The billiards room is one of the most common rooms to draft, and solving the dartboard puzzle provides you with keys: usually normal keys to unlock doors, but sometimes special keys you’ll only find once in a while.

Note: this guide won’t contain the solution for every dartboard puzzle, but it’ll explain how it works and how to solve it, which really only requires basic math once you know what you’re doing.

Your first step to solving the puzzle is knowing what the four colors you’ll see on the dartboard mean.

Dartboard colors and what they mean

The colors you see on the dartboard tell you what to do to the numbers they’re adjacent to. Remember this, or write it down:

Blue = Add
Yellow = Subtract
Pink = Multiply
Purple = Divide

These colors and the numbers around the edges of the dartboard form a math puzzle. When you’ve solved the puzzle, click the number you think is the answer. That will take you to the next stage of the puzzle, and after you’ve correctly guessed a few stages, the dartboard will rise and you’ll be able to collect your key or keys. If you guess incorrectly, you return back to the first stage to try again.

Note: the dartboard puzzle will get a little bit harder each time you solve it, and there are some variations you’ll run into the more times you see it.

The order of operations

To know the order in which to perform the steps of the puzzle, you’ll need to begin with the bullseye and work your way out from the center toward the edges.

Here’s an example of the order of operations:

Closest to the bullseye is the color blue (6), in the next ring, yellow (3), in the next ring, pink (5), then finally, purple (15).

So in the example above, starting at zero, you’d add, then subtract, then multiply, then divide.

0 + 6 = 6
6 – 3 = 3
3 x 5 = 15
15 ÷ 15 = 1
Solution: 1

That’s almost everything you need to know. Just follow the order of operations from the center outwards, and do what the colors indicate. It can get tricky, and sometimes even involve negative numbers, so use a calculator if you need to.

There are some variations that come into play the more you see this puzzle, and I’ve covered them below.

Variation: Square bullseye

You will sometimes see a square in the bullseye. That means you square one of the numbers. But perform the color operation first, then square the result. Here’s an example:

Order: Blue, square, yellow, purple
Add, square, subtract, divide

0 + 8 = 8
8 squared = 64
64 – 20 = 44
44 ÷ 11 = 4
Solution: 4

You will sometimes see other colors in the bullseye with the square. That means wait to square the number until you reach that color in the order of operations. Example:

Order: Blue, yellow, pink, square, purple
Add, subtract, multiply, square, divide

0 + 20 = 20
20 – 1 -13 = 6
6 x 1 = 1
6 squared = 36
36 ÷ 12 = 3
Solution: 3

Variation: Diamond bullseye

If the square is tilted 45 degrees inside the bullseye, like a diamond, that means you transpose the number’s digits when you get to that color, after you’ve performed that color’s operation. Example:

Order: Blue, Pink, Yellow, Transpose
Add, multiply, subtract, transpose digits

0 + 10 = 10
10 x 10 = 100
100 – 9 = 91
Transpose 91 = 19
Solution: 19