How to solve the Billiard Room dart puzzle in Blue Prince

The darts puzzle in the Billiard Room is a Blue Prince puzzle you’ll encounter early during your daily expeditions through Mt. Holly.

While not essential for reaching the fabled Room 46, it’s still worth taking the time to solve the darts puzzle on each run. Solving the darts puzzle rewards you with a randomized key (or two!), which can help you get through locked doors.

Here’s how to solve the Billiard Room dart puzzle in Blue Prince.

How to solve the darts puzzle in the Billiards Room

Every time you draft the Billiard Room, you’ll be able to access the darts puzzle. As with every good dive, it’s located on the far wall behind the pool table.

At its core, the darts puzzle is a series of randomized mathematical equations. Each color represents a mathematical function to its corresponding number on the darts board. You can find what function each color represents by using the magnifying glass on a document in the Nook, which reveals the following:

• Blue = addition
• Yellow = subtraction
• Pink = multiplication
• Purple = division

Note that PEMDAS — the parentheses, exponents, multiplication, division, addition, subtraction order of operations — doesn’t apply here. Rather, the order of operations for each darts puzzle equation starts from the ring closest to the bullseye and moves its way outward.

Also in our testing, at least in the early goings, the first equation consists of just one blue number. Since X number + 0 = X number, select the number that’s highlighted in blue and you’ll move on to the second equation. At that point, though, you have to actually do some math.

Let’s go through a full series of examples for the darts puzzle:

For this one, 20 is marked blue and 3 is marked yellow.

20 – 3 = 17.

In this one, 1 is blue and 17 is pink.

1 x 17 = 17 (again!)

In this one, 10 is blue and 2 is purple. Since 2 / 10 doesn’t divide into a number that exists on a dartboard…

10 / 2 = 5.

Here’s where it gets more complicated. Remember the rule about the order of operations? In this case, the blue 13 is your base number, then the yellow 3, the pink 5, and the purple 10. Breaking it down…

13 – 3 = 10
10 x 5 = 50
50 / 10 = 5

Dart puzzle rewards

Once you solve the final puzzle, the dartboard will shift upward, revealing your reward of either keys, a silver key (which leads to rooms with multiple doorways), a Secret Garden Key, or an electronic keycard (which unlocks electronically locked doors).

Advanced darts puzzle symbols

According to our testing, the more times you complete the darts puzzle, the more complicated each equation gets — even folding in some newer, more flummoxing math symbols.

Here are some additional symbols — set in either the bullseye or order border of the dartboard — we’ve encountered alongside brief definitions of what they mean. You’ll apply these symbols after doing whatever steps correspond with the color of the bullseye.

• Square = ^2
• Diamond = reverse the numbers
• Red dots = repeat this step based on how many dots are displayed
• Red X = skip this step
• Red / = slash your final number in half
• Two squiggly lines = round up to the nearest 1
• Four squiggly lines = round up to the nearest 10
• Six squiggly lines = round up to the nearest 100
• The section of the dartboard is 1/3 full = divide that number by 3

As one Polygon staffer put it in our Slack channel, “there was a time when i liked the billiards room puzzle but now that i am on day 50 or so, i hate the billiards room puzzle.”

For more Blue Prince guides, check out our full walkthrough on how to reach Room 46, learn how to solve the breaker box puzzle, how to find the terminal password, where to find the Secret Garden Key, or read how to open the Garage door, Orchard Gate, and West Gate.