Blue Prince: How to Solve the Dartboard Puzzle in the Billiard Room
Blue Prince’s complexity is not limited to its procedurally generated room layouts. The puzzles are equally mind-bending. One such puzzle is in the billiard room. Also known as the dartboard puzzle, this mathematical teaser may leave you feeling off-target (pun intended), especially since the game offers sparse clues to guide you through it.
The first clue can be found in the Guest room. A note is placed on the desk. Click on it to read. It’s written by a guest who had a thrilling time on the hunt with Lord Evanson. He mentions about a new game in the billiard room and that he enjoys “mathematical puzzles”, suggesting that the dart puzzle is a math brain teaser.
The second clue is displayed right next to the board. Pay attention to the dart cabinets on the left and right side of the board. You can see arithmetic operators ( +, – , x ) on the cabinets. They also hint at a math puzzle.
The third clue is in the Nook. Click on the Note to read it. Use the magnifying glass om the lower-right corner of the note to reveal a hidden clue within the note. It shows the color-coded sections and the associated operations. You can purchase the magnifying glass from the commissary or find it in certain rooms, such as the study room, archive room, parlor room or the nook room.
Here’s how to solve the dartboard puzzle in the Billiard room:
A dartboard has 20 sections. A color-coded section represents a mathematical operation (addition, subtraction, multiplication, division).
| Color | Mathematical operation |
| Blue (innermost section) | Addition |
| Yellow | Subtraction |
| Pink | Multiplication |
| Purple | Division |
The screenshot below will make things a bit easier to understand:
In the beginning, when you start the dartboard puzzle, an innermost section will be highlighted as blue. It’s the starting value. Note the number associated with the blue section and click on it to begin the first equation.
Next, start solving an equation with the help of the color-coded sections/operations and their associated numbers. But here’s the twist. Instead of the standard mathematical order of operations, i.e BODMAS or PEMDAS, you will have to perform operations starting from the center of the dartboard and working your way outward. In the above screenshot, the order goes: subtraction, then multiplication, and division.
Always pay attention to the color of the sections as they might change places as the puzzle gets more complex every time you draft the billiard room on a new day. But order will always be from the innermost ( center of the board ) to the outermost section.
Note: In case of addition, there should be two blue sections on the board, only then you can add two numbers associated with the two blue sections on the board. If it’s only one, we will use it to identify the starting number.
With the help of the above screenshot as an example, let’s find out how to solve an equation on a dartboard.
1. Start with the number associated with a innermost colored section, ie. a section closest to the bullseye. In this example it’s 20.
2. Note down the colored section associated with that number to perform the operation. In this case it’s a single blue section, so we have identified 20 as the starting number.
3. Move to the next outer section, identify the color and the number associated with it. The number associated with the yellow section is 10.
Subtract 10 from 20 (20 – 10 = 10)
4. Move to the next outer section. Note down its color to identify the operation and the number associated with it. It’s pink (multiplication) and the number is 2.
Multiply 10 by 2 (10 x 2 = 20)
5. Finally, identify the operation associated with the color on the outermost section of the dartboard. It’s purple/dark blue (division) and the number associated with it is 4.
Divide 20 by 4 (20 ÷ 4 = 5)
The correct answer is 5. Click on 5 on the dartboard to start the next equation. Keep solving equations with colored sections and their corresponding numbers until you complete the puzzle. The board slides up, revealing a reward.
The first few equations will be easy to solve, but as you progress, the number of operations will increase. Follow the same sequence, from the center of the board and work your way outward to solve it.
Note: If you see a number aligned with a pink and a blue section, just multiply the number by itself.
Advance Modifiers
As you continue to draft Billiard room in each new in-game day, the complexity of the dartboard puzzle in the room will increase. You will dicover new symbols and modifiers.
Square □
If you see a square appear on the bullseye, it denotes the square function (x²).
Example: A square appears on the bullseye and its background color is blue. Identify the number associated with the blue section and multiply that number by itself.
If the number associated with the blue section is 2, just multiply 2 by itself. The answer is 4.
Things get more complex when solving a larger equation:
A square appears on the bullseye. Note down the background color of the bullseye. If it’s pink, then multiply the input by itself in the later steps.
Assuming the background color of the bullseye is pink. We will be multiplying the input with itself in step 2. Here’s one example:
1. Innermost: 20 (Blue)
2. Next section: 11 (Yellow) and 3 (Yellow)
3. Next section: 1 (Pink)
4. Outermost section: 2 (Purple/Blue)
1. Subtract 3 and 11 from 20 (20 – 11- 3 = 6)
2. Multiply 6 by 1 (6 x 1 = 6 ). In this step the square modifier comes into play. Multiply 6 by itself as you will need to follow the square modifier and the background color of the bullseye. The answer is 36.
3. Divide 36 by 2 (36 ÷ 2 = 18). 18 is the correct input. Click on 18 to move to the next equation.
Diamond ◇
If a diamond appears on the bullseye, flip the number in the later steps or as per the color in the bullseye background.
Example: You see a diamond in the bullseye. Note down the background color of the diamond. If it’s pink, the diamond modifier will come into effect after Multiplying 6 by 8.
1. Innermost: 6 (Blue)
2. Next section: 8 (Pink)
3. Next section: 6 (Purple)
1. Multiply 6 by 8 (6 x 8 = 48)
2. Flip the number 48. It becomes 84.
3. Divide 84 by 6 ( 84 ÷ 6 = 14)
14 is the correct input. Click on 14 to proceed to the next equation.
Red Dots
Red dots may show up on the area surrounding the numbered segments, making the overall equation more complex. Repeat the same operation based on how many red dots are shown above a number. Here you will have to note down the colored segments associated with the number to begin the operation . If there are two dots, repeat the operation twice.
Red X
If you see a red X on the area surrounding the numbered segments, it means to ignore that particular step. The red X will be displayed above a number, so any operations (colored sections) associated with that number should be ignored.
Rewards
The more complex the puzzle, the greater the rewards you can earn. For simple puzzles, you will get standard keys to unlock doors. But as you progress and solve complex puzzles, you will get:
Silver key: Use the key to unlock a door that will lead to a room with multiple doors.
Electronic keycards: Can be used to unlock hard-to-breach security doors.
Secret garden key: A key to the secret garden.
