How to solve the Billiard Room dart puzzle in Blue Prince

The darts puzzle located within the Billiard Room represents an early-game challenge you’ll frequently encounter during daily expeditions through the mysterious corridors of Mt. Holly. While not mandatory for reaching the legendary Room 46, mastering this puzzle provides substantial benefits for your overall progression.

Completing the darts challenge rewards players with randomly generated keys—sometimes even two at once—that prove invaluable for accessing locked areas throughout the estate. This makes it a worthwhile investment of time during each expedition run, especially when you’re struggling to find specific keys through other means.

Accessing the puzzle requires entering the Billiard Room during your draft, where you’ll find the dartboard positioned strategically on the far wall behind the pool table. Its consistent location makes it easy to incorporate into your regular exploration routine once you’ve mastered the solving process.

At its core, the darts puzzle presents players with randomized mathematical equations where each color corresponds to a specific mathematical function applied to the numbers on the dartboard. To decipher these color-function relationships, examine the document in the Nook using the magnifying glass tool, which reveals the crucial decoding information needed for successful puzzle resolution.

Unlike standard mathematical conventions, the puzzle completely disregards PEMDAS—the traditional order of operations involving parentheses, exponents, multiplication, division, addition, and subtraction. Instead, calculations proceed systematically from the ring closest to the bullseye outward toward the board’s perimeter, creating a unique solving sequence that requires adjustment for those accustomed to conventional mathematics.

During initial testing phases, the first equation typically features only a single blue number, creating a simplified entry point for players. Since the mathematical principle of X number + 0 = X number applies here, simply selecting the blue-highlighted number advances you to subsequent, more complex equations that demand actual mathematical computations.

Many players mistakenly apply traditional mathematical rules to these puzzles, leading to calculation errors and failed attempts. The outward-solving sequence represents the most critical adjustment for veteran puzzle solvers, as it reverses conventional computation approaches. Developing this specialized solving mindset significantly improves success rates.

Early-game simplification serves as an intentional design choice to ease players into the puzzle mechanics. These single-color equations function as tutorial stages, allowing you to familiarize yourself with the interface and basic concepts before confronting more complex multi-color combinations that require actual mathematical operations.

For efficiency optimization, experienced players recommend solving the darts puzzle immediately upon entering the Billiard Room rather than backtracking later. This integrates puzzle completion seamlessly into your exploration flow and ensures you don’t forget this valuable key source during time-pressed expeditions. The randomized key rewards can dramatically impact your ability to access restricted areas, making consistent puzzle solving a high-value activity.

Let’s examine complete solving sequences for typical darts puzzle configurations to illustrate the practical application of these principles:

Example 1: Single Color Simplicity
When only one number appears highlighted in blue, the solution remains straightforward. For instance, if the number 20 displays blue highlighting, simply select 20 to proceed. The equation effectively resolves as 20 + 0 = 20, requiring no complex calculations.

Example 2: Dual Color Combination
Consider a scenario where 20 appears in blue and 3 displays yellow highlighting. First, identify the mathematical function associated with yellow from the Nook document—let’s assume multiplication for this example. The solving process begins with the innermost (blue) number: 20, then applies the yellow function: 20 × 3 = 60. The correct solution would be 60.

Example 3: Complex Multi-Color Equation
For more advanced puzzles featuring multiple colors, maintain the outward-solving sequence. If 1 appears blue and 17 displays pink, apply the respective functions in bullseye-outward order. Assuming pink represents addition based on the Nook document, the calculation would be: 1 (blue) + 17 (pink) = 18. This systematic approach ensures accuracy regardless of equation complexity.

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