Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

The Goal

Your task is to implement a scoring calculator for a game called Entanglement. According to the given rules, your program must determine how many points the player earns and which path they follow.

Rules

The game is played on a hexagonal grid. The player places one hexagonal tile at a time. Each tile has 12 entrances numbered 0–11, forming 6 distinct path segments — each entrance connects exactly once. It follows that one path segment is represented by 2 integers entranceA and entranceB.

Example of a single tile with numbered entrances.

Gameplay:

The game starts on the base tile at position [0, 0], at entrance 7.
Each turn, the player places a new tile on the empty cell directly ahead (first move: [0, -1]).
After placing a tile, the player follows the connected path.
The path continues until it reaches an empty cell, the board edge, or returns to the base tile.
The game ends once the path reaches the board edge or the base tile.

Scoring:

Each turn consists of placing one tile and following the resulting path. For every segment of the path passed through during this turn, the player scores 1, 2, 3, ... points respectively.

Examples:

If the path passes through 1 segment this turn, the score increases by 1
If the path passes through 2 segments this turn, the score increases by 3 (1+2)
If the path passes through 3 segments this turn, the score increases by 6 (1+2+3)
If the path passes through 4 segments this turn, the score increases by 10 (1+2+3+4)
If the path passes through 5 segments this turn, the score increases by 15 (1+2+3+4+5)
and so on...

Coordinate System:

The board has a fixed size, with all cells located at most 3 units away from the center. Your task is to print placement of all visited path segments, so make sure you understand the coordinate system used:

Coordinate system:
y increases towards the south
x increases towards the north-east

Additional Info

- Click the gear icon in the viewer to access display options.
- This puzzle is inspired by the logic game Entanglement.
- Source code available on GitHub.
- Design available on Figma.

Game Input / Output

Turn input

Each turn, you receive information about the tile placed on the board:

6 lines: 2 space-separated integers entranceA and entranceB that form a path segment of the tile.

Turn output

Line 1: The current total score.

Line 2: A list of semicolon-separated (;) path segments. Each segment is defined by a quadruplet of space-separated integers:
x y entranceA entranceB, representing a visited tile at position [x, y] and the two entrances connected on that tile.

Turn output example:

0 -1 3 7; 0 -2 0 5; 1 -2 10 8 – represents three path segments:

0 -1 3 7 – first segment: the player starts this turn at [0, -1] and connects entrances 3 and 7.
0 -2 0 5 – second segment: the player continues at [0, -2] and connects entrances 0 and 5.
1 -2 10 8 – third segment: the player ends this turn at [1, -2] and connects entrances 10 and 8.

Note 1: The referee will trim spaces around ; for convenience.

Note 2: Path segment entrances are unordered: (3 7) is equivalent to (7 3).

Constraints

Response time for the first turn: ≤ 1s
Response time for subsequent turns: ≤ 50ms

Solve it

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