Irregular grids

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Here are some types of irregular grids common in WPC-style puzzles.

Hexagonal[edit]

Examples of originally hexagonal puzzles includes Boomerangs.

Row/Column: Translated into 3 directions. For example, this is hexagonal Easy as AB from PGP IB.

Example
Solution

Straight/Right Turn: Some puzzle forbids 60° turns at all. Some puzzle introduces different notation for loop being straight, making 60° turn, making 120° turn.

2x2-Constraint: Traslated into no "triangles" (three cells adjacent to each other) being completely shaded. For example, this is hexagonal Nurikabe from WPC 2019 IB.

Example
Solution

Triangular[edit]

Triangular: Translated into 3 directions. For example, this is triangular Lighthouses from WPC 2019 IB.

Example
Solution

Straight/Right Turn: Loop makes 120° turn in every cells.

Pyramidal[edit]

Geometrically identical to hexagonal grids, but the overall shape of the grid is triangular. An example of originally pyramidal puzzles are Pyramid and Trid.

Trid Example
Trid Solution

Cairo Pentagonal[edit]

Row/Column: Undefined, since there are no straight direction.

Straight/Right Turn: Translated into: "when edges that the loop crosses when entering and leaving the cell are adjacent, the loop "makes a turn" in the cell." This is Cairo Pentagonal Masyu from WPC 2019 IB.

Example
Solution

2x2-Constraint: Translated into; No interior point is completely surrounded with black cells. For example, this is Cairo Pentagonal Nanro Signpost from WPC 2019 IB.

Example
Solution

General Graph[edit]

If the puzzle rules only require the concept of edgewise connectivity, then the puzzle can be presented on any graph. For example this is "3D" Fillomino from WPC 2019 IB.

Example
Solution

Cylindrical, Toroidal, Möbius strip[edit]

In a cylindrical grid, the leftmost and the rightmost rows are considered adjacent.

In a toroidal grid, the topmost and bottom rows and the leftmost and the rightmost rows are respectively considered adjacent. For example, this is a toroidal Snake from WPC 2019 IB.

Example
Solution

In a Möbius strip grid, the topmost cell of the leftmost row are connected to the bottom cell of the rightmost row, et cetera.