Cuttings

Cuttings are puzzles where you divide a shape made of unit squares (a polyomino) by drawing cuts along the grid lines. Each cut goes between two adjacent cells. Your goal is to split the shape into a given number of parts that satisfy the rules (e.g. equal area, or exactly one circle per part).

Shapes can be simple squares or rectangles, or more complex polyominoes. Sometimes puzzles use triangular cells (half-squares) as well; the same idea applies: cuts follow the grid, and parts are connected regions.

The Rules

• Grid: The shape is made of unit cells on a grid (squares, or in some puzzles, triangles).
• Cuts: You place cuts along the edges between adjacent cells. Cuts do not go through cells.
• Parts: After cutting, the shape is split into connected regions (pieces). Two cells are in the same piece if you can walk between them along cell edges that are not cut.
• Goals: Typically you must get exactly k parts, often with equal area (same number of cells per part), and sometimes with exactly one marker (circle) per part or identical-shaped parts.

Strategy

• Count the total number of cells; if the goal is k equal parts, each part must have (total ÷ k) cells.
• For "one circle per part", place cuts so that each connected region contains exactly one marker.
• Try to balance the shape: avoid leaving one part much larger or smaller than the others.

Practice Problems

Use the problems below to practise. Click an edge between two cells to add or remove a cut. When your partition matches the goal, the puzzle is solved!