Squares and Rectangles
Squares and Rectangles is a region-division puzzle genre invented by Anurag Sahay in 2022. The author recalls creating it while thinking about a puzzle by Cihan Altay (likely titled Geometric Figures), which explores a similar idea rooted in spatial geometry.
The puzzle blends geometric reasoning with grid-based area division, requiring solvers to analyze shapes, proportions, and spatial relationships as they partition the grid into valid regions. This emphasis on geometry gives the genre a distinctive, visual character compared to more arithmetic-driven division puzzles.
Original version included also clues in the grid nodes and edges, but in later refinements, the ruleset was simplified to use only clues inside cells, removing any dependence on grid vertices. This streamlining improved clarity while preserving the core geometric logic of the puzzle.
The puzzle blends geometric reasoning with grid-based area division, requiring solvers to analyze shapes, proportions, and spatial relationships as they partition the grid into valid regions. This emphasis on geometry gives the genre a distinctive, visual character compared to more arithmetic-driven division puzzles.
Original version included also clues in the grid nodes and edges, but in later refinements, the ruleset was simplified to use only clues inside cells, removing any dependence on grid vertices. This streamlining improved clarity while preserving the core geometric logic of the puzzle.
Rules
Divide the grid into nonoverlapping regions. Each region should contain exactly one circle. Any region containing a black circle should be a square. Any region containing a white circle should be a rectangle not a square. Regions of the same area can not share an edge (but can share a corner).
Click to see the answer.