The Mathematics of Jigsaw Puzzles – Edge Matching

A jigsaw puzzle is a tiling problem with uniquely shaped pieces. The computational complexity of solving one is NP‑complete. For a standard puzzle, the number of possible pairings is enormous. An n×n puzzle has about (n²)! arrangements. The probability of matching all edges correctly is tiny. Humans solve by using colour, pattern, and shape. The mathematics of edge matching is used in computer vision (reassembling shredded documents), protein folding (matching surfaces), and the design of puzzles with unique solutions.