Spegni!

Lights Out in SwiftUI — with a real solver inside. Tap a light and it toggles together with its four neighbours; turn everything off to win. Spegni is Italian for "turn it off", usually shouted from another room.

Boards from 3×3 to 7×7, per-size best scores, and a hint button backed by linear algebra.

The interesting part: the solver

Two facts make Lights Out a linear system over GF(2): pressing a cell twice undoes it, and press order doesn't matter. So a solution is just a set of cells, and "solve the board" becomes solving Ax = b where A says which presses touch which cells and b is the current lights.

Solver.swift does Gaussian elimination over GF(2) (rows are UInt64 bitmasks, so a row XOR is one instruction), finds a particular solution, then walks the null space — the famous quiet patterns, 5×5 has four — and keeps the solution with the fewest presses. That gives:

• "Solvable in N" in the UI: the true minimal press count, live after every move
• Hints that are always part of an optimal solution (using one disqualifies the game from setting a record — fair is fair)
• unsolvability detection: on 5×5 only a quarter of light patterns can be switched off at all; the solver proves it instead of guessing

Boards are still generated the cheap way — scrambling from the solved state with random presses, which guarantees solvability without any of the above. Generation and verification meeting in the middle is the fun of this project.

Code

• Board.swift — game state, pure logic, no SwiftUI
• Solver.swift — GF(2) elimination + null-space minimization
• GameView.swift — the whole UI
• Tests/ — board mechanics and solver correctness across sizes, including a known-unsolvable position (11 tests)

swift test

Runs on iOS 17 / macOS 14. Open the package in Xcode and use the #Preview in GameView.swift, or drop the sources into an app target and add @main.

MIT license.