The Hamiltonian Circuit is a challenging puzzle game available on iPhone. The objective of the game is to find a path that visits every square in the grid, avoiding walls and never crossing itself, to create one continuous circuit.

The game starts with simple 4x4 grids to help players get the hang of things. It requires careful plotting of moves and thinking ahead by several squares. If a mistake is made, players can trace back over their line to make it disappear. Hints are available for those who get stuck, with mistakes turning red and disappearing while correct moves are added to the line.

Each puzzle has only one solution, and players will know when they find it. The puzzles start with 4x4 grids and progress all the way up to 20x20, offering increasingly challenging gameplay that can take hours to solve. Players can quit in the middle of a puzzle and their progress will be automatically saved.

The Hamiltonian Circuit is not just a game, but also an exercise for abstract thinking skills and a challenge for the brain. Inspired by a puzzle created by Irish mathematician William Rowan Hamilton in 1856, this game offers a range of difficulty levels that will test players' problem-solving abilities. Good luck!