Robert Abbott · logic mazes
Eyeball Mazes
In these mazes, your path depends on colour, shape and the direction you face. A goal can disappear behind you once you leave it.
Most mazes consist of paths separated by walls. Eyeball Mazes are different: the board is filled with coloured symbols. You choose which square to move to, but a legal move depends on more than the positions of the squares.
Mazes with rules
American game inventor Robert Abbott created logic mazes in which finding a route requires attention to the rules of movement and the player's state. His other works include Theseus and the Minotaur and Alice Mazes.
In September 2003 Abbott announced his new Eyeball Mazes series on his Logic Mazes website. MathPuzzle featured it as a puzzle of the week. The surviving author’s page later offered thirteen mazes.
Which way are the eyes looking?
The player is shown as a circle with two eyes. They indicate which way you face: you can move straight ahead or sideways, but not backwards. Turning changes your direction. Returning to a familiar square can therefore leave you in a different state, with different moves available.
You may travel any distance horizontally or vertically. The destination must match your starting square in colour, symbol, or both. You cannot cross blank squares. Finding a route means choosing both a matching symbol and a way to approach it from the right direction.
Disappearing goals
The first puzzles have one goal; some later ones have several. When you leave a goal you have visited, its square becomes blank and cannot be crossed. The order matters: a convenient first goal may close the route to the others.
Mazes 12 and 13 contain purple lightning bolts. You may cross them but cannot stop on them: no other symbol matches a bolt in either colour or shape. They allow long passages without adding places to stop.
Creating the puzzles
Abbott said he made most of the layouts by hand. Mazes 5 and 6 were exceptions: their layouts were generated by James Stephen’s PuzzleBeast program. Abbott observed that the program sometimes produced difficult puzzles whose difficulty was not obvious even to him.
In 2004 Abbott corrected Maze 4 after Bobbie Jo Riddle found an unintended short solution. In 2008 he wrote that the Catalan Culture Ministry had used the mazes in a competition with its own book theme.
On this site
Our collection contains the thirteen layouts from the archived author’s page, in their original order. You can choose any maze, undo moves and resume an attempt in the same browser. The server verifies each result; stars depend on route length and can be improved by replaying.