The History of Alice Mazes

In an ordinary maze, knowing where you are is enough. In an Alice maze, you must also remember how far you can travel. Return to a familiar square with a different step length and you may find a different way forward.

Alice in Mazeland

American game inventor Robert Abbott created “mazes with rules”: finding the way through depends on understanding how movement works as well as reading the map. His creations also include Theseus and the Minotaur and the card game Eleusis.

One of these puzzles, Alice in Mazeland, appeared in Abbott’s 1990 book Mad Mazes. He later explained that, when writing the book, he had not yet thought of making several mazes with the same rules.

The name recalls Lewis Carroll’s Alice’s Adventures in Wonderland, in which Alice grows and shrinks. In the maze, the player does not change size; instead, the distance travelled in a move changes.

From book to collection

In 2001 Abbott programmed the first eight Alice mazes for his Logic Mazes website. On 24 February that year, MathPuzzle featured them as an interactive puzzle of the week. Abbott continued adding layouts until the collection contained twenty.

The maze from the book became number 16 in the online collection. On his archived page, Abbott named maze 15 as his favourite, while noting its difficulty: a seven-by-seven board does not necessarily make a simple puzzle.

A familiar square, a different problem

Follow an arrow from your current square, travelling exactly your present step length. Landing on a red arrow increases the next step; landing on a yellow arrow decreases it. You can jump over squares and return to a position with a different set of possible moves.

Solutions can involve loops. Abbott described discovering a loop in one maze that returns to its original state only after several circuits of the board. A familiar square can be part of either the solution or a detour.

Number seven or eighteen?

One maze was number 7 in the early 2001 set. In the later twenty-maze collection it became number 18. MathPuzzle preserves Abbott’s comments and a diagram by Andrea Gilbert; Abbott’s own page explains the change of number.

Abbott stated that its shortest solution takes 57 moves. His description and Gilbert’s diagram on MathPuzzle reveal the solution.

On this site

The first twenty layouts come from Abbott’s archived page and retain his numbering. Mazes open in sequence; after solving one you can return and try to find a shorter route.

Visit the original page and other sources using the links below.