The stepping-stone mazes
(by Andrea Gilbert & Robert Abbott)


Can you count to three? That's all you really need for these nifty mazes. Step, step, step, change colour, repeat. Each visit to each group of coloured stones must involve exactly three steps, no more no less. These mazes were designed during 2011 in collaboration with Robert Abbott (www.logicmazes.com).

These mazes were designed an atypical way. By following a few basic ground rules (regarding the shape and size of the colour groups) it turns out that a remarkable number of grid arrangements naturally yield good mazes, requiring little or no refinement. A key underlying reason for such a high yield is the relative ease of arranging the grid such that the resulting state-diagram is fully connected (all states are both reachable and escapable) despite also being a directed graph (where moves are non-reversible). This type of state-diagram is technically known as a strongly connected digraph which, perhaps not surprisingly, turns out to yield some very nice mazes.

January 2012: Games Magazine (USA) features a stepping-stone maze entitled Three Flask Task on its cover (March 2012 issue).

 

sample puzzle
click below to play

 

Aim
Cross the grid, from left to right, visiting exactly three stepping stones of the same colour and then switching colour. U-turns not permitted, but you may revisit the same stepping stone several times.

Controls
Use the puzzle drop-list to select a puzzle.
Use mouse clicks or cursor-keys for movement.
Use restart (action) or the space key to reset.

Movement
Use the cursor keys to move, or click on a stepping stone.
Press "u" (undo) to jump back as far as the last colour-change.

Hints
You cannot get completely stuck in this maze, as long as you plan ahead at least one step.


applet – © Andrea Gilbert 2011
concept & puzzle set - © Andrea Gilbert & Robert Abbott 2011-2012