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The stepping-stone mazes

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).

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.

Controls

Use the puzzle drop-list to select a puzzle.
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.
U-turns not permitted.

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.

A stepping stone maze featured on Games Magazine (USA) cover - March 2012


applet - © Andrea Gilbert 2011
concept & puzzle set - © Andrea Gilbert & Robert Abbott 2011-2012
applet JS conversion - cheerpj transpiler from Leaning Technologies - 2020