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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).

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

concept & puzzle set - © Andrea Gilbert & Robert Abbott 2011-2012
puzzlescript implementation - © Matthieu Haller - 2021