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The Clockwork Mouse

G. P. Jelliss
Chessics #10, problem 350, December 1980.
Clockwork Mice.
Helpmate in 5 (2 ways) with set play, duplex.

The Clockwork Mouse can also be described as a Rotating Directed Wazir. It moves either one step forward in the direction it is facing, or turns 90 degrees to left or right. It cannot turn and step in the same move. I show them as pawns, moving head-first. A turn can be shown by simply stating the new direction in which the piece faces, N, S, E or W.

Solution:1...d4 2.N N† 3.d6 d5† 4.d7 d6† 5.d8 d7‡
1.N d4 2.W c4 3.c5 b4 4.b5 a4 5.a5 N‡
1.S S 2.d4 e3 3.d3 e2 4.d2 e1 5.d1 W‡

The duplex play is the same reflected (which I call "pseudoduplex").

G. P. Jelliss Chessics #10, December 1980, problem 368: Place a Clockwork Mouse anywhere on the chessboard, wind it up and allow it to wander round the board in such a way that it spends the same amount of time (measured by the number of moves) in every cell and ends up where it started.

Solution, Chessics #11, January-June 1981:

Surprisingly the path is uniquely determinate. A turning move in a cell counts as one unit, while a move into or out of a cell counts as a half unit, so the piece spends two time units in each cell. The pattern can also be interpreted as a type of Rook tour visiting each cell once, provided a non-stop move through a cell counts as a half-visit.

Historical Note: In an article by Rudolfo Pozzi "The Mongolian and Tuvinian Chess Sets and their Symbolism" published for the 8th Convention of Chess Collectors International (Vienna May 19-24 1998), and sent to me by Mike Pennell in 1999, there is a photo (Figure 11) of two Queens from among the Lewis Chess pieces, showing the designs on the back of their thrones. One of these is a celtic knot (i.e. a representation of a ribbon that passes alternately over and under itself) that shows the same pattern as the Clockwork Mouse tour, but rotated 45 degrees. However I have not been able to locate a similar image on the internet. The Lewis pieces featured in the BBC "History of the World in 100 Objects" and are said to date from 1150-1200.