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## Re: Need help fellow board gamers

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• I tried posting this before, but the server hung up... I dunno what DAO is, but I looked up the rules to Susan and Abalone on Richard s PBeM server at
Message 1 of 141 , Apr 2, 2001
I tried posting this before, but the server hung
up...<br>I dunno what DAO is, but I looked up the rules to
Susan and<br>Abalone on Richard's PBeM server at
www.gamerz.net<br>By those rules, the board for each game is the same
hexagonal<br>grid of 61 cells. In lieu of scratching out this board
in the<br>dirt, maybe you could print the grid out
on your piece of paper.<br>After all, if the rules
are simple, they can be memorized.<br>Hex has even
simpler rules, and the board uses a hexagonal<br>grid,
although it's in the shape of a rhombus not a
hexagon.<br>Rules to hex are on Richard's server.<br><br>David
• ... The Cairo tiling is one of those 14. It has advantages over many other non-regular tilings in that it is monohedral (all the same face) and isohedral
Message 141 of 141 , Feb 11, 2002
>For instance, one page shows the 14
> different types of pentagon that will tile a plane.

The Cairo tiling is one of those 14. It has advantages over many
other non-regular tilings in that it is monohedral (all the same
face) and isohedral (every face has the same "relative position" to
the surrounding faces). However, you can't easily start at one Cairo
pentagon and move in a straight line to a row of other cells, as you
can on a square or hexagonal grid. Blobz (= Cairo-ized "Blobs"
or "Ataxx" or "Spot") is a good example of a game that allows this
kind of transplanting, because it doesn't involve pieces moving long
distances.

There are plenty of monohedral tilings, though as John Lawson says,
the only regular polygons that will tile the plane are equilateral
triangles, squares, and regular hexagons. I can't think of any games
on other monohedral tilings either, apart from original ones that
haven't been tested (or that haven't passed).

One idea that I haven't done anything with involves a non-convex
equilateral pentagon, angles 36 degrees, 108 degrees, 108 degrees, 36
degrees, and (a reflex angle) 252 degrees. This pentagon has the
property of being able to tile the plane in a great many ways -- you
can hardly put the tiles together in such as way as to make it
impossible to fit another one in. Also, they're mirror-symmetric, so
they could be flipped over without disturbing the array.

I would make a good number of these in stiff cardboard, black on one
side and white on the other like Othello pieces, and play them on a
mat with a large ellipse drawn on it, where they aren't allowed to
lap over the edge of the ellipse. The idea would be that the first
player places a tile with his color showing, then the players
alternately place tiles edge-adjacent to a tile already played, and
somehow a player "captures" pieces of the other color by flipping
them, as in Othello. That's the rule that I haven't figured out.
But if one could find such a rule that would lead to a good game, it
would have the interesting property of being completely abstract and
yet having an infinite number of possible opening moves...

Mark Thompson
Chicago, IL
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