Many people know about the (Martian) Chess Boards designed by Elliot C. Evans, see http://www.ee0r.com/tri-chess. They are perfect for Martian Chess, but I found them wanting for games where the pyramids need to lie down, such as Pikemen or Branches and Twigs and Thorns: a 3-pip pyramid (a large) can't comfortably lie on its side within every "square" or in every direction.
So, I designed my own boards that I want to share with you. In addition to playing Martian Chess, you can now play all the other pyramid games--that require a chess board--with 2, 3, 4, 5 and 6 players (if the rules allow for it).
The boards are all diamond shaped and they come in three different patterns--that does not matter for the amount of cutting or laminating. You need two copies of each (six in total) to make all the different multiplayer boards (see attachments for boards and examples).
Properties.
Note.
Some possible arrangements are sub-optimal as they do not preserve at least one diagonal along the edges. You might get puzzled without some examples, so take a look. To be honest, I suffered from bewilderment myself for a while. Preparing this post, I took pictures yesterday of all the boards, but I was shocked to notice that one example was not correct! I thought I had overlooked something that turned my design useless! I was relieved to find that I had only been impatient . . . Hence the examples to spare you the unjustified disappointment.
Technical Info.
The reason my boards work so well is that most 2x2 squares of neighboring cells use but two colors (distributed nicely over the diagonals), so you could call them "correct". Each of my boards has 6 "correct" 2x2 squares, while Evans' boards have only 4 "correct" 2x2 squares. In addition, my boards can be arranged to preserve this property along edges for one (in the case of 3-player board) or even two 2x2 squares (in the case of a 6-player board); in any case, all other 2x2 squares have at least one diagonal of the same color. Also, adjacent cells with identical colors can always be avoided! (Evans' boards always have some adjacent cells with the same color across edges and do not preserve any diagonal across edges--except for 2- and 4-player configurations.)
In the attachments, I provide examples of multi-player arrangements for 2-, 3-, 4-, 5-, and 6-player boards. There are a few other arrangements possible, but I leave that for you to figure out.
Have fun!
Let me know your observations, remarks or questions. Thank you.
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Neat idea!
very cool - can you post a picture of them?
Sure, Kristin, I was still learning about the interface.
So, here are the pictures. They are small versions of the boards in Boards.zip.
Below are some pictures of the boards in Boards V2.0.zip (no multiplayer configurations yet, but I assure you it's possible!). Again, you will need two copies of each to make all multi-player options!
[Technical info. I designed these today (Jan 25, 2016) after playing with some other options. These boards are also released under the cc-by-nc 4.0 creative common license (see https://creativecommons.org/licenses/by-nc/4.0/ for more details).]
I added a photo album with comments explaining how to form each board and the number of solutions.
Have fun!
Impressive, good job. Thank you fFor all the demonstrative pictures, as well. Very nice.
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