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This makes no sense.
I think I get what the author/inventor was trying to do. Label the 5x5 board a-e and 1-5. From the description there doesn't seem to be a square c3--that's where the 4x4 board lives. Label the 4x4 board w-z and 6-9 (as if it were the upper right of a 26x10 board). I think b4 is supposed to be touching w9, so conceivably you could step a piece from w9 to b4 and vice-versa. I'm not sure about diagonal steps, like from b4 to w8 or x9, but hey, I'm not designing a game here, just trying to figure out the board. The 5x5 square c4 looks to be touching x9 and y9, so you could probably step back and forth there too. The 5x5 board looks like it rests on the intersection xy-78. Adjacencies to x8 are probably a3, a4, a5, b5, c5, which is a lot of squares. I think it'd be awful hairy to design a game for this board. I'm certainly not going to try it. :)
You could use this for a varint skrink chess. Capture a piece and it goes to next smallest borad. Captures on the smallest borad remove the piece! p.s Kings can be captured expect on the smallest bored. Sorry about the spelling mistakes.
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