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Tetraktys Chess. Squares are Pythagorean ascending 4-3-2-1, each square half offset right and left: in other words, a row of one sits over a row of two squares, over three, over four. Squares are numbered top-down: 1, 2-3, 4-5-6, 7-8-9-10. Two piece types are drop-placed in the first two moves. Lateral one-step move always available. Piece 'A' has one-step-up option if there is any piece (of either colour) adjacent to it; otherwise 'A' can go one step down. Piece 'K' has one-step-down option if there is any piece adjacent; else 'K' can go one step up. In addition, there is an 'off-board'(notionally one-step sideways) allowed from any of 1,2,3,4,6,7,or 10 to any other non-adjacent and vacant square from among those seven. Squares 5,8, and 9 are excluded from this off-board non-capturing move. Sqs. 5,8,9 can of course be reached variously by normal one-s-u, one-s-d, or ordinary one-step lateral(from one or two of 4,6,7,10). Move is required, no null move. No piece may remain in the 7-8-9-10 row for four turns. If and when only two pieces left, no piece may remain in the 7-8-9-10 row for three turns. Goal: capture the other's two pieces. Inability to move also loses.