George Duke wrote on Mon, Apr 10, 2017 07:40 PM UTC:
There are other integer number sequences. You could add diagonal directions and make these sliders too. Then the board could be fixed at 30x30. Huygens is orthogonal leaper but a variant piece would be Queenlike to the prime number squares five and over or more inclusively three and over.
Then there are more pieces to expand the idea to other sequences. Fibonacci moves Queenlike to 3,5,8,13, and 21 distance. Triangular number piece moves along radial lines exactly 3,6,10,15, 21, or 28. Square number piece to 4,9,16, and 25, a weak piece. Deficient number sequence piece (since perfect numbers are so rare) is the strongest going to 4,5,7,8,9,10,11,13,14,15,16,17,19,21,22,23,25,26,27,29. Tetrahedral number 4,10,20, weak mover again. Abundant number to 12,18,20,24 (keeping all these less than 30 to fit the board). Lucas to 3-distance, or 4, 7, 11,18 or 29. Pawns should be Man to all eight directions one or two steps, squares which the mathematical pieces cannot any of them reach from the same starting square.
Lucky number unit can go radially 3 or 7 or 9 or 13 or 15 or 21 or 25 only. Pancake number type moves 4, 7, 11, 16, 22, or 29.
However, never design a chess piece based on Weird Numbers. They are too few and too large. '70' is the first weird number because it is abundant being less than (1+2+5+7+10+14+35, its factors), but no set of those divisors sum to 70 itself. The only other less than 4-digit weird number is 836, and the sequence 70, 836, 4030, 5830 is unsuitable -- except on that infinite board.
There are other integer number sequences. You could add diagonal directions and make these sliders too. Then the board could be fixed at 30x30. Huygens is orthogonal leaper but a variant piece would be Queenlike to the prime number squares five and over or more inclusively three and over.
Then there are more pieces to expand the idea to other sequences. Fibonacci moves Queenlike to 3,5,8,13, and 21 distance. Triangular number piece moves along radial lines exactly 3,6,10,15, 21, or 28. Square number piece to 4,9,16, and 25, a weak piece. Deficient number sequence piece (since perfect numbers are so rare) is the strongest going to 4,5,7,8,9,10,11,13,14,15,16,17,19,21,22,23,25,26,27,29. Tetrahedral number 4,10,20, weak mover again. Abundant number to 12,18,20,24 (keeping all these less than 30 to fit the board). Lucas to 3-distance, or 4, 7, 11,18 or 29. Pawns should be Man to all eight directions one or two steps, squares which the mathematical pieces cannot any of them reach from the same starting square.
Lucky number unit can go radially 3 or 7 or 9 or 13 or 15 or 21 or 25 only. Pancake number type moves 4, 7, 11, 16, 22, or 29.
However, never design a chess piece based on Weird Numbers. They are too few and too large. '70' is the first weird number because it is abundant being less than (1+2+5+7+10+14+35, its factors), but no set of those divisors sum to 70 itself. The only other less than 4-digit weird number is 836, and the sequence 70, 836, 4030, 5830 is unsuitable -- except on that infinite board.