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Haynie's high power fairy chess 64. With orthodox chess set but different stronger movements for most pieces. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]

George Duke wrote on Wed, May 12, 2010 10:59 PM UTC:

Chimera is {R,B,NN,Camel,Zebra} getting close in value to Conway's 
Angel, who can leap to any square away n=x, x anything you want. Angel n=7 on 8x8 leaps to any other square, covering the whole board.  Maximum unobstructed range of centralized Chimera here of Haynie device is not that 63 squares of British mathematician Conway, but 55 squares. Add Antelope 3,4 and Giraffe 1,4. Then super-Chimera is {R,B,NN,Camel,Zebra,Antelope,Giraffe}. Super-Chimera reaches all 63 squares from the four central squares but the radial ones arrived by sliding. Make Rook Buddha and Bishop Rakshasa and Nightrider Grandmaster. Then that hyper-Chimera as all-leaping {Buddha,Rakshasa,Grandmaster,Camel,Zebra,Antelope,Giraffe} encompassess when centralized  Conway Angel n=4 (only) including all that one's squares and more, but not Angel n=5 on enlarged boards. How many hyper-Chimeras would defeat single Conway Angel n=19 on 20x20? As few as four or many as twenty, what one number between suffices? If they are all aligned adjacent in line from a corner along one edge, how many moves will it take to spread them out and kill the Angel?

George Duke wrote on Thu, May 13, 2010 03:24 PM UTC:

Six. Six hyper-Chimeras suffice and are necessary on 20x20. (Six mere super-Chimeras would work likewise.) The problem amounts to placing as many hyper-Chimeras so all the squares are covered and they mutually protect one another. By definition in the last comment, hyper-Chimera is Angel n=4, controlling surrounding set of 9x9 squares from any starting square. 20x20 board is a to t files and 1 to 20 ranks. So, efficiently place hyper-Chimeras protecting themselves orthogonally at e5, e16, p5 and p16. That leaves corridors of ranks 10 and 11 and files j and k not yet fully covered and just out of those sitting four's reach. It takes two more hyper-Chimera centrally placed at either both j10 and k11 or else both j11 and k10. Strongish to say the least, enemy Angel n=19 reaches every square singly on the board any turn at will. We assume alternating turns whilst the hyper-Chimera spread out from a1, a2, a3, a4, a5 and a6. There would be no other solution of so few as 6 pieces only. They have to be e5, e16, p5, p16 plus what is on the central pair. Only the j10/11-k10/11 guarantee both full rank/file coverage of the gaps, self-preservation, and triumph over the Angel. /// The other question is how many moves to get there from the a-file positions? Assuming for follow-up related, similar but somewhat weaker super-Chimera, not hyper-Chimera, is more interesting. Any super-Chimera dangling unprotected en route is a loss, sacked at once by opposing Angel n=19; and five pieces left are unable ever to terminate endless deadlock since Angel n=19 here only needs 2 free squares to live forever.

George Duke wrote on Sat, May 15, 2010 03:04 PM UTC:

Actually there appears to be one more solution for three only altogether. The two already described are much alike and the third is rather different.

George Duke wrote on Wed, May 19, 2010 03:53 PM UTC:

Also working would be a1, t20, f6, f15, o6, o15. And also the pair just as well a20, t1 with f6, f15, o6, o15, making four total solutions. 'a1' and 't20' protect each other across long diagonal from the Angel, and whereever Angel last was, she has no move and loses. Or the same thing, whoever she would try to take is guarded by one of the other five super-Chimeras, who one or another reach every other board square than their sittings.

Greg Strong wrote on Fri, Oct 9, 2020 01:20 AM UTC:Poor ★

The design of this game makes no sense to me. The Rook is upgraded to a Dragon King. The Knight is upgraded all the way to an Amazon. The Queen is upgraded to the most powerful piece I have ever heard of. But the poor Bishop is downgraded to a Wazir - a piece that moves only one step horizontally or vertically. One problem is that the board has so much power that it will be a tactical smash-fest. Another problem is that the Wazirs will never move. I cannot imagine any circumstance in which a player would waste a move on them, except possibly to get them out of the way to allow castling, and probably not even then. With all the nightriders, castling will likely be impossible anyway.

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