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Hey, George, you didn't notice the hint of chagrin and a delicate sarcasm in that statement of mine? To boldly invent the rhino for the umpteenth time doesn't do a lot for one's image. Imagine my thrill when I found out the Muse of Redundancy had visited me with another used idea. But to put together a little system that pops out pieces like that among other common and some very rare and unique pieces isn't all that bad. [I may need to continue that thought on your 91.5 Trillion thread, George]. I do have to disagree about independent invention of ideas, though. It has happened repeatedly throughout history, and will happen more and more in CVs because there are more and more of them. With luck, people with experience will catch the duplications. But this doesn't lessen the creativity of the designer, merely the bragging rights... :-)
A color-alternating piece with mating potential? You must be joking. For the purpose of mating a bare King, the mirror Rhino is equivalent to the (FN), which has mating potential of boards upto 16x16 (where it takes 100 moves), see: http://www.chessvariants.org/index/listcomments.php?subjectid=12x12_checkmate
In fact, mating with the mirror-rhino can be more complicated than mating with a simple FN, because the additionaly attacked zebra square provides lot of stalemate traps. A key position in the mirror-rhino's mating manoeuvre is the following: Black King on a1,a2,or b1; White king on c3, mirror-rhino on f6. Black to move. Only now the white king can complete the confinement of the black king --- BTW, the rhino is not colourswitching at all, it is a slider continuing its way after WN squares to C NN2 .... Adding the wazir to the Gnu essentially gives it the can-mate property.
The Rhino is an interesting and inspiring piece and this article is well written.
None of this page's long-range pieces are switching. The Rhino's first three destinations are those of the Wazir, Knight, and Camel. Knight plus Camel equals famously triangulating Gnu. Likewise the even destinations (exactly as with the Mirror Rhino) are destination of the Nightrider - a straight linepiece like the Bishop and Rook and so able to make two moves in the same direction and return in a single move the same length as the two together. Indeed not even a Waverer, a Rhino restricted to moves of odd numbers of steps, is switching as a Camel move can be reversed in four Wazir ones. Nor is a Feverer, a Mirror Rhino so restricted, as a Ferz move can be reversed in two Zebra ones. It may be more difficult when what I am for short calling Camel/Zebra moves are stepping ones here, but it is posible.
'On an eight by eight Chess board, I don't believe a Rhino or a Mirror-Rhino plus a King can mate a King, but a Double-Rhino plus a King can. A Monster should be able to mate unaided.'
I'm pretty sure an ordinary Rhino can, like so:
d e f g h ---+---+---+---+---+ | | | | k | 8 ---+---+---+---+---+ | R | | | | 7 ---+---+---+---+---+ | | | | K | 6 ---+---+---+---+---+ | | | | | 5
Correct me if I'm wrong.
'...but can the rhino+king force the opposing king into this position?' Good point - the diagram works for a Gnu too, but it doesn't follow that a Gnu can force mate.
@charles: ... but can the rhino and the king force this position? Yes they can, and they can do so easily: Essentially, after forcing the opposite king to the edge of the board, the rhino pushes forward using the wazir move.
@J�rg: I don't follow. Unlike a rook, the rhino cannot confine a king to an edge without assistance. In fact, it cannot confine the enemy king ANYWHERE without assistance--its attack pattern is porous. The friendly king needs to stay close to the enemy king to plug the gaps. It's not even clear to me that rhino+king could force the enemy king to an edge in the first place. If you take the diagram nnz posted, the rhino delivers the check, so it must have been the last piece moved. Which means the lone king's last move must have been from g8 to h8. So: black king g8, white king h6. In order to force the king into the corner, the rhino needs to be some place that attacks both f8 and f7, and to deliver the checkmate it also needs to be able to reach e7 in one move. That pattern of three adjacent squares does not appear anywhere in the rhino's movement diagram. You can't rewind the position shown even one move. Therefore, the rhino cannot force the exact position shown. HOWEVER, a similar mate might still be possible; the rhino could also deliver the mate from c6 or a5. A rhino at e5 threatens f7 and f8 and can also reach c6 to deliver the mate. Perhaps you might also do better to locate the friendly king at g6 instead of h6. So the exact diagram nnz posted is not possible without collusion, but I still don't know whether it's possible to force a mate or not. My suspicion is not, but I haven't given it extensive thought.
I suggest that you take a chess board, two kings and some piece representing the rhino (a knight works well for me) and try it out. I must admit, that I didn't analyse the specific position nnz gave here, the placement of the supporting King is a bit awkward here. Both of your proposals to repair the situation work out fine. For similar pieces: A gnu and a king can drive the king to the edge, but cannot give mate; the same holds for the quintessence (of quintessential chess).
A weird piece idea where all wazir movements are crooked
So this is supposed to be a rhino-mirror rhino alternating?
@Aurelian Florea
This is a Rhino where all Wazir movements are crooked compared to the previous one
Note that it must be trivially easy to checkmate a bare King with a Rhino, powerful as the latter is, in addition to covering two orthogonally adjacent squares. The checkmating applet cannot really do crooked sliders, but assuming that blocking doesn't play a significant role with only another King on the board, you can let it calculate a piece that directly leaps to the squares a Rhino would attack.
As is well known, the Gnu/Wildebeest, whose targets all fall on the Rhino paths, has no mating potential. This is due to a coincidental collision with the King. But just adding a single W move to the Gnu (say fW) already cricumvents this problem. So WNC, which is a subset of the Rhino (but leaping) already has an easy mate (maximally 19 moves).
The Mirror Rhino fares even better, as FN in itself has already mating potential (maximally 22 moves). The longer distance moves of the Rhino were only needed because without them no two orthogonally adjacent squares would be attacked.
How about a 135° Rhino '(abz)W'? A Pine. ...989.. ...767.. ...545.. 97531357 86410146 97531357 ...545.. ...767.. And it's mirror version. ...787.. ...565.. ...343.. 75312135 86420246 75312135 ...343.. ...565..
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