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MatPlus.Net Forum Helpmates Unusual twinning and unusual AUW.
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(1) Posted by seetharaman kalyan [Saturday, Jun 14, 2014 20:23]; edited by seetharaman kalyan [14-06-14]

Unusual twinning and unusual AUW.

I was delighted to publish this nice problem by Nikola Predrag showing a novel twinning method to show AUW by the same white pawn. Your comments welcome.
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(2) Posted by Kevin Begley [Sunday, Jun 15, 2014 04:32]; edited by Kevin Begley [14-06-15]

Interesting twinning idea.

The concept is not entirely original -- I vaguely recall some problems twinned by removal of the mating unit, for example (which is quite similar); in fact, I made a fairy problem based upon twinning from the final position, with only alteration of the diagram's retro-content, and I seem to recall that somebody had partially anticipated even that idea -- but, this specific change might be new.

And, this idea does suggest the possibility for a broader set of options, in altering the mating unit...
I'd like to hear any ideas to shorten the text required, while preserving alternative options for replacement.

I'd especially like to hear Nikola's thoughts; until we do, here's my suggestion (hopefully others can improve upon it):

0) AMU->... = Alter Mating Unit in some way (where the specific alteration is designated by "...").

1) AMU->UPPER-CASE : specifies alteration of mating unit's type, from the solution to the original diagram.
e.g., "b),c),d),e) AMU->Q,R,B,S" = alter mating unit's type to Queen, Rook, Bishop, Knight), and solve again by identical stipulation.
How about that -- maybe you can show an AUW in this twinning method, too!?

2) AMU->*... : specifies continuous alteration of mating unit (for each twin, make the same alteration in the mating diagram from the preceding twin).
e.g., "b),c),d) AMU*->P" = b) AMU->P (from final mate of diagram), c) AMU->P (from final mate of b), and d) AMU->P (from final mate of c).
Interestingly, here the solver's final solution may be adequate proof of all preceding solutions.

3) AMU->lower-case : specifies alteration of mating unit's type color.
e.g., b) AMU->n = alter mating unit's color to neutral, and solve again by identical stipulation.

4) AMU->#° : specifies alteration of mating unit's type rotation (note: works only with fairy units present).
e.g., b) AMU->90° = alter mating unit's rotation 90° clockwise, and solve again by identical stipulation.

5) AMU->lower-case UPPER-CASE : specifies alteration of mating unit's type and color.

6) AMU->(x) : specifies annihilation of mating unit (e.g., remove the mating unit, and solve again by identical stipulation).

7) AMU->() : specifies no alteration of mating unit... (e.g., do nothing, just solve again from the final mate position, applying new retro assumptions).


Are there other possibilities? Are there better ways to cover these possibilities?

Are there any issues with this type of twinning?
1) If checkmate is delivered by double-check (or n-tuple-check), must the twin apply to all mating units, simultaneously?
2) What about stalemates?
3) Is there cause to expand this to alteration of the final position (where specific alterations can be stipulated, such as Q->R, R->B, etc)?
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(3) Posted by Kevin Begley [Sunday, Jun 15, 2014 05:20]; edited by Kevin Begley [14-06-15]

ps: here's an AUW I made, in a single solution, by the same neutral pawn (which experiences a peculiar kind of duel)...
I sent it somewhere, but never heard back, so I presume this was never published.

K.B. (scheme)
(= 2+9+2N )
Relegation Chess

Relegation Chess (aka Degradierung) - upon moving onto its own 2nd rank (home-rank for pawns of a given color), an officer (except King) immediately demotes to pawn.

1.g8=nB! …nBh7(=nP) 2.h8=nQ+! …nQxd4 3.nQd1 …nQd7(=nP) 4.d8=nS! …nSb7(=nP) 5.bxa8=nR!#

I liked the single-unit having a duel (reminds me of Good-Kirk vs Bad-Kirk), and showing AUW...
Unfortunately, the use of Maximummer (as usual, when it used to force play, and is not thematically necessary) cheapens the idea far too much.
The judge (whomever that was) deserves credit, if this was the reason for neglecting my problem (many fairy judges fail to appreciate significant differences in fairy element usage, particularly in excessively constraining conditions).
Plus, my construction was rather shoddy...

A much better AUW, with a single white pawn, is seen in the following:

Kurt Smulders
3rd Prize, The Problemist, 1982
(= 2+9 )
Relegation Chess

1.g8=S! 2.Sh6 3.Sxg4 4.Sxh2(P) 5.h4 6.h5 7.h6 8.h7 9.h8=B! 10.Bxb2(P) 11.b4 12.b5 13.b6 14.bxa7 15.a8=R! 16.Rxa4 17.Rxa2(P) 18.a4 19.a5 20.a6 21.a7 22.a8=Q! 23.Qxf3 24.Qxg3 25.Qg7 =

By comparison, I quite liked Nikola's method of achieving this -- even if it might be a stretch to claim this is a single pawn (the same could be said, but only to a lesser degree, in the fairy methodology) -- because his creative interpretation appears entirely orthodox (which constitutes a spectacular realization of what we might incorrectly believe to be a fairy theme)!
Maybe, if we think slightly outside the box, any Chess rules (including orthodox) might be sufficient to express any theme!?
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(4) Posted by seetharaman kalyan [Sunday, Jun 15, 2014 07:50]; edited by seetharaman kalyan [14-06-15]

You are right Kevin that twins where the mating piece is removed is done several times. Twins shifting the black king from mating position has also been done before but not so frequent. This specific twinning, of changing mating piece is, I thought, novel. Your interesting suggestions for notation appear simple and should be examined by experts.

Hm....AMU is already a fairy condition. it may or may not be relevant.
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(5) Posted by Kevin Begley [Sunday, Jun 15, 2014 15:56]; edited by Kevin Begley [14-06-15]

You are correct -- "AMU" is not the most universal notation either...
Ideally, the notation for both twinning and stipulation should be language independent; therefore, symbols are better.
Perhaps it's time we consider some unicode symbols (they are far more accessible today, and they might be helpful in expressing some ideas more clearly).

Also, the "*" (which I used to suggest successive alteration of the mating unit) is a poor choice -- the symbol is already taken for setplay.
Probably the latter can be improved with the ampersand ("&") -- which already denotes successiveness in twinning...

The notation we can fix fairly easily (providing folks do not become prematurely attached to a sub-optimal expression -- luckily, I see little need for that, here).
I'm more concerned about additional options not considered.
I'm confident that I have not covered all possibilities, which means unforeseen alterations are likely to be necessary.
Better to get this right the first time (at the very least, strive for a framework which has room to grow).
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(6) Posted by Nikola Predrag [Sunday, Jun 15, 2014 18:27]; edited by Nikola Predrag [14-06-15]

I made that h#2 as an example for the discussion about a twinning principle. I was not sure whether it should be published as an original, because of the uncommon twinning and the possible troubles with a short and clear explanation of it.

And the very discussion was about the short and clear symbols for a whole class/family of a twinning principle:
>a new twin starts from the mate-position of the previous twin. Of course, after some "Change" which allows Black to play some legal move(s).<

I wrote down various attempts but not enough systematically and clearly to paste it here. Anyway, the symbols should come when the essence of a concept is clear.
The essence is "Solve>Change>Solve(Again)>Change>Solve...", shortly "S-C-S" twinning, or any better symbolization.
My problem would be e.g. >4xh#2; S-C-S(Twins),C=Demotion<
Demotion (default) affects the pieces promoted during the play
4xh#2 tells that Mate&Change must happen after every 2+2 halfmoves, 4 phases altogether

"DemotionGradual" might mean Q-R-B-S-P, starting with any rank (in case of less than 5 twins)
"PromotionGradual" might mean P-S-B-R-Q etc., without a mandatory "real" Pawn-promotion on the last rank.

Perhaps a fairy condition could be defined >kxh#n; S-C-S(Condition)<:
"after each n+n halfmoves, Mate&Change must happen and a complete solution would require kxn+kxn halfmoves"
bK has k-"lives" and after each "partial mate", the "Fairies" save bK at the cost of 1 "life"

S-TC-S might symbolize the twinning and S-FC-S the condition.

There are various possibilities but the fundametal concept and symbolization are hardly needed for just a few composed problems.
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(7) Posted by seetharaman kalyan [Sunday, Jun 15, 2014 20:44]; edited by seetharaman kalyan [14-06-15]

I believe that this simple symbol would be understandable. " ># " implying that any change occurs from the previous mating position.

># remove g7, ># g7 to g6, ># g7=P, >#g7=S etc.. There can only be three changes possible in the mating position: Move the king, change/remove the mating piece or insert a pawn/piece in the mating line.
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(8) Posted by Nikola Predrag [Sunday, Jun 15, 2014 22:18]

Yes, but why to specify the change for each twin, if they are many and the change is always the same. Rough example:
(= 9+8 )
8xh#1.5 S-Demotion-S

If I could make it in a minute (without the pieces and board), there is surely a possibility to make much more twins. Specifying each twin separately requires space and work.
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(9) Posted by Kevin Begley [Sunday, Jun 15, 2014 23:02]; edited by Kevin Begley [14-06-15]

The idea of using fairy conditions to alter the mating unit is a good one, but we still require a twinning symbol indicating the metamorphosis of a mating unit.
I like ">#", but I think Δ (or δ) are better symbols for change. For example: b) #Δ P or b) Δ# ♙ .

Maybe ∫ can symbolize succession: b),c),d) ∫ #δ ♙ -- it's a pity we can't easily show that the integration goes from x=diagram to x=twin d).
Also, maybe the path integral shows up better -- b),c),d) ∮ #δ ♙ -- this might even be more logical.

At least we can put some calculus in our twinning mechanism!
I'm sure some math major will argue that we are integrating over the mating unit, so maybe this form is better: b),c),d) ∮ ♙ δ#

Note: "8xh#1.5 S-Demotion-S" does not read like a twin -- in fact, this is an interruption of the stipulation; clearly, this information does not belong in the stipulation.
Furthermore, whether you mean "Demotion" (I think you mean "relegation chess", or "Degradierung" -- Demotion Chess is a slightly different fairy condition, invented by Dan Meinking), because those fairy conditions change officers moved upon specific ranks (their own 2nd rank, or their own 8th rank) -- neither one alters mating units, spanning the entire board.

Moreover, I don't agree that the essence here is "solve-change-solve" -- the essence of this idea is a twin, first and foremost, which changes the mating unit in a particular way (in this specific case, we alter the type of unit, but we could as easily alter the color, or rotate the unit, or remove the mating unit, or make no change to the unit, and proceed; some thought is required for how fairy conditions might work here).

Finally, as I've explained, there is the option to draw multiple twins from the final position of the diagram, or to draw them from each successive twins.
The "solve change solve" formula might have proved a useful framework to build Nikola's problem, but it fails to envision a means to cope with alternative architectures, based upon the true essence of this idea.

By the way, there is a subtle point to Nikola's twinning, which demonstrates that the twinning mechanism is not as orthodox as you might first think; to fully appreciate this, just consider what happens if a mating unit occurs on the 1st (or last) ranks. Obviously, this is a possibility for which the composer will deliberately go out of their way to disallow, but according to the first rule of chess composition, somebody, someday, is going to want to put this oddity to good use. Therefore, plan for it (which would be easier, if problem chess had insisted upon a consistent default rule for all pawns on the 1st rank -- and the obvious solution there is to make pawns behave as they would on every other rank, with the exception of the 2nd last ranks).

So, strangely enough, Nikola has helped to demonstrate that orthodox and fairies are actually more interconnected than some folks like to pretend. :-)
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(10) Posted by Nikola Predrag [Monday, Jun 16, 2014 01:59]

I'm not eager to propose the symbols, I'll eventually accept whatever might be proposed. I care more about their meaning.

8xh#1.5 indeed interferes with the stipulation but in case of a fairy condition it might be a stipulation. And it's not clear that S-Demote-S is a twinning principle, it looks more as a condition.

I wrote it that way as a possible(?) example of a condition which not only "demotes" a promoted piece after the mate. It also allows 2 consequent white moves, White mates and after demotion, White continues.
If such sequence W-B-W>W-B-W... looks unacceptable, the very act of "demotion" might be taken as a black move.
But I'm not much interested in new conditions (before having an idea for a problem), that might be explored or abandoned by those who are interested.

Actually, sending that problem to Seetharaman, I wrote under the diagram:
h#2(x4) #=PromotionsCancelled-PlayContinued 5+11
where (x4) is supposed not to affect the meaning of the stipulation, but to indicate its repetition through 4 twins.

Solve-Change-Solve could be a twinning or a condition, so I wrote S-C-S(Twins)
and S-C-S(Condition), or shorter S-TC-S and S-FC-S (TwinChange and FairyChange).

The essence of the idea (S-TC-S) is indeed a twin, but not only "which changes the mating unit in a particular way". "Change" could be "Relocation", "Addition" or "Removal" of some piece. "Change" could be "ColorChange" or "CancellAllAndernachColorChange" or "CancellParticularAndernachColorChange" etc.

h#2; #(a>b>c)=Relocate(bK)
might suggest that in mate-position of a/b, bK is relocated to f8/b3, and there's h#2 again.
h#2(x3); #=Relocate
might suggest the same twinning principle (for 3 twins) but not only bK is relocated.

Any clear and short symbolization would be good, so go on.

In orthodox problems, the twinning with Pawns on 1st/8th rank would be simply incorrect. The author must care about it. A great restriction for the construction of that h#2 AUW, was getting the first 3 mates from 7th rank. A mate from 6th rank would mean a mate by promotion in the next twin, leaving wP on 8th rank for the next twin.

Fairy chess might allow anything and some general "general theory" would have to care about everything.
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(11) Posted by Joost de Heer [Monday, Jun 16, 2014 08:43]

If there are two solutions in a), and only one of them leads to a solution, after the change, in b), is the second solution in a) a cook or an invalid solution?
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(12) Posted by Georgy Evseev [Monday, Jun 16, 2014 08:45]

This discussion has gone into unneeded details.

I have long ago resolved this difficulty for myself, declaring that there are two kinds of twins: technical and constructive.

Technical twins are used when they are needed because of technical difficulties or formal limitations. The change should be as small as possible. The kinds of technical twins are well documented and most probably we will not see anything new is this field.

In the constructive twins the mechanics of twinning is itself a part of the author's idea. So, everything is allowed, until the idea is emphasized enough. Unfortunately, this is exactly the reason why no sensible classification is possible: generally, a new problem with the same mechanics of twinning is, really, significantly anticipated. From the other hand this means that we will be able to see a new finds in this area.

I had given a small lecture about this kind of twins in Marianka in 2011. Unfortunately, I had not prepared the text separately, but the problems shown during lecture are available in Marianka 2011 bulletin (, starting from page 49.
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(13) Posted by Kevin Begley [Monday, Jun 16, 2014 08:49]; edited by Kevin Begley [14-06-16]


You make many good points... and it's important to reiterate my appreciation for your original problem.
I'd like to see more creative ideas actually encouraged -- it's particularly enjoyable, when such an original idea can be expressed with thematic artistry!
My favorite art is that which gives the reader something to think and talk about... it expands the genre... it teaches me something that logically should not fit on a chessboard.

I was stirred by your problem...
I thought it appropriate to raise some larger issues, offer some suggestions, and ask for improvements, here.
I am confident that my suggestion is not the best (there are many things I have not considered -- for example, relocation of mate units, as you noted in your last post). Like you, I look forward to the improvements, which will surely enhance our ability to express such creative new twinning options (as you have demonstrated, and as we may extrapolate plausible). Hopefully, I helped to push a remarkable twinning idea forward...

I know some will consider it tangential to encourage further suggestions, and improvements, in this thread, but for me, such a discussion seems the natural residual impact of your work (which you can definitely take as a compliment). I hope it gets the editors, and the software developers talking to one another... searching for the best way to universally express such twinning possibilities.
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(14) Posted by Nikola Predrag [Monday, Jun 16, 2014 09:20]

in case of twinning, a second solution, such as you described, would be a cook.
In case of fairy condition, h# in kxn moves (with k Parts or k "partial mates"), any "partial" solution which doesn't lead to a "complete solution", might be considered as simply "not solution". However, such fairy condition should be precisely defined and I don't know how.

I agree that it's not likely to see many problems with such twinning. This twinning principle itself makes the main content, the play is not interesting (but the construction might be). Still, instead of AUW, something else probably could be shown.

the possibilities are unlimited and to anticipate all of them in some general classification looks impossible. Still, some flexible frame would be a welcome and brave contribution.
I have indeed tried to "play" with a twinning which looks like a fairy condition, to achieve an illusion of continued play as h#8(4x2)
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MatPlus.Net Forum Helpmates Unusual twinning and unusual AUW.