﻿﻿ MatPlus.Net

Website founded by
Milan Velimirović
in 2006

12:16 CET

Remember me

 CHESS SOLVINGTournamentsRating lists01-Oct-2019
 B P C F

MatPlus.Net Forum Promenade An almost joke question

Page: [Previous] [Next] 1 2

### An almost joke question

SH, original, but probably anticipated

A given legal pawnless position with Black to move is drawn. If all pieces swap color and White is to move, the position is...
a) won for White
b) illegal

Where is the white king after the color swap?

Mark the text to see the solution:
a) on e1 (castling)
b) in check (for example bBa8 wKb7)

I consider your solution to be incomplete -- the full position is required (at least one, with the possible admission that many positions may satisfy your stipulation).

And your solution to b) is not the only solution. Consider the following position:

(= 2+8 )

Nice catch here!

The most economic that I see for b) without check is the beneath:

(= 2+3 )

And for a) even four units are enough...

(= 2+2 )

So, maybe a better setting of that idea (with the above unique [??] solutions) could be:

a) To a knight on f8 add a minimum of white and black units (no pawns) for a position with no king in check and Black to move that is drawn. If all pieces swap color and White is to move, the position is won for White.

b) To a knight on f8 add a minimum of white and black units (no pawns) for a position with no king in check and Black to move that is drawn. If all pieces swap color and White is to move, the position is illegal.

What are the positions?

EDIT: No, now I see that the bK can also be on g6 in b)...

And for b) with Siegfried's question and without check also 4 units are enough...

(= 2+2 )

This seems even be a unique position (besides mirrored) with 4 units.

Another try for unique solutions...

a) To a unit on h7 add a minimum of white and black units (no pawns) for a position with no king in check and Black to move that is drawn. If all pieces swap color and White is to move, the position is won for White.

b) To a unit on h8 add a minimum of white and black units (no pawns) for a position with no king in check and Black to move that is drawn. If all pieces swap color and White is to move, the position is illegal.

What are the positions?

Will let you try before I post my position for a)!

Good find with the 4-piece position for b)! Unfortunately, it is not entirely unique - it is still drawn if Black has a rook instead of a bishop on f7.

Is a) possible with 4 pieces? I have found various 5-piece positions, e.g. like this:

(= 2+3 )

(= 2+2 )

Or R, Se6, so much for unique ;-)

Then you have Ka8 Bb8 - Kb6 Nd6 and Ke1 Ra1 - Kg1 Nd6. Unless
I misunderstood something, which is probable :-), this IS unique.
(Kh1 loses!)

Hauke

If king can be in check.... sorry it is the first post itself !

Looks like you are right, Hauke. Nice find!

@Hauke, you had it ALMOST right - it's just switching White and Black for a) and it is perfect with two 4-units!

So, here is the entrance for FIDE-Album 2013-15 (oh no! - some of my co-authors do not like that, although it would be so nice for the study section...):

SH, HR, GSTO & AT

To a knight on d6 add a minimum of white and black units (no pawns) for a position with no king in check and Black to move that is drawn.

a) If all pieces swap color and White is to move, the position is won for White.
b) If all pieces swap color and White is to move, the position is illegal.

What are the positions?

Solutions:

a) wKg1 wSd6 - bKe1 bRa1; with swapped colors 1.0-0-0+ wins.
b) wKa8 wBb8 - bKb6 bSd6; with swapped colors illegal as there is no last move for Black.

The joke is gone but the solutions seem uniquie!

If there was already something like that, most likely Werner Keym did it...
See on http://www.thbrand.de/2013/02/22/werner-keym/ a position similar to our b)-solution with a different question. It shows that instead of swapping colors you could also just rotate the board!

Actually in this case, the effect is the same.

I have no issue with the album anymore, Arno. Send it in! :-)

@Arno: Yes - flipping the board is easier, because of the CPT theorem
(H. Reddmann, Schwalbe article, issue...eh, must be ages).

For those who don't know that article, I quickly recap it here because
it is very fundamental. In physics, any situation is equivalent under
CPT operation (C=replace all matter by antimatter,P=mirror space,
T=reverse time). Intuitively, because nothing else than time, space
and matter exists. Be this as is (CPT proof DOES have some very weak
conditions, and instant Nobel to those who would find a CPT violation),
in Chess this is certainly true. C=swap color, P=flip board horizontally,
T=change right to move. It's obvious that "white" and "black" are
only labels (e.g. the "Immortal" was played with Andersen playing
black and beginning - or so I heard). Unless you have a fairy condition which
treats white and black unfairly (e.g. the common "black maximummer"),
CPT holds.

And yes, I did observe that you must either switch the knights color
between a and b or the order of the stipulations (which I'd prefer).

Hauke

EDIT: So here would be the (simpler) CPT-switched version:

To a knight on d3 add a minimum of white and black units (no pawns) for a position with no king in check and White to move that is drawn.

a) If the board is flipped horizontally, the position is won for White. wKe8 wRa8 - bKg8 bSd3
b) If the board is flipped horizontally, the position is illegal. wKb3 wSd3 - bKa1 bBb1

(Or "rotated by 180°" instead of "flipped", and knight e3)

Hauke

(= 4+3 )

It's an easy Nalimov check to verify that this position flips between
won and lost on board mirroring. Can you improve on that (or at least
find a version with Nd6? :-)

Hauke

At least it is possible to have 1 piece less.

(-white knights; +wpc7; bkd8->d5)

Georgy, the task is to do it without pawns.

I managed with six pieces:

(= 3+3 )

I didn't manage with Nd6, but at least there is a piece on d6 :)

So did "Karan" from schachfeld.de (since the problem is already published
on a public board, I took the liberty to let them have fun with it too),
and he found two different settings with 6 pieces too. One (or so I
think) can be included and it's unique with a Nd6 again (or so I think)!

Karan, schachfeld.de, Version HR
Add to a Nd6 blablaetc.; after a 90° rotation (!)
the position switches from Black wins to White wins.
Everyone, please check! Author solution here:

Hauke