Minichess puzzle

[petero2]

I enjoy a lot these minichess puzzles and I always get the same outcome: close, but no cigar.

Same, except I don't even get close.

Here is another puzzle.

In 4x4 chess, the kqqqqrrnkp ESM has 2,375,527 unique legal positions. Only two of them are checkmates (the rarest per ESM for up to 12 pieces). What are they? To be clear, the side with the 4 queens is checkmated. Also, the two positions must not be convertible to each other by any combination of symmetries or color swaps. Pawn is allowed on the first rank.

[d]QR2/QR2/QNpk/QK2 w
This is actually a rotation of the other position but it is not equivalent because of the pawn.

[Ajedrecista]

Hello Alex:

[d]2k1/2p1/RRNK/QQQQ

White to move of course, not Black.

Alex

The funny question here is what was black last move.

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I can't find any other solution through logic.

Alex

There is a list of requirements:

• The black pawn must give check, so the white king must be immediately Southwest (SW) or Southeast (SE) to that pawn.

• The black pawn must be defended by the black king in order to be a checkmate and not only check [i.e. the white king (wK) can not capture the pawn]. Following the former cardinal notation, the black king must be immediately NE, N, NW, W (if wK is SW) or E (if wK is SE) to the pawn.

• The black pawn can not be captured by any other white piece. The white knight being immediately W, E or S to the pawn seems key. It is reasonable that the four queens are in one side of the board (a or d files, or 1 and 4 ranks) in order to be cramped, avoiding checks or capturing the pawn.

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[d]QR2/QR2/QNpk/QK2 w
This is actually a rotation of the other position but it is not equivalent because of the pawn.

In the meantime, I see that Peter brings a solution that enables a black last move (c2#).

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello:

[d]Q7/8/2K5/8/8/8/8/7k w - - 0 1
The task of the Untouchable King
White has a king on c6 (c3, f6 or f3) and a queen, black has a king. Can white always checkmate without moving his king?
The solution was obtained using a computer (A. L. Brudno and I. J. Landau, 1969). Checkmate is given no later than the 23rd move for any position of the queen and the black king.
In other positions, the white king and the free black king cannot be checked.
Will your program be able to checkmate?
PS: The white king can't walk!

Just to bring context to this problem, I found the original source of 1969. I learnt the Russian wording «Неприкасаемый король» (The Untouchable King) thanks to this link and Google Translator, and that was publisshed at «Шахматы» magazine. I found that it was at issue Nº19 thanks to this link.

The issue Nº19 of 1969 of «Шахматы» magazine can be downloaded in DJVU format from here:

https://publ.lib.ru/ARCHIVES/SH/''Shahm ... hmaty.html (The index page).
https://publ.lib.ru/ARCHIVES/SH/''Shahm ... %b919.djvu (Issue Nº19 of 1969 of «Шахматы»).

The problem is at the bottom half of page 23 of the issue, with the white king on c3, the white queen on f7 and the black king on h8. The given solution is in 22 moves (starting with 1.- Qf6+, Kh7 and finishing with 21.- Qg2, Ke1; 22.- Qf1#), but the next paragraph says somethink about 'maximum' and 23-move. Since I do not know Russian language and I am in a hurry, I can not translate the short article right now, which ends with a draw of a walking rook with legs and a chessboard under its arm.

Regards from Spain.

Ajedrecista.

[Brunetti]

The funny question here is what was black last move.

Hello,
AFAIK for the purpose of determining legality, this is not required according to Kiril.

Alex

[Ajedrecista]

Hello:

The funny question here is what was black last move.

Hello,
AFAIK for the purpose of determining legality, this is not required according to Kiril.

Alex

Good to know. What about this position?

[d]Q1QQ/R1RQ/1pN1/K1k1 w

Regards from Spain.

Ajedrecista.

[Brunetti]

Good to know. What about this position?

It's never possible to mate the King in the corner because you have to cover two excape squares, one with the King and the other one by blocking the square with the Knight (sliders could take the pawn). Then you simply can't place the 6 sliders without attacking the King or the pawn.

So your positions can't be checkmate, look better

Alex

[Ajedrecista]

Hello:

Good to know. What about this position?

It's never possible to mate the King in the corner because you have to cover two excape squares, one with the King and the other one by blocking the square with the Knight (sliders could take the pawn). Then you simply can't place the 6 sliders without attacking the King or the pawn.

So your positions can't be checkmate, look better

Alex

That is true! I checked that neither white piece could capture the pawn and I completely forgot about the king escape through a2. Thanks for pointing out.

Regards from Spain.

Ajedrecista.

[Kirill Kryukov]

Very nice! Alex and Peter get the cookie. I added these positions to my page.

[Kirill Kryukov]

[d]2k1/2p1/RRNK/QQQQ w

The funny question here is what was black last move.

Any of the 10 different captures by the pawn, no problem here, because pawns are allowed on their first rank.

I found it more interesting to try reconstructing the history of one of the previous positions:
[d]1pBQ/1KRQ/nnNP/1k1b w

[Ajedrecista]

Hello Kirill:

Understood. I was aware that black pawns can be at the fourth rank (their first rank). My problem was that the black king was already on c4, so the pawn move c4-c3# was impossible. I completely overlooked the fact of captures, so either bxc3# or dxc3# are possible, each of them capturing P, N, B, R or Q, hence 2•5 = 10 possible captures you wrote.

Long time to master the 4x4 game... Imagine in 8x8!

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I do not understand the suggested task of 'reconstructing the history' of the other position. Try to find previous moves that lead to the position? If that, it looks difficult indeed.

Regards from Spain.

Ajedrecista.