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What does it mean when a retrograde analysis problem is qualified as being "monochromatic" ?

2 Answers 2

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"Monochromatic" (or "monochrome") is a popular fairy condition with nearly 450 examples in the PDB database: https://pdb.dieschwalbe.de/overview.jsp?expression=K%3D%27Monochromatic%27

It is frequently used in retrograde analysis, but can appear with purely forward stipulations having no retro content.

Each piece move must end on the same colour square it began. This is a comically severe restriction:

  • Knights cannot move at all
  • Pawns can only capture (after any initial double step)
  • only K-side castling is legal.

On the other hand, en passant is fine and indeed often exploited in problems to help a pawn promote.

Here is a simple but fun example, by A.Buchanan 1991:

[Title "Show a promotion route, indicating units captured. Monochromatic."]
[fen "3qk3/6p1/8/8/8/8/1P1P1P2/4K3 w - - 0 1"]

Solution at https://pdb.dieschwalbe.de/P1339843

[Note that solutions in PDB use German piece names, so KQRBNP translates to KDTLSB (König, Dame, Turm, Läufer, Springer und Bauer). White/Black translates to w/s (weiss/schwarz). Finally, if there is ever castling, kingside & queenside translate to k & g (kleine = short & grosse = long).]

In most problems, "checks are fairy". This means that a King is only in check by enemy units standing on same-colored square, when capturing the King would be a monochromatic move. So that e.g. the two Kings can happily be in contact.

The monochromatic constraint has been used several times in the popular Sherlock Holmes book by Raymond Smullyan. However in Smullyan's compositions, checks are not fairy: the kings could not be adjacent.

Another variant relies on the concept that castling is considered to be a king's move (with the rook just a "passenger") In this context, queenside castling is ok.

Monochromatic allows some deep compositions. For example, here's one by the renowned French composer Thierry Le Gleuher:

[Title "What unit captured Ng1? Monochromatic."]
[fen "1N4B1/2p2p2/2Q3k1/p2p1RPp/P4P1b/7P/2PPPrrK/8 w - - 0 1"]

Solution sketch at https://pdb.dieschwalbe.de/P0001761.

Note that wKh2 is not considered to be in check. This won the 1st prize in diagrammes for 1989 and appeared in the FIDE Album 1989-1991.

See also: Max number of promoted units on the board in a monochromatic game

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    Do you have a solution for the Buchanan one written in algebraic notation? I can't quite understand the notations there. (also, the puzzle is to get a pawn to promote with the image as the starting position? or is it a retrograde puzzle?)
    – justhalf
    Dec 21, 2023 at 9:43
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    @justhalf In the solution to P1339843, PDB's entry for Andrew Buchanan's problem, people are using German letters for units: K=king, D=queen, T=rook, L=bishop, S=knight, B=pawn (not bishop!).
    – Rosie F
    Dec 21, 2023 at 10:47
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    Thanks. I can understand it now. Although the first sentence is confusing since it uses "[Sb8] was captured by [Ph2]" where the Ph2 also means pawn. And lowercase "s" as in "sD" means "black" as in "black queen", right?
    – justhalf
    Dec 21, 2023 at 11:48
  • I've added a paragraph on German chess notation, which is worth learning, to open the door to the wonderful resource which is PDB.
    – Laska
    Dec 21, 2023 at 13:31
  • @justhalf if you understood it can you write the solution in algebraic notation? I couldn't get it, and I don't see how it's possible either. The pawns can't move except to capture, and there are only two possible pieces to capture.
    – Allure
    Dec 22, 2023 at 12:34
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This type of problem is defined in the book "The Chess Mysteries of Sherlock Holmes" by Raymond Smullyan as being retrograde analysis puzzles where the pieces have the additional rule that they may not change color. That is, a piece may not move from a white square to a black square or vice versa.

This has a number of consequences:

  1. Knights may not move
  2. en passant is allowed, so in that particular case a white squared piece can capture a piece on a black square
  3. Castling is only possible on the king side because queenside castling involves the rook changing color of square.

Here is an example:

[Title "What color is the pawn on g3?"]
[fen "4k3/8/8/8/1K6/6P1/3P1P2/8 w - - 0 1"]

The logic is as follows:

  1. The white king started on e1, so must have castled kingside to escape to the center of the board
  2. If the pawn on g3 is white then it must have come from a dark square, h2. But in that case the white king could not escape from the castled position.
  3. Therefore the pawn on g3 must be a black pawn
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  • On this specific example, why couldn't d2 pawn be black? (so original white d2 pawn was captured, king go out, then another black pawn comes in). Or is it only g3 pawn with the color undetermined?
    – justhalf
    Dec 21, 2023 at 9:46
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    @justhalf Your last sentence is correct. It is only the g3 pawn which is undetermined. The other two pawns are definitely white. This is a problem in Smullyan's The Chess Mysteries of Sherlock Holmes. In the book, the g3 pawn is printed half white, half black.
    – Rosie F
    Dec 21, 2023 at 10:49

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