Monochromatic chess problem

Raymond Smullyan, 1979



Monochromatic chess. A white bishop stands at e3 or e4. which?

Originally posted by David113
Raymond Smullyan, 1979

[fen]4k3/8/8/8/8/8/3P1P2/4K3[/fen]

Monochromatic chess. A white bishop stands at e3 or e4. which?

There is no bishop on either square.

Do I win?

😀😛

I'd never heard of monochromatic chess before, so I googled it:

In monochromatic chess, no piece may make a move in which it changes the colour of its square. As a result, rooks may move only an even number of squares, knights are immobile, kings can only move diagonally, etc. Pieces still give check on squares they cannot reach but would have been able to reach in a normal chess game. All other rules remain as in orthodox chess.

"Pieces still give check on squares they cannot reach but would have been able to reach in a normal chess game" - according to the Retrograde analysis corner (http://www.janko.at/Retros/Glossary/Monochromatic.htm) this is not true. Maybe different people use different conventions.

Originally posted by David113
"Pieces still give check on squares they cannot reach but would have been able to reach in a normal chess game" - according to the Retrograde analysis corner (http://www.janko.at/Retros/Glossary/Monochromatic.htm) this is not true. Maybe different people use different conventions.

I've never heard of this variation of monochrome, and with good reason. What sense does it make for pieces to give check on squares they can't reach? This is inconsistent with the definition of check.

Part of the fun of chess variants is that you have to think about their logical implications for the game as a whole. In monochrome chess, Kings can sit on adjacent squares, Rooks can never change square color, etc. Why ruin a simple, elegant rule with a clumsy exception?

This is what the Retrograde analysis corner has to say about the "Maximummer" condition:
"Checks are not fairy: the wh. King is under check even if capturing him would not be Black's longest move. Thus all moves in a Maximummer are legal moves in the usual sense."

I agree that it should only be check if the king can be taken next move with a legal monochromatic move. E.g. a Black rook on f1 would not give check to a White king on e1.

I can't work out much from this position. Obviously the White king hasn't moved. Black's last move must have been d7-e8 or f7-e8.

If White didn't have a bishop on e3 or e4 then Black's last move must have been a capture. Perhaps there's some way to prove that this must have been White's white squared bishop?

Originally posted by Fat Lady
I agree that it should only be check if the king can be taken next move with a legal monochromatic move. E.g. a Black rook on f1 would not give check to a White king on e1.

I can't work out much from this position. Obviously the White king hasn't moved. Black's last move must have been d7-e8 or f7-e8.

If White didn't have a bishop on e3 or e4 then Bla ...[text shortened]... Perhaps there's some way to prove that this must have been White's white squared bishop?

Try playing a legal game to reach the position.

The bishop is on e3 - I've played through a game (and certainly not the shortest one to get there).

Either side could have moved last, I think, probably a black K capture (is it possible to force a win with KQ v K in this?).

The most obvious thing to think of is that the rooks need releasing early on, whites black B can't do this without the b pawn being removed first of all. So a capture on h7 or h5 to get things going?

The proof is much simpler.

Originally posted by Peakite
The bishop is on e3 - I've played through a game (and certainly not the shortest one to get there).

Either side could have moved last, I think, probably a black K capture (is it possible to force a win with KQ v K in this?).

The most obvious thing to think of is that the rooks need releasing early on, whites black B can't do this without the b pawn being removed first of all. So a capture on h7 or h5 to get things going?

Now comes the harder question: Why can't you play through a game and end up with a Bishop on e4?

Originally posted by David113
The proof is much simpler.

Of course, but how many are going to see that right off the bat? By trying to play out a PG with Be3 and then a PG with Be4, the proof will become painfully obvious.

Originally posted by BigDoggProblem
Now comes the harder question: Why can't you play through a game and end up with a Bishop on e4?

Black has no pieces left on the board and the two white pawns and King have obviously not moved and are all on black squares.

Since Blacks King cannot capture pieces on Black squares and Black has no remaining pieces on black squares, the last capture on black squares must have been by White.

As we know that White's other three remaining pieces have not moved, we know that the one remaining White piece must be on a black square. To say it another way, if White's bishop was on a white square, Black would have another piece on a black square.

True 🙂