Weird checkmate contest

The position below is legal! 18 Queens are actually possible in a game of chess. Just mate in 1.

In this position, white has only one legal mate in one.

That’s not a checkmate.

I am fighting with the puzzle interface. Try to get it right! Edit: now it is right!

That’s alright.

First puzzle: Qxe4#

Second puzzle: Qxe4#

One of the two is correct. (Note: I just switched the 2 diagrams but the correct answers remain as they were)

Then what is the answer?

Both are correct

I'll answer it tomorrow giving others a chance to chew on it.

Note: I just switched the 2 diagrams but the correct answers remain as they were

Agreed

In both positions Black still has 16 units, so White couldn't have made any prior captures. Assuming it's White to play, what was Black's last move? It wasn't made by any of the pieces on the 7th rank or the g-file, because such a piece (Q or R) would've been illegally checking White (on the 8th rank or h-file) while it was Black's turn. Black's last move wasn't by the d5-N either, because that implies it has just intercepted a check by the c5-R, but this R couldn't have delivered a check when (as mentioned) no white capture has taken place and Rxc5+ is needed for such a check to have occurred. That leaves Black's other N as the potential last mover, and its position is different in the 2 diagrams:

(A) On d6 the N could have made the last move, in response to a non-capturing check by the c7-Q. Therefore Black could have made the last move and it's possible to be White's turn in the diagram. The mate-in-1 is thus 1.Qxe4.

(B) On f4 the N couldn't have made the last move either, as that implies the g3-B has given an illegal check. That's because with no white captures possible, this B couldn't have just played Bxg3+, and the non-capturing Bg3+ would mean that the h2-Q was already checking while it was White's turn - again an impossibility. Therefore we've proved that Black couldn't have made the last move in the diagram. And since the diagram is a legal position, it could have arisen only if White had made the last move. Hence it's Black to play in the diagram and the mate-in-1 is 1...Qg8.

Sweet retro problem with cute starting positions!

EDIT: I forgot that we also need to rule out a black N capture on d5 or (in the second diagram) f4 as the last move. Such a capture would have meant Black wasn't in check from the c5-R or g3-B, so that there's no need for White to have made a capturing check and the diagram is legal with White to play.

How do we know there's no spare white unit for either black N to capture on d5 or f4? White has 11 units in the diagram, of which 5 are promoted pieces (4 Qs + 1 B). The 5 white Ps must have marched straight down their files to promote without making any captures (as Black has no missing units). To get out of their way, their respective opposing black Ps had to make one capture each (before promoting themselves), for a total of 5 captures. These captures account for all 5 of White's missing units. That means there's no spare unit for either black N to capture as the last move in the diagram.

Almost the same as post #61.

Thanks Rocky64 for that great analysis! Some people around here believe you ought to construct a proof game for these problems but I much prefer it this way.

More could be done with these ideas but I won't give up the 4x4 and 5x5 squares for the gold of the world! Marching a Roman infantry square across a chessboard is my taste in weirdness, which is the topic!

No worries @Arisktotle, and congrats on getting it sound! It must have been a challenge to juggle all three aspects of the problem: (1) retro-analysis, (2) forward mates-in-1, and (3) square shapes.

An improved version of post # 109. It's a triplet of problems with a switch of 2 units between them. All problems require a checkmate in 1 move. Solutions follow later.

1. Diagram 1.

2. Diagram 2 = Diagram 1 plus a switch of Rf4 and Pf6

3. Diagram 3 = Diagram 1 plus a switch of Bf3 and Pf6

1. Bxe4#

2. Rxe5#

3. fxe4#

Consider giving me a trophy for solving these problems! I really had to spend some quality time.