Do you know checkmate?

Beginners have trouble recognising checkmate. Do you?

1

2

Trophy for correct explanation of the checkmates!

(retro) (problems without words - enjoy)

^^ Good luck!

I think Problem 1 is cooked (-1. c6-c5 cxb8=B), but I haven't really analyzed that line, so haven't figured out whether that's actually impossible.

I haven't touched Problem 2.

So in problem #1 white is already in checkmate, and in #2 white moves Nxa6#. What am I missing?

First, in both cases White is in check. (So 1. Nxa6?? is illegal.)

Second, in both cases White might be able to do en passant. The problem is, can White?

Oh, Problem 1 solved, I think. Yes, White can do en passant. The analysis is too hard to type from phone though, so I'll leave it for now for others.

Great and awesome

Problem 2 is easier than Problem 1. :/ But that's a really neat cage; interesting use of tempo.

finnerz1999's puzzle is unrelated to Remellion's, and might be better given in its own thread.

2) is checkmate. Black's last move could have been ...b6-b5, which means white, by convention, cannot take en passant.

Problem 2 is trickier than Problem 1. But despite the gigantic clunk of pieces at the bottom left, the analysis is terribly straightforward - except that uncapturing NxR is the key as BigDogg found. Not uncapturing, or uncapturing B, is retropat. Trophy!

Of course while making it I ran into maybe 3 other cages/structures that I'd have liked to use but couldn't, due to space/material constraints. Maybe in another setting. e.p. mate-on-mate situations restrict the king positions quite severely.

I miscounted Black's available pieces. :/ Just explains you shouldn't do retro on bed.

Problem 1 (aka the problem I didn't fail)

Black's last move was by the c5 pawn. Either it comes from c7, in which 1. bxc6 e.p.# mates Black, or it comes from c6. Let's see whether the latter is possible.

White's last move wasn't by the rook (blocked), the knight (can only come from c8, which is giving check), or the king (c5 is in contact with king, d5/e5/d3 are double contact checks). Not the pawn on b5, c2, d2 either (nowhere to retract). Not the bishop coming from c7 either, but it's possible that the bishop was new (cxb8=B). The only remaining moves are cxb8=B and bxc3.

Black made eight captures by pawns (cxbxa, dxc, exd, fxexdxcxb); White is missing eight pieces. So all pieces are captured by pawns. In other words, White's dark bishop gets out from c1. So retracting bxc3 is out of the question, as it would lock the bishop in c1 and thus not enough captures. The problem is now whether cxb8=B is possible.

White made two pawn captures (axb, bxc). If the bishop was promoted, it must come from e-file or to the right, which requires three more captures to b-file. Black is missing five pieces, so that's equality achieved: White's bishop might have been a promoted e-pawn (but not further to the right).

But if this is the case, White needs all captures, including Black's g/h-pawns. Similarly, Black needs all captures, including White's g/h-pawns. Meanwhile, these four pawns can't capture (too many captures), and can't get past each other for promotion either. (White's f-pawn can, after letting Black's f-pawn to capture a piece to e-file, as it's also required.) So this is impossible.

Thus the last move was indeed c7-c5, allowing White to do en passant and mate.

In diagram 1, white can take en passant and mate if the black pawn moved from c7, if from c6, white is mated

In diagram 2, white can take en passant and mate if the black pawn moved from b7, if from b6, white is mated

@SmartMocha: That's your problem; figure out whether Black's pawn came from rank 6 (White is checkmated) or from rank 7 (Black is checkmated after White's en passant move).

Well explained for problem 1. Trophy for you sir! (Final triviality: -1...c7-c5 allows -2. Nc6 or -2. Kd5 retractions and hence is legal.)

These two sentences are incoherent. Instead, the captures could have been dxcxbxa instead of dxc and cxbxa... unless the comma separators didn't have any meaning in the first place.

Yet, this means that the captures happened on a4, b5, c6, b3, c4, d5, d6 and e7.

All of white's pieces were captured, so every missing pawn (e,f,g,h) was captured. I don't see how this can be done.

Probably missing something. (either that or e.p. is illegal and it's mate)

Promotions. And/or captures to get the white pawns where they need to be. That was a typo by chaotic_iak too though.

Right, I forgot to specify that retracting -1. c7-c5 allows -1... Nc6-a7 (and apparently -1... Kd5-d4 too).

cxbxa means the c7 pawn made captures to move to b-file, then a-file. dxc means the d7 pawn made a capture to move to c-file. It's not known on which ranks precisely. It's easier to write "cxbxa" than "c7-pawn captured to move to b-file, then a-file". It might also be the case that there was dxcxbxa instead, the original c-pawn staying in the file (as in the actual solution), but the point is that we count Black's captures.

The pawns were captured after promotion, just like the case when I tried whether cxb8=B is possible as White's last move. (Or by capturing to move to a different file, but it's still not enough.)

Also, typo where?

Typo exactly there. Last move c7-c5 and captures cxbxa?

Captures were dxcxbxa, exd, fxexdxcxb, uniquely determined.

Oh, yes, there. Before deducing c7-c5 was the last move, the captures might have been cxbxa and dxc however, instead of dxcxbxa. You only know it's dxcxbxa after you find c7-c5 as last move, in which it no longer matters.

No, you have missed the point. The point is that there are possible histories of the game in which white can't take ep - meaning that white has been checkmated. Again, this is convention for retro problems.