A retro problem

So here is a problem I composed.

Is the following position legal?

Another one. Where was black’s queen captured?

We need to account for both the possibilities of the last move being White's or Black's. Looking at the position, I could easily rule out the last move being a king move. I can also rule out a few other chess pieces, leaving as only candidates for the last move:

• 1.the c3 pawn  (0.c3 or 0.bxc3)
• 2.the e3 pawn (0.e3 or 0.fxe3)
• 3.the g3 pawn (0.fxg3)
• 4.the e6 pawn (0.dxf6 or 0.e6 or 0.fxe6)
• 5.the d6 pawn (0...exd6)
• 6.the b7 knight (0...Nxb7)

White has 7 pawns and Black has 7 pawns, so at most one promotion is available for either side. But probably not White. We can deduce the pawn on g3 must originate from f2, so 0.fxe3 is out of the question and the pawn from e3 must originate from e2. We can also decuce Black has not enough material for White to have a pawn come from the b file to the e file (3), to have a pawn come from the f file to the g file(1), and to have a pawwn promote (1+) all at once. In fact, Black has 12 of his original 16 chess pieces, so promotion is out of question for White.

Now, since Black's pawns originating from a7 to e7 weren't taken, non-king black pieces needed to be taken. fxg3 also requires a minor or major black piece being taken since the g7 pawn is still on g7... Which means Black promoted one of its pawns! And capture-wise, the h2 pawn requires two captures from Black and the d6 one requires one, and White still has 12 of his original 16 chess pieces, so there is no concern here.

So yep, the first one is legal. The 7 possibilities are:

• the last move was 0...exd6
• the last move was 0.dxe6
• the penultimate move was -1...exd6 and the last move was 0.e6
• the last move was 0.fxg3
• the penultimate move was -1...exd6 and the last move was 0.c3
• the penultimate move was -1...exd6 and the last move was 0.e3
• the last move was 0.Nxb7

There are so many possibilities.

@daStrwbrry For your last puzzle, I guess your answer was d7 (trying to get in your head). However, there are just so many answers... When I started retro puzzles, I struggled with pawn captures. Here, the black queen could have been captured by any of the pawns present on a3, c5, d4, e3 and f3 in your position, as far as I know.

Here would be an easy fix to your second problem.

Some decent analysis for the first position, KlekleLegacy! Deducing the last move is quite important here, and you have reduced it to only a few possibilities. However, you can rule out even more possibilities for the last move. There are some things you need to be careful about: the position is not that simple.

Try to link white’s captures with black’s missing pieces (and vice versa), since this allows you to keep track of the inventory for both sides. For example, neither Nxb7 nor exd6 cannot be the last move - why not? Looking at whether a side can promote or not is generally not how to start the analysis - analysing the inventory and pawn captures is easier to do first.

Also, to show that the position is legal, it helps to make a proof game for the position: start with the initial array of pieces on the board, and make legal moves to reach the position. This will fully convince yourself that the position is legal. (If you are more experienced with retros, you may just post the critical ending moves, but your starting position must be legal too, and shows that the pieces can easily get out of their configuration.) If you think the position is illegal, you could write an illegality proof (similar to how you wrote a [faulty] legality proof for this position, but showing the opposite, that the position cannot be reached legally).

Retro problems are difficult to solve for many people, but you have the right approach and a good start. I believe you can solve this one!

The second problem is difficult too, since it is not clear at first where black's several missing pieces were captured, so it seems they could be captured anywhere, especially the queen. But then again, making a proof game to this position might help you gain an understanding about the problem, and why there is only one square where the queen could be captured. Your "fix" wouldn't work though, as the queen could be captured on almost any square. There is a reason why the white pawns are precisely placed there...

This position is very tough though, and it seems that you are stuck, so here are some hints:

• How does white's king get to f7?
• How do the pieces at the top (ranks 6-8 and g5) get there legally?

I realized I can rule out 0...exd6 since the Black bishop needs to escape, and 0.Nxb7 since there ain't enough material.

You can eliminate 3 more of your last move possibilities, as black cannot retract exd6 yet until their dark-squared bishop gets back home on f8. You also mentioned that white cannot promote because it does not have a capture left: does this tell you anything about this pawn? How was it captured?

Once you have analysed the captures properly, another thing to think about is how the pieces reach their positions - these are called retro-cages. For example, how do the pieces in the a5-a8-d8-d5 square get there - what was the last move which locked the cage? Similar logic with the pawns, h1 and h3 in the bottom right corner - what move locks that cage?

I did try yesterday to build a proof game to show for the first position but I haven't succeed yet. I had already figured the g1-h4 cage is locked by fxg3. I have gotten somewhat close to replicating the position, but had trouble with the king in the a5-d8 cage (which is a big deal), which makes me think my pawn moves were incorrect and I need another approach for the a5-d8 cage.

Still cooking .

Doing a bit more retrograde analysis first would be useful for you on your way to constructing a proof game for the position. The analysis will help you figure out the specific move orders, how to reach the cages, what the captures were etc. It is much easier to develop a strategy with this analysis, rather than playing random moves and not knowing what to do.

Yes, it is legal.

That is correct, BigDoggProblem! Those were the last moves I had in mind, well done. A nice try is -1. d5xBe6?, but this turns out to be one move too slow for black, causing white to run out of pawn moves at the end. Uncapturing the white a-pawn is key to avoid white from running out of moves, and only the black rook can get there without the white pawn getting in the way.

The idea behind this was to create a position without bishops but force a bishop promotion to happen. Making the last move be PxB would be trivial for experienced solvers, so I tried to improve on this. Eventually I got lucky enough and discovered this position, which I thought would be a harder challenge.

Have you tried the second problem?

bQ was captured on e5. During retraction, a black unit must sit on e5 for a few moves. If it was a black N, white would be in check.

One further comment: the black pawn can only retract back to a6. wK must have entered thru b6.

Also correct. The rook must get back home to a8 as quickly as possible too, which is why it was captured at d6. Anyway, that’s both problems solved, fantastic work!

@KlekleLegacy: You might wonder why I asked you to make a proof game after you claimed that there were multiple possibilities for the first position. This is just to show you that if you think there are multiple releases for a position, you would struggle to make a proof game via these releases; there is an illegality which prevents you from reaching the position this way (unless you can make a proof game - then the position is cooked!). In that case, it would require you to re-analyse the position and find out why it is impossible with other releases.

Just my advice to you when solving retros. But usually though, if you think you find cooks, it means you need to do more analysis. The proof game is just if you’re unsure and need further convincing that the “cooks” don’t work.