Your first retro problem

Welcome to the second part of the retrograde analysis tutorial series. We will look at a simple and classic problem that you can try to solve.

Before we begin, two reassurances. Don’t worry if you can’t solve it at first. I took a terribly long time seeing it myself when I first encountered it as an inexperienced (with regard to problems) chessplayer.

And certainly don’t worry if the solution looks wordy. It’s not because it’s complicated! In this series I will try to explain every step of reasoning in detail; after all, it’s a tutorial. Solution pages in problem magazines tend to be very concise and omit “elementary” details, which is excellent to avoid lengthy paragraphs; we will eventually reach that point.

A simple problem

So, as promised, for your first retro problem we have an instructive classic.

You’re told that white is to move in the position, so black must have just moved. Your task is to figure out what that last move was. Feel free to stop here for a while and try finding the answer yourself.

Although I said it’s simple, this problem can be challenging for those not used to retros. There are a few common mistakes most new solvers make when solving this. Read the below hints before checking the solution, since a few common mistakes are caught there!

First of all, it’s clear that black’s last move must have been with the black king. (It can’t be with a black piece that got captured, since black made the move leading to the diagram. Convince yourself of this.)

Where did the black king come from? From b7 or b8? That would have been a position with the two kings adjacent to each other, which is illegal! So the black king didn’t come from those squares after all. That leaves the square a7. So you might be tempted to say “The black king went from a7 to a8,” and leave it at that.

If you noticed the bishop on g1 would check the king on a7, good! It’s not illegal in general for the black king to have come from a square when it was in check (please convince yourself of this: the black king moved from a7 to a8 escaping a check from the bishop). However, we should always ensure that the position was legal. How did white give check with the bishop on g1?

…It is perfectly normal to be confused here. White couldn’t have moved the bishop to give the check, not from h2 (the white pawn is already there), and not from along the a7-f2 diagonal (where it would have been giving check to black’s king with white to move). It’s also not a promotion, as the white bishop is indeed on g1 and there is no silly trick like an upside-down board here. (There is never any such silly trick. We’d tell you if your task is to figure out which way the board is.) So… is the problem actually impossible?

I assure you there is a solution. Please convince yourself once again that the arguments we made above are correct! Yes, the black king came from a7, but go back to the problem diagram anyway (black king on a8) and think again. If you need a final hint, here you go: the black king indeed went from a7 to a8, but did it simply move from a7 to a8?

Solution

I will now reveal the solution. All the above reasoning is correct, but we overlooked something. “The black king went from a7 to a8,” yes, but there can be two kinds of moves: non-captures, and captures! The black king could have captured something on a8. Does that solve the impossible bishop check? Go through the possibilities for the captured unit one by one: not a pawn (pawn on the 8th?), not a bishop, rook nor queen (they don’t help solve the bishop check)… a knight? Yes! That gives white the last move of Nb6*a8+, a discovered check from the bishop on g1! (This last knight move could have been a simple move or a capture of something; we can’t tell which.)

The solution is thus: Black’s last move was Ka7xNa8.

Learning points

In the process of solving this problem, we’ve already touched upon a few important points. I’ll elaborate a bit more below:

Legal moves and positions

The concept of “legality” lies at the heart of all retro problems.

A move is legal if it follows the rules of chess.

A position is legal if there is a way to reach it from the normal chess starting position via legal moves.

Outside of retro problems, almost all positions you will ever see are easily shown to be legal or illegal. Retro problems however deal with positions which are right on the edge, where it is difficult to prove it to be either. Once we have to consider side-to-move, castling rights and en passant rights, this will be very true. (That’s for later on, though).

Move notation

A completely-described move should indicate if it was a capture or not, and if so, which type of piece was captured.

As seen in the above problem, saying “The last move was Ka8” is too vague, and even specifying “a7 to a8” is insufficient. The solution to the problem can only be Ka7xNa8, specifying the piece moved (king, K), the start and end squares (a7, a8), that it was a capture (x), and the piece captured (knight, N). This is also sometimes written as Ka7xa8(N).

For a move without capture, we would write Ka7-a8. For a move that could be either a capture or non-capture we write Ka7*a8. Finally, for a capture of an unknown unit, we write Ka7x~a8 or just Ka7xa8.

Checks

You might have encountered difficulties while reasoning about the checks in the above problem, especially if you were thinking like this: “the position before was like this. Then black played this. So before that white played something, but black was in check before that… or was it after that?”

It’s very easy to get lost when thinking in terms of side-to-move and playing moves forward while going backwards in time, so to speak. The human brain struggles to go in both directions at once.

Wow is it hard to think in reverse.

Indeed it is! So we use a little trick. Instead of thinking about regular forward moves while going back, we think about unplaying moves backwards while going back. No cognitive dissonance there.

This skill of retracting moves is the key to dealing with retros. Knowing how to do it makes finding the solution to problems like the one above almost trivial. Think of it as learning a new set of rules for a different game that happens to look very much like regular chess. This will be our topic for next time.