Vampires in Chess V - Running Water

Happy Halloween! This year, I would like to open with a challenge for you: can you construct a legal position where en passant MUST be possible? That is, a position that would be illegal without the en-passant right.

It is easy to set up a position where a certain pawn moved last. But how can you make sure it was a double step, not a single one?

Take a moment to think about it.

Hint: use a king to prevent the single step.

A classic from 1922

Here is a famous problem by William Langstaff that does it in a cute way:

The answer is yes! If Black cannot castle, 1. Ke6 followed by 2. Rd8# does the job. On the other hand, if Black still preserves castling rights, their last move must have been g7-g5 (from g6 it would have been attacking White's king) and thus White can play 1. hxg6!, mating next move, e.g. 1... O-O 2. h7#.

An extra requirement

The above diagram, with White to move and Black still able to castle, is an example of what we were looking for: a position where en passant MUST be possible.

But what if I asked you to achieve the same goal with both sides still able to castle? This extra condition prevents you from using the king trick.

With this twist, our innocent puzzle suddenly becomes a formidable challenge. To this day, only one technique is known to solve it: summoning a chess vampire.

The legend of the river

In this series, we have searched the woods and found vampires where en passant is possible or where en passant CANNOT be possible, and we even discovered their castle! But our quest is far from over. Today, we are on the trail of a very special specimen: a vampire where en passant MUST be possible. Do they even exist?

Every hunter knows that vampires cannot set foot in running water. A vampire can leap over a river in a single bound, but the leap is fatal: once on the other bank, it vanishes. So vampires always prefer another path, a bridge further down, a way around.

Yet old hunters still tell the tale of a very special vampire. It is said that it reaches the river just before dawn, with no time left to hesitate. It has no choice but to leap. A patient hunter on the far bank could catch a glimpse of it in mid-flight. Many have tried, but no one has ever witnessed such an extraordinary event.

Tonight, my dear reader, you will.

The vampire that had to leap

Here it is, caught in mid-flight, a moment before it vanishes:

Let us uncover its secret together.

Solution

It is useful to first explore where the missing pieces were captured.

• White's queen and light-squared bishop were captured at home, blocked by their own pawns (and the white king never moved, since 3 castling rights still remain). Since Black's pawn on b6 came from c7 by capture, White's missing knight was captured on b6.
• Black's dark-squared bishop was captured at home, while Black's queen was captured by White's f-pawn, which is now on g5.

Importantly, the black queen escaped through c7, so c7xNb6 took place while she was still on d8. This capture also cornered (literally) the remaining white knight on a8, which cannot have moved after that (on c7 it would have checked a king that never moved).

So, after c7xNb6, White had at most 4 moves left, all with pawns (a2-a3 and at most three f-pawn moves). Meanwhile, the black queen had to leave d8 and get captured.

The queen's last journey

Let us consider where the black queen was captured:

• On g3: she needs 2 moves to get there from d8, but White could only make 1 move (with the a-pawn) before having to capture on g3. Not possible.
• On g4: she needs 3 moves to get there, but White could only make 2 moves (with the a-pawn and f2-f3) before capturing on g4. Not possible either.
• On g5: the only option.

To reach g5 in 3 moves (fewer is impossible), she can take 4 different paths:

• c7-g3-g5
• c7-f4-g5
• c7-e5-g5
• c7-c5-g5

The path through g3 is not possible, since with f2 already empty, she would be checking the white king from g3. The path through f4 fails because the f-pawn needs to pass through f4 while she is standing there.

The other two paths are plausible, but they pass through f5, so the black f-pawn arrived there after the queen. Thus, Black's last four moves were 3 with the queen, followed by 1 with the f-pawn. Since White only had 4 moves after c7xNb6, in the challenge position Black made the last move, and it must be White to move (note that the turn had not been specified).

A leap or a step?

Black's last move was f7-f5 or f6-f5. Either way, every possible game goes back to the following position, with the f-pawn on f7 or f6 respectively. Here it is with the f-pawn on f7:

Let us conclude with our usual parity argument. Ignoring the black f-pawn, to reach the position right before c7xNb6:

• White made an even number of moves: the white knights stand on squares of different colors so, together, they moved an even number of times; no other white piece moved (all pawn moves came after c7xNb6).
• Black made an odd number of moves: an even number of knight moves and an odd number of moves with the queenside rook.

Since that position is Black to move, White must have made one more move than Black, so the parities must differ. That only works if the black f-pawn had not moved yet, i.e. if it was still on f7.

So, the answer to the challenge is: Yes! White can capture en passant. And the position would be illegal otherwise!

Conclusion

The challenge position is a vampire (only White could have started the game): a legal position whose mirror image is illegal.

The legend was true: this vampire had no choice but to leap, right in front of the hunter. A moment later the sun rises: whatever White plays, the en-passant right is gone, and with it, the vampire.

Which raises a question I find fascinating: can a vampire where en passant is possible ever survive the next move? Every case I know says no. But that is a tale for another night.

Bonus challenge for the reader

From the above vampire position, find a helpmate in 2.5 moves: find a sequence of moves that leads to Black getting checkmated on White's 3rd move (White starts and both sides cooperate to achieve this task).

There are two solutions. Can you find both? Post them in the comments!

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Have a spooky night!