The Castle of Chess Vampires

I hope you had a nice Halloween! Let me challenge you with the following somewhat unusual chess puzzle.

Your goal is to "adoube" the ambiguously placed rook. Should it be on g1 or on h1?

M. Ambrona, December 2023 (Madrid). Published at The Hopper Magazine - Issue 5.

Yes, only one of the two options is possible for the position to be legal (reachable in a game of chess).

Please, give it a try!

Hint: What were the last moves in this game?

But what does this have to do with Halloween?

Solving this puzzle requires a subtle parity argument, one that gives birth to a thrilling realm in chess composition: chess vampires.

A chess vampire is a legal position without a mirror image (whose mirror image is illegal). Check out our first post on chess vampires for more details about how the mirror image of a position is defined and to learn about these unique creatures.

The Vampire's Castle

Last year we encountered vampires where en-passant is possible. We even searched the woods and discovered that vampires with promoted pieces exist, but they can only be found when the night is late, almost at dawn. Still, one mystery remained unsolved.

Could the legend be true? Could there truly be a castle of vampires? It is said to be hidden deep within the dark, only revealing itself under the pale light of a full moon. Tales of ghostly apparitions have fueled speculation for centuries. Some claim to have seen the castle's silhouette through the trees. Others insist it is merely a myth designed to keep curious souls away. Despite numerous expeditions, no one had ever found it.

Today, reader, you have the opportunity to discover it for yourself. The solution to the above puzzle is a castling vampire, a vampire that has survived a castling move. What an incredible find!

Solution

Following the hint, let us forget for a second about the rook and ask: what were the last moves in the game that led to the puzzle position?

It is Black's turn, so White moved last. There are many apparent possible retractions for White, but what was Black's previous move? If it was a7-a6, what was Black's move before that? We are in a hurry to make a Black knight reappear on the board that could keep retracting for Black.

Black's knights were captured on b3 and c3.

• We need 3 White retractions to make a Black knight reappear on b3. Too many...
• We cannot retract dxc3 until the white bishop (in expedition) goes back to c1...

It seems we have reached a dead end. However! We can gain an extra retraction if we make a black pawn reappear on h6 when retracting the bishop.

It is not hard to get convinced that the last 5 moves (plies) in this game must have been as follows (we are still disregarding the rook):

We can now conclude with our usual counting argument. Ignoring the rook, to reach the position right before dxc3:

• White performed an odd number of moves (an even number of knight moves + one pawn move axb3).
• Black performed an even number of moves (squares b3 and c3 have different colors).

However, in a position with White to move, both players must have performed the same number of moves. This means, we need to flip White's parity, which can only be done by placing the mysterious rook on g1.

Conclusion

This composition solves the long-standing open question of whether there are vampires where a side has castled. I am still amazed by the fact that they exist.

This has implications for our classification of vampires by "clans," but that's a tale for another time.

I hope you enjoyed the post! If you did, make sure you share it with your friends! All the best!