A Christmassy Delight

by Frederic Friedel
12/28/2023 – Problemists love to construct problems in shapes that symbolize something auspicious. The great composer (and World Championship candidate) Pal Benkö sent us a problem shaped like a candle. Today we bring you two problems shaped like Christmas trees. They are not too hard, which we cannot say about the third problem, which taxes the brain.
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A decade ago, our dear friend Pal Benko, one of the most inventive problem composers in the world, had a special Christmas Day treat for our readers.

Pal Benkö, 2015

White to play and mate in five

Pal's problem symbolized a Christmas candle. It is now easy to solve, as we can testify. Get a chess board and pieces – they are there on the shelf somewhere – and try to work out the solution. If that fails you can use computer assistance.

This year our problem expert Anirudh Daga sent us two Christmas Tree problems for you to solve. They are not his own compositions, and the source will be given to you together with the solutions we provide in the first week of January. Let us start with a direct mate:

Big hint: the perfectly symmetrical tree is not in the center of the board. That makes the problem correct. Try to figure out why. And enjoy the mates that follow the key move.

And here's another, shaped even more like a Christmas tree:

How can Black (to play) and White cooperate to get the black king mated in three moves?

Were the above two problems too easy. Then here is a helpmate that is harder, especially the very deep question that is attached to it:

If you are good at these things, you may find a way to construct a position in which the black king is mated after two move (by each side). You can make them on the diagram above –remember, it is Black who makes the first move.

If you have a very agile mind, you can find a second solution that also leaves the black king mated. So apparently the problem has two solutions, which is perfectly normal in helpmates, as long as the solutions are strategically different. So we could leave it at that – we can say bravo, you have solved the problem. 

But if you are a true problem expert, then there is a further question for you: why is only one of these two solutions legal? This requires deep retroanalytical reasoning, and is quite difficult to work out.

The solutions to all three problems will be provided in the first week of January, with video explanations by our consummate problem expert, Anirudh Daga. Once again, please do not give away any solutions in the open discussion section below.

Previous Christmas 2023 puzzles

Editor-in-Chief emeritus of the ChessBase News page. Studied Philosophy and Linguistics at the University of Hamburg and Oxford, graduating with a thesis on speech act theory and moral language. He started a university career but switched to science journalism, producing documentaries for German TV. In 1986 he co-founded ChessBase.

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Frits Fritschy Frits Fritschy 1/1/2024 04:41
I think I got the solution to the helpmate in 2, with a proof game for the only solution, the other solution being illegal.
JoshuaVGreen JoshuaVGreen 1/1/2024 03:15
@Frits Fritschy, I too recall seeing that #2 before. IIRC, it was here at ChessBase but with the all-important wPe7 omitted.
Frits Fritschy Frits Fritschy 12/30/2023 04:23
Of course for the right solution, the position of the helpmate should be legal as well... although normally, it's the composer's job to proof that.
Frits Fritschy Frits Fritschy 12/30/2023 09:44
Edward, I can assure you that there seem to be two solutions where white mates on the second move (however, only one of them is legal).
edwardsp edwardsp 12/29/2023 11:59
A minor point of clarification. In the two-solution helpmate above, does the question require that both solutions provide for White to give mate in 2 moves (with Black making the first move)? I can find a second helpmate, but it requires more than 2 moves by White.
Michael Jones Michael Jones 12/29/2023 12:49
The convention that a direct mate problem must have a unique solution makes the first one a lot easier - the number of unique first moves available (i.e. moves whose reflection is not possible) is very small, which limits the possibilities which require checking. I'm sure if reflected solutions were "allowed", it would be possible to create a similar problem which was much more difficult.

In the third problem, it is clear what the reason must be that one of the solutions is illegal - there are only two cases in chess where it is not immediately obvious from a glance at the position whether or not a particular move is legal. Proving that it is so is much harder: there are enough clues in the position to deduce a considerable amount about how it was arrived at, but I haven't yet managed to follow a line of reasoning to reach the desired result.
Frits Fritschy Frits Fritschy 12/28/2023 09:54
I don't know where, I don't know when, but I've seen (and solved) the mate in two before.
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