Christmas Puzzles: solutions (2)

by Frederic Friedel
1/4/2021 – In our December 31 puzzle page we showed you problems ranging from mate in one to mate in 203 – expecting this record from decades ago to have been broken. And indeed it was: there is now a direct mate problem in which you have to play 226 accurate moves to mate the opponent (i.e. it is dual-free). In our second solutions page we also provide the answer to the ominous train problem, which has eluded some of the brightest minds in the world.

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The twin problems by artist Abraham Jacob Bogdanove (reconstructed from a painting by Luke Neyndorff) were fairly simple.

White to mate in two moves
White to mate in one move

In both diagrams there is an engine waiting to play defensive moves and prevent White from mating in two and one moves. So it will be fairly easy for you to follow the solutions:

Problem 1: 1.Ne2 Kxd2 (1...cxd2 2. Nf4#; 1... Ra1 2. Nf4#; 1... Nc2 2. Nxc1#) 2. Nf4#. 
Problem 2: 1.exf8=N#.

To help you get over the one-mover we showed you two unusually long problems by James Malcom. In the first Black will gladly move his bishop between g1 and h2, unless we force him to play something else – which should be a mate.

In the second problem White's goal is to castle long, while Black is bent on preventing exactly this! It turns out that White needs 67 moves to force Black to allow O-O-O. This sounds insane, but it is quite logical once you have understood the basic logic.


So who is the author of these imaginative many-move problems. Some elderly problemist with decades of experience, you may think? Well, think again.

James Malcolm is a 17-year-old high-school student! He lives in Iowa, USA, and just like chess enthusiasts his age, loves playing online games. But he is different in one aspect, he also takes a lot of pleasure in composing chess problems, and he is especially fond of record tasks, jokes, and anything related to the three special moves of chess: castling, promotion, and en passant.

A rather uncommon interest for a young man!


Christmastide Solving Contest

On December 25 our colleagues at ChessBase India staged a solving contest in which around a large number of enthusiasts took part. They were not just from within India, but also from various parts of the world, like Germany, Romania, Russia, USA – to name just a few! What was surprising was the outstanding quality of these entries. At least 17 readers who wrote in had perfect solutions, and twice more scored more than fifty percent. This is what a solution to the 76-mover looks like in Hindi.

How many moves to mate?

In 1986 John Nunn sent us a chess problem by Danish composer Walther Jørgensen. It was, at the time, the longest dual-free direct-mate with a legal starting position that had ever been devised. You can replay this astonishing 203-mover on our replay board below, and understand everything, thanks to the comments by John Nunn.

On our December 31 puzzle page I predicted that this 44-year-old record would probably have been broken. Within a day problemist Werner Keym informed me that it had indeed been increased to 226 moves – by the same Walther Jørgensen, using the same basic pattern.

The picture of Walther Jørgensen (1916-1989) was taken from Thema Danicum, the publication of the Danish Chess Problem club.


Note that you can click the Autoplay icon to have the entire solution replayed for you – while you sit back and enjoy your coffee or mate tea?! Shift+Autoplay click is slowest replay, Ctrl+click is faster and Alt+click is fastest.

A logical non-chess problem

What have I done? Ten years ago, at a German railway station, I had asked young grandmaster Anish Giri why the overhead power lines ran zigzag instead of straight. I posed this innocent question to our readers.

Looking from above (even from a bridge) you can clearly see that the power line trace a zigzag path above the trains, and that this has been done purposefully: the masts have longer and shorter arms.

Anish was baffled, and when I brought it up a few weeks ago he still didn't have an answer. Neither did a dozen 2750+ GMs, who have been working on the problem for weeks now. Some days ago Anish got it, but only after I had helped him – I gave him a video showing the bow collector (pantograph) getting power from the overhead line. You can watch some of this seven-minute video and see if you also hit on the answer.

Interestingly two readers had the correct solution. One of them, Albitex, is an electronic technician and who worked for a railway signalling company. No wonder. Also Vishy Anand solved it – his father worked in the railways. But even highly educated scientists – quantum physicists, astronomers, mathematicians – as well as the super-GMs – didn't even get close.

Now for the answer. The reason for the zigzagging is incredibly simple: if the power wire was straight it would cut through the bow collector, like a chain saw, in a couple of miles! The wire need to glide back and forth over the collector for it to last. Watch the video above.

This is what would happen after a mile or two if the power line were straight. The wire would stay in the groove and continue to cut through the bow collector. 

Sorry to have spent such a lot of time on this – it spun unexpectedly out of control. And now a dozen close friends will be cursing me. I must be more careful in the future. For the “gimme-more” friends and readers here are a few more non-chess New Year’s 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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enfant enfant 1/9/2021 11:39
Once again, I enjoyed the problems this year. However late I got to try solving them!

I would agree the railway problem is not really a logical non-chess problem. There are
other reasons, such as arcing for instance, that could have been the reason for the
notching, and the zigzag design.

Here is a good logical non-chess problem:

1) Imagine three circles of different sizes on a plane, not overlapping.

2) For each pair of circles, draw the (two) lines which are tangent to both circles,
and mark the point at which the two lines cross each other. Call this the crossover
point for that circle pair.

3) Fact: the three crossover points for the three circle pairs will always lie on the same

Although you can prove 3 mathematically, ( either analytically or geometrically),
there is a very simple LOGICAL argument also why it must always be true.

What is that simple logical argument?
Frits Fritschy Frits Fritschy 1/5/2021 11:59
It's the same with sharpening a chisel on a grinder: you should move the chisel back and forth to prevent the stone being hollowed out in the middle.
Joshua Green Joshua Green 1/5/2021 02:38
I'm not a close friend of yours, nor will I be cursing your name. However, I do disagree with your (implicit) characterization of the train riddle as "a logical non-chess problem" that anyone should be able to solve with careful thought. For starters, the "View from above" is a far clearer demonstration of what you're referring to than anything you've provided previously, and it was hardly fair to hold that particular graphic back. More relevantly, it seems that this explanation hinges on some specific knowledge, e.g.:
1) The materials used will wear away at each other to a significant degree.
2) The above wear can be reduced by zig-zagging the wires.
3) Though (2) doesn't completely eliminate that wear, its benefits are sufficient to override the costs (such as longer wires).
Sorry, but that's too much for me to consider this a purely logical puzzle, especially when compared to other logical puzzles that you've shared. I will grant that this is an interesting factoid, though.
rgorn rgorn 1/4/2021 11:52
If you rub two materials against each other, abrasion will mostly affect the softer material. Installing, repairing, and maintaining an overline contact system is time consuming and expensive, replacing pantograph strips every month or so isn't. So they use a very hard copper alloy for the overline wire and rather soft graphite for the pantograph strips. This increases the lifetime of the precious part at the cost of the inexpensive and easily replacable one. The zig-zag line is just an optimization of this idea that makes it feasible. (And the lubricating effect of graphite particles you mentioned is of course also helpful.)
Frederic Frederic 1/4/2021 10:08
@Chaber: "There is also cutting technology based on this rule - wire cutting." Yes, here is a picture of a machine that cuts through metal with a wire: And here is someone cutting through a log with a wire:
@rgorn: Pantograph strips are made of steel, copper alloy, pure carbon, and metal-impregnated carbon. Carbon strips are proved to be the most suitable material to copper and copper alloy contact wires. Carbon strips have good self-lubrication in high-speed pantographs. They replace the strip every few weeks or months.
Gad, what's happening? I am becoming an expert in electric trains and pantographs...
Chaber Chaber 1/4/2021 09:26
Zig-zag cable will not wear too quick because its local time contact takes miliseconds while pantograph (collector) is in constant contact.
There is also cutting technology based on this rule - wire cutting.
rgorn rgorn 1/4/2021 06:38
Followup trick question to the zig-zag problem. Why is the collector made of such a weak material (graphite)? Isn't it obvious that even with this zig-zag it will wear off quickly and has to be replaced constantly?