The Magic of Logic (13)

The electric train riddle and more

Over Christmas I traditionally run a chess puzzle contest on the news page of my company. The problems have to be “computer resistant” — it has become trivially easy, and also very tempting, to simply switch on a “chess engine” to get the solution in seconds. So I use unorthodox variants of the game, like “checkless chess” (checks are not allowed except when it is checkmate), or selfmate (White forces Black to mate him, Black tries his best to avoid that), or add-a-piece. Let me give you a taste of this last one:

In these “twin” problems (by Bengt Giöbel) you are asked to add a white queen on the board and then mate Black in one move. The additional question is: why are the solutions quite different in the two diagrams that are clearly 1:1 horizontal reflections?

The answer is that the queen must be placed to the left of the king to make the position “legal”. Since all the pawns are on their original squares the queen could never have reached a square to the right of the king — or moved to any square in front of the pawns. So the solutions are: +wQc1 and 1.d3 mate and +wQa1 and 1.b3 mate.

The final instalment of my Christmas puzzles dealt with very short problems, like a difficult mate in one move, and very, very long ones. The record is a forced mate, with no “duals” (alternate lines of play), in 226 moves! And at the end of the instalment I added a little non-chess problem. It was the ten-year anniversary of my giving it to a young super-talent.

In 2010 I was at a railway station in Emsdetten, Germany, with a 14-year-old lad who had just become a full chess grandmaster. The lad was Anish Giri, who is currently number 11 in the world.

The electric trains passing by had bow collectors (or pantographs) that drew electricity from power lines (catenaries) above.

Looking at the power cables, we could clearly see that they did not run in a straight line. They were mounted in a way that made them trace a (mild) zigzag path:

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

My question to Anish was: why did the overhead contact wire not follow a straight line? Why did it have a zigzag pattern, as shown in the picture above? He could not tell me why. This was the problem I added to my December 31 Christmas Puzzle quiz. And all hell broke loose.

I need to mention that I have been trying to find out whether chess super-talents are generally smarter than regular kids? Now other exceptional chess players, most with GM titles and under 15 years old, but some adult GMs in the top of the world rankings, were confronted with this logical problem. I also gave it to a math professor, to a quantum physicist, to the head of a project group at Intel, to a doctor of engineering — and generally numerous boffins in my acquaintance. Just two got it right: the Prof after a day of pondering, and the engineer after a few dozen milliseconds. And one reader: Turns out he is an electronic technician and who worked for a railway signalling company.

Just three? This amazed me: shouldn’t the solution, which is very simple, be immediately obvious to everyone? Perhaps you, dear readers, can figure it out?! Watch a few minutes of this video and draw your conclusions.

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

Groans from around the world. But also “gimme-more” messages. So here are a few additional New Year’s puzzles. Wishing you a bearable 2021.

Another train question

This is what the axle of a train looks like.

The question is: what keeps it on the track, what is the main reason why trains don’t derail? Remember: both wheels are connected and turn at the same speed.

Why doesn’t a train go off the track, even in curves — when one wheel has a greater distance to cover?

Shorties

• A cup of coffee and a biscuit cost $1.10 (one dollar and ten cents). The coffee costs one dollar more than the biscuit. How much does the biscuit cost?
• In a hotel ten maids can clean ten rooms in ten minutes. How long does it take 100 maids to clean 100 rooms?
• Enders starts giving half his money plus 50 cents to Hennes, each day. After five days Enders has one dollar left. How much did he start with?
• You have a glass of red wine and a glass of white wine. You take a spoonful of the red wine from the glass, put it into the white wine glass and mix. Now you take a spoonful of the mixture from the white wine glass and put it into the red wine glass. Which glass has more of the other wine?
• And finally:

I am not giving you the solutions to these problems here. If you cannot get enough of this kind of thing, here are previous articles:

Logic

• The Magic of Logic (1)
• The Magic of Logic (2)
• The Magic of Logic (3)
• The Magic of Logic (4)
• The Magic of Logic (5)
• The Magic of Logic (6)
• The Magic of Logic (7)
• The Magic of Logic (8)
• The Magic of Logic (9)
• The Magic of Logic (10)
• The Magic of Logic (11)
• The Magic of Logic (12)
• Piet Hein and the Soma Cube
• The Café Wall Illusion
• Tricking the brain
• IQ test: weighing the coins
• Lie to your kids — it’s good for them
• He had a dream — a logical puzzle