Black and White

ceriani puzzle

Luigi Ceriani published this curiously ambivalent retrograde puzzle in Europe Echecs in 1960. White is to mate in two moves.

The answer turns on whether White can castle kingside and whether Black can castle queenside. Castling is always deemed to be legal unless it can be proven otherwise. The question of White’s castling comes down to the origin of the rook on a6. If that started on h1, then White may not castle because the rook that’s currently on h1 obviously must have moved in order to get there. If the rook on a6 started on a1, then again White may not castle, because in that case the rook must have got to its present position via e1, since the pawn originally on a2 can have reached its present position on b3 only after the knight on a1 had itself moved there from b3.

That means that if the rook on a6 is not a promoted piece, White cannot castle. If it is a promoted piece, then Black cannot castle, because the white pawn that was promoted must have passed over either d7 or f7 first, which would have forced the black king to move if it had been on its original square. Hence either castling by White or castling by Black is impossible.

Well, if castling by Black is impossible, then White can win by castling himself, since then Black has no escape from 2. Rf8#. And if castling by White is impossible, then White can capture the b5 pawn en passant (followed by mate with the queen), because if Black’s king and rook have not moved then Black’s last move must have been b7-b5. (His last move cannot have been b6-b5 because that would leave White no possible previous move. As it is, with Black’s last move being b7-b5, White’s preceding move must have been R[c6]xa6+.)

(Via John M. Rice, An ABC of Chess Problems, 1970.) (Maybe I’m being obtuse, but isn’t it possible that neither side can castle? In that case both proposed mates fall apart and I don’t see how White can succeed.)

02/03/2020 UPDATE: Ach, I’d just given the answer to my own question: Castling is deemed to be legal unless it can be proven otherwise, and it can’t be proven that neither side can castle. (Thanks, David and Daniel.)


Reader Jack McLachlan found this curious entry among the marriage notices in the Scots Magazine of January 1790:

At Newburn, near Newcastle, Mr William Dormand, to Miss Hannah Hoy, of that place. The ceremony was attended by the father, mother, brother, sister, aunt, nephew, two husbands, and two wives, and yet there were only four persons present at the marriage.

No explanation is given. How is such an arrangement possible?

Click for Answer

Moving Art

The 2018 Halloween parade in Kawasaki, Japan, included a procession of famous paintings. The group took home the year’s grand prize, around $4,400. (The last entry is a reference to Cecilia Giménez’s 2012 failed restoration attempt of Elías García Martínez’s Ecce Homo.)


“Lion-Eating Poet in the Stone Den”

Chinese-American linguist Yuen Ren Chao composed this passage in classical Chinese; when read in modern Mandarin, every syllable has the sound “shi,” with only the tones differing.

In a stone den was a poet called Shi Shi, who was a lion addict, and had resolved to eat ten lions.
He often went to the market to look for lions.
At ten o’clock, ten lions had just arrived at the market.
At that time, Shi had just arrived at the market.
He saw those ten lions, and using his trusty arrows, caused the ten lions to die.
He brought the corpses of the ten lions to the stone den.
The stone den was damp. He asked his servants to wipe it.
After the stone den was wiped, he tried to eat those ten lions.
When he ate, he realized that these ten lions were in fact ten stone lion corpses.
Try to explain this matter.

Aaron Posehn gives an explanation, including the full text in Chinese, here.

(Thanks, Brad.)

Marden’s Theorem
Image: Wikimedia Commons

If f(z) is a cubic polynomial with complex coefficients, and if the roots of f are three distinct non-collinear points A, B, and C in the complex plane, then the roots of the derivative f′ are the foci of the unique ellipse inscribed in triangle ABC and tangent to the sides at their midpoints.

The theorem is named for Morris Marden, but it had been proven about a century earlier by Jörg Siebeck.

(Dan Kalman, “The Most Marvelous Theorem in Mathematics,” Math Horizons 15:4 [April 2008], 16-17.)

An Early Voice

On October 21, 1889, Prussian field marshal Helmuth von Moltke the Elder made two audio recordings on Thomas Edison’s new cylinder phonograph. The first contains a congratulatory message to Edison and an excerpt from Faust, the second a line from Hamlet.

This is the only voice recording we have of a person born in the 18th century — Moltke had been born in 1800, technically the last year of that century. Ironically, he had been known as der große Schweiger, “the great silent one,” for his taciturnity.

Podcast Episode 282: Helga Estby’s Walk

In 1896, Norwegian immigrant Helga Estby faced the foreclosure of her family’s Washington farm. To pay the debt she accepted a wager to walk across the United States within seven months. In this week’s episode of the Futility Closet podcast we’ll follow her daring bid to win the prize, and its surprising consequence.

We’ll also toast Edgar Allan Poe and puzzle over a perplexing train.

See full show notes …

Applied Chemistry

On his May 1997 final exam at the University of Oklahoma School of Chemical Engineering, a Dr. Schlambaugh asked, “Is hell exothermic or endothermic? Support your answer with proof.” Most students based their responses on Boyle’s law, but one gave this answer:

First, we postulate that if souls exist, they must have some mass. If they do, then a mole of souls must have a mass. So at what rate are souls moving into hell and at what rate are souls leaving? I think we can safely assume that once a soul gets to hell it does not leave. Therefore, no souls are leaving. As for souls entering hell, let’s look at the different religions that exist in the world today. Some of the religions state that if you are not a member of their religion, you will go to hell. Since there are more than one of these religions and people do not belong to more than one religion, we can project that all souls go to hell. With the birth and death rates what they are, we can expect the number of souls in hell to increase exponentially. Now, we look at the rate of change in the volume of hell. Boyle’s Law states that in order for the temperature and pressure in hell to stay the same, the ratio of the mass of the souls to the volume needs to stay constant. (1) If hell is expanding at a slower rate than the rate at which souls enter hell, then the temperature and pressure in hell will increase until all hell breaks loose. (2) If hell is expanding at a rate faster than the increase in souls in hell, then the temperature and pressure will drop until hell freezes over. So which is it? If we accept the postulate given to me by Theresa Banyan during Freshman year, ‘It will be a cold night in hell before I sleep with you’ and take into account the fact that I still have not succeeded in having sexual relations with her, then (2) cannot be true. Thus hell is exothermic.

“The student, Tim Graham, got the only A.”

(Dave Morice, “Kickshaws,” Word Ways 31:2 [May 1998], 140-149.)

01/28/2020 This is a legend, apparently starting at the Taylor Instrument Company in the 1920s and accumulating some entertaining variations since then. The text of the Applied Optics piece is here. (Thanks, Dan and Pete.)

An Unexpected Party

J.R.R. Tolkien received this letter in March 1956:

Dear Sir

I hope you do not mind my writing to you, but with reference to your story ‘Lord of the Rings’ running as a serial on the radio under the item on the programme ‘for the schools’ Home Service once a week in the afternoons I was rather interested in how you arrived at the name of one of the characters named Sam Gamgee because that happens to be my name. I haven’t heard the story myself not having a wireless but I know some who have, one being my nephew, bearing the same surname, who is a school teacher and it caused a laugh among his class when it came on. Another, my great neice and the latter’s daughter 9 yrs of age a pupil at a different school, also heard it and caused some surprise among the class when it came on at her school. I know it’s fiction, but it is rather a coincidence as the name is very uncommon, but well known in the medical profession.

The above address is my brothers as I have no permanent address.

Yrs faithfully

Sam Gamgee

Tolkien wrote back, “It was very kind of you to write. You can imagine my astonishment, when I saw your signature! I can only say, for your comfort I hope, that the ‘Sam Gamgee’ of my story is a most heroic character, now widely beloved by many readers, even though his origins are rustic. So that perhaps you will not be displeased by the coincidence of the name of this imaginary character (of supposedly many centuries ago) being the same as yours.”

He later said, “For some time I lived in fear of receiving a letter signed ‘S. Gollum’. That would have been more difficult to deal with.”