A Hazy Mate

smullyan undetermined mate

Raymond Smullyan presented this oddity in his Chess Mysteries of Sherlock Holmes in 1980. Suppose we come upon this abandoned chess game. Can White mate in two moves? The answer seems to be yes. If Black can’t castle, then White can play 1. Ke6 and then promote his g-pawn, giving mate. If Black can castle, that means that neither his king nor his rook has yet moved, and hence he must just have moved his pawn to e5. That permits White to capture the pawn en passant. Now if Black castles then 2. b7 is mate, and if he plays any other move then the g-pawn promotes. Either way, White mates Black on his second move.

But that’s odd. We’ve decided that a mate in two exists, but we can’t show it — and we don’t even know how White commences!

(F. Alexander Norman, “Classicists and Constructivists: A Dilemma,” Mathematics Magazine 62:5 [December 1989], 340-342. See Donkey Sentences.)

02/17/2025 UPDATE: Reader Eugene Kruglov points out that 1. Ke6 works in Smullyan’s position whether or not Black castles — if he does, then 2. a8=Q is mate. The position below works as Smullyan intended — when Black castles, only the en passant capture leads to mate in two. (Thanks, Eugene.)

kruglov improvement

| Oddities

One World at a Time

Thomas Jefferson to the Rev. Isaac Story, Dec. 5, 1801, on the afterlife:

When I was young I was fond of the speculations which seemed to promise some insight into that hidden country, but observing at length that they left me in the same ignorance in which they had found me, I have for very many years ceased to read or to think concerning them, and have reposed my head on that pillow of ignorance which a benevolent Creator has made so soft for us, knowing how much we should be forced to use it.

“I have thought it better, by nourishing the good passions & controlling the bad, to merit an inheritance in a state of being of which I can know so little, and to trust for the future to him who has been so good for the past.”

| Death · Religion

Shipshape

https://commons.wikimedia.org/wiki/File:Cmglee_Cambridge_Trinity_College_punt_names.jpg
Image: Wikimedia Commons

These are the punts of Trinity College, Cambridge, moored on the River Cam. What is the significance of their names?

Click for Answer
| Puzzles · Trivia

Escort

https://pixabay.com/photos/moon-full-moon-sky-night-sky-lunar-1859616/

Steaming from New York to the Azores in 1867, Mark Twain noted a curious companion overhead:

We had the phenomenon of a full moon located just in the same spot in the heavens at the same hour every night. The reason of this singular conduct on the part of the moon did not occur to us at first, but it did afterward when we reflected that we were gaining about twenty minutes every day because we were going east so fast — we gained just about enough every day to keep along with the moon. It was becoming an old moon to the friends we had left behind us, but to us Joshuas it stood still in the same place and remained always the same.

(From The Innocents Abroad.)

02/11/2025 Reader Catalin Voinescu writes:

Mark Twain is talking absolute nonsense here.

The moon is in (almost) the same phase as seen from all over the world. It rises and sets at roughly the same local time, regardless of longitude, and the relation between phase and time of day when the moon is visible is the same everywhere (the full moon peaks at midnight; a week later, the last-quarter moon rises around midnight, peaks in the morning and sets around noon; and so on).

Even ignoring moon phase and local time, the moon rises, peaks and sets almost 50 minutes later every day, so gaining 20 minutes every day would not be enough.

(Thanks, Catalin.)

| Science & Math

Narrow Meaning

https://archive.org/details/strand-1899-v-18/page/238/mode/2up?view=theater

Reader J. William Hook submitted this curiosity to the Strand in August 1899. Holding the page level with the eyes foreshortens the characters and reveals a love poem:

Art thou not dear unto my heart?
Oh, I search that heart and see
And from my bosom tear the part
That beats not true to thee.

But to my bosom thou art dear,
More dear than words can tell,
And if a fault be cherished there,
‘Tis loving thee too well.

There seems to have been a little vogue for this kind of thing — C. Field submitted a similar image three months later.

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Small Talk

(Until William Herschel’s advances in telescopes, stars seemed to have “rays” or “tails.”)

At a dinner given by Mr Aubert in the year 1786, William Herschel was seated next to Mr Cavendish, who was reputed to be the most taciturn of men. Some time passed without his uttering a word, then he suddenly turned to his neighbour and said: ‘I am told that you see the stars round, Dr Herschel’. ‘Round as a button’, was the reply. A long silence ensued till, towards the end of the dinner, Cavendish again opened his lips to say in a doubtful voice: ‘Round as a button?’ ‘Exactly, round as a button’, repeated Herschel, and so the conversation ended.

— Constange A. Lubbock, The Herschel Chronicle, 1933

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