A Stressful Game

A puzzle by Ezra Brown and James Tanton:

Three gnomes sit in a circle. An evil villain puts a hat on each gnome’s head. Each hat is either rouge or puce, the color chosen by the toss of a coin. Each gnome can see the color of his companions’ hats but not of his own.

At the villain’s signal, all three gnomes must speak at once, each either guessing the color of his own hat or saying “Pass.” If at least one of them guesses correctly and none guesses incorrectly, all three gnomes will live. But if any of them guesses incorrectly, or if all three pass, they’ll all die.

They may not communicate in any way during the game, but they can confer beforehand. How can they arrange a 75 percent chance that they’ll survive?

Click for Answer
| Puzzles

Small World

The Sherlock Holmes story “The Adventure of the Priory School” concerns the Duke of Holdernesse and the kidnapping of his son, Lord Saltire. The family name of the duke is never given in the story, but Holmes mentions in “The Adventure of the Blanched Soldier” that his real title is Duke of Greyminster.

Greyminster calls to mind Lord Greystoke, the title of Tarzan’s father, John Clayton, in Edgar Rice Burroughs’ Tarzan adventures. Greystoke is marooned on the west coast of Africa while investigating a political intrigue there, and his wife gives birth to a son who becomes lord of the apes.

Is there a link here? Did Burroughs discreetly alter Clayton’s title from Greyminster to Greystoke in telling his story?

Writing in the Baker Street Journal in 1960, Princeton English professor H.W. Starr points out that John Clayton is also the name of the driver of the cab in which Stapleton trails Sir Henry and Dr. Mortimer in The Hound of the Baskervilles.

That’s an interesting coincidence. Can Tarzan’s father and the cab driver be the same man? No, the timing doesn’t work: Tarzan’s father was marooned in 1888 and never returned to England, and the John Clayton of Baskervilles appears at 221B Baker Street in 1889.

But the cabbie could be Tarzan’s grandfather. In the Tarzan stories, when Tarzan’s father disappears off Africa, the title passes to his younger brother (the cabbie’s other son, in our hypothesis), and we are told that that son bore a son of his own, William Cecil Clayton. William Cecil Clayton was 19 or 20 in 1909, similar to the age of Lord Saltire, the kidnapped son of the Duke of Holdernesse in “Priory.” Starr writes, “This seems too close a correspondence of facts to be mere coincidence.”

If all this is true, and assuming that Burroughs changed “Greyminster” to “Greystoke,” then John Clayton the cab driver is really the fifth Duke of Greyminster, father of two sons: John Clayton (“Lord Greystoke” in Burroughs’ rendering) and the “sixth Duke of Holdernesse” (in Doyle’s rendering). And the “Lord Saltire” who is kidnapped in “The Adventure of the Priory School” is the latter’s son, William Cecil Clayton, seventh Duke and the first cousin of John Clayton III, who is the eighth Duke of Greyminster and Tarzan of the Apes.

(All this might also help to explain Holmes’ whereabouts during his supposed death in the period 1891-1894 — possibly the British government had sent him to Africa to investigate Greystoke’s disappearance.)

(H.W. Starr, “A Case of Identity, or The Adventures of the Seven Claytons,” Baker Street Journal, New Series X, i, January 1960.)

Philip José Farmer hatched an even more elaborate theory in 1972.

| Literature

The Stairs of Reconciliation

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Image: Flickr

The Burg, the official headquarters of the regional government in Graz, Austria, contains a double spiral staircase, two flights of stairs spiraling in opposite directions that “reunite” at each floor, a masterpiece of architecture designed in 1499.

Bonus: Interestingly, several facades of the building bear the inscription A.E.I.O.U., a motto coined by Frederick III in 1437, when he was Duke of Styria. It’s not clear what this means, and over the ensuing centuries heraldists have offered more than 300 interpretations:

  • “All the world is subject to Austria” (Alles Erdreich ist Österreich untertan or Austriae est imperare orbi universo)
  • “I am loved by the elect” (from the Latin amor electis, iniustis ordinor ultor)
  • “Austria is best united by the Empire” (Austria est imperio optime unita)
  • “Austria will be the last (surviving) in the world” (Austria erit in orbe ultima)
  • “It is Austria’s destiny to rule the whole world” (Austriae est imperare orbi universo)

At the time Styria was not yet part of Austria, so here it would refer to the House of Austria, or the Habsburg dynasty — which historically adopted the curious motto itself.

| Art · History · Language

Intentions

In 1983 Paul Desmond Taafe imported certain packages into England. He thought they contained currency, which he erroneously believed was illegal to import. The packages actually contained cannabis, which was illegal to import. Was he “knowingly concerned in [the] fraudulent evasion” of any prohibition on importing goods?

He was convicted but appealed. “If we describe his action in terms of his own beliefs (about the facts and about the law), it obviously constituted an attempt to commit (indeed, it constituted the actual commission of) that crime,” writes R.A. Duff in Criminal Attempts. But Taafe wasn’t “knowingly concerned” in evading the ban on cannabis — he didn’t know he was importing cannabis. And however guilty he may have felt for smuggling currency, that wasn’t a crime.

He was acquitted.

(Taaffe [1983] 1 WLR 627 (CA); [1984] 1 AC 539 (HL).)

| Crime

Podcast Episode 308: Nicholas Winton and the Czech Kindertransport

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Image: Wikimedia Commons

In 1939, as the shadow of war spread over Europe, British stockbroker Nicholas Winton helped to spirit hundreds of threatened children out of Czechoslovakia. In this week’s episode of the Futility Closet podcast we’ll describe Winton’s struggle to save the children and the world’s eventual recognition of his achievements.

We’ll also consider some ghostly marriages and puzzle over a ship’s speed.

See full show notes …

| History · Podcast

Fact and Fiction

In 2012, the admissions department at the University of Chicago received a package addressed to Indiana Jones — or to Henry Walton Jones Jr., Indiana’s full name. “The package contained an incredibly detailed replica of ‘University of Chicago Professor’ Abner Ravenwood’s journal from Indiana Jones and the Raiders of the Lost Ark,” the university posted on its Tumblr page. It included photos, maps, and even handwritten text (“I was able to speak through an interpreter with the Guardian of Ark who told me that no other man beside himself could lay eyes on the Ark, that it was an absolutely holy object, and that the world would not pollute it by looking at it,” Ravenwood warns. “He added that he and the villagers would protect the Ark with their lives if necessary.”)

“This package was a little perplexing because we couldn’t find the staff member or the professor [it was intended for] in the directory,” undergraduate outreach Garrett Brinker told Wired.

The university set up an email tip line and inquired with Lucasfilm, which only responded, “We were just as surprised to see this package as you were!”

It turned out that the the replica was one of several that had been shipped from Guam to Italy; it had somehow fallen out of the package in Honolulu, and the post office had delivered it faithfully to the address it bore. “We believe that the post office wrote on our Zip code on the outside of the package and, believing the Egyptian postage was real, sent it our way. From Guam to Hawaii en route to Italy with a stopover in Chicago: truly an adventure befitting Indiana Jones.”

In exchange for some University of Chicago merchandise, the original “prop replicator” in Guam agreed to let the school keep the journal — it’s now on display in the main lobby of the Oriental Institute there.

See Afoot.

| Entertainment · Oddities

A Perfect Bore

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If we assume the existence of an omniscient and omnipotent being, one that knows and can do absolutely everything, then to my own very limited self, it would seem that existence for it would be unbearable. Nothing to wonder about? Nothing to ponder over? Nothing to discover? Eternity in such a heaven would surely be indistinguishable from hell.

— Isaac Asimov, “X” Stands for Unknown, 1984

| Religion · Science & Math

An Unexpected Party

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At long last, after the three volumes were successfully launched, he became what [C.S.] Lewis called ‘cock-a-hoop’ and talked with great enthusiasm of the fate of the pirated paperback version and the astonishing growth of the Tolkien cult. He enjoyed receiving letters in Elvish from boys at Winchester and from knowing that they were using it as a secret language. He was overwhelmed by his fan mail and would-be visitors. It was wonderful to have at long last plenty of money, more than he knew what to do with. He once began a meeting with me by saying: ‘I’ve been a poor man all my life, but now for the first time I’ve a lot of money. Would you like some?’

— George Sayer, “Recollections of J.R.R. Tolkien,” in Joseph Pearce, ed., Tolkien: A Celebration, 1999

| Literature