A problem proposed by Richard Hoshino and Sarah McCurdy for Crux Mathematicorum, September 2008:
Five points lie on a line. Here are the 10 distances between pairs of points, listed from smallest to largest:
2, 4, 5, 7, 8, k, 13, 15, 17, 19
What’s k?
In this week’s episode of the Futility Closet podcast we’ll explore some curiosities and unanswered questions from Greg’s research, including a novelist’s ashes, some bathing fairies, the mists of Dartmoor, and a ballooning leopard.
We’ll also revisit the Somerton man and puzzle over an armed traveler.
In the first James Bond novel, 1953’s Casino Royale, Bond orders a drink of his own invention:
‘A dry martini,’ he said. ‘One. In a deep champagne goblet.’
‘Oui, monsieur.’
‘Just a moment. Three measures of Gordon’s, one of vodka, half a measure of Kina Lillet. Shake it very well until it’s ice-cold, then add a large thin slice of lemon peel. Got it?’
‘Certainly monsieur.’ The barman seemed pleased with the idea.
‘Gosh, that’s certainly a drink,’ said Leiter.
Bond laughed. ‘When I’m … er … concentrating,’ he explained, ‘I never have more than one drink before dinner. But I do like that one to be large and very strong and very cold, and very well-made. I hate small portions of anything, particularly when they taste bad. This drink’s my own invention. I’m going to patent it when I think of a good name.’
The name he thinks of is the Vesper, ostensibly inspired by the character Vesper Lynd. But in fact the recipe wasn’t original to Bond — Fleming had first received the drink from the butler of an elderly couple in Jamaica — it was named after vespers, a service of evening prayer. Bond says, “It sounds perfect and it’s very appropriate to the violet hour when my cocktail will now be drunk all over the world.” He’d have trouble getting one today — Kina Lillet was discontinued in 1986, and the strength of Gordon’s Gin was reduced in 1992.
On September 19, 1968, as the Soviet Union’s Zond 5 spacecraft was circling the moon, Jodrell Bank Observatory and the CIA were shocked to intercept the voices of cosmonauts Valery Bykovsky, Vitaly Sevastyanov and Pavel Popovich reading out telemetry and computer data and even discussing the prospect of a landing. The Zond mission had been thought to be uncrewed; now it sounded as though the Soviets might beat the United States to a moon landing. Apollo 17 astronaut Eugene Cernan said that the incident “shocked the hell out of us.”
It was a hoax. Popovich recalled later, “When we realized we would never make it to the moon, we decided to engage in a little bit of hooliganism. We asked our engineers to link the on-the-probe receiver to the transmitter with a jumper wire. Moon flight missions were then controlled from a command centre in Yevpatoria, in the Crimea. When the probe was on its path round the Moon, I was at the center. So I took the mike and said: ‘The flight is proceeding according to normal; we’re approaching the surface …’ Seconds later my report — as if from outer space — was received on Earth, including [by] the Americans. The U.S. space advisor Frank Borman got a phone call from President [Johnson], who asked: ‘Why is Popovich reporting from the moon?’ My joke caused real turmoil.
“In about a month’s time. Frank came to the USSR, and I was instructed to meet him at the airport. Hardly had he walked out of his plane when he shook his fist at me and said: ‘Hey, you, space hooligan!'”
(From Strand, May 1911.)
The location of Alexander the Great’s tomb is a mystery. After Alexander’s death in Babylon in 323 B.C., his body was taken first to Memphis and then to Alexandria, where Pompey, Julius Caesar, Cleopatra, Augustus, and Caligula all visited his tomb. But by the 4th century A.D. the tomb’s location was no longer known. Egypt’s Supreme Council for Antiquities has now recognized more than 140 search attempts, but none has succeeded conclusively.
On May 10, 1933, in the Bebelplatz in central Berlin, members of the National Socialist Student Union burned 20,000 books, objecting to the “un-German spirit” of many Jewish, communist, and liberal authors. Joseph Goebbels declared that “the era of exaggerated Jewish intellectualism is now at an end … and the future German man will not just be a man of books … this late hour [I] entrust to the flames the intellectual garbage of the past.”
In 1995, Israeli sculptor Micha Ullman created a memorial room under the plaza, with empty shelves enough to accommodate 20,000 books. A plaque set into the cobblestones bears a quote by Heinrich Heine:
That was but a prelude;
where they burn books,
they will ultimately burn people as well.
You’re in a dark room. The only light comes from an old LED digital alarm clock with four seven-segment displays. The time is displayed in 24-hour format, HH:MM (no seconds), and the leading digit is blank if not used. How much time passes between the room’s darkest state and its lightest?
Friend John, whose (:) was removed,
When asked why he had lately proved
So free of caution and of fear,
Said, “I’ve no (*), my dear.”
— Willard R. Espy
