This paragraph jumped out at me last night from B.G. Wilson’s Unusual Railways (1958) — he’s writing about the Mount Washington Cog Railway in New Hampshire, one of the world’s steepest, with an average grade of 25 percent:

Before leaving this line, mention must be made of a method of riding down the track employed by track maintenance men and long since banned. Wood and metal seats some 3 ft. × 1 ft. were made to fit over the rack rail. These were known as slide-boards, or more popularly, as ‘Devil’s Shingles’. Seated on these, controlling (sometimes) the speed with hand brakes, the men would career down the mountainside. The record time for the trip — as we have said, 3 1/4 miles — was 2 3/4 minutes!

That’s 70 mph! For comparison, the modern train takes 40 minutes to descend at 4.6 mph. And this was in the late 19th century — the railway opened in August 1869. Wilson writes, “After one man had been killed and another seriously injured, the Devil’s Shingles were banned.” I don’t know any more than that.

All Hands on Deck?

A reader named Hamp Stevens sent this conundrum to Martin Gardner, who published it in his Mathematical Magic Show (1965). Can these 25 cards be arranged to form five poker hands, each of them a straight or better (that is, straight, flush, full house, four of a kind, straight flush, or royal flush)? If it’s possible, find the five hands; if it’s not, prove that it’s impossible.

“This ingenious puzzle is quickly solved if you go about it correctly,” Gardner wrote. “A single card is the key.”

Click for Answer

Hard Target

In a special football game, a team scores 7 points for a touchdown and 3 points for a field goal. What’s the largest mathematically unreachable number of points that a team can score (in an infinitely long game)?

Click for Answer


la rochefoucauld

More maxims of François VI, Duc de La Rochefoucauld (1613–1680):

  • “We always love those who admire us; but we don’t always love those whom we admire.”
  • “There are people who would never have been in love, if they had never heard talk of Love.”
  • “The Generality of People judge of Men by their Reputation, or Fortune.”
  • “Men would not live long in Society, if they were not the mutual Dupes of one another.”
  • “Titles, instead of exalting, debase those who don’t act up to them.”
  • “Prosperity is a stronger Trial of Virtue than Adversity.”
  • “Weak People can’t be sincere.”
  • “‘Tis more difficult to be faithful to a Mistress when on good Terms with her, than when on bad.”
  • “‘Tis not so dangerous to do Ill to most Men as to do them too much Good.”
  • “A Man often imagines he acts, when he is acted upon; and while his Mind aims at one thing, his Heart insensibly gravitates towards another.”
  • “When great Men suffer themselves to be subdued by the Length of their Misfortunes, they discover that the Strength of their Ambition, not of their Understanding, was what supported them; and that, bating a little Vanity, Heroes are just like other Men.”
  • “Cunning and Treachery proceed from Want of Capacity.”
  • “If we took as much Pains to be what we ought, as we do to deceive others by disguising what we are; we might appear as we are, without being at the Trouble of any Disguise.”

And “‘Tis a Mistake to imagine that only the violent Passions, such as Ambition and Love, can triumph over the rest. Laziness, languid as it is, often masters them all; she indeed influences all our Designs and Actions, and insensibly consumes and destroys both the Passions and the Virtues.”

Pleased, I’m Sure

A problem by Atlantic College mathematician Paul Belcher:

Anna and Bert invite n other couples to a dinner party. Before the meal begins, some people shake hands. No one shakes hands with their own partner, no one shakes hands with themselves, and no two people shake hands with each other more than once. Afterward, Anna asks all the other 2n + 1 people how many times they shook hands, and she gets a different answer from each of them. How many times did Anna shake hands?

Click for Answer

In a Word

n. excessive reverence for a place

Of the million or so Japanese who visit Paris each year, about 12 have to be repatriated due to “Paris syndrome,” a transient psychological disorder brought on when the mundane reality of the city clashes with their romanticized expectations.

The syndrome was first diagnosed by Hiroaki Ota, a Japanese psychiatrist working in France. Symptoms include delusional states, hallucinations, feelings of persecution, and anxiety.

“Fragile travellers can lose their bearings,” psychologist Hervé Benhamou told Le Journal du Dimanche. “When the idea they have of the country meets the reality of what they discover, it can provoke a crisis.”

(A. Viala et al., “Les japonais en voyage pathologique à Paris : un modèle original de prise en charge transculturelle,” Nervure 5 (2004): 31–34.)

Podcast Episode 85: Raising Chicago

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In 1868, visiting Scotsman David Macrae was astonished to see Chicago transforming itself — dozens of buildings were transplanted to the suburbs, and hotels weighing hundreds of tons were raised on jackscrews. In this week’s episode of the Futility Closet podcast we’ll follow the city’s astounding 20-year effort to rid itself of sewage and disease.

We’ll also learn how a bear almost started World War III and puzzle over the importance of a ringing phone.

Sources for our feature on the raising of Chicago:

David Young, “Raising the Chicago Streets Out of the Mud,” Chicago Tribune, date strangely withheld (retrieved Dec. 7, 2015).

Robin Einhorn, “Street Grades, Raising,” Encyclopedia of Chicago (accessed Dec. 6, 2015).

Josiah Seymour Currey, Chicago: Its History and Its Builders, 1918.

Alfred Theodore Andreas, History of Chicago: Ending With the Year 1857, 1884.

David Macrae, The Americans at Home, 1870.

There’s a very extensive collection of contemporaneous news accounts here.

Listener mail:

Aaron Tovish, “The Okinawa Missiles of October,” Bulletin of the Atomic Scientists, Oct. 25, 2015.

Wikipedia, “Norwegian Rocket Incident” (retrieved Dec. 12, 2015).

Wikipedia, “Volk Field Air National Guard Base” (retrieved Dec. 12, 2015).

Chris Hubbuch, “False Alarm: How a Bear Nearly Started a Nuclear War,” La Crosse [Wis.] Tribune, Jan. 30, 2009.

This week’s lateral thinking puzzle is from Matthew Johnstone’s 1999 book What’s the Story?

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at Thanks for listening!

Putting Words

In 1946, when Japanese prime minister Hideki Tojo was being held prisoner by the victorious Allies, he asked for a set of dentures so that he could speak clearly during his war crimes trial.

The dentures were made by 22-year-old military dentist E.J. Mallory. “I figured it was my duty to carry out the assignment,” Mallory remembered in 1988. “But that didn’t mean I couldn’t have fun with it.”

An amateur ham radio operator, he inscribed the phrase “Remember Pearl Harbor” in Morse code into the dentures and delivered them to Tojo.

Mallory and his colleague George Foster told a few friends, but the secret got out and the two had to awaken Tojo in the middle of the night to borrow back the dentures and grind out the message. The next day, when a colonel confronted them, they were able to say truthfully that there was no message.

It’s not known whether Tojo ever found out what had happened. He was executed in 1948.

“It wasn’t anything done in anger,” Mallory remembered in 1995. “It’s just that not many people had the chance to get those words into his mouth.”