The Cornish Cliff Mystery

dudeney cliff puzzle

Police have chased two thieves to the Cornish coast. There they find that two sets of footprints depart the hard road and cross soft soil to the edge of a cliff, where they end. The cliff juts out 200 feet above sea-washed boulders. No one could survive a fall from this height, there is no way to descend the cliff, and there are no other footprints.

The police have proven that the footprints match those of the fleeing criminals. The small foot belongs to Marsh, who apparently takes relatively long strides, walking heavily on his heels. Lamson takes shorter strides, treading more on his toes and evidently following behind Marsh, as he sometimes treads over the smaller man’s footprints.

The two men did not walk to the cliff edge and then return to the road by walking backward in their own footprints — such precision over a course of 200 yards is impossible. Accordingly the inspector says he will report that the criminals, hopeless to escape justice, have hurled themselves to their death.

“Then you will make a fatal mistake,” says Henry Melville, a visiting member of the Puzzle Club. “The men are alive and in hiding in the district.” He proves to be right, but how did the men get away from the edge of the cliff?

Click for solution …

First and Last

The fifth power of any one-digit number ends with that number:

05 = 0
15 = 1
25 = 32
35 = 243
45 = 1024
55 = 3125
65 = 7776
75 = 16807
85 = 32768
95 = 59049

11/26/2016: UPDATE, after hearing from some readers who are thinking more deeply than I am:

First, this immediately implies that any integer raised to the fifth power ends with the same digit as the original number.

Second, the same effect occurs regularly at higher powers, specifically 9, 13, 17, and x = 1 + 4n where n = {0, 1, 2, 3, …}.

Does anyone know what this rule is called? I found it in Reuben Hersh and Vera John-Steiner’s 2011 book Loving + Hating Mathematics — Eugene Wigner writes of falling in love with numbers at his school in Budapest: “After a few years in the gymnasium I noticed what mathematicians call the Rule of Fifth Powers: That the fifth power of any one-digit number ends with that same number. Thus, 2 to the fifth power is 32, 3 to the fifth power is 243, and so on. At first I had no idea that this phenomenon was called the Rule of Fifth Powers; nor could I see why it should be true. But I saw that it was true, and I was enchanted.”

I actually can’t find a rule by that name. Perhaps it goes by a different name in English-speaking countries?

(Thanks, Evan, Dave, and Sid.)

Sommelier!

https://commons.wikimedia.org/wiki/File:13_rackham_poe_caskofamontillado.jpg

Edgar Allan Poe’s “The Cask of Amontillado” may be a classic horror story, but it’s full of “weird wine howlers,” according to Clifton Fadiman.

Fortunato, who is immured in the story, “prided himself on his connoisseurship in wine,” and Montresor, who does the immuring, adds, “I was skilful in the Italian vintages myself, and bought largely whenever I could.”

But Fortunato tells him, “Luchesi is quite incapable of telling Amontillado from Sherry,” and, later, “Amontillado! You have been imposed upon; and as for Luchesi, he cannot distinguish Sherry from Amontillado.”

But Amontillado is a sherry! H. Warner Allen points out that André Simon’s wine encyclopedia defines Amontillado as “one of the most popular types of Sherry, neither too dry nor too sweet.”

Compounding this error, Montresor tells Fortunato that he wants Luchesi’s opinion of a pipe of Amontillado that he has received. But a pipe is a cask of port; a cask of sherry is a butt.

Also, Poe seems to have thought that Amontillado is an Italian wine, perhaps judging by the look of the word. Fadiman writes, “What he thought ‘a flagon of De Grâve’ could be is almost beyond conjecture.”

(Clifton Fadiman, Dionysus: A Case of Vintage Tales About Wine, 1962.)

Midnight Oil

In 1960, MIT mathematician George B. Thomas Jr. received a letter from a waterfowl farmer in Maine. The farmer thought he had discovered an error in a problem in Thomas’ influential textbook Calculus and Analytic Geometry. A little bewildered, Thomas looked into it and discovered that there was indeed an error. He thanked the writer and promised to correct the mistake in future editions.

The two corresponded intermittently thereafter, but four years went by before Thomas realized that the farmer was novelist Henry Roth, author of Call It Sleep. Suffering a disastrous case of writer’s block, Roth had turned to farming and tutoring to support his family, and he had worked his way through every problem in Thomas’ book, ninety per chapter, “often struggling long into the night before arriving at the solution,” according to biographer Steven Kellman.

A copy of the textbook, “inscribed with notes,” is listed among Roth’s papers. In the preface to the fourth edition, Thomas wrote, “One of the author’s friends, Mr. Henry Roth, wrote that he feared that the new edition would be ‘rife with set theory.’ I believe that he, and others who have used the third edition, will find that only modest additions of set theory have been made.”

Togetherness

https://commons.wikimedia.org/wiki/File:Whittier,_Alaska.jpg
Image: Wikimedia Commons

Nearly everyone in Whittier, Alaska, lives under the same roof. The 14-story Begich Towers was built after World War II, and the building was converted to a condominium when the military withdrew. About 200 people live in 150 two- and three-bedroom apartments, and they can go weeks without leaving the building, which contains a post office, a grocery, a medical clinic, the mayor’s office, a general store, the police department, a Methodist church, a laundry, a small hotel, a conference room, and a play area with an indoor pool. A tunnel system leads to the community school and a general store.

By most accounts, life in the tower is pretty agreeable. But “because we have four elevators, sometimes people pull pranks on you and hit every button,” resident June Miller told CBC News. “And it’s like, ‘Really? This again?'”

(Thanks, Ginny.)

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Podcast Episode 130: The Unlikely Ultramarathoner

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

Australia’s Westfield ultramarathon had a surprise entrant in 1983: A 61-year-old potato farmer named Cliff Young joined a field of elite professional runners for the 500-mile race from Sydney to Melbourne. In this week’s episode of the Futility Closet podcast we’ll describe Young’s fortunes in the race and the heart, tenacity, and humor that endeared him to a nation.

We’ll also learn the difference between no and nay and puzzle over a Japanese baby shortage.

Intro:

Thomas Wedders exhibited his 7.5-inch nose throughout Yorkshire in the 1770s.

Two meteorologists played ping-pong on a solid block of snow atop Scotland’s Ben Nevis in 1902.

Sources for our feature on Cliff Young:

Julietta Jameson, Cliffy: The Cliff Young Story, 2013.

Phil Essam, ed., I’ve Finally Found My Hero, 2016.

Matthew Ricketson, “Cliff’s Not Finished Yet,” The Age, Nov. 29, 1983.

J. Freeman, “Cliff Calls It a Day,” Telegraph, April 17, 1985.

Greg Truman, “A Long-Running Favorite Draws to an End,” The Advertiser, May 5, 1986.

Louise Evans, “Cliff, the Battler’s Hero, Refuses to Shuffle Off Into the Sunset,” Sydney Morning Herald, June 4, 1988.

R. Reed, “Westfield Highway Closed to Cliff: Old Shuffler ‘Saved’ From Himself,” Sunday Herald, March 11, 1990.

G. Legg, “Cliff, 70, Has Enough Puff for 170km,” Courier-Mail, May 23, 1992.

Derek Ballantine, “For Cliff, a Long Road to Nowhere,” The Advertiser, April 10, 1993.

Alan Rider, “‘Where’s Cliffy?’: In Hobart Run-Walk!,” Hobart Mercury, April 20, 1993.

Tony Baker, “An Epic of Eccentricity,” Hobart Mercury, April 25, 1997.

“End of the Road for Cliff,” Sydney Morning Herald, Nov. 3, 2003.

Graeme Leech, “Shy Runner Shuffled Into a Nation’s Heart,” The Australian, Nov. 7, 2003.

Charles Happell, “A Gumbooted Forrest Gump, Cliff Young Ran His Own Race,” The Australian, March 23, 2013.

“Running Legend’s Cup Will Return to District,” Colac Herald, April 17, 2015.

Here’s Neil Kearney’s 1983 documentary Cliffy, made shortly after Young’s victory and showing his trademark shuffling gait:

And Clock End Films made a TV movie about Young in 2013. (Thanks, Julie.)

Listener mail:

“Frenemies — Churchill’s Planned 1945 Surprise Attack on the Soviets,” Military History Now, Oct. 15, 2012.

Wikipedia, “Operational Unthinkable” (accessed Nov. 18, 2016).

Historical Board Gaming: Operation Unthinkable Custom Map & Rules.

BoardGameGeek: Castle Itter.

Digital Capricorn Studios: Castle Itter.

National Public Radio, “No, Yes, Definitely: On the Rise of ‘No, Totally’ as Linguistic Quirk,” Morning Edition, April 12, 2015.

Kathryn Schulz, “What Part of ‘No, Totally’ Don’t You Understand?”, New Yorker, April 7, 2015.

This week’s lateral thinking puzzle was contributed by listener Jon Sweitzer-Lamme, who sent this corroborating link (warning: this spoils the puzzle).

You can listen using the player above, download this episode directly, or subscribe on iTunes or Google Play Music or via the RSS feed at http://feedpress.me/futilitycloset.

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

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!