Legerdemain

Apart from being mathematically true, ONE + TWELVE = TWO + ELEVEN is also famously an anagram — the same group of letters appears on each side of the expression.

In numerical form (1 + 12 = 2 + 11) it’s both an anagram and a palindrome — the same numerals appear on either side of the equal sign, and in opposite order.

Expressed in Roman numerals (I + XII = II + XI) it remains an anagram and a palindrome — again, the same numerals appear on both sides, and in reverse order.

In a square font the equation remains the same when each character is turned upside down:

In Word Ways, contributor Charles Melton points out a further coincidence: Write the original equation in a square font, turn it upside down, and twist the first plus sign 45 degrees to make a multiplication sign:

legerdemain 2

A similar trick works in Roman numerals: Start with the original expression, turn it upside down, and change the plus signs to minus. If IIX is taken as 8, then we get another valid expression:

I + XII = II + XI
IX + II = IIX + I
IX – II = IIX – I

(Anil, “One + Twelve = Two + Eleven,” Word Ways 35:4 [July 2012], 308. See also Spanagrams and Immortal Truth.)

November 29, 2016October 10, 2024 | Language

Podcast Episode 131: Escape From Libby Prison

Libby Prison was one of the most infamous prison camps of the Civil War — thousands of Union prisoners were packed together in a converted warehouse, facing months or years of starvation and abuse. The Confederates thought the prison was escape-proof, and in this week’s episode of the Futility Closet podcast we’ll show how a determined group of prisoners set out to prove them wrong.

We’ll also duel with a barrel and puzzle over why an admitted forger would be found innocent.

See full show notes …

November 28, 2016October 2, 2017 | History · Podcast

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?

	Select Click for Answer
From the road, Marsh alone walked to the edge of the cliff, carrying Lamson’s boots in his hands. At the edge of the cliff he changed boots and walked backward to the road, carrying his own boots. “This little maneuver accounts for the smaller footprints showing a deeper impression at the heel, and the larger prints a deeper impression at the toe, for a man will walk more heavily on his heels when going forward, but will make a deeper impression with the toes in walking backwards. It will also account for the fact that the large footprints were sometimes impressed over the smaller ones, but never the reverse; also for the circumstance that the larger footprints showed a shorter stride, for a man will necessarily take a smaller stride when walking backwards.” From Henry Dudeney’s The Canterbury Puzzles, 1907.

Click for Answer

November 27, 2016December 4, 2016 | Puzzles

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?

12/08/2016 UPDATE: It’s a consequence of Fermat’s little theorem, as explained in this extraordinarily helpful PDF by reader Stijn van Dongen.

(Thanks to Evan, Dave, Sid, and Stijn.)

November 26, 2016December 8, 2016 | Science & Math

Sommelier!

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.)

November 25, 2016November 23, 2016 | Literature

In a Word

forfex
n. a pair of scissors

November 23, 2016December 13, 2016 | Language

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.”

November 23, 2016November 22, 2016 | Literature · Science & Math

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.)

November 22, 2016 | Oddities

Misc

AGAMEMNON is made up of three consecutive palindromic triads.
South Africa has three capital cities.
In 1984, Newspeak is never spoken.
A good licking is a bad licking.
“A thing is not necessarily true because a man dies for it.” — Oscar Wilde

November 22, 2016November 21, 2016 | Language · Literature · Quotations · Trivia

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.

See full show notes …

November 21, 2016October 2, 2017 | Podcast