Another conundrum from Henry Dudeney’s The Canterbury Puzzles:
A squire has drawn a portrait of King Edward III with a single continuous stroke of his pen. “‘Tis a riddle to find where the stroke doth begin and where it doth also end. To him who shall first show it unto me will I give the portraiture.” What is the answer?
Roman craftsmen made a remarkable coup around 300 A.D. — they produced a cup that is red when lit from behind and green when lit from the front. The effect occurs because the glass contains tiny proportions of gold and silver nanoparticles that reflect light of certain wavelengths. The workers themselves may have discovered the technique by accident, and may not have understood it fully; only a few pieces of 4th-century Roman glass display this “dichroic” property. Art historian Donald Harden called it “the most spectacular glass of the period, fittingly decorated, which we know to have existed.” It now resides in the British Museum.
In 1948, retired clock maker Lawrence Wahlstrom acquired a surplus World War II bomb sight bearing a complicated cluster of gears, restored it to operation, and began adding more gears to it over a period of 15 years. He resolved on adding 50 each year, and succeeded so well that today the total number isn’t known.
Popular Mechanics wrote in 1954, “We all know someone who works harder doing nothing than most of us work doing something, but we can’t possibly know anything that works harder at nothing that a machine built by a California hobbyist. The machine has over 700 working parts that rotate, twist, oscillate and reciprocate — all for no purpose except movement.”
In a review for the New Yorker in 1959, film critic Kenneth Tynan mistakenly referred to “the late Eric Blore,” and the magazine’s famously vigilant fact-checking department failed to note that the English comic actor was still alive.
Blore’s lawyer demanded a retraction, and a chastened Tynan prepared an apology, which was scheduled to appear in the following issue.
After that issue had been printed, though, the actor really did die … so while that day’s newspapers were reporting Blore’s death, the New Yorker was apologizing for saying he was no longer alive.
(Thanks, Johnny.)
James Riffel’s 1991 film Night of the Day of the Dawn of the Son of the Bride of the Return of the Revenge of the Terror of the Attack of the Evil, Mutant, Alien, Flesh Eating, Hellbound, Zombified Living Dead Part 2 in Shocking 2-D spawned three sequels: Night of the Day of the Dawn of the Son of the Bride of the Return of the Revenge of the Terror of the Attack of the Evil, Mutant, Hellbound, Flesh-Eating Subhumanoid Zombified Living Dead, Part 3 (2005), Night of the Day of the Dawn of the Son of the Bride of the Return of the Revenge of the Terror of the Attack of the Evil, Mutant, Hellbound, Flesh-Eating Subhumanoid Zombified Living Dead, Part 4 (2005), and Night Of The Day Of The Dawn Of The Son Of The Bride Of The Return Of The Revenge Of The Terror Of The Attack Of The Evil, Mutant, Hellbound, Flesh-Eating, Crawling, Alien, Zombified, Subhumanoid Living Dead — Part 5 (2011).
The 2015 direct-to-video film The Scorpion King 4: Quest for Power is the sequel to the sequel to the prequel to the prequel to the sequel to the remake of Universal’s original 1932 The Mummy, starring Boris Karloff.
“Certainly I was typed,” Karloff said of his long career in horror. “But what is typing? It is a trademark, a means by which the public recognizes you. Actors work all their lives to achieve that. I got mine with just one picture. It was a blessing.”
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:
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.)
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.
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?
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.)
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.)