You’re locked on the roof of a building that’s 800 feet tall, and you want to reach the ground uninjured. You can safely fall only about 5 feet. The walls of the building are completely smooth and featureless, except that one wall has a small ledge that’s 400 feet above the ground. There’s a hook on this ledge, and another hook directly above it at the edge of the roof.
You have 600 feet of rope and a knife. How can you reach the ground?
A man who enters a public restroom has to make a complex choice quickly. He wants to choose a urinal that maximizes his chances of maintaining privacy — that is, that minimizes the chance that someone will occupy a urinal next to him. Which choice is best?
Computer scientists Evangelos Kranakis and Danny Krizanc modeled a number of strategies: lazily choosing the closest urinal that provides privacy; tacitly cooperating in the decision with other men; maximizing one’s distance from other occupants; and making the choice randomly. Happily, their findings support the general intuition:
Our main conclusion is that when faced with the decision of what urinal to choose upon entering the men’s room, in order to maximize your privacy, you should probably choose the one furthest from the door if it is available and the one next to it is unoccupied. For a vast majority of the (what we consider) natural behaviors that men choosing urinals might follow, this choice is optimal.
Related: In 1984 Donald E. Knuth noticed that the toilet paper dispensers in Stanford’s computer science department hold two rolls of tissue, both of which are available for use. Suppose there are two sorts of people in the world, those who are disposed to draw from the larger roll and those who draw from the smaller roll, and that each user takes exactly one sheet from his favored roll. What’s the expected number of sheets remaining just after one of the two rolls has been emptied? Donald E. Knuth’s Toilet Paper Problem.
(Evangelos Kranakis and Danny Krizanc, “The Urinal Problem,” in Paolo Boldi and Luisa Gargano, eds., Fun With Algorithms: 5th International Conference, Fun 2010, Iscia, Italy, June 2010: Proceedings.)
In his Musical Biography of 1824, John R. Parker attempts to characterize musical keys in words:
“It is sufficient to have hinted at these effects,” he writes. “To account for them, is difficult; but every musician is sensible of their existence.”
battailous
adj. ready for battle; warlike
scious
adj. possessing knowledge
didascalic
adj. pertaining to a teacher
Among Union Army regiments, the 33rd Illinois became known as the “brains” regiment because it contained so many teachers. “It was stated derisively that the men would not obey orders which were not absolutely correct in syntax and orthography and that men who were discharged from it for mental incapacity, at once secured positions as officers in other regiments.” Many of them came from Illinois State Normal University; of the 97 teachers and pupils on the university’s rolls in 1860-1861, 53 entered the army.
(Charles A. Harper, Development of the Teachers College in the United States, With Special Reference to the Illinois State Normal University, 1935.)
Amazingly, we have a photograph of a man who crossed the Delaware with George Washington. This is Conrad Heyer, born in 1749 and photographed in 1852 at age 103. He served in the Continental Army during the Revolutionary War, crossed the Delaware with Washington in December 1776, and fought in several major battles. The Maine Historical Society says that this makes him the earliest-born human being ever to be photographed.
The footage below shows Despina, the grandmother of Balkan film pioneers Yanaki and Milton Manaki, spinning and weaving in the Ottoman Balkans in 1905. She was 114 years old at the time, which means we have video of a person born in the 1700s.
Just offering this as a curiosity:
It was devised by the late Japanese cryptogramist Kyoko Ohnishi, and praised by puzzle maven Nob Yoshigahara. If each letter stands for a unique digit, what product is encoded here?
When this appeared in MIT Technology Review in November 2012, it attracted 20 responses, but it appears that all of them used computers to find the solution. If there’s a way to reason it out, I don’t think anyone has found it yet.
If we assume that neither of the factors has a leading zero, and that the partial products have five and four digits, as shown, then the solution is unique. I’ll put it in the spoiler box below, in case you want to work on it yourself.
In 1854, English aristocrat Roger Tichborne disappeared at sea. Twelve years later, a butcher from Wagga Wagga, Australia, claimed he was the long-lost heir. In this week’s episode of the Futility Closet podcast, we’ll tell the sensational story of the Tichborne claimant, which Mark Twain called “the most intricate and fascinating and marvelous real-life romance that has ever been played upon the world’s stage.”
We’ll also puzzle over why family businesses are often more successful in Japan than in other countries.
In 1866, writing in the Virginia City Territorial Enterprise, Mark Twain accused San Francisco police chief Martin Burke of corruption, and “some leather-head” misinterpreted the column to suggest that Burke kept a mistress. Twain wrote to the San Francisco Examiner with a clarification:
EDITOR EXAMINER:–You published the following paragraph the other day and stated that it was an ‘extract from a letter to the Virginia Enterprise, from the San Francisco correspondent of that paper.’ Please publish it again, and put it in the parentheses where I have marked them, so that people who read with wretched carelessness may know to a dead moral certainty when I am referring to Chief Burke, and also know to an equally dead moral certainty when I am referring to the dog:
‘I want to compliment Chief Burke — I do honestly. But I can’t find anything to compliment him about. He is always rushing furiously around, like a dog after his own tail — and with the same general result, it seems to me; if he (the dog, not the Chief,) catches it, it don’t amount to anything, after all the fuss; and if he (the dog, not the Chief,) don’t catch it it don’t make any difference, because he (the dog, not the Chief,) didn’t want it anyhow; he (the dog, not the Chief,) only wanted the exercise, and the happiness of “showing off” before his (the dog’s, not the Chief’s,) mistress and the other young ladies. But if the Chief (not the dog,) would only do something praiseworthy, I would be the first and the most earnest and cordial to give him (the Chief, not the dog,) the credit due. I would sling him (the Chief, not the dog,) a compliment that would knock him down. I mean that it would be such a first-class compliment that it might surprise him (the Chief, not the dog,) to that extent as coming from me.’
He added: “I think that even the pupils of the Asylum at Stockton can understand that paragraph now.”
Four be the things I’d been better without:
Love, curiosity, freckles, and doubt.
— Dorothy Parker
By M. Techritz. Place the black and white kings on the board so that White can mate in one move.
