A stick is broken at random into 3 pieces. It is possible to put them together into the shape of a triangle provided the length of the longest piece is less than the sum of the other 2 pieces; that is, provided the length of the longest piece is less than half the length of the stick. But the probability that a fragment of a stick shall be half the original length of the stick is 1/2. Hence the probability that a triangle can be constructed out of the 3 pieces into which the stick is broken is 1/2.
In contemporary secretary schools, training emphasizes the inhibition of reading for meaning while typing, on the assumption that such reading will hinder high-speed performance. Some support for this assumption derives from the introspections of champion speed typists, who report that they seldom recall the meaning from the source material incidentally.
— William E. Cooper, Cognitive Aspects of Skilled Typewriting, 2012
We don’t even know the keyboard. A 2013 study at Vanderbilt asked 100 subjects to take a short typing test; they were then shown a blank QWERTY keyboard and given 80 seconds to label the keys. On average they typed at 72 words per minute with 94 percent accuracy but could correctly label only 15 letters on a blank keyboard.
“This demonstrates that we’re capable of doing extremely complicated things without knowing explicitly what we are doing,” said graduate student Kristy Snyder.
It had formerly been believed that typing starts as a conscious process that becomes unconscious with repetition. But it appears that typists never memorize the key locations in the first place.
“It appears that not only don’t we know much about what we are doing, but we can’t know it because we don’t consciously learn how to do it in the first place,” said psychologist Gordon Logan.
Above: From Paris, 1927: a novelty car that can “sidle” into parking spaces.
Below: Someone was actually working on this in the 1950s (thanks, Martin):
A related puzzle from The Chicken From Minsk, Yuri B. Chernyak’s 1995 collection of math and physics problems: Why is it easier to parallel-park a (conventional) car by backing into the space rather than pulling in directly?
Imagine pulling out of the space. With the front wheels turned sharply to one side, the center of rotation is close to the car’s rear end; the front of the car swings out of the space, avoiding the car in front, and then the rear follows it. Because the center of rotation is so close to the rear of the car, it would be hard to back out of a tight space. Now play the scenario in reverse: By backing into the space, the driver is putting the least maneuverable end of the car into position first and can then rotate the rest into place.
On Saturday night last, a man who resided in Twenty-ninth-street was killed in a most singular manner. The following are the peculiar circumstances, as far as our reporter has been able to learn them — for, in consequence of the opinion entertained concerning his relatives by the deceased, who was a man of considerable wealth and respectability, they have made great effort to keep the particulars from the public ear. It appears that nearly a year ago the deceased, who was fifty-three years of age, became strongly impressed with an idea that, when he should die, the parsimonious disposition of his relatives would lead them to put him in a cheap coffin, while he had a strong desire to be buried in one of polished rosewood, lined with white satin and trimmed with silver. Soon after this strange idea got possession of his mind, he discovered an elegant coffin in one of the principal warehouses, which suited him. He purchased it for $75; had it sent to his residence at nightfall, and stowed it away in a small closet adjoining his bed-room, where it remained until the time of the accident. How it occurred is not known to a certainty, for the first intimation the family had of the lamentable occurrence was from a servant, who, on going to call him to breakfast, found the door wide open and the deceased lying upon the floor, dead, with his coffin at his side. She screamed, which soon brought the family, and on raising the body the skull was found crushed in upon the brain. He was discovered about 8 o’clock yesterday morning, when, to all appearance, he had been dead several hours. On examining the closet, a bottle containing a quantity of sherry wine was found, and as Saturday night was excessively warm, he is supposed to have gone to the closet in order to procure the wine to use with some ice-water he had on a small table by his bedside. It is thought that he must have sought for it in the dark, and by some mistake upset the coffin, which stood nearly upright. Becoming sensible that it was falling, he probably made an effort to get away, when he fell, and the outer end struck his head with sufficient force to fracture his skull and cause almost immediate death. The inquest will be held with all possible secrecy. The unfortunate impression of the deceased concerning his relatives is a sufficient reason for withholding the names of the parties.
Mayfield gives 94 additional narrative alphametics, including the remarkable BRUTUS + STABS = CAESAR, in the article. He provides no answers, but if you get stuck you can derive them using this nifty calculator.
Pick a positive integer, list the positive integers that will divide it evenly, add these up, and subtract the number itself:
10 is evenly divisible by 10, 5, 2, and 1. (10 + 5 + 2 + 1) – 10 = 8.
Now do the same with that number, and continue:
8 is evenly divisible by 8, 4, 2, and 1. (8 + 4 + 2 + 1) – 8 = 7.
7 is evenly divisible by 7 and 1. (7 + 1) – 7 = 1.
1 is evenly divisible only by 1. (1) – 1 = 0.
Many of these sequences arrive at some resolution — they terminate in a constant, or an alternating pair, or some regular cycle. But it’s an open question whether all of them do this. The fate of the aliquot sequence of 276 is not known; by step 469 it’s reached 149384846598254844243905695992651412919855640, but possibly it reaches some apex and then descends again and finds some conclusion (the sequence for the number 138 reaches a peak of 179931895322 but eventually returns to 1). Do all numbers eventually reach a resolution? For now, no one knows.
“The smallest, oldest and most famous magic square of all is the specimen of Chinese origin known as the Lo shu. In this, the numbers from 1 to 9 are so placed that their sum taken in any row, column or diagonal is 15. This is another way of saying that the sum of any three of them lying in a straight line is 15. Less well known is the ‘Egyptian’ Lo shu (seen below) in which the same numbers are rearranged in a triangular formation that exhibits the same property.”
(From his book Geometric Magic Squares, 2013.) (Thanks, Lee.)
In 1800 a 12-year-old boy emerged from a forest in southern France, where he had apparently lived alone for seven years. His case was taken up by a young Paris doctor who set out to see if the boy could be civilized. In this week’s episode of the Futility Closet podcast we’ll explore the strange, sad story of Victor of Aveyron and the mysteries of child development.
We’ll also consider the nature of art and puzzle over the relationship between salmon and trees.
