Weighing in Verse

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How can you find one bad coin among 12 using only three weighings in a pan balance? We published the classic solution in November 2013, but a clever alternative appeared in Eureka in October 1950. Here the aspiring counterfeiter is named Felix Fiddlesticks, and he’s trying to find the coin for this mother:

F set the coins out in a row
And chalked on each a letter, so,
To form the words: “F AM NOT LICKED”
(An idea in his brain had clicked).

And now his mother he’ll enjoin:

weighing in verse table

This plan will reveal the bad coin no matter which it is. For instance, if the coin marked O is heavy, then in the first two weighings the left pan will drop, and in the third weighing it will rise; no other bad coin will produce this result. The plan will also reveal reliably whether the bad coin is heavy or light.

Such cases number twenty-five,
And by F’s scheme we so contrive
No two agree in their effect,
As is with pen and patience checked:
And so the dud is found. Be as it may
It only goes to show CRIME DOES NOT PAY.

(Cedric Smith, “The Twelve Coin Problem,” The Mathematical Gazette, Vol. 89, No. 515 [July 2005], pp. 280-281. A generalized algorithm for solving such a problem for any number of coins is given by Michael Weatherfield in the same issue, pp. 275-279.)

| Puzzles

Riddles in the Dark

http://puzzling.stackexchange.com/questions/15763/the-lord-of-the-puzzles

In 1904, a 12-year-old J.R.R. Tolkien sent this rebus to a family friend, Father Francis Morgan. What does it say?

Click for Answer
| Puzzles

The Road Not Taken

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“You know, many a man realizes late in life that if when he was a boy he had known what he knows now, instead of being what he is he might be what he won’t; but how few boys stop to think that if they knew what they don’t know instead of being what they will be, they wouldn’t be?” — Stephen Leacock, How to Make a Million Dollars, 1910

There was a young man of Cadiz,
Who inferred that life is what it is,
For he early had learnt,
If it were what it weren’t,
It could not be that which it is.

— J. St. Loe Strachey (editor of The Spectator)

| Quotations

Practical Politics

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On May 22, 1856, South Carolina representative Preston Brooks approached Massachusetts senator Charles Sumner as he sat writing at his desk in the U.S. Senate chamber. “Mr. Sumner,” he said, “I have read your speech twice over carefully. It is a libel on South Carolina, and Mr. Butler, who is a relative of mine.” Then he began to beat Sumner savagely with his gold-headed walking cane. Blinded with blood, Sumner at first was trapped under the desk, which was bolted to the floor, but he wrenched it free and staggered up the aisle, Brooks raining blows on his head until the cane snapped and Sumner collapsed unconscious. Even then Brooks held him by the lapel and continued to beat him with half the cane until the two were separated.

Sumner had denounced South Carolina senator Andrew Butler in a speech two days earlier in a dispute over slavery in the new territories of Kansas and Nebraska. Brooks was convicted of assault and fined $300, but he received no prison sentence, and his constituents returned him to office. Pro-slavery Southerners sent him hundreds of new canes, one inscribed “Hit him again.”

On Nov. 9, 1889, Col. A.M. Swope encountered Col. William Cassius Goodloe in the corridor of the Lexington, Ky., post office. The two had been battling for control of the state Republican party, and tragically they had adjoining mailboxes.

“You obstruct the way,” said Goodloe.

“You spoke to me,” said Swope. “You insulted me.”

Goodloe drew a knife. Swope drew a Smith & Wesson .38. Goodloe stabbed Swope 13 times, piercing his heart and nearly cutting off his hand. Swope shot Goodloe twice, tearing up his belly and setting his clothes afire. Swope died on the post office floor, and Goodloe staggered to a doctor’s office. He died two days later.

One witness said he never thought he would witness “such a magnificent display of manly courage and bravery.” Goodloe’s uncle, Cassius M. Clay, said of his nephew’s conduct, “I couldn’t have done better myself.”

| History · Society

Overtime

At Labuan, a British possession in North Borneo, there are only two English officials, Governor Leys and Lieut. Hamilton. The latter gentleman combines in himself the offices of colonial secretary, postmaster, treasurer, magistrate, inspector of police, inspector of the prison, chief commissioner of woods, colonial engineer, and master attendant. In these various capacities he corresponds from himself to himself in the most stately official style, and carefully copies and registers his numerous despatches.

— Poverty Bay Herald, Feb. 24, 1888

| Oddities

Surprise Appearance

Suppose we put eight white and two black balls into a bag and then draw forth the balls one at a time. If we repeat this experiment many times, which draw is most likely to produce the first black ball?

Most people answer 4, but in fact the first black ball is most likely to appear on the very first draw:

surprise appearance table

By symmetry, the second black ball is most likely to appear on the final draw.

(A.E. Lawrence, “Playing With Probability,” Mathematical Gazette, vol. 53 [December 1969], 347-354.)

| Science & Math

Early Adopter

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Mark Twain boasted both that “I was the first person in the world that ever had a telephone in his house” and that “I was the first person in the world to apply the type-machine to literature.” The latter may be true — Twain began experimenting with a Remington No. 2 typewriter in 1874. He reckoned that the book must have been Tom Sawyer; in fact it was probably Life on the Mississippi.

Other writers have been slower to adopt new technology. “This is a nervous letter,” wrote Flannery O’Connor to Cecil Dawkins in 1959. “I am congratulating you on the electric typewriter. It is very nice but I am not used to it yet. I keep thinking about all the electricity that is being wasted while I think what I am going to say next.”

| Literature · Technology

The Weight of the World

kinmont 8 natural handstands

In 1969 artist Robert Kinmont produced 8 Natural Handstands, a series of photographs of himself standing on his hands in various locations.

Each, he said, depicted an upside-down view of Atlas holding up the earth.

“This world,” wrote Thoreau, “is but canvas to our imaginations.”

| Art

Public Enemy

In his 1880 autobiography, Henry Armitt Brown recalls a strange incident from his student days. While a law student in November 1865, he had gone to bed one midnight and dreamed that he was lying on the cobblestones of a narrow street, held down by a “low-browed, thick-set man” who was bent on killing him. He threw the man off and bit at his throat, but the man smiled and brought out a bright hatchet. Brown’s friends leaped to his aid, but as they did so “I saw the hatchet flash above my head and felt instantly a dull blow on the forehead.” He tasted blood and seemed to hover in the air over his own body, where he could see “the hatchet sticking in the head, and the ghastliness of death gradually spreading over the face.”

The following morning, as they walked to school, a friend of his remarked that he’d had a strange dream that night. “I fell asleep about twelve and immediately dreamed that I was passing through a narrow street, when I heard noises and cries of murder. Hurrying in the direction of the noise, I saw you lying on your back fighting with a rough laboring man, who held you down. I rushed forward, but as I reached you he struck you on the head with a hatchet, and killed you instantly.” At Brown’s inquiry he described the murderer as “a thick-set man, in a flannel shirt and rough trousers: his hair was uncombed, and his beard was grizzly and of a few days’ growth.”

A week later Brown called at a friend’s house in New Jersey:

‘My husband,’ said his wife to me, ‘had such a horrid dream about you the other night. He dreamed that a man killed you in a street fight. He ran to help you, but before he reached the spot your enemy had killed you with a great club.’

‘Oh, no,’ cried the husband across the room; ‘he killed you with a hatchet.’

“I remembered the remark of old Artaphernes,” Brown wrote, “that dreams are often the result of a train of thought started by conversation or reading, or the incidents of the working time, but I could recall nothing, nor could either of my friends cite any circumstance ‘that ever they had read, had ever heard by tale or history,’ in which they could trace the origin of this remarkable dream.”

| Oddities