Starting Funds

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Three men play a game, agreeing that in each round the loser will double the money of each of the other two. After three rounds, each man has lost one time, and each man has $24. How much did each have at the start of the game?

Click for Answer

A Geometric Illusion

geometric illusion

Which of the two shaded areas is larger, the central disc or the outer ring?

Surprisingly, they’re equal. Each of the concentric circles has a radius 1 unit larger than the last. So the area of the central disc is π × 32 square units, and the area of the outer ring is π × 52 – π × 42 = π × 32 square units. So the two areas are the same.

A Cool Customer

A brewery stored its beer in a cellar some distance from the bottling plant. The cellar was cooled by pipes that circulated a saline solution from a central cooling unit. The main pipe that connected this cooling unit and the cellar happened to pass near the cellar of a retailer.

The brewery’s owner eventually discovered that the retailer was using the saline solution to cool his own cellar. He sued the retailer for theft, but the judge ruled, “In accordance with Article 242 of the Criminal Code, theft is the unlawful appropriation of commodities belonging to another party. In the present case no theft has been committed, since the saline solution was not misappropriated; rather, it was returned in its entirety to the brewery’s main pipe.”

The brewery owner appealed the case, arguing, “The issue is not the theft of saline solution but the theft of energy. If the saline solution is used to cool the defendant’s cellar in addition to my own, I have to pay more for electricity to operate the central cooling unit.”

The court of appeals ruled: “The saline solution acquires heat from the retailer’s cellar; therefore, energy belonging to the brewery is not being stolen. On the contrary, the brewery is receiving gratuitous energy from the retailer.”

This story appeared in a German scientific monograph, “Questions of Thermodynamical Analysis,” by P. Grassman. In propounding it in May 1990, Quantum added, “We all agree the judge was wrong, but not everyone can correctly explain his error. Can you?”

Progress

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Letters to the Sydney Morning Herald during the planning of the Sydney Opera House:

“Faced with the nightmare illustrated in your columns, some 25th century Bluebeard’s lair, its ominous vanes pointed skywards apparently only for the purpose of discharging guided missiles or some latter-day nuclear Evil Eye, words fail.”

— W.H. Peters, Sydney, Jan. 31, 1957

“To me, the winning design suggests some gargantuan monster which may have wandered over the land millions of years ago. It certainly is right out of place beside the dignity of the Harbour Bridge.”

— M. Rathbone, Kensington, Jan. 31, 1957

“This whale of a monument to the clever ugliness of ‘modern’ art will be a constant eyesore. Its over-finished roof with many curved surfaces all covered with white tiles will be a glaring monstrosity. Could not the suffering which it will cause be more equitably distributed by constructing the fins in such a way that they will act as giant megaphones and thus keep residents on the north supplied with the dying screams of melodramatic sopranos?”

— J.R.L. Johnstone Beecroft, Feb. 1, 1957

“With all respects to so-called modern art, I feel that the design is completely unbefitting our foreshores. Perhaps the judges had in mind the installation of a Big Dipper on the peak of the roof to help the opera company balance its budget.”

— Jack Zuber, Kingsgrove, Feb. 1, 1957

In 2003 Danish architect Jørn Utzon received the Pritzker Architecture Prize, architecture’s highest honour. The citation read, “There is no doubt that the Sydney Opera House is his masterpiece. It is one of the great iconic buildings of the 20th century, an image of great beauty that has become known throughout the world — a symbol for not only a city, but a whole country and continent.”

Ear and Eye

Peculiarly British limericks:

There was a young fellow of Beaulieu,
Who loved a fair maiden most treaulieu.
He said, “Do be mine,”
And she didn’t decline,
So the wedding was solemnized deaulieu.

There was a young maid of Aberystwyth,
Who took corn to the mill to make grystwyth,
The miller, named Jack,
With a pat on her back,
Pressed his own to the lips that she kystwyth.

There was a mechalnwick of Alnwick,
Whose opinions were anti-Germalnwick;
So when war had begun,
He went off with a gun
The proportions of which were Titalnwick.

There was a young lady of Slough,
Who went for a ride on a cough.
The brute pitched her off
When she started to coff;
She ne’er rides on such animals nough. (Langford Reed)

A bald-headed judge called Beauclerk
Fell in love with a maiden seau ferk
Residing at Bicester,
Who said when he kicester,
“I won’t wed a man without herk.”

See This Sceptred Isle and Sound Rhymes.

A Wand’ring Minstrel

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Gilbert and Sullivan gained fame around the world for their operettas. But where W.S. Gilbert could be impatient and irascible, Arthur Sullivan was full of lively good humor. Vernon Blackburn remembered a curious incident from his travels:

It so happened that I journeyed to Rome almost immediately after my hearing for the first time The Yeomen of the Guard. I was full of its melodies, full of its charm; and one night walking through the Piazza di Spagna, I was whistling the beautiful concerted piece, ‘Strange Adventure,’ whistling it with absolutely no concern and just for the love of the music. A window was suddenly opened and a little face looked out in the moonlight, while a thin voice exclaimed in apparent seriousness: ‘Who’s that whistling my music?’ I looked up with astonishment and with some awe, and told the gentleman that if he were Sir Arthur Sullivan it was his music that I was whistling; and, said I, I thought that the copyright did not extend to Italy. I remember how he convulsed with laughter somewhat to my discomfiture, and closed the window to shut out the chill of the night. I never dared at that period of life to make any call upon one whom I considered to be so far above the possibilities of intercourse.

In his 1908 memoir, baritone Rutland Barrington remembered: “There was invariably enormous competition for seats at the Savoy premieres, and it was difficult to find room for all friends. On one occasion a great personal friend of Sullivan’s, Mr Reuben Sassoon, had applied too late, and backed his application with a piteous appeal to Sullivan for help. He at once said to Carte, ‘If he’ll change the first letter of his name, I’ll give him a seat in the orchestra.'”

“The Roadside Littérateur”

There’s a little old fellow and he has a little paintpot,
And a paucity of brushes is something that he ain’t got,
And when he sees a road sign, the road sign he betters,
And expresses of himself by eliminating letters.

Thus THROUGH ROAD
Becomes ROUGH ROAD
And CURVES DANGEROUS
Is transformed to CURVES ANGER US
And 24-HOUR SERVICE
Turns into 24-HOUR VICE
And MEN AT WORK IN ENTRANCE
Is reduced to MEN AT WORK IN TRANCE
An SLOW DOWN BRIDGE ONE WAY
Is triumphantly condensed to
LOW DOWN BRIDE ON WAY

But the old fellow feels a slight dissatisfaction
With the uninspiring process of pure subtraction.
The evidence would indicate he’s taken as his mission
The improvement of the road signs by the process of addition.

Thus TRAFFIC LIGHT AHEAD
Becomes TRAFFIC SLIGHT AHEAD
And GAS AND OIL
Is improved to GASP AND BOIL
And simple REST ROOMS
Appear as QUEEREST ROOMS
And UNDERPASS ONE WAY
Emerges as UNDERPASS GONE AWAY
And (perhaps his masterpiece)
RIGHT
EAST BOUND
TUNNEL

Is elaborated to

FRIGHTENED
BEASTS ABOUND
IN TUNNEL

Thus we see the critical mood
Becomes the creative attitude.

— Morris Bishop

Podcast Episode 359: Stranded in Shangri-La

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Image: Wikimedia Commons

In 1945, a U.S. Army transport plane crashed in New Guinea, leaving three survivors marooned in the island’s mountainous interior. Injured, starving, and exhausted, the group seemed beyond the hope of rescue. In this week’s episode of the Futility Closet podcast we’ll describe the plight of the stranded survivors and the remarkable plan to save them.

We’ll also reflect on synthetic fingerprints and puzzle over a suspicious notebook.

See full show notes …

Triple Threat

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Image: Wikimedia Commons

Designed in Belgium in 1860, the Apache centerfire revolver attracted a following in the French underworld because it combined three weapons in one: a single-action six-shot revolver, a dual-edged bayonet, and a set of brass knuckles that doubles as the revolver’s grip. The knife and the knuckle duster fold inward, so the whole apparatus can fit easily into a pocket or bag.

Without sights, trigger guard, or safety, the gun is tricky to operate, but then you probably won’t want it for long-range shootouts. “It was designed for self-defence and to be used at very close quarters,” said Charles Hartley, who auctioned off one of the few specimens in 2014. “There is no barrel to the gun so the user would have had to have had it pressed up against someone’s chest.”

Though its pinfire bullets are now obsolete, the weapon’s novelty still attracts collectors — another Apache, auctioned in 2013, drew $2,850.

(Thanks, Carlos.)