The Three-Hat Problem

In the October 2003 issue of MIT Technology Review, Donald Aucamp offered this conundrum:

Three logicians, A, B, and C, are wearing hats. Each hat displays a positive integer, and each logician can see his companions’ numbers but not his own. All of them know that the numbers are positive integers and that one of the numbers is the sum of the other two. The three then take turns in a contest to see who can determine his number first. In the first round, all three pass, but in the second round A correctly states his number is 50. What are the other two numbers, and how did A know that his was 50?

Click for Answer


  • Queen Victoria and her future husband, Albert, were born with the help of the same midwife.
  • Ulysses Grant and Harry Truman had the same meaningless middle initial.
  • SLICES OF BREAD is an anagram of DESCRIBES LOAF. (Dean Mayer)
  • France’s longest land border is with Brazil (via French Guiana).
  • “A creed is an ossified metaphor.” — Elbert Hubbard

(Thanks, Tony.)

All God’s Creatures,_with_a_description_of_the_habits_and_economy_of_the_most_interesting_(1883)_(14752342245).jpg

“Animals seen as sport become to the mind meat, and cease to be individual creatures, so that you may feed fishes, but catch fish, ride elephants, but hunt elephant, fatten turkeys and pigs, but chase turkey and pig, throw bread to ducks, but shoot duck; and some creatures, whom God would seem to have created merely for the chase, such as grouse and snipe, require no plural forms at all. And even as few as two pigs become pig if hunted.” — Rose Macaulay

In Thomas Tryon’s Country-Man’s Companion (1684), the birds upbraid man, “O thou Two-Leg’d unfeather’d unthinking Thing,” for his slaughter:

How many thousands of our innocent kind have been murthered by Guns, Traps, Snares, &c? and many thousands both of our Males and Females have lost their loving Mates by the like Stratagems, and no Pity or Compassion taken by Man on our miserable Sufferings, but rather they encourage each other to our destruction, and cry, Hang these scurvey Birds, shoot them, destroy them, they are good for nothing but to eat up our Corn: As if God that created us had done it in vain, as if he intended us not a subsistance and Food? What right I pray, has Man to all the Corn in the world? or why should he grumble and repine if we take a few Grains to supply our Necessities, whilst he squanders away such Heaps upon his Lusts? Wherein I fear he has so much besotted himself, and by continual Practice is become so harden’d, and has so powerfully irritated the dark Wrath in himself, that all our Remonstrances to him to move him to Mercy and Compassion, and to forbear polluting himself with the Blood of the Innocent, will be but in vain, and that we must still sigh and groan under his Cruelty and Tyranny, which as long-run will return seven fold upon his own guilty Head.

The Chemists’ Drinking Song

In a 1963 essay, Isaac Asimov pointed out that paradimethylaminobenzaldehyde can be sung to the tune of “The Irish Washerwoman.” Inspired, John A. Carroll wrote this jig:

(chorus:) Paradimethylaminobenzaldehyde
Sodium citrate, ammonium cyanide
Phosphates and nitrates and chlorides galore
Just have one o’ these and you’ll never need more.

Got messed up last night on furfuryl alcohol
Followed it down with a gallon of propanol
Drank from mid-morning til late afternoon
Then spat on the floor and blew up the saloon.

(repeat chorus)

Powdered aluminum, nitrogen iodide
Slop it around and add some benzene
Then top off the punch with Fluorescein

(repeat chorus)

Whiskey, tequila and rum are too tame,
The stuff that I drink must explode into flame.
When I break wind it strips all the paint in the room,
And rattles the walls with an earthshaking boom.

(repeat chorus)

Go soak your head in a jar of formaldehyde
Scrub very hard, then rinse out your mane
In dichlorodiphenyltrichloroethane!

Imitation Game

Hemingway said, “The step up from writing parodies is writing on the wall above the urinal.” Yet the International Imitation Hemingway Competition attracted more than 24,000 entries in its first 10 years, as well as celebrity judges including Ray Bradbury, George Plimpton, and Joseph Wambaugh. The annual contest started when owners Jerry Magnin and Larry Mindel sought a way to promote their tavern, Harry’s Bar & American Grill in Century City, Calif. From there the competition passed from sponsor to sponsor until United Airlines adopted it for its in-flight magazine, Hemispheres. The final winner, in 2005, was “Da Moveable Code,” by Illinois cardiologist Gary Davis:

Paris could be very fine in the winter when it was clear and cold and they were young and in love but that winter of 1924 they quarreled badly and she left for good. Paris, the city of light, turned dark and sodden with sadness. But it was still a damn fine place and he hated to leave it so he sat in the cafés all day and drank wine and thought about writing clean short words on bright white paper.

He preferred Café des Amateurs, on the Place St-Michel. The waiters in their long aprons respected him and he did good work there, defeating them all in the arm wrestling and the drinking and the dominoes and the boxing. They told him timeless stories of love and cruelty and death. That was good, because his Michigan stories had dried up, his jockeys and boxers had worn out, and sometimes he worried his oeuvre might be over.

One afternoon in late autumn two gypsies came into the café, a ragged old man and his daughter. She carried a crystal ball between her arms. They went table to table telling fortunes. Soon they came to him. Dark eyes stared at his palm, then into the ball. Two fair arms well cradled it in her lap.

‘Guapa, I am not one for whom the ball tells –‘ he started, but she put a finger to his lips. She studied his face. Her dark eyes were like deep forest pools where trout the color of pebbles hang motionless in the cool flowing eddies, waiting for the good larvae, the tasty larvae. Sun-burned, confident, loving eyes the color of the sea. He wrote that down.

‘Inglés, my ball shows what you must write.’

‘Americain.’ It was like saying hello to a statue. He wrote that down, too.

‘Picture this,’ she started, ‘First I see a corpse in the Louvre, by the Mona Lisa. A gruesome ritual murder. The police suspect you, an obscure professor. You flee, through the Tuilleries, then across the river.’

‘Into the trees?’

‘Murders in churches, arcane symbols and codes, Opus Dei, Swiss bankers, split-second escapes, powerful sects …’

‘Powerful sex?’

She paused. ‘I see a mysterious redhead at your side.’

‘Powerful sex?’

Her eyes found his. ‘I see a major motion picture.’

‘No,’ he shook his head earnestly. ‘Not now. I must master the art of narration in the best and simplest way. Lean hard narrative prose.’

She rolled her eyes, sunburned eyes. ‘Isn’t it pretty to think so …’

‘I write terrific stuff here, guapa,’ he said, writing that down. ‘True sentences. Not the words above the urinal.’

‘Don’t call me guapa, Papa.’

‘Drop the Papa, guapa.’

‘Whatever,’ she sighed and turned to the ball again. ‘Try this, loser Americain. An old fisherman loves baseball. He catches a big fish, but sharks eat it.’

He slapped her hard across the ear. It was a good ear, sunburned and confident. And just like that, the old man and the seer disappeared.

To celebrate his win, Davis said he was “toying with the idea of growing a beard and fishing Lake Michigan for marlin.”

A Game Afoot

In “The Adventure of the Final Problem,” Sherlock Holmes flees London, pursued by his archenemy, James Moriarty. Both are headed to Dover, where Holmes hopes to escape to the continent, but there’s one intermediate stop available, at Canterbury. Holmes faces a choice: Should he get off at Canterbury or go on to Dover? If Moriarty finds him at either station he’ll kill him.

In their 1944 Theory of Games and Economic Behavior, mathematician John von Neumann and economist Oskar Morgenstern address this as a problem in game theory. They set up the following payoff matrix showing Moriarty’s calculations:

canterbury game

Von Neumann and Morgenstern conclude that “Moriarty should go to Dover with a probability of 60%, while Sherlock Holmes should stop at the intermediate station with a probability of 60% — the remaining 40% being left in each case for the other alternative.”

As it turns out, that’s exactly what happens in the story — Holmes and Watson get out at Canterbury and watch Moriarty’s train roar past toward Dover, “beating a blast of hot air into our faces.” “There are limits, you see, to our friend’s intelligence,” Holmes tells Watson. “It would have been a coup-de-maître had he deduced what I would deduce and acted accordingly.”

(It’s not quite that simple — in a footnote, von Neumann and Morgenstern point out that Holmes has excusably replaced the 60% probability with certainty in his calculations. In fact, they say, the odds favor Moriarty — “Sherlock Holmes is as good as 48% dead when his train pulls out from Victoria Station.”)

The Burger Savant

Phyllis Brienza, a waitress at Manhattan’s Bun & Burger since the day it opened on Oct. 26, 1970, became famous for a unique gift — she had “such an extraordinary memory for the niceties of appetite that regular clients do not have to speak their wishes aloud,” reported Israel Shenker in the New York Times in 1975.

She recognized a customer in a Nehru jacket as “medium with half a bun and French.” A man in a raincoat was a “well,” a well-done hamburger.

“If you order it once one way, that’ll stick in my mind,” she said. “When someone new comes in, I think to myself, ‘That’s a medium,’ or ‘that’s a rare.’ Sometimes they have this serious look and I think, ‘That must be a well.’ Usually I’m right.”

In 1974 she received a Christmas card from a customer whom she remembered at once. It was signed “Medium rare, pressed.”

Odd Clocks

With the help of Australian engineer David Cox, the Swedish design firm Humans Since 1982 created this “clock clock,” a clock made of clocks whose hands stop every 60 seconds to display the military time in square numerals.

The clock fountain at Osaka’s South Gate Building, below, “prints” the time (and some surprisingly complex graphics) in sheets of water, somewhat like a dot matrix printer.


At the beginning of 1983’s Return of the Jedi, the third film in the original Star Wars trilogy, an alien script could be seen on monitor readouts on the second Death Star. Devised by artist Joe Johnston, these lines weren’t intended to be read, but West End Games art director Stephen Crane gave each character a name, creating an alphabet for gamers to use.

With Lucasfilm’s approval, this has become “Aurabesh,” a 34-letter writing system named for its first two letters, aurek and besh. And Aurabesh has now found its way into Star Wars films, books, comics, and TV series. Since the 2004 DVD release of A New Hope, the original film in the series, the words on the Death Star’s tractor beam control have appeared in Aurebesh, bringing the alphabet’s adoption full circle.

“The Aurebesh is a lot like Boba Fett,” Crane wrote. “It is a facet of the Star Wars phenomenon that had its origin as a cinematic aside, but which has come to be widely embraced, far out of proportion to its humble origins.”


On Sept. 2, 1945, an American Navy squadron came ashore at Sagami Bay near Yokohama to demilitarize the Japanese midget submarines in the area. They found this notice on the door of a marine biological research station there, left by embryologist Katsuma Dan.

The Americans honored his wish: On the last of 1945 he was summoned by an officer of the U.S. First Cavalry and handed a document releasing the station back to the University of Tokyo.

The notice is on display at the Woods Hole Oceanographic Institution’s Marine Biological Laboratory (here’s the full story).