“Counting the Wounded”

A puzzle by Henry Dudeney:

When visiting with a friend one of our hospitals for wounded soldiers, I was informed that exactly two-thirds of the men had lost an eye, three-fourths had lost an arm, and four-fifths had lost a leg. ‘Then,’ I remarked to my friend, ‘it follows that at least twenty-six of the men must have lost all three — an eye, an arm, and a leg.’ That being so, can you say exactly how many men were in the hospital? It is a very simple calculation, but I have no doubt it will perplex a good many readers.

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Flying Ash

Images: Wikimedia Commons

Here’s a striking sign of the pervasive influence of the Industrial Revolution: It darkened England’s moths. Before 1811, the peppered moth, Biston betularia, had a white body. But as soot darkened trees, lighter-bodied insects became more visible to birds and other predators. By 1848 the frequency of dark-bodied moths in industrial regions had increased dramatically, one of the first documented instances of Darwin’s principle of natural selection. American geneticist Sewall Wright called it “the clearest case in which a conspicuous evolutionary process has actually been observed.”

Somewhat related: A curious wartime observation by Gertrude Stein, in Alsace, from The Autobiography of Alice B. Toklas:

Another thing that interested us enormously was how different the camouflage of the french looked from the camouflage of the germans, and then once we came across some very neat camouflage and it was american. The idea was the same but as after all it was different nationalities who did it the difference was inevitable. The colour schemes were different, the designs were different, the way of placing them was different, it made plain the whole theory of art and its inevitability.


In 1837 English journalist Albany Fonblanque wrote, “Sir Robert Peel was a smooth round peg, in a sharp-cornered square hole, and Lord Lyndenurst is a rectangular square-cut peg, in a smooth round hole.”

Which of these is the better fit? In other words, which is larger, the ratio of the area of a circle to a circumscribed square, or the area of a square to a circumscribed circle?

In two dimensions, these ratios work out to π/4 and 2/π, respectively, so a round peg fits better into a square hole than a square peg into a round hole.

But, strangely, Berkeley mathematician David Singmaster discovered in 1964 that this is true only in dimensions less than 9. For n ≥ 9 the n-dimensional unit cube fits more closely into the n-dimensional unit sphere than vice versa.

There’s a moral in there, but I don’t know what it is.

(David Singmaster, “On Round Pegs in Square Holes and Square Pegs in Round Holes,” Mathematics Magazine 37:5 [November 1964], 335-337.)

Spun Wool

Image: Flickr

The wordplay journal Word Ways has made a tradition of revising the familiar rhyme “Mary Had a Little Lamb” under various constraints. Some examples:

Alliteration: James Puder, WW February 1998

Astral Aries’ avatar, alabaster “Aly,”
Ann adopted; allies are Ann and Ann’s argali.
Ann, an able autodidact, academic angst avoids;
And arch Aly’s Argus-eyed act awes astonished anthropoids.

Pangram (uses all 26 letters): A. Ross Eckler, WW February 1989

Mary had a little lamb with fleece extremely white;
Instead of grazing, all alone, the lamb kept her in sight.
It followed her to school one day, which was against the rule;
The children thought it quite a joke to view a lamb in school.

Words formed of chemical element symbols: WW February 2008

In ClAsS ONe MoRn SHe TaKEs HEr PLaCe; TeAcHEr CrIEs “SHoO! RUN!”
HeAr THoSe LaSSiEs ScReAm “HoW CuTe!” ThIS AgNUS — PURe FUN!”

Four-letter words: Dave Morice, WW November 2006

Mary kept some tiny lamb with wool hued just like snow,
Each spot that this girl, Mary, went, that lamb went also (slow).
Once lamb went past home room with girl. That bent some rule last year.
This made kids loud, glad, made them play: they eyed lamb very near.

Three-letter and shorter words: Jeff Grant, WW May 2004

Amy had an ewe so wee, it was an icy hue,
And any way our Amy led, the ewe it did go too.
It ran in to her den one day (an act not in the law).
Oh, the fun for boy and gal! The ewe so wee all saw.

Child Abuse


Nominative determinism is the theory that people gravitate toward occupations that reflect their names. In 1994 New Scientist noted that a new book, Pole Positions: The Polar Regions and the Future of the Planet, had been written by one Daniel Snowman, and that another, London Under London: A Subterranean Guide, received just two weeks later, had been written by Richard Trench. Psychologist Jen Hunt of the University of Manchester pointed out an article on incontinence in the British Journal of Urology whose authors were A.J. Splatt and D. Weedon.

If the theory is valid, then the naming of children is more momentous than we think. Harry Truman’s vice president, Alben William Barkley, above, was originally named Willie Alben Barkley, and contended that no one named Willie Alben could be elected superintendent of the county poorhouse. He changed his name to Alben William.

“In fact,” he wrote in his autobiography, “I think one of the graver shortcomings of my long career as a lawmaker was my failure to introduce a bill making it mandatory for parents to postpone the naming of their children until the youngsters are old enough to pick out a name for themselves.”

The 7-11 Problem

A man goes into a 7-11 store, buys four items, and notices that the bill totals $7.11. Even more interestingly, the product of the four prices is 7.11. What are the prices?

The answer is $1.20, $1.25, $1.50, and $3.16. There’s no thunderbolt insight to find; the problem yields to patient consideration.

Who came up with it? The most common credit I’ve seen is Doug Brumbaugh of the University of Central Florida. I found it in Crux Mathematicorum; see problem M203 in the September 2006 issue for Richard K. Guy’s solution.

The Floating Water Bridge

When a high voltage difference is applied, a liquid bridge of deionized water can sustain itself between two beakers even when they’re separated by 25 millimeters.

British engineer William Armstrong first reported this in an 1893 lecture. The phenomenon is known to be founded in surface polarization, but it’s still not completely understood.

No Exit

On Feb. 23, 1950, a railroad signal worker discovered the badly mangled body of a man in a tunnel south of Salzburg, Austria. Among its torn clothes police found the diplomatic passport and service identification of U.S. Navy captain Eugene S. Karpe, who’d been returning to the United States after serving for three years as naval attaché in Rumania.

It appeared that Karpe had fallen from the door of the Arlberg-Orient Express as the train sped around a curve in the dark of night. The train car had very small windows, and the doors had been locked automatically before the train had entered the tunnel. A student testified that he’d had breakfast and lunch with Karpe on the day he was killed; Karpe had had an ordinary breakfast and only a bottle of mineral water for lunch, eliminating the theory that he’d been drunk.

Karpe was the second-highest-ranking American mysteriously killed in Austria since the end of World War II. The first had been found stabbed and beaten to death after having been seen in the company of four men wearing Russian uniforms. Karpe was a close friend of Robert Vogeler, who had just been convicted as a spy and saboteur in Bucharest and sentenced by a people’s court to five years in prison.

The Austrian police contended that Karpe’s death was not a suicide and didn’t appear to be an accident. Formally the case remains unsolved.

(From Scott Baron and James Wise Jr., Dangerous Games: Faces, Incidents, and Casualties of the Cold War, 2013.)