A Fashion Puzzle

According to a British censorship manual from World War II (PDF, page 14), this sketch, published in a wartime newspaper, contained a secret message, ostensibly hidden in Morse code in the arrangement of dots and lines on the women’s dresses. The message is “Heavy reinforcements for the enemy expected hourly,” or, in the German original, “Massive Feindverstärkungen werden stündlich erwartet.”

A second message is hidden in the signature, written in a French shorthand. In English this read “Before Arras”; in German it was probably “Vor Arras.”

Unfortunately, the manual doesn’t explain the method by which these messages were hidden, and to date no one has been able to re-establish it. Where are these messages to be found in the image? Encryption expert Klaus Schmeh writes, “So far, I could neither find the morse message nor the shorthand message. I even went to the British Archive in London to look at the original document and to take high resolution photographs. It didn’t help.”

On his blog, Schmeh presents one of these high-resolution images, as well as a second mystery from the same manual. See the comments on that post for some suggestions from his readers.

May 16, 2019May 16, 2019 | History

Geography

Brad Taylor offered this baseball puzzle in the October 2001 issue of MIT Technology Review:

The Red Sox beat the Orioles 9 to 4 in 17 innings. Where was the game played?

	Select Click for Answer
Baltimore. In order to win by more than 4 in extra innings a team must bat first. So the Red Sox were visiting the Orioles. (Thanks, Bruce.)

May 16, 2019May 15, 2019 | Puzzles

Black and White

I don’t know who came up with this, but I thought it was cute. Can White checkmate Black in two moves from this position?

	Select Click for Answer
Yes. 1. Rb3 forces 1. … Ka5, and now 2. Ra3 is mate. From the r/chess subreddit.

May 15, 2019May 15, 2019 | Puzzles

Unwholesome

Prove that if n is a positive integer greater than 1, then

$\displaystyle 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}$

is not an integer.

	Select Click for Answer
Find the least common multiple of 2, 3, …, n, and recast each fraction using this denominator. Now all the numerators will be even except for one term, the one whose original denominator had been the highest power of 2 that doesn’t exceed n. Thus the sum of the numerators is odd while the common denominator is even.

May 15, 2019May 14, 2019 | Puzzles

Growing Room

corbusier spiral

How can an art gallery accommodate a growing collection? In 1931 Le Corbusier proposed a Musée à croissance illimitée that would grow like a snail’s shell, coiling in a rectangular spiral as needs required and as funds became available.

“The means of orienting one’s self in the museum is provided by the rooms at half-height which form a ‘swastika,'” he explained. “Every time a visitor, in the course of his wanderings, finds himself under a lowered ceiling he will see, on one side, an exit to the garden, and on the opposite side, the way to the central hall. The Museum can be developed to a considerable length without the square spiral becoming a labyrinth.”

He presented the idea as a museum for Philippeville in North Africa in 1939, in a town planning project for Saint-Dié in 1945, and in a competition design to reconstruct the center of Berlin in 1958, but it was never realized.

(From Ulrich Conrads and Hans G. Sperlich, The Architecture of Fantasy, 1962.)

May 14, 2019May 14, 2019 | Art

Multimedia

For his 1938 film Alexander Nevsky, Sergei Eisenstein worked so closely with composer Sergei Prokofiev that individual shots in the climactic “battle on the ice” were timed to correspond to the length of musical phrases.

Their collaboration during editing to marry music and imagery set the modern standard for filmmakers; Valery Gergiev, principal conductor of the London Symphony Orchestra, called Prokofiev’s score “the best ever composed for the cinema.”

May 14, 2019May 13, 2019 | Art

Unquote

“The enemy of art is the absence of limitations.” — Orson Welles

May 13, 2019May 13, 2019 | Quotations

Podcast Episode 248: Smoky the War Dog

In 1944, an American soldier discovered a Yorkshire terrier in an abandoned foxhole in New Guinea. Adopted by an Army photographer, she embarked on a series of colorful adventures that won the hearts of the humans around her. In this week’s episode of the Futility Closet podcast we’ll tell the story of Smoky the dog, one of the most endearing characters of World War II.

We’ll also contemplate chicken spectacles and puzzle over a gratified diner.

See full show notes …

May 13, 2019May 20, 2019 | History · Podcast

Red and Blue

A problem from the 1996-1997 Estonian Mathematical Olympiad:

A square tabletop measures 3n × 3n. Each unit square is either red or blue. Each red square that doesn’t lie at the edge of the table has exactly five blue squares among its eight neighbors. Each blue square that doesn’t lie at the edge of the table has exactly four red squares among its eight neighbors. How many squares of each color make up the tabletop?

	Select Click for Answer
The tabletop measures 3n × 3n, so we can divide it evenly into n² 3 × 3 squares that together tile the surface completely. For each of these 3 × 3 squares: If the unit square at the center is red, there are 5 blue squares and hence 3 red squares adjoining it. If the unit square at the center is blue, there are 4 red squares and hence 4 blue squares adjoining it. That means that each of our 3 × 3 squares is made up of the same constituents: 5 blue squares and 4 red squares. So the 3n × 3n tabletop is made up of 5n² blue squares and 4n² red squares. It remains to show that such a coloring is possible. See the link below, pages 31-32, for a diagram. (From “The Olympiad Corner,” Crux Mathematicorum 29:1 [February 2003], 22-36.)

Click for Answer

May 12, 2019 | Puzzles

“Oscar’s Morning Work”

https://commons.wikimedia.org/wiki/File:Oscar_Wilde_Statue.JPG — Image: Wikimedia Commons

Oscar Wilde, among his various stories told here of which he was always the aesthetic hero, related that once while on a visit to an English country house he was much annoyed by the pronounced Philistinism of a certain fellow guest, who loudly stated that all artistic employment was a melancholy waste of time.

‘Well, Mr. Wilde,’ said Oscar’s bugbear one day at lunch, ‘and pray how have you been passing your morning?’ ‘Oh! I have been immensely busy,’ said Oscar with great gravity. ‘I have spent my whole time over the proof sheets of my book of poems.’ The Philistine with a growl inquired the result of that.

‘Well, it was very important,’ said Oscar. ‘I took out a comma.’ ‘Indeed,’ returned the enemy of literature, ‘is that all you did?’ Oscar, with a sweet smile, said, ‘By no means; on mature reflection I put back the comma.’ This was too much for the Philistine, who took the next train to London.

— Syracuse [N.Y.] Standard, May 21, 1884

May 11, 2019 | Literature