Double Trouble

http://commons.wikimedia.org/wiki/File:M%C3%B6bius_strip.jpg
Image: Wikimedia Commons

The properties of the simple Möbius strip are well understood: Take a strip of paper, give it a half-twist, and tape the ends together. Now an ant can traverse the full length of the loop, on both sides, and return to its starting point without ever crossing an edge.

But try doing the same thing with two strips of paper. Pair the strips, give them a half-twist, and connect the ends. Now it’s possible to insert a toothpick between the bands and to draw the toothpick along the entire length of the loop, which seems to show that they’re two distinct objects. But if you draw a line along either strip, starting anywhere, you’ll find that you traverse both strips and return to your starting point.

“I have known people to ponder this for hours while listening to Pink Floyd without ever fully appreciating what they have beheld,” writes Clifford Pickover in The Möbius Strip. Are you holding one object or two?

Words and Numbers

THREE NONILLION THIRTEEN TRILLION NINETEEN BILLION contains:

1 B
2 Hs
3 Rs
4 Os
5 Ts
6 Ls
7 Es
8 Is
9 Ns

At least two numbers produce similar results in Spanish:

SEISCIENTOS ONCE NONILLONES SETECIENTOS DIECISEIS

UN OCTODECILLÓN DOSCIENTOS CINCO NONILLONES SEISCIENTOS CINCO

(Thanks, Claudio.)

Black and White

smullyan sherlock holmes chess problem 1

Raymond Smullyan presented this puzzle on the cover of his excellent 1980 book The Chess Mysteries of Sherlock Holmes. Black moved last. What was his move?

Click for Answer

A Poet’s Life

A letter from Wallace Stevens to his wife, July 19, 1916:

Eminent Vers Libriste Arrives in Town; Details of Reception

St Paul, Minn. July 19, 1916. Wallace Stevens, the playwright and barrister, arrived at Union Station, at 10.30 o’clock this morning. Some thirty representatives of the press were not present to greet him. He proceeded on foot to the Hotel St. Paul, where they had no room for him. Thereupon, carrying an umbrella and two mysterious looking bags, he proceeded to Minnesota Club, 4th & Washington-Streets, St. Paul where he will stay while he is in St. Paul. At the Club, Mr. Stevens took a shower-bath and succeeded in flooding not only the bath-room floor but the bed-room floor as well. He used all the bath-towels in mopping up the mess and was obliged to dry himself with a wash-cloth. From the Club, Mr. Stevens went down-town on business. When asked how he liked St. Paul, Mr. Stevens, borrowing a cigar, said, ‘I like it.’

Dear Bud:

The above clipping may be of interest to you. Note my address. I am waiting for some papers to be typed — ah! Give my best to the family.

With love,

Wallace

Lazy Tennis

You’ve just won a set of singles tennis. What’s the least number of times your racket can have struck the ball? Remember that if you miss the ball while serving, it’s a fault.

Click for Answer

Spring Fever

http://www.google.com/patents/US2808807

Inventors Neil and William Winton patented this “parakeet exercise perch” in 1957, in hopes of improving bird morale:

Parakeets are fast becoming common household pets and one of the first objectives of the new owner of a parakeet is to teach the parakeet to utter words that will amuse the owner thereof. …

An object of the present invention is to provide an exercising perch which will facilitate getting a parakeet in a cheerful state of mind so as he will talk or chatter more profusely.

The coil is designed so that “when a parakeet alights on any one of the coils, it will bounce up and down, sway with the weight of the bird, and oscillate back and forth.” The cage-mounted version shown here is only one option; the Wintons also envisioned a free-standing model and one that can be mounted on a wall (which is “entertaining to a parakeet possessing the ability to nose dive through a sleeve member”).

I don’t know how the parakeets responded. If they conquer the earth someday, perhaps they’ll give each of us a trampoline.

Exeunt

In 1853, a writer to Notes & Queries observed that the third line of Gray’s Elegy can be transposed 11 different ways while retaining its sense:

The ploughman homeward plods his weary way.
The weary ploughman plods his homeward way.
The weary ploughman homeward plods his way.
The ploughman, weary, plods his homeward way.
The ploughman weary homeward plods his way.
Weary the ploughman plods his homeward way.
Weary the ploughman homeward plods his way.
Homeward the ploughman plods his weary way.
Homeward the ploughman weary plods his way.
Homeward the weary ploughman plods his way.
The homeward ploughman weary plods his way.
The homeward ploughman plods his weary way.

“It is doubtful whether another line can be found, the words of which admit so many transpositions, and still retain the original meaning,” he wrote. Forty-two years later, the editors of Miscellaneous Notes and Queries filled four pages with 252 transpositions:

Plods the ploughman, weary, his homeward way.
His weary way the homeward ploughman plods.
Homeward plods his way the ploughman, weary.
His homeward way the weary ploughman plods.
The weary ploughman homeward plods his way.
The homeward ploughman, weary, his way plods.
The weary ploughman plods his way homeward.
Plods the weary ploughman his way homeward.
Weary, the ploughman plods his homeward way.
His way homeward plods the weary ploughman.
Plods, weary, the ploughman his way homeward.
Weary his way plods homeward the ploughman.
The ploughman, weary, homeward plods his way.
His way plods homeward the ploughman, weary.
Homeward, weary, the ploughman his way plods.

They even offered a year’s subscription to any reader who could add to the list. I can’t tell whether anyone took them up on it — perhaps they were too tired.

Riddling Letters

http://books.google.com/books?id=9OEvAAAAMAAJ

In 1891 the Strand ran two features on oddities encountered by the British post office, which kept facsimiles of the most puzzling letters in three great scrapbooks. “Many a pictorial curiosity passes through the post; and the industrious letter-sorter is often bewildered as to where to despatch missives, the envelopes of which bear hieroglyphics which would positively out-Egypt Egypt.”

Some examples are merely helpless, such as the direction above or a letter intended for Pamber, near Basingstoke, Hants., which was addressed “Pambore near Beas and Stoke, Ence.” Elsewhere, “A seafaring man evidently expected at the Sailors’ Home is addressed, ‘Walstrets, Selorshom Tebiekald for’; which, being interpreted, means, ‘Sailors’ Home, Wells-street: To be called for.”

But others seem deliberately elusive — one letter bore only these lines:

http://books.google.com/books?id=9OEvAAAAMAAJ

This one:

http://books.google.com/books?id=9OEvAAAAMAAJ

… was intended for Swansea in South Wales.

“One envelope has an ingenious direction on it. It is intended for S.S. Kaisow, lying in the Red Sea. It shows a very deliberate-looking sow labeled K, with a belt round it in the form of the letter C painted red.”

But at least those letters had envelopes. One thrifty correspondent simply wrote his message on the back of a postage stamp and dropped it in the mail:

http://books.google.com/books?id=9OEvAAAAMAAJ

“Meet me to-night without fail. Fail not — I am hard up.” “Though he probably parted with his last penny,” note the editors, “considering the state of his exchequer, he ran a great risk of remaining still hard up, owing to non-delivery of his communication.”

Amazingly, many of these letters actually found their recipients, a testament to the diligence and imagination of the postal authorities. “But we are rather in doubt as to whether a communication from the United States addressed to ‘John Smith, Esq., or any intelligent Smith, London, England,’ or possibly a proposal from some unknown admirer for ‘Miss Annie W—, London, address not known,’ ever reached their rightful owners.”

Countrymen

An ignorant Yorkshireman having occasion to go to France, was surprised on his arrival to hear the men speaking French, the women speaking French, and the children jabbering away in the same tongue. In the height of the perplexity which this occasioned, he retired to his hotel, and awakened in the morning by the cock crowing, whereupon he burst into a wild exclamation of astonishment and delight, crying, ‘Thank goodness! there’s English at last!’

Tit-Bits From All the Most Interesting Books, Periodicals and Newspapers in the World, Dec. 10, 1881