Growing Pains

A problem from the Soviet Mathematical Olympiad:

Two hundred students are arranged in 10 rows of 20 children. The shortest student in each column is identified, and the tallest of these is marked A. The tallest student in each row is identified, and the shortest of these is marked B. If A and B are different people, which is taller?

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Driver’s Ed

http://books.google.com/books?id=_icDAAAAMBAJ&printsec=frontcover#v=onepage&q&f=false

From Popular Science Monthly, April 1933: “A mechanical horse that trots and gallops on steel-pipe legs, under the impulse of a gasoline engine, is the recent product of an Italian inventor. With this horse, he declares, children may be trained to ride. The iron Dobbin is said to canter along a road or across a rough field with equal ease. Its design recalls the attempts of inventors, before the days of the automobile, to imitate nature and produce a mechanical steed capable of drawing a wagon.”

That kid might be happier in a cart.

Flashback

http://commons.wikimedia.org/wiki/File:Richard_Porson.JPG

English scholar Richard Porson (1759-1808) may have had the most prodigious memory of the 18th century. “He knew almost the whole of Homer, Horace, Cicero, Virgil and Livy,” recounts Henry H. Fuller in The Art of Memory (1898). “He could repeat whole plays from Shakespeare and complete books from Paradise Lost, scenes from Foote, and scores of pages from Gibbon’s Decline and Fall, or Rapin’s works. He knew by heart the whole of Mortal Tale of the Dean of Badajos, and Edgeworth’s Essays on Irish Bulls, and could repeat from beginning to end Smollett’s Roderick Random and other noted English novels. He could recite a newspaper page after one reading, and said that he would undertake to repeat the entire contents of a week’s issues of the London Morning Chronicle.”

Eliezer Cogan recalls that one day Porson called on a friend who asked him the meaning of a word in Thucydides. Without looking at the book, Porson repeated the passage. His friend asked how he knew which passage he’d been reading. “Because,” Porson replied, “the word occurs only twice in Thucydides, once on the right-hand page in the edition which are using, and once on the left. I observed on which side you looked, and accordingly knew to which passage you referred.”

Some Mirror Puzzles

some mirror puzzles

Hold a match horizontally before a mirror. If the match’s head is to the right, then so is that of its reflection — the match is not reversed left to right. But now hold up the matchbox. Its writing is reversed. Why?

“Here is a related puzzle,” writes psychologist Richard Gregory in Mirrors in Mind (1997). “Hold a mug with writing on it to a mirror. What do you see in the mirror? The reflection of the handle is unchanged — but the writing is right-left reversed. Can a mirror read?!

Set two mirrors together at a 60° angle and rotate the pair around your line of sight. Your image is preserved despite the mirrors’ rotation. This is not the case if the mirrors are set at 45° or 90°. Why?

Unquote

http://commons.wikimedia.org/wiki/File:Franciszek_Zmurko_-_In_delightful_dream.jpg

“Sleep is death enjoyed.” — Friedrich Hebbel

Misc

  • Hastie Love was convicted of rape in Tennessee in 1968.
  • Zebra stripes are white.
  • 14641 = (1 + 4 + 6)4 × 1
  • Spain’s national anthem has no words.
  • LION + TIGER = LOITERING
  • “Character is that which can do without success.” — Emerson

It Begins

http://www.flickr.com/photos/urbansheep/14642636/

Image: Flickr

Moscow’s stray dogs have begun using the city’s subway system. Zoologist Andrey Poyarkov of the Moscow Ecology and Evolution Institute, who has been studying the city’s 35,000 strays for 30 years, says some dogs scavenge downtown during the day and board trains in the evening to travel to industrial complexes in the suburbs, where they sleep.

“Because the best scavenging for food is in the city center,” Poyarkov told the Sun, “the dogs had to learn how to travel on the subway — to get to the center in the morning, then back home in the evening, just like people.”

This seems to be a sinister trend:

  • In 2006 a Jack Russell terrier named Ratty began taking the Number 10 bus from his farm in Dunnington, North Yorkshire, to a pub five miles away, where regulars would feed him sausages. When barred from one pub he switched to another nearby.
  • In 2007 a cat nicknamed Macavity began boarding the Number 331 bus in Wolverhampton, riding 400 meters, and alighting near a fish-and-chip shop. “He sat at the front of the bus, waited patiently for the next stop and then got off,” passenger Paul Brennan told the Daily Mail. “It was was quite strange at first, but now it just seems normal.”
  • In 2009 the BBC reported that a cat named Casper was boarding buses in Plymouth, Devon, and sitting in a favorite seat for the entire 11-mile trip through the city center. The driver would let him off when they returned to the bus stop opposite his house.
  • This year a ginger cat named Dodger began hopping onto buses near his home in Bridport, Dorset. “I hadn’t seen him all morning until my daughter Emily told me one of her friends had just seen him on the bus at Charmouth,” five miles away, owner Fee Jeanes told the Telegraph. “I couldn’t believe it and panicked. I got into my car to go off and look for him, and then at that moment the bus pulled up near our house, and lo and behold he got off.”

It gets worse: Poyarkov’s graduate student Alexei Vereshchagin says that stray dogs in Moscow have been observed obeying traffic lights.

Black and White

loquin chess problem

By Paul Loquin. White to mate in two moves.

Click for Answer

“He and She”

When I am dead you’ll find it hard,
Said he,
To ever find another man
Like me.

What makes you think, as I suppose
You do,
I’d ever want another man
Like you?

— Eugene Fitch Ware, Some of the Rhymes of Ironquill, 1900

Odd and Even

Put the integers 1, 2, 3, … n in any order and call them a1, a2, a3, … an. Then form the product

P = (a1 – 1) × (a2 – 2) × (a3 – 3) … × (ann).

Now: If n is odd, prove that P is even.

Click for Answer