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?

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.

“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

Nine Lives Left

http://commons.wikimedia.org/wiki/File:Hans_Thoma_Die_Katze_Abendfrieden.jpg

I don’t know what to make of this — on Sept. 7, 1950, the London Times reported that a 10-month-old kitten had climbed the Matterhorn.

The story, “from our correspondent,” claims that the black-and-white kitten lived in the Hotel Belvedere at 10,820 feet, where he would watch departing alpinists as they left for the summit. One morning, apparently, he decided to follow them. “After a long and lonely climb” he reached the Solway hut at 12,556 feet, and the next day “bivouacked in a couloir above the shoulder.” A climbing party passed him on the third day, and he caught them up at the summit (14,780 feet), “miauing and tail up,” and was rewarded with a share of their meal. He was carried back down in a rucksack.

This is all reported very earnestly, and there’s even a photograph of the cat, but I can’t find a corroborating account anywhere. Both The Canadian Nurse and The Veterinary Record picked up the story, but they both credit the Times. The Guinness Book of World Records cited the cat for its feat, but presumably they’re relying on the same account.

Is this preposterous? Do I overestimate the Matterhorn? Do I underestimate kittens? Can anyone shed any light on this?

The Case of the Self-Stealing Store

In 1983, Jacob Henderson was convicted of burglarizing a Maaco paint shop in Jackson, Miss. He appealed on the ground that the indictment was illiterate:

The Grand Jurors for the State of Mississippi, … upon their oaths present: That Jacob Henderson … on the 15th day of May, A.D., 1982.

The store building there situated, the property of Metro Auto Painting, Inc., … in which store building was kept for sale or use valuable things, to-wit: goods, ware and merchandise unlawfully, feloniously and burglariously did break and enter, with intent the goods, wares and merchandise of said Metro Auto Painting then and there being in said store building unlawfully, feloniously and then and there being in said store building burglariously to take, steal and carry away; And
One (1) Polaroid Land Camera,
One (1) Realistic AM/FM Stereo Tuner
One (1) Westminster AM/FM radio
One (1) Metal Box and contents thereof,

… the property of the said Metro Auto Painting then and there being in said store building did then and there unlawfully, feloniously and burglariously take, steal and carry away the aforesaid property, he, the said Jacob Henderson, having been twice previously convicted of felonies, to-wit: … .

Henderson called an English teacher as an expert witness. She pointed out that the district attorney’s indictment doesn’t charge Henderson with any wrongdoing; instead it charges the merchandise itself with breaking into the paint store.

“This case presents the question whether the rules of English grammar are a part of the positive law of this state,” wrote Justice Robertson for the court. “If they are, Jacob Henderson’s burglary conviction must surely be reversed, for the indictment in which he has been charged would receive an ‘F’ from every English teacher in the land.”

“Though grammatically unintelligible, we find that the indictment is legally sufficient and affirm, knowing full well that our decision will receive of literate persons everywhere opprobrium as intense and widespread as it will be deserved.”