Al writes the numbers 1, 2, …, 2n on a blackboard, where n is an odd positive integer. He then picks any two numbers a and b, erases them, and writes instead |a – b|. He keeps doing this until one number remains. Prove that this number is odd.
Search Results for: in a word
Misc
- To burn up is to burn down.
- Litotes is an anagram of T.S. Eliot.
- 1012658227848 × 8 = 8101265822784
- Three U.S. presidents died on July 4.
- “Grasp the subject, the words will follow.” — Cato the Elder
Ironically Apt
In 2013, Japanese refrigeration company Fukushima Industries introduced a new mascot, a happy winged egg:
“I fly around on my awesome wings, patrolling supermarket showcases and kitchen refrigerators. I can talk to vegetables, fruit, meat, and fish and can check on their health! I was born in a Fukushima refrigerator! I love eating and I’m full of curiosity. I think of myself as kind, with a strong sense of justice, but my friends say I’m a bit of a klutz. But I’m always working hard to make myself shine!”
Unfortunately the company named the character “Fukuppy,” a combination of Fukushima and the English word happy.
After the name began to make news in English-speaking countries, Fukushima issued an apology and withdrew it.
Catastrophe
In Seven Types of Ambiguity (1949), William Empson describes a particularly inscrutable English newspaper headline:
ITALIAN ASSASSIN BOMB PLOT DISASTER
Bomb and plot, you notice, can be either nouns or verbs, and would take kindly to being adjectives, not that they are anything so definite here. One thinks at first that there are two words or sentences, and a semicolon has been left out as in telegrams: ‘I will tell you for your penny about the Italian Assassin and the well-known Bomb Plot Disaster’; but the assassin, as far as I remember, was actually not an Italian; Italian refers to the whole aggregate, and its noun, if any, is disaster. Perhaps, by being so far separated from its noun, it gives the impression that the other words, too, are somehow connected with Italy; that bombs, plots, and disasters belong both to government and rebel in those parts; perhaps Italian Assassin is not wholly separate in one’s mind from the injured Mussolini.
In fact it’s not clear what the intended meaning had been. Empson says that the main rhythm conveys the sense “This is a particularly exciting sort of disaster, the assassin-bomb-plot type they have in Italy.” In The Wordsworth Book of Usage & Abusage (1995), Eric Partridge suggests that the writer may have meant ITALIAN DISASTER ASSASSIN’S BOMB-PLOT, “There has been in Italy a disaster caused by a bomb in an assassin’s plot.” But he agrees that “even after an exasperating amount of cogitation by the reader,” the meaning is unclear.
To the Point
In What a Word!, his 1936 examination of English usage, A.P. Herbert takes up a letter written in “officese”:
Madam,
We are in receipt of your favour of the 9th inst. with regard to the estimate required for the removal of your furniture and effects from the above address to Burbleton, and will arrange for a Representative to call to make an inspection on Tuesday next, the 14th inst., before 12 noon, which we trust will be convenient, after which our quotation will at once issue.
He reduces this to:
Madam,
We have your letter of May 9th requesting an estimate for the removal of your furniture and effects to Burbleton, and a man will call to see them next Tuesday forenoon if convenient, after which we will send the estimate without delay.
This shortens the letter from 66 words to 42. Then he cuts it again, to 35 words, or 157 letters against the original 294, a savings of nearly 50 percent:
Madam,
Thank you for your letter of May 9th. A man will call next Tuesday, forenoon, to see your furniture and effects, after which, without delay, we will send our estimate for their removal to Burbleton.
In a large firm, he estimates, cutting “verbose and indolent, obscure, inelegant, and time-devouring monkey-talk” could save a week’s work for two typists.
Elsewhere he considers a memo that reads “Hot-Water Bottles: With reference to the above matter I should like an opportunity of discussing same with you.” The improvement he suggests is “Could we, please, have a talk about Hot-Water Bottles?”
Cube Route
A centered hexagonal number is a number that can be represented by a hexagonal lattice with a dot in the center, like so:
Starting at the center, successive hexagons contain 1, 7, 19, and 37 dots. The sequence goes on forever.
The sum of the first n centered hexagonal numbers is n3, and there’s a pretty “proof without words” to show that this is so:
Instead of regarding each figure as a hexagon, think of it as a perspective view of a cube, looking down along a space diagonal. The first cube here contains a single dot. How many dots must we add to produce the next larger cube? Seven, and from our bird’s-eye perspective this pattern of 7 added dots matches the 7-dot hexagon shown above. The same thing happens when we advance to a 3×3×3 cube: This requires surrounding the 2×2×2 cube with 19 additional dots, and from our imagined vantage point these again take the form of a hexagonal lattice. In the last image our 33 cube must accrete another 37 dots to become a 43 cube … and the pattern continues.
Reflections
Epigrams of poet Ralph Hodgson:
- Oaths in anguish rank with prayers.
- The wink was not our best invention.
- When crises pall, humdrum is sensational.
- But Woman — in whose image made?
- A sparrow in a snowstorm with a feather in his bill: that is Faith.
- Forget the slush, but keep the snow / Of Christmasses of long ago.
- Anniversary: Familiarity breeds content.
- Some things have to be believed to be seen.
- Who shall paraphrase a tear!
- There’s one thing to be said for sin — it does give conscience exercise.
- Why not Foremothers?
- The Golden Rule was called new-fangled, once upon a time.
- Blessed are the children of a nobody.
- The handwriting on the wall may be a forgery.
And “The ‘last word’ is only the latest.”
Misc
- Vatican City has 2.27 popes per square kilometer.
- Skylab was fined for littering.
- Five-syllable rhyming words in English: vocabulary, constabulary
- 8767122 + 3287682 = 876712328768
- “We die only once, and for such a long time!” — Molière
Above is the only known film footage of Mark Twain, shot at Twain’s Connecticut home in 1909. The women are thought to be his daughters Clara and Jean.
Term Limits
Little-used words:
anopisthograph
adj. having writing on one side only
antapology
n. a reply to an apology
antephialtic
n. something that prevents nightmares
centesimate
v. to select one person in every hundred for a punishment
citramontane
adj. relating to this side of the mountains
demonachize
v. to remove monks from
frounce
n. a canker in the mouth of a hawk
hendecad
n. a period of eleven years
laquearian
adj. armed with a noose
pastinaceous
adj. of the nature of a parsnip
philosophunculist
n. an insignificant philosopher
spartostatics
n. the study of the strength of ropes
swinehood
n. pigs collectively
togated
adj. clad in a toga
trouserdom
n. the domain of those who wear trousers
yealing
n. a person of one’s own age
See Specialists.
Good News
From an 1897 Strand feature on odd Bibles:
Perhaps the rarest of all the curious Bibles is the famous ‘Bugge’ Bible, an edition of Matthew’s Bible, published in 1551. In this we read, at Psalms xci., 5, ‘So that thou shalt not nede to be afrayed for anye bugges by nyghte.’
Possibly “bugge” was understood as equivalent to the modern word bogie, or ghost. See Oops.