By Royal V. Heath:
12 + 43 + 65 + 78 = 87 + 56 + 34 + 21
That’s not terrifically impressive on its face. But:
- Each side uses the digits 1-8.
- The whole equation is a palindrome.
- It remains valid if you square each term.
Teamwork
At the start of her career, NIH immunologist Polly Matzinger disliked writing in the passive voice and felt too insecure to adopt the first person. So she listed her dog, Galadriel Mirkwood, as a coauthor and wrote as “we.”
Their paper was published in 1978 in the Journal of Experimental Medicine. When the editor learned Galadriel’s species, he barred Matzinger from his pages for the rest of his life.
Antique Spam
In July 1833 the Earl of Stamford and Harrington received a letter signed “Martha Turner.” “It is with shame, indescribable shame, I presume to address your Lordship with these lines,” she wrote, “but from having a knowledge of your Lordship’s person from my infancy, and through the report of your Lordship’s sympathising and benevolent character, I am about entrusting a most unfortunate affair to your Lordship’s honour and secrecy.”
She had left her widowed mother at Christmas, she said, with a man who had promised to marry her but had left her “ruined and undone.” She begged for “a small pecuniary assistance,” pleading with the earl to rescue her “from entire destruction” and “a miserable death.”
Martha Turner didn’t exist. Her appeal was contrived and arranged by Joseph Underwood, one of about 250 letter-writing impostors who plagued England’s wealthy in the 1830s. Underwood had invented and written Martha’s letter in a woman’s hand, and he forged corroborating messages from her supposed seducer and from a clergyman supporting her story.
Underwood earned nearly £1,000 a year at this, which apparently made his frequent incarcerations worthwhile. “If the faculty of creation be one of the principal attributes of genius,” wrote John Grant in 1838, “Underwood was a genius of the first magnitude. The force and felicity of his imaginative facts were remarkable. Had he turned his attention to novel-writing, instead of to the profession of a begging-letter impostor, there is no saying how high his name might at this moment have stood in the current literature of the country.” Underwood chose otherwise — he died in Coldbath Fields Prison in 1838.
Sibling Rivalry
Do men have more sisters than women do? Intuitively it seems they must. In a family with two children, a boy and a girl, the boy has a sister but the girl doesn’t. In a family with four children, two boys and two girls, each boy has two sisters but each girl has one. It seems inevitable that, on average, men must have more sisters than women.
But it isn’t true. There are four possible two-child families, all equally likely: BB, BG, GB, GG. Half of the children in these families have a sibling of the same sex, and half have a sibling of the opposite sex. This observation can be extended to larger families. So men have the same number of sisters as women.
Cut the Knot has a good discussion of the statistics, including a javascript simulator.
The Right Moment
The second Earl of Leicester sat in Parliament for 67 years without saying a word.
His son, the third earl, was silent for 32 years.
His grandson, the fourth earl, said nothing for 23 years.
His great-grandson, the fifth earl, Thomas William Edward Coke, kept his silence for 22 years, then in 1972 rose and said, “I hope we shall use safer chemicals in place of those which have devastated the countryside.”
“My record of silence is not all that remarkable because I know that my family have not been overtalkative in this house,” he said later.
First Base
The earliest mention of baseball may be in Northanger Abbey, of all places:
… it was not very wonderful that Catherine, who had by nature nothing heroic about her, should prefer cricket, baseball, riding on horseback, and running about the country at the age of fourteen, to books.
Jane Austen wrote that passage in 1798, 41 years before Abner Doubleday supposedly invented the game in 1839. Evidence now suggests that “America’s game” evolved in England and was imported to the New World in the 18th century.
UPDATE: A reader alerts me that the town of Pittsfield, Mass., passed an ordinance in 1791 forbidding inhabitants from playing “Baseball” and certain other games near a new meeting house. This is believed to be the first written reference to baseball in North America. But a researcher at the Oxford English Dictionary tells me that the OED now has an example dating from 1748: “Now, in the winter, in a large room, they divert themselves at base-ball, a play all who are, or have been, schoolboys, are well acquainted with.” The letter writer was English, so, for the moment, England has the ball.
Lightning Monopoly
What’s the shortest possible game of Monopoly if each player plays optimally? Richard I. Hess of Palos Verdes, Calif., found this solution:
You roll 1, 1, land on Community Chest, and win $10 as second prize in a beauty contest. Then you roll 5, 5 and buy Electric Co. for $150. You end your turn by rolling 1, 3 and buying St. James for $180. Now you have $1180.
Each other player rolls 1, 3 and pays 10 percent Income Tax, reducing their balance to $1350 each.
Your turn again. You roll 1, 1 and buy Tennessee for $180, then roll 2, 2 and draw a Chance card, which sends you back three spaces, where you buy New York for $200. Now you roll 1, 2 and draw another Chance card, which advances you to GO and yields $200. You have exactly $1000, which you use to buy 10 houses, four on St. James and three each on Tennessee and New York.
The other players roll 4, 4 and pay $32 rent on Electric Co., then roll 2, 2 and pay $750 on St. James. They conclude ignominously by rolling 1, 2 and going bankrupt on New York, where they owe $600 and have only $568.
That’s if every player does his best. What if your opponents play a stupid but legal game?
You roll a 3 and buy Baltic for $60. Every other player buys Baltic from you for $1500 and sells it back for $3. Then each rolls 1, 2, lands on Baltic, and, having $3 but owing $4, goes bankrupt.
(From the Journal of Recreational Mathematics, 15(1))
11/21/2011 UPDATE: Kevin Tostado points out that a player who draws the Community Chest card “Bank Error in your Favor: Collect $200” would not need to draw the “Advance to GO card”; that it’s unnecessary to purchase Electric Company; and that the 10% income tax option was phased out in 2008. He offers the following improvement, which requires one less roll by the first player and one less property purchased:
You roll 1, 1, land on Community Chest, and collect $200 for a bank error in your favor. Then you roll 4, 4, land on Just Visiting, then roll 1, 5 and buy St. James for $180, ending your turn. Now you have $1370.
Each other player rolls 1, 3 and pays $200 Income Tax, reducing their balance to $1300 each.
Your turn again. You roll 1, 1 and buy Tennessee for $180, then roll 1, 3 and draw a Chance card, which sends you back three spaces, where you buy New York for $200. You have $1140, which you use to buy 11 houses, four each on St. James and New York and three on Tennessee.
The other players roll 3, 3, land on Just Visiting, then roll 3, 3 and pay $750 on St. James. They conclude ignominously by rolling 1, 2 and going bankrupt on New York, where they owe $800 and have only $550.
“Also, in the course of filming my documentary, one player I interviewed described how in an actual tournament game, he bankrupted three opponents in under 15 minutes, all actually trying to win (and not just throw the game), through acquiring a natural monopoly on the light blues on his 2nd full turn of the game.” (Thanks, Kevin.)
Unquote
“History is all explained by geography.” — Robert Penn Warren
Horse Sense
From the U.K. Schools Mathematical Challenge, a multiple-choice competition for students ages 11-14:
Humphrey the horse at full stretch is hard to match. But that is just what you have to do: move one match to make another horse just like (i.e. congruent to) Humphrey. Which match must you move?
Quiet Study
When French-American philanthropist Stephen Girard founded Philadelphia’s Girard College in 1830, he explicitly excluded religion from the campus:
I enjoin and require that no ecclesiastic, missionary or minister of any sect whatsoever, shall ever hold or exercise any station or duty whatever in the said college; nor shall any such person ever be admitted for any purpose, or as a visitor, within the premises appropriated to the purposes of the said college.
“In making this restriction, I do not mean to cast any reflection upon any sect or person whatsoever,” he wrote, “but, as there is such a multitude of sects, and such a diversity of opinion amongst them, I desire to keep the tender minds of the orphans, who are to derive advantage from this bequest, free from the excitement which clashing doctrines and sectarian controversy are so apt to produce.”