Ogden Nash invented a streamlined limerick he called the “limick”:
An old person of Troy
In the bath is so coy
That it doesn’t know yet
If it’s a girl or a boy.
Two nudists of Dover,
When purple all over,
Were munched by a cow,
When mistaken for clover.
A cook called McMurray
Got a raise in a hurry
From his Hindu employer,
By flavouring curry.
A young flirt of Ceylon,
Who led the boys on,
Playing “Follow the Leda,”
Succumbed to a swan.
Based on an ancient Hindu game, Snakes and Ladders (Chutes and Ladders in ophidiophobic America) is at heart a morality lesson: As you progress by die roll from square 1 to square 100 and spiritual enlightenment, your way is complicated by virtues and vices. Landing on a snake (or chute) will send you back to an earlier square, and landing on a ladder will send you ahead to a later one. Each of these shortcuts is associated with a precept — “Carelessness” leads to “Injury,” “Study” leads to “Knowledge,” and so on.
In 1993 University of Michigan mathematician S.C. Althoen and his colleagues considered the game as a 101-state absorbing Markov chain. The shortest possible game lasts seven moves, the longest is infinite, and according to their calculations the expected number of moves in the Milton Bradley version of Chutes and Ladders is
which is about 39.2.
Troublingly, the average length of a game without snakes or ladders (just the 100-square board) is almost exactly 33 moves: “Apparently the snakes lengthen the game more than the ladders shorten it.” And, while adding a ladder will generally shorten the game and adding a snake will lengthen it, this isn’t always the case: In the original game, adding a ladder from square 79 to square 81 lengthens the expected playing time by more than two moves (to about 41.9), since it increases the chance of missing the important ladder leading from square 80 to square 100. And adding a snake from square 29 to square 27 shortens the game by more than a move (to about 38.0), since it offers a second chance at the long ladder from 28 to 84.
So, arguably, we might advance more quickly through life with more vice and less virtue.
(S.C. Althoen, L. King, and K. Schilling, “How Long Is a Game of Snakes and Ladders?”, Mathematical Gazette 77:478 [March 1993], 71-76.)
I just ran across this in Benjamin Glover Laws’ The Two-Move Chess Problem, from 1890. It’s by G. Chocholous. White is to mate in two moves.
Discovered by State Farm research agents in 2001:
Antonio Parkway crosses Avenida de las Banderas in Rancho Santa Margarita, California.
Grinn Drive meets Barret Road in West Chester, Ohio.
East Ho Road meets North Hum Road in Carefree, Arizona.
Dock Street connects Hickory Avenue and Dickory Avenue in Harahan, Louisiana.
On its 35th anniversary, THX, the sound quality assurance company founded by George Lucas, released the original score of “Deep Note,” its audio trademark, which debuted at the premiere of Return of the Jedi in 1983 and is now familiar from countless films. Essentially it’s a stupendous D chord; the U.S. trademark registration reads:
The THX logo theme consists of 30 voices over seven measures, starting in a narrow range, 200 to 400 Hz, and slowly diverting to preselected pitches encompassing three octaves. The 30 voices begin at pitches between 200 Hz and 400 Hz and arrive at pre-selected pitches spanning three octaves by the fourth measure. The highest pitch is slightly detuned while there are double the number of voices of the lowest two pitches.
“I like to say that the THX sound is the most widely-recognized piece of computer-generated music in the world,” says James A. Moorer, who wrote it. “This may or may not be true, but it sounds cool.” And now that we have the score you can do this:
286 = 77371252455336267181195264
That’s the largest known power of 2 with no zeros in its decimal representation.
Are there higher such powers? No one knows.
any-lengthian
adj. unscrupulous
anythingarianism
n. the fact or phenomenon of not holding any fixed or established beliefs
Created by Franz Armbruster in 1967, “Instant Insanity” was the Rubik’s Cube of its day, a simple configuration task with a dismaying number of combinations. You’re given four cubes whose faces are colored red, blue, green, and yellow:
The task is to arrange them into a stack so that each of the four colors appears on each side of the stack. This is difficult to achieve by trial and error, as the cubes can be arranged in 41,472 ways, and only 8 of these give a valid solution.
One approach is to use graph theory — draw points of the four face colors and connect them to show which pairs of colors fall on opposite faces of each cube:
Then, using certain criteria (explained here), we can derive two directed subgraphs that describe the solution:
The first graph shows which colors appear on the front and back of each cube, the second which colors appear on the left and right. Each arrow represents one of the four cubes and the position of each of the two colors it indicates. So, for example, the black arrow at the top of the first graph indicates that the first cube will have yellow on the front face and blue on the rear.
This solution isn’t unique, of course — once you’ve compiled a winning stack you can rotate it or rearrange the order of the cubes without affecting its validity. B.L. Schwartz gives an alternative method, through inspection of a table, as well as tips for solving by trial and error using physical cubes, in “An Improved Solution to ‘Instant Insanity,'” Mathematics Magazine 43:1 (January 1970), 20-23.
“If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple. But if you have an idea and I have an idea and we exchange these ideas, each of us will have two ideas.” — George Bernard Shaw
“He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me. That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density in any point.” — Thomas Jefferson
The end of the Civil War opened a new era of fossil hunting in the American West — and a bitter feud between two rival paleontologists, who spent 20 years sabotaging one another in a constant struggle for supremacy. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Bone Wars, the greatest scientific feud of the 19th century.
We’ll also sympathize with Scunthorpe and puzzle over why a driver can’t drive.
