Bookmarks (195)

A puzzle by Russian mathematician Sergei Berlov: Here are two decagons. Suppose that a positive integer is written at each of the 20 vertices such that the sum of the numbers around each decagon is 99. Prove that it’s possible to mark some number of successive vertices on each decagon so that the two sums of marked numbers are equal. (The marked segment on...

I just found this in a 1950 issue of Pi Mu Epsilon Journal: Question: How many legs has a horse? Answer: Twelve; two in front, two behind, two on each side, and one in each corner. Later in the same volume, Marlow Sholander shows that in fact every horse has an infinite number of legs. That’s to say nothing of color. And see Chasing...

Suppose your dog eats the ace of spades and you’re forced to play poker with a 51-card deck. Does this make it more or less likely that you’ll be dealt a two-pair hand? The answer is not immediately clear. The loss of the ace means that fewer two-pair hands are possible, but the total universe of possible five-card hands is also reduced. Surprisingly, the...

Demetri Martin composed this palindromic poem as part of a project for a fractal geometry class at Yale in spring 1993. The first two and last two lines are palindromes, the middle line (“Be still if I fill its ebb”) minus its last letter is a palindrome, and the entire poem is a palindrome: Dammit I’m mad Evil is a deed as I live....

An odd incident from the memoir of Lt. John Worsham of the 21st Virginia Infantry — during the Battle of Saunders Field in May 1864, two opposing soldiers found themselves in a gully and agreed to a fistfight to decide which had captured the other: Then they decided that they would go into the road and have a regular fist and skull fight, the...

These verses can be interpreted to support either the Stuarts or the Hanovers, according as they’re read. If each is addressed separately, from top to bottom, they’ll seem to support the Hanoverian regime; read together, right across the page, they declare for the Stuarts: From Reuben Percy, Relics of Literature, 1823.

In this conundrum by Mitsunobu Matsuyama, when four congruent quadrilaterals are rotated about their centers, their area seems to increase. What has become of the red square? The answer is that each side of the large square is slightly shorter after the rotation. If θ is the angle between two opposing sides in each quadrilateral, then the ratio of the areas of the two...

J. Bryan III used to challenge his friends to think of an English word that contains either of the following strings of letters: ILIL ILIW “I’ve never played the game with anyone who could solve either of these combinations.” Can you?

“Improprieties in pronunciation” among the people of New England in 1808, collected by Caleb Bingham and published in The Child’s Companion: afraid: afeard apron: apun audacious: outdacious bonfire: burnfire brittle: brickle cards: cairds caught: cotch coin: quine cucumber: cowcumber dictionary: dixonary drain: dreen earth: airth fanciful: fancical five pence: fippence gown: gound grasshopper: hoppergrass jaundice: janders musician: musicianer poplar: popple quart: quairt quotient: coshun...

How can we make sense of this passage, composed by Willard R. Espy? The Optic Reed has a Haste Harm. It Hose, one assumes, not to be Lever; it neither Heats the Ripple, nor Hides the Razed sinner for his Rude Rime; it is not Old. Then Leave to it; ere thy grave Loses, thou mayst find here the Hart to the Rest thou...

A circle is divided into six sectors, into which are written (say, counterclockwise) these numbers: 1, 0, 1, 0, 0, 0 You can increase any two neighboring numbers by 1. By doing this repeatedly, is there a way to make all six numbers equal?

A problem by Nikolai Rozov: “If the brainteaser you solved before you solved this one was harder than the brainteaser you solved after you solved the brainteaser that you solved before you solved this one, was the brainteaser you solved before you solved this one harder than this one?”

This remarkable phenomenon was discovered by Cambridge mathematician James Grime. Number five six-sided dice as follows: A: 2, 2, 2, 7, 7, 7 B: 1, 1, 6, 6, 6, 6 C: 0, 5, 5, 5, 5, 5 D: 4, 4, 4, 4, 4, 9 E: 3, 3, 3, 3, 8, 8 Now, on average: A beats B beats C beats D beats E beats...

Excerpts from letters received by the British pensions office, quoted in George Lyttelton’s Commonplace Book, 2002: Mrs R. has no clothes, has not had any for many years. The clergy have been visiting her. In reply to your letter, I have already cohabited with your officers, so far without any result. You have changed my little boy to a little girl. Will this make...

By Wikimedia user Efbrazil. Fill in four squares to make a continuous dark path connecting the stars. No diagonal moves are allowed.

When I went out to throw the discus I went and sprained some little viscus. Since that disruption of my viscera I don’t go out and throw the discera. — Don Laycock

subagitate v. to have sex with verecund adj. bashful; modest reme v. to cry or call out cacoëpistic adj. badly pronounced [Sir Walter Raleigh] loved a wench well; and one time getting up one of the Mayds of Honour up against a tree in a Wood (’twas his first Lady) who seemed at first boarding to be something fearfull of her Honour, and modest,...

“Whenever you observe an animal closely, you feel as if a human being sitting inside were making fun of you.” — Elias Canetti

In his 1954 book Language in Relation to a Unified Theory of the Structure of Human Behavior, Kenneth Pike presents a toy language in which meaning is determined by the relative order of the elements. If these expressions have the indicated meanings: 1. los "It is smoke" 2. mif "It is a ball" 3. kap "They are eyes" 4. losmif "The ball is smoking"...

When the news of [Richelieu’s] passing was brought to Urban VIII, the old Pope sat for a moment in pensive silence. ‘Well,’ he said at last, ‘if there is a God, Cardinal Richelieu will have much to answer for. If not, he has done very well.’ — Aldous Huxley, Grey Eminence, 1941

You see, when you learn to read you will be born again into another world and it is a pity to be born again so young. I should put off reading, if I were you. As soon as you learn to read you will not see anything again quite as it is. It will all the time be altered by what you have read...

In his Table Talk, W.H. Auden says that La Rochefoucauld “simply says what one has always known.” Robert Craft added, “Yes, but without him some of us would not have known that we knew.”

“Conjugated nouns,” offered by Ohio State University linguist Arnold M. Zwicky in Verbatim in 1975: I steal the keel. I stole the coal. I have stolen the colon. They choose the hues. They chose the hose. They have chosen the hosen. They mow the banks of the row. They mowed the banks of the road. They have mown the banks of the Rhone. I...

Dedication of P.G. Wodehouse’s 1926 book The Heart of a Goof: To My Daughter Leonora Without Whose Never-Failing Sympathy and Encouragement This Book Would Have Been Finished in Half the Time

Oh Lord, Thou knowest that I have lately purchased an estate in fee simple in Essex. I beseech Thee to preserve the two counties of Middlesex and Essex from fire and earthquakes; and as I have also a mortgage at Hertfordshire, I beg of Thee also to have an eye of compassion on that county, and for the rest of the counties, Thou may...

“Ingliz menuyu” presented to writer William Dalrymple at a family restaurant in Turkey in 1986: SOAP Ayas soap Turkish tripte soap Sheeps foot Macaront Water pies EATS FROM MEAT Deuner kepab with pi Kebap with green pe Kebap in paper Meat pide Kebap with mas patato Samall bits of meat grilled Almb chops VEGETABLES Meat in earthenware stev pot Stfue goreen pepper Stuffed squash...

Wikimedia user Tarquin points out that the natural rhythm of spoken language can be used to teach polyrhythms. Above: The phrase “cold cup of tea,” spoken naturally, approximates a rhythm of 2 against 3. Below: The phrase “what atrocious weather” approximates 4 against 3.

A gentleman walked up to another gentleman, who was standing before the fire in a Coffee Room, and immediately said, ‘I beg your pardon, Sir, but may I ask your name?’ ‘I am not in the habit, Sir,’ said the other man, ‘of giving my name to strangers, but, as you are so pertinacious, Sir, my name is Thompson, Sir.’ ‘Then, Mr. Thompson, Sir,’...

Remarkable names of real people, collected in the 1980s by John Train: Mac Aroni Cigar Stubbs Legitimate Jones Halibut Justa Fish Daphne Reader’s Digest Taione Halloween Buggage Eucalyptus Yoho Solomon Gemorah Asa Miner Carlos Restrepo Restrepo Restrepo de Restrepo Cranberry Turkey Breckenridge Jr. Demetrius Plick F.G. Vereneseneckockkrockoff Rev. Fountain Wetmore Rainwater Grecian T. Snooze July August September Lobelia Rugtwit Hildebiddle Tarantula Turner Theanderblast Mischgedeigle...

When James Cameron was serving as second unit director on Galaxy of Terror (1981), he was asked to film an insert of a severed arm that’s being eaten by maggots. The team made a fake arm, covered it with mealworms, lit the shot, and rolled the camera, but the mealworms didn’t move. “They looked completely inert,” Cameron said. “So I thought, well, what would...

If your nose is close to the grindstone And you hold it there long enough In time you’ll say there’s no such thing As brooks that babble and birds that sing These three will all your world compose Just you, the stone and your poor old nose. — “From a two hundred-year-old stone in a country cemetery,” quoted in Christina Foyle, So Much Wisdom,...

Two rhapsodies on the name of French philosopher Michel Onfray, by Basile Morin. In the chain ambigram above, the first name is transfigured (at some point) into the last. In the tessellation ambigram below, the two names appear simultaneously as figure and ground.

From Pi Mu Epsilon Journal, November 1950: (1/2)3 < (1/2)2. Taking the logarithm to the base 1/2 of each member of the above inequality, we write 3 log1/2(1/2) < 2 log1/2(1/2). But logbb = 1. Therefore 3 < 2.

Back in 2017 I wrote about the Feynman ciphers, three coded messages that had been presented as challenges to Richard Feynman in the 1950s. Feynman couldn’t crack them, and even at the time of my post only the first of the three had been decoded — it turned out to be a transposition of the opening of Chaucer’s Canterbury Tales in Middle English. But...

Smith College mathematician Jim Henle published this retrograde analysis puzzle in the Mathematical Intelligencer in 2018 as part of an appreciation of Raymond Smullyan. “After many moves, the chessboard appears as above. What were the last two moves?”

Several claimants have been put forth as the originators of the modern tropical cyclone ‘naming’ system. Australian weather meteorologist, Clement L. Wragge, is one of the best-established holders of the title. … Most ingeniously, he gained a measure of personal revenge by christening some of the nastiest storms with politicians’ names such as Drake, Barton, and Deakin. Modern hurricane researcher Chris Landsea noted that,...

In 1900, Louis Philip Perew of Tonawanda, New York, built a “gigantic man” of wood, rubber, and metal that “walks, talks, runs, jumps, [and] rolls its eyes.” Standing 7 foot 5 in size 13 1/2 shoes and clothed in white duck, the nameless man “walked smoothly, and almost noiselessly” at an exhibition for the Strand, circling the hall twice without stopping. Perew was cagey...

In 2005, Jeremy Winterson bought a bootleg copy of Revenge of the Sith in Shanghai and noticed something wrong with the English subtitles. The movie’s dialogue had been translated mechanically into Chinese and then translated back again into English, leaving it almost incomprehensible. (A similar disaster had befallen a Portuguese-French phrasebook in 1883.) Fans replaced the movie’s original audio dialogue with voice actors reading...

A Polish problem longlisted for the 19th International Mathematical Olympiad in Yugoslavia, July 1977: A room contains nine men. Among every three of them there are two who are mutually acquainted. Prove that four of them are mutually acquainted.

We have a strong intuition that it’s wrong to punish someone for a crime he hasn’t committed, but is this always the case? Algy, an Alaskan motorist, and Ben, a traffic policeman, both know reliably that Algy intends to speed on a remote, unpatrolled, but radar-surveyed highway at 10:31 tomorrow morning. They also know that, if this happens, police won’t be able to reach...

No, no; for my virginity, When I lose that, says Rose, I’ll die: Behind the elms last night, cried Dick, Rose, were you not extremely sick? — Matthew Prior Time magazine called this perhaps the only naughty verse that can’t be bowdlerized. (While we’re at it: In 1680 John Wilmot published a poem about premature ejaculation.)

This 1904 comic by Gustave Verbeek (click to enlarge) is a sort of visual palindrome — the first six panels are presented conventionally, and then they’re displayed again in reverse order and upside down to compose the story’s second half. Even the written messages change their meaning: why big buns am mad u! becomes in pew we sung big hym, and so on. Only...

Two leaps the water from its race Made to the brook below, The first leap it was curving glass, The second bounding snow. — William Allingham

Man is so intelligent that he feels impelled to invent theories to account for what happens in the world. Unfortunately, he is not quite intelligent enough, in most cases, to find correct explanations. So that when he acts on his theories, he behaves very often like a lunatic. Thus, no animal is clever enough, when there is a drought, to imagine that the rain...

A problem by British puzzlist Hubert Phillips: In writing home about an examination, five schoolgirls each made one true statement and one untrue one. The relevant passages: Betty: Kitty was second in the examination. I was only third. Ethel: You’ll be glad to hear that I was top. Joan was second. Joan: I was third, and poor old Ethel was bottom. Kitty: I came...

It’s illegal to mispronounce Joliet. G.K. Chesterton left an unfinished poem titled Plakkopytrixphylisperadaulantiobatrix. Alms has no singular. The Spanish village Trasmoz has been cursed and excommunicated by the Catholic Church. “The wink was not our best invention.” — Ralph Hodgson An Irish riddle: Yonder he is through the stream, a man without a coat, a man without a belt, a man of hard slender...