1. By A.F. Rockwell. White to mate in two moves. (Solutions are below.)
2. In 1866 Sam Loyd asked: Suppose you’re playing White against an opponent who’s required to mirror every move you make — if you play 1. Nf3 he must play 1. … Nf6, and so on. Can you design a game in which your eighth move forces your opponent to checkmate you with a nonmirror move?
3. An endgame study by J.A. Miles. “White to play and draw the game.”
It seems a bit arrogant that those of us in the United States refer to ourselves as “Americans” when more than half a billion other people live in the Americas. But what should we call ourselves instead?
“You have properly observed that we can no longer be called Anglo-Americans,” noted Thomas Jefferson in a letter after the Revolution. “That appellation describes now only the inhabitants of Nova Scotia, Canada, &c. I had applied that of Federo Americans to our citizens, as it would not be so decent for us to assume to ourselves the flattering appellation of free Americans.”
What’s a better term? In 1992 Columbia University etymologist Allen Walker Read compiled a list of suggestions that have been made over the years:
Perhaps we’re all counterfeit: In early usage “Americans” applied not to European colonists but to the native Indians whose territory they were invading. John Locke wrote in 1671: “So if you should ask an American how old his son is, i.e., what the length of duration was between his birth and this moment, he would … tell you his son was 30 or 40 moons old as it happened.”
(Allen Walker Read, “Derivative Forms From the Name United States,” paper read at the 31st annual Names Institute sponsored by The American Name Society, Baruch College of The City University of New York, May 2, 1992.)
Artist Thomas Cole took up a grand theme in 1833 — The Course of Empire, a series of five paintings that depict the rise and fall of a civilization. The Savage State shows a prehistoric wilderness in which the only artificial note is a circle of teepees:
The Arcadian or Pastoral State shows the beginning of agriculture, with a primitive temple, farmers, and shepherds:
The Consummation of Empire shows a thriving city, with an imperial procession crossing a triumphal bridge:
Destruction shows barbarians sacking the city and nature herself punishing human presumption:
And Desolation shows the return of nature, with trees growing up through the ruins of the city:
Interestingly, all five paintings depict the same scene: In the foreground is a natural port, and in the background is a distinctive mountain precipice. The time of day passes from dawn to dusk.
In 1836 more than 2,000 people attended the paintings’ exhibition at the National Academy of Design, an audience unprecedented in the United States. “The philosophy of my subject is drawn from the history of the past, wherein we see how nations have risen from the savage state to that of power and glory, and then fallen, and become extinct,” Cole had written to his patron Luman Reed. “You will perceive what an arduous task I have set myself; but your approbation will stimulate me to conquer difficulties.”
(Thanks, Cody.)
A puzzle by Princeton mathematician John Horton Conway:
Last night I sat behind two wizards on a bus, and overheard the following:
A: I have a positive integral number of children, whose ages are positive integers, the sum of which is the number of this bus, while the product is my own age.
B: How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages?
A: No.
B: Aha! AT LAST I know how old you are!
“This is an incredible puzzle,” writes MIT research affiliate Tanya Khovanova. “This is also an underappreciated puzzle. It is more interesting than it might seem. When someone announces the answer, it is not clear whether they have solved it completely.”
We can start by auditioning various bus numbers. For example, the number of the bus cannot have been 5, because in each possible case the wizard’s age and the number of his children would then uniquely determine their ages — if the wizard is 3 years old and has 3 children, then their ages must be 1, 1, and 3 and he cannot have said “No.” So the bus number cannot be 5.
As we work our way into higher bus numbers this uniqueness disappears, but it’s replaced by another problem — the second wizard must be able to deduce the first wizard’s age despite the ambiguity. For example, if the bus number is 21 and the first wizard tells us that he’s 96 years old and has three children, then it’s true that we can’t work out the children’s ages: They might be 1, 8, and 12 or 2, 3, and 16. But when the wizard informs us of this, we can’t declare triumphantly that at last we know how old he is, because we don’t — he might be 96, but he might also be 240, with children aged 4, 5, and 12 or 3, 8, and 10. So the dialogue above cannot have taken place.
But notice that if we increase the bus number by 1, to 22, then all the math above will still work if we give the wizard an extra 1-year-old child: He might now be 96 years old with four children ages 1, 1, 8, and 12 or 1, 2, 3, and 16; or he might be 240 with four children ages 1, 4, 5, and 12 or 1, 3, 8, and 10. The number of children increases by 1, the sum of their ages increases by 1, and the product remains the same. So if bus number b produces two possible ages for Wizard A, then so will bus number b + 1 — which means that we don’t have to check any bus numbers larger than 21.
This limits the problem to a manageable size, and it turns out that the bus number is 12 and Wizard A is 48 — that’s the only age for which the bus number and the number of children do not uniquely determine the children’s ages (they might be 2, 2, 2, and 6 or 1, 3, 4, and 4).
(Tanya Khovanova, “Conway’s Wizards,” The Mathematical Intelligencer, December 2013.)
Two similar puzzles: A Curious Conversation and A Curious Exchange.
Unfortunate newspaper headlines, collected by Robert Goralski for Press Follies, 1983:
TOWN OKS ANIMAL RULE (Asheville Citizen)
TRAVIS MAN DIES AFTER ALTERATION (Sacramento Bee)
INDIAN OCEAN TALKS (The Plain Dealer)
JUVENILE COURT TO TRY SHOOTING DEFENDANT (Deseret News)
TRAIN ROLLS 0 MILES WITH NO ONE ABOARD (New York Times)
LAWMEN FROM MEXICO BARBECUE GUESTS (San Benito [Texas] News)
FLIES TO RECEIVE NOBEL PRIZE (New York Times)
CARTER TICKS OFF BLACK HELP (San Francisco Examiner)
MAULING BY BEAR LEAVES WOMAN GRATEFUL FOR LIFE (Herald-Dispatch, Huntington, W.Va.)
SILENT TEAMSTER GETS CRUEL PUNISHMENT: LAWYER (The Home News, Brunswick, N.J.)
MANCHESTER MAN BURSTS, HALTS TRAFFIC (Hartford Times)
SKELETON TIED TO MISSING DIPLOMAT (Philadelphia Evening Bulletin)
POET DOESN’T WANT AUDIENCE OF ILLERATES (Raleigh Times)
GLASS EYE IS NO HELP IN IDENTIFYING CORPSE (Deseret News)
FORMER MAN DIES IN CALIFORNIA (Freemont County [Calif.] Chronicle News)
MATH IMPROVEMENT INDICATES LEARNING IS TIED TO TEACHING (New York Times)
PAIR CHARGED WITH BATTERY (Denver Post)
TUNA RECALLED AFTER DEATH (Chicago Daily News)
TWO CONVICTS EVADE NOOSE; JURY HUNG (Oakland Tribune)
JERK INJURES NECK, WINS AWARD (Buffalo News)
TEACHERS’ HEAD GOES OFF TO JAIL (Sarasota Herald-Tribune)
SIX SENTENCED TO LIFE IN CLARKSVILLE (Nashville Banner)
POPE LAUNCHES TALKS TO END LONG DIVISION (Pomono Progress Bulletin)
A GRATEFUL NATION BURIES SAM RAYBURN (New York Herald Tribune)
SHOUTING MATCH ENDS TEACHER’S HEARING (Newsday)
DOCTOR TESTIFIES IN HORSE SUIT (Waterbury Republican)
Some are inspired: When the New York Times reported that a mansion-hunting Aristotle Onassis had visited Buster Keaton’s former estate, it chose the headline ARISTOTLE CONTEMPLATING THE HOME OF BUSTER.
For centuries, May 1 brought chaos to New York, as most tenants had to move on the same day, clogging the streets with harried people and all their belongings. In this episode of the Futility Closet podcast we’ll review the colorful history of “Moving Day” and wonder how it lasted through two centuries.
We’ll also recount some surprising escapes from sinking ships and puzzle over a burglar’s ingenuity.
H.M. Small found it difficult to sleep in railway seats in 1889 — so he invented a hammock.
It’s actually possible to sleep at full length if the seat in front is pushed forward — but that might be going too far.
interfector
n. a death-bringing planet
mundicidious
adj. likely or able to destroy the world
In 2012 an online petition urged the Obama administration to build a Death Star like the one in Star Wars. The campaign amassed 25,000 signatures, enough to require an official response, and it fell to Paul Shawcross, chief of the Science and Space Branch at the Office of Management and Budget, to reject the project. He gave three reasons:
I leave my front door, run on a level road for some distance, then run to the top of a hill and return home by the same route. I run 8 mph on level ground, 6 mph uphill, and 12 mph downhill. If my total trip took 2 hours, how far did I run?
Sahara geology presented as a flan recipe, from French naturalist Théodore Monod’s Méharées: Explorations au vrai Sahara, 1937:
Take a flan-tray, which represents the basement (our Mauretanian and Tuareg granites).
- Place some pastry in the flan-tray in irregular masses (A) — these are the Precambrian mountain chains, the Saharides.
- Level this off with a knife (B) so that the folds, as in erosional peneplanation of the Sahara, are seen only in the ravines which cross the plain; the mountains are now vigorously planed down.
- First event: a tap (from which, fortunately, jam flows) floods the garnished mould (C). Similarly the sea at the beginning of the Palaeozoic invaded the Saharan basement, which it then partly occupied, until the middle Carboniferous — what an enormous amount of jam! All this time the Sahara is under water, and sandstones, limestones, conglomerates and shales were deposited — all the sediments of the Tuareg and Mauritanian plateaux.
- A new event (the djinns must have been at work here) — the bottom of the flan-tray experiences an uplift; the dish, pastry and jam emerge (D). This is the time of the coal measures; the sea retreats, and the Sahara is left high and dry, basking in the sun.
- But whoever says dry land, implies erosion; the sediments rise up, are corroded, and the spoon cuts so deeply that it exposes the jam, pastry, and sometimes even the metal of the flan-tray (E).
- And while this continues for millions of years, erosion is unable to evaporate its own debris and the eroded sediments are not washed away to the sea — they just accumulate, and what is lost in some districts is gained by others, whilst gradual infilling continues (F).
- Then one fine day, while iguanodons are blundering around in Picardy, and swarms of ammonites are scudding around in the Parisian sea, a second tap is turned on again and adds another layer, this time of cream (for convenience of explanation) (G). The sea re-invades a good part of the Sahara and deposits the usual sediments — Cretaceous and Eocene.
- A new retreat of the sea and a new continental phase occur, with customary erosion and deposition (H).
- Gradually, the country comes to be like it is today; sprinkle with granular sugar (fresh-water Quaternary deposits), and icing sugar dunes (I).
- And there we are! Serve hot or chilled.
“Very well — that will teach me to invent foolish nonsense for my neophyte when it is so easy to explain the influence of Saharidian tectonics on the orientation of Hercynian virgations, the suggestion of angular discordnce separating the basal congomerate of the continental beds from the post-Visean argillites, or more simply the origin of the bowlingite included in the pigeonite andesite with diabase facies of Telig. But I doubt that he would understand it any better …”
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