Here are six new lateral thinking puzzles to test your wits and stump your friends — play along with us as we try to untangle some strange situations using only yes-or-no questions.
Author: Greg Ross
A Second Career
In Willy Wonka & the Chocolate Factory (1971), just after Charlie buys a chocolate bar, he discovers a commotion at a newsstand: The finder of the fifth ticket, a “gambler from Paraguay,” has been declared a fraud.
“Can you imagine the nerve of that guy, trying to fool the whole world?” says one man.
“Boy, he really was a crook,” says another.
The man pictured in the newspaper is Martin Bormann, Adolf Hitler’s private secretary.
Express
This paragraph jumped out at me last night from B.G. Wilson’s Unusual Railways (1958) — he’s writing about the Mount Washington Cog Railway in New Hampshire, one of the world’s steepest, with an average grade of 25 percent:
Before leaving this line, mention must be made of a method of riding down the track employed by track maintenance men and long since banned. Wood and metal seats some 3 ft. × 1 ft. were made to fit over the rack rail. These were known as slide-boards, or more popularly, as ‘Devil’s Shingles’. Seated on these, controlling (sometimes) the speed with hand brakes, the men would career down the mountainside. The record time for the trip — as we have said, 3 1/4 miles — was 2 3/4 minutes!
That’s 70 mph! For comparison, the modern train takes 40 minutes to descend at 4.6 mph. And this was in the late 19th century — the railway opened in August 1869. Wilson writes, “After one man had been killed and another seriously injured, the Devil’s Shingles were banned.” I don’t know any more than that.
All Hands on Deck?
A reader named Hamp Stevens sent this conundrum to Martin Gardner, who published it in his Mathematical Magic Show (1965). Can these 25 cards be arranged to form five poker hands, each of them a straight or better (that is, straight, flush, full house, four of a kind, straight flush, or royal flush)? If it’s possible, find the five hands; if it’s not, prove that it’s impossible.
“This ingenious puzzle is quickly solved if you go about it correctly,” Gardner wrote. “A single card is the key.”
Fitting
If two unit circles are tangent externally as shown, and from a point P on one circle rays PQ and PR are drawn intersecting both circles, then arc lengths x + y = z.
From Claudi Alsina and Roger B. Nelsen, Icons of Mathematics, 2011.
Black and White
Hard Target
In a special football game, a team scores 7 points for a touchdown and 3 points for a field goal. What’s the largest mathematically unreachable number of points that a team can score (in an infinitely long game)?
Unquote
More maxims of François VI, Duc de La Rochefoucauld (1613–1680):
- “We always love those who admire us; but we don’t always love those whom we admire.”
- “There are people who would never have been in love, if they had never heard talk of Love.”
- “The Generality of People judge of Men by their Reputation, or Fortune.”
- “Men would not live long in Society, if they were not the mutual Dupes of one another.”
- “Titles, instead of exalting, debase those who don’t act up to them.”
- “Prosperity is a stronger Trial of Virtue than Adversity.”
- “Weak People can’t be sincere.”
- “‘Tis more difficult to be faithful to a Mistress when on good Terms with her, than when on bad.”
- “‘Tis not so dangerous to do Ill to most Men as to do them too much Good.”
- “A Man often imagines he acts, when he is acted upon; and while his Mind aims at one thing, his Heart insensibly gravitates towards another.”
- “When great Men suffer themselves to be subdued by the Length of their Misfortunes, they discover that the Strength of their Ambition, not of their Understanding, was what supported them; and that, bating a little Vanity, Heroes are just like other Men.”
- “Cunning and Treachery proceed from Want of Capacity.”
- “If we took as much Pains to be what we ought, as we do to deceive others by disguising what we are; we might appear as we are, without being at the Trouble of any Disguise.”
And “‘Tis a Mistake to imagine that only the violent Passions, such as Ambition and Love, can triumph over the rest. Laziness, languid as it is, often masters them all; she indeed influences all our Designs and Actions, and insensibly consumes and destroys both the Passions and the Virtues.”
Pleased, I’m Sure
A problem by Atlantic College mathematician Paul Belcher:
Anna and Bert invite n other couples to a dinner party. Before the meal begins, some people shake hands. No one shakes hands with their own partner, no one shakes hands with themselves, and no two people shake hands with each other more than once. Afterward, Anna asks all the other 2n + 1 people how many times they shook hands, and she gets a different answer from each of them. How many times did Anna shake hands?
In a Word
topolatry
n. excessive reverence for a place
Of the million or so Japanese who visit Paris each year, about 12 have to be repatriated due to “Paris syndrome,” a transient psychological disorder brought on when the mundane reality of the city clashes with their romanticized expectations.
The syndrome was first diagnosed by Hiroaki Ota, a Japanese psychiatrist working in France. Symptoms include delusional states, hallucinations, feelings of persecution, and anxiety.
“Fragile travellers can lose their bearings,” psychologist Hervé Benhamou told Le Journal du Dimanche. “When the idea they have of the country meets the reality of what they discover, it can provoke a crisis.”
(A. Viala et al., “Les japonais en voyage pathologique à Paris : un modèle original de prise en charge transculturelle,” Nervure 5 (2004): 31–34.)