Here’s a subtly impossible figure devised by UC-Santa Cruz computer scientist David Huffman. If it’s a three-sided pyramid, then its edges define the intersections of three planes and should meet in a single point. But they don’t:
This is intriguing because the figure doesn’t immediately look impossible. In Vagueness and Contradiction, philosopher Roy Sorensen writes, “The impossibility of an appearance is sometimes concealed without overloading our critical capacities.”
Possibly this is because we sense that other solutions are possible that can reconcile the error. Zenon Kulpa points out that the pyramid becomes intelligible if we imagine that the farther side hides a fourth edge, giving the figure four sides rather than three. He describes two families of such solutions in “Are Impossible Figures Possible?”, Signal Processing, May 1983.
In March 2013, New Mexico art dealer Forrest Fenn announced that he had hidden a bronze treasure chest in the Rocky Mountains north of Santa Fe. In the chest, he says, are gold coins, artifacts, and jewelry worth more than $1 million.
Fenn said he’d conceived the idea when diagnosed with cancer in 1988, planning to bury the treasure as a legacy. The cancer went into remission, but he decided to bury the chest anyway. In a self-published memoir he offered the following poem, which he says contains nine clues:
As I have gone alone in there
And with my treasures bold,
I can keep my secret where,
And hint of riches new and old.
Begin it where warm waters halt
And take it in the canyon down,
Not far, but too far to walk.
Put in below the home of Brown.
From there it’s no place for the meek,
The end is ever drawing nigh;
There’ll be no paddle up your creek,
Just heavy loads and water high.
If you’ve been wise and found the blaze,
Look quickly down, your quest to cease,
But tarry scant with marvel gaze,
Just take the chest and go in peace.
So why is it that I must go
And leave my trove for all to seek?
The answers I already know,
I’ve done it tired and now I’m weak.
So hear me all and listen good,
Your effort will be worth the cold.
If you are brave and in the wood
I give you title to the gold.
Fenn has been releasing further clues periodically as he follows the search (“No need to dig up the old outhouses, the treasure is not associated with any structure”). A number of people claim to have found the chest, but none has provided evidence, and Fenn says that to the best of his knowledge it remains undiscovered.
In 1935 a shark in an Australian aquarium vomited up a human forearm, a bizarre turn of events that sparked a confused murder investigation. This week’s episode of the Futility Closet podcast presents two cases in which a shark supplied key evidence of a human crime.
We’ll also learn about the Paris Herald’s obsession with centigrade temperature, revisit the scary travel writings of Victorian children’s author Favell Lee Mortimer, and puzzle over an unavenged killing at a sporting event.
A water jug is empty, and its center of gravity is above the inside bottom of the jug. Water is poured into the jug until the center of gravity of the jug and water (considered together) is as low as possible. Explain why this center of gravity must lie at the surface of the water.
If P is the center of gravity of the system, then as long as P is above the surface of the water, it will fall as the surface rises. When P reaches the surface, adding any more water will raise the water level and hence the level of P.
From Edward Barbeau, Murray Klamkin, and William Moser, Five Hundred Mathematical Challenges, 1995.
Avon, Colorado, has a bridge called Bob. The four-lane, 150-foot span, built in 1992, connects Avon with the Beaver Creek ski resort across the Eagle River. The town council held a naming contest and received 85 suggestions, including Avon Crossing and Del Mayre Bridge. It was 32-year-old construction worker Louie Sullivan who said, “Oh, heck, just name it Bob,” a suggestion that set city manager Bill James “laughing so hard he had to leave the room.”
Sullivan said he was surprised at the town’s vote; previously he had considered Avon a bit stuffy. “It raises my faith in their sense of humor,” he said.
The Swedish pop group Caramba has an odd claim to fame — their eponymous 1981 album consists entirely of nonsense lyrics. No one’s even sure who was in the band — the album sleeve lists 13 members, all using pseudonyms. It was produced by Michael B. Tretow, who engineered ABBA’s records, and singer Ted Gärdestad contributed some vocals, but these are the only two participants who have been named.
The band broke up (apparently) after the first album, so we’ll never get more of this. Here are the lyrics to the single “Hubba Hubba Zoot Zoot”:
Hubba hubba zoot zoot
Num
Deba uba zat zat
Num
A-hoorepa hoorepa a-huh-hoorepa a-num num
A-num
Hubba hubba zoot zoot
Num
Deba uba zat zat
Num
A-hoorepa hoorepa a-huh-hoorepa a-num num
A-num
Hubba hubba zoot zoot
Deba uba zat zat a-num num
Hubba hubba zoot zoot
Deba uba zat zat a-num num
A-hoorepa hoorepa a-huh-hoorepa a-num num
A-hoorepa hoorepa
HAH
A-huh-hoorepa a-num num
A-num
Hubba hubba zoot zoot
Deba uba zat zat a-num num
Hubba hubba zoot zoot
Deba uba zat zat a-num num
A-hoorepa hoorepa a-huh-hoorepa a-num num
A-hoorepa hoorepa a-huh-hoorepa
HAH
A-num num
A-num
Hubba hubba zoot zoot
A-huh zoot a-huh
Deba uba zat zat a-num num
Hubba hubba zoot zoot
Deba uba zat zat a-num num
A-hoorepa hoorepa a-huh-hoorepa a-num num
Num
A-hoorepa hoorepa a-huh-hoorepa a-num num
Deba uba zat zat
A-hoorepa hoorepa a-huh-hoorepa a-num num
a-num
Hubba hubba zoot zoot
deba uba zat zat
HAH
A-hoorepa hoorepa a-huh-hoorepa a-num num
A-num
Hubba hubba zoot zoot
Deba uba zat zat a-num num
Hubba hubba zoot zoot
Duuh
Deba uba zat zat a-num num
A-hoorepa hoorepa a-huh-hoorepa a-num num
A-hoorepa hoorepa a-huh-hoorepa a-num num
HAH
A-num
Hubba hubba zoot zoot
Deba uba zat zat a-num num
Hubba hubba zoot zoot
Deba uba zat zat a-num num
A-hoorepa hoorepa a-huh-hoorepa a-num num
A-hoorepa hoorepa a-huh-hoorepa a-num num
HAH
Hubba hubba zoot zoot
Deba uba zat zat a-num num
HOH
Hubba hubba zoot zoot
Hubba hubba mo-re mo-re
Deba uba zat zat a-num num
A-hoorepa hoorepa a-huh-hoorepa a-num num
A-hoorepa hoorepa a-huh-hoorepa a-num num
A-num
A puzzle from Martin Gardner’s column in Math Horizons, November 1995:
Driving along the highway, Mr. Smith notices that signs for Flatz beer appear to be spaced at regular intervals along the roadway. He counts the number of signs he passes in one minute and finds that this number multiplied by 10 gives the car’s speed in miles per hour. Assuming that the signs are equally spaced, that the car’s speed is constant, and that the timed minute began and ended with the car midway between two signs, what is the distance from one sign to the next?
We can answer this without knowing the car’s speed. If x is the number of signs that the car passes in one minute, then the car will pass 60x signs in an hour. We’re told that the car is traveling at 10x miles per hour, so in 10x miles it will pass 60x signs, and in one mile it will pass 60x/10x signs, or 6. So the signs are 1/6 mile, or 880 feet, apart.
Thomas Huxley’s Evolution and Ethics took China by storm — phrases such as the strong are victorious and the weak perish resonated in the national consciousness and “spread like a prairie fire, setting ablaze the hearts and blood of many young people,” noted philosopher Hu Shih.
People even adopted Darwin’s ideas as names. “The once famous General Chen Chiung-ming called himself ‘Ching-tsun’ or ‘Struggling for Existence.’ Two of my schoolmates bore the names ‘Natural Selection Yang’ and ‘Struggle for Existence Sun.’
“Even my own name bears witness to the great vogue of evolutionism in China. I remember distinctly the morning when I asked my second brother to suggest a literary name for me. After only a moment’s reflection, he said, ‘How about the word shih [fitness] in the phrase “Survival of the Fittest”?’ I agreed and, first using it as a nom de plume, finally adopted it in 1910 as my name.”
There must be a story behind this one: In 1900 Ludwig Ederer patented an “alarm bed” to wake an attendant when a greenhouse grows too cold.
If the steam pressure in the boiler drops, the bed suddenly tilts upright, “so that the sleeper will slide or roll off, thus reminding him that the steam within the pipe system is below a certain point, endangering the life of the plants within the greenhouse.”
After he’s stoked the fire the attendant can go back to bed and dream about getting a better job.
A group of children are standing outside a room. Each wears a hat that’s either red or blue, and each child can see the other children’s hats but not her own. At a signal they enter the room one by one and arrange themselves in a line partitioned by hat color. How do they manage this without communicating?
The first child stands in the center of the room, and the second stands at her side. Thereafter each entering child follows a rule: If she sees that the line of children are all wearing hats of the same color, then she stands at one end of the line. If they’re wearing both red and blue hats, then she inserts herself at the break between the two colors.
