Flip Sum
A problem from the 1999 St. Petersburg City Mathematical Olympiad:
Fifty cards are arranged on a table so that only the uppermost side of each card is visible. Each card bears two numbers, one on each side. The numbers range from 1 to 100, and each number appears exactly once. Vasya must choose any number of cards and flip them over, and then add up the 50 numbers now on top. What’s the highest sum he can be sure to reach?
Out of This World
Tunisia has an unique tourist draw — its southern desert contains the abandoned sets of five Star Wars movies, in which the Sahara stood in for the planet Tatooine.
A list, complete with photos and geographical coordinates, is here.
They’re popular with European tourists, but they won’t last — the 20-building set of Mos Espa, Anakin Skywalker’s hometown, is being engulfed by sand dunes.
In a Word
aurigation
v. the act or art of driving a chariot or coach
“When I Loved You”
When I loved you
And you loved me,
You were the sea,
The sky, the tree.
Now skies are skies,
And seas are seas,
And trees are brown
And they are trees.
— Charles A. Wagner
Busy
Male bees come from unfertilized eggs, so they have mothers but no fathers. Females come from fertilized eggs, so they have parents of both sexes. This produces an interesting pattern: The number of males in a given generation equals the number of females in the succeeding generation. And the number of females in a given generation equals the number of females in the succeeding two generations:
So the total number of bees, male and female, in generation n is the Fibonacci number Fn.
W. Hope-Jones discovered the relationship in 1921; this example is from Thomas Koshy’s Fibonacci and Lucas Numbers With Applications, 2001.
Self-Service
William Lance invented this “improved serving table” in 1866. It bears a set of food-laden shelves that revolve continuously past the diners, driven by steam. The shelves are “so loaded with viands, to move at the rate of fifteen or twenty feet per minute, or to pass before each guest at such speed as to exhibit before each guest the entire bill of fare once per minute, giving each one ample opportunity to help him or herself to such viands as may suit their tastes.”
“All persons at this table are put upon an equality and free to act for themselves, and these shelves so arranged as not only to contain the full bill of fare, and that kept hot by lamp or otherwise, but also to contain all the necessary dishes, knives, forks, spoons, glasses, &c.”
The attendant in the hidden “pantry” at the bottom replenishes the offerings and discreetly removes dirty dishes from the bottom shelf, where they’re left by departing diners. Lance estimates that such a table might serve 150 diners with only two attendants, “except those required in the pantry to put away the last dishes of each guest and brush off the crumbs and adjust the chair.”
From the Heart
Banker James M. Fail repeatedly donated money to his alma mater, the University of Alabama, which he credited for his success in the business world. But he declined opportunities to give his name to an Alabama facility. “After all,” he said, “who would want anything with the name ‘Fail’ on it?”
In 2008 he found a way to support the school and accept credit — he put his name on the visitors’ locker room.
The Bermagui Mystery
In 1880, 29-year-old Australian geologist Lamont Young set out in a fishing boat to survey the gold fields north of Bermagui in New South Wales. With him were his assistant, two fishermen, and the vessel’s owner. The boat was spotted sailing north the following morning, but it was discovered deserted that afternoon inside a shoal at Mutton Fish Point, 16 kilometers north of Bermagui.
Inside the boat were clothes, books, and research papers belonging to Young and his assistant, whose spectacles were laid out neatly on the seat. The oars and mast had been lashed to supports, but the sails and anchor were missing, and there was a single bullet hole in the starboard side. Near a campfire on the beach nearby were tins of salmon and butter, a jar of honey, half a loaf of bread, and three mother-of-pearl studs. There was no evidence of a struggle, but the copper case of a cartridge was found in the sand 30 yards from the boat.
The Colonial Office offered a reward of 200 pounds for information leading to the location of the missing men, and Young’s father hired a private detective, but the five were never found, and their disappearance has never been explained. The inlet where the boat was found is now named Mystery Bay in their honor.
The Little Man
In 1525, more than 100,000 German peasants demanded an end to serfdom and were massacred by the well-organized armies of the ruling class. After observing the ornate memorials with which the aristocrats congratulated themselves, Albrecht Dürer proposed a similarly baroque monument to the slain peasants:
Place a quadrangular stone block measuring ten feet in width and four feet in height on a quadrangular stone slab which measures twenty feet in length and one foot in height. On the four corners of the ledge place tied-up cows, sheep, pigs, etc. But on the four corners of the stone block place four baskets, filled with butter, eggs, onions, and herbs, or whatever you like. In the centre of this stone block place a second one, measuring seven feet in length and one foot in height. On top of this second block place a strong chest four feet high, measuring six and a half feet wide at the bottom and four feet wide at the top. Then place a kettle upside down on top of the chest. The kettle’s diameter should be four and a half feet at the rim and three feet at its bottom. Surmount the kettle with a cheese bowl which is half a foot high and two and a half feet in diameter at the bottom. Cover this bowl with a thick plate that protrudes beyond its rim. On the plate, place a keg of butter which is three feet high and two and a half feet in diameter at the bottom. Cover this bowl with a thick plate that protrudes beyond its rim. On the plate, place a keg of butter which is three feet high and has a diameter of a foot and a half at the bottom, and of only a foot at the top. Its spout should protrude beyond this. On the top of the butter keg, place a well-formed milk jug, two and a half feet high, and with a diameter which is one foot at its bulge, half a foot at its top, and is wider at its bottom. Into this jug put four rods branching into forks on top and extending five and a half feet in height, so that the rods will protrude by half a foot, and then hang peasants’ tool on it – like hoes, pitchforks, flails, etc. The rods are to be surmounted by a chicken basket, topped by a lard tub upon which sits an afflicted peasant with a sword stuck into his back.
What would that look like?
