Posts Tagged ‘Puzzle’
“Advantage! What is advantage?”*…
Pradeep Mutalik unpacks the magic and math of how to win games when your opponent goes first…
Most games that pit two players or teams against each other require one of them to make the first play. This results in a built-in asymmetry, and the question arises: Should you go first or second?
Most people instinctively want to go first, and this intuition is usually borne out. In common two-player games, such as chess or tennis, it is a real, if modest, advantage to “win the toss” and go first. But sometimes it’s to your advantage to let your opponent make the first play.
In our February Insights puzzle, we presented four disparate situations in which, counterintuitively, the obligation to move is a serious and often decisive disadvantage. In chess, this is known as zugzwang — a German word meaning “move compulsion.”…
Four fascinating examples: “The Secrets of Zugzwang in Chess, Math and Pizzas,” from @PradeepMutalik.
* Fyodor Dostoyevsky, Notes from Underground
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As we play to win, we might recall that it was on this date in 2011 that scientists involved in the OPERA experiment (a collaboration between CERN and the Laboratori Nazionali del Gran Sasso) mistakenly observed neutrinos appearing to travel faster than light. OPERA scientists announced the results with the stated intent of promoting further inquiry and debate. Later the team reported two flaws in their equipment set-up that had caused errors far outside their original confidence interval: a fiber optic cable attached improperly, which caused the apparently faster-than-light measurements, and a clock oscillator ticking too fast; accounting for these two sources of error eliminated the faster-than-light results. But even before the sources of the error were discovered, the result was considered anomalous because speeds higher than that of light in a vacuum are generally thought to violate special relativity, a cornerstone of the modern understanding of physics for over a century.
“Then we got into a labyrinth, and when we thought we were at the end, came out again at the beginning, having still to seek as much as ever.”*…
On the heels of Wordle‘s extraordinary success, there have been a rash of variations: e.g., Crosswordle, Absurdle, Quordle, even the NSFW Lewdle.
Now for the National Gallery of Art, another nifty puzzle: Artle.
Enjoy!
* Plato, Euthydemus
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As we play, we might recall that it was on this date in 1934 that Mandrake the Magician first appeared in newspapers. A comic strip, it was created by Lee Falk (before he created The Phantom)… and thus its crime-fighting, puzzle-solving hero is regarded by most historians of the form to have been America’s first comic superhero.
“In a world of diminishing mystery, the unknown persists”*…
But what is it for?…
In the first episode of Buck Rogers, the 1980s television series about an astronaut from the present marooned in the 25th century, our hero visits a museum of the future. A staff member brandishes a mid-20th-century hair dryer. “Early hand laser,” he opines. As an observation of how common knowledge gets lost over time, it’s both funny and poignant. Because our museums also stock items from the past that completely baffle the experts.
Few are as intriguing as the hundred or so Roman dodecahedrons that we have found… In 1739, a strange, twelve-sided hollow object from Roman times was discovered in England. Since then, more than a hundred dodecahedrons have been unearthed.. We know next to nothing about these mysterious objects — so little, in fact, that the various theories about their meaning and function are themselves a source of entertainment.
So, what do we know?
Roman dodecahedrons — or more properly called Gallo-Roman dodecahedrons — are twelve-sided hollow objects, each side pentagonal in shape and almost always contain a hole. The outer edges generally feature rounded protrusions.
Most of the objects are made from bronze, but some are in stone and don’t have holes or knobs. The dodecahedrons are often fist-sized yet can vary in height from 4 to 11 cm (about 1.5 to 4.5 in). The size of the holes also varies, from 6 to 40 mm (0.2 to 1.5 in). Two opposing holes typically are of differing sizes.
Objects of this type were unknown until the first one was found in 1739 in Aston, Hertfordshire. In all, 116 have been dug up from sites as far apart as northern England and Hungary. But most have been found in Gaul, particularly in the Rhine basin, in what is now Switzerland, eastern France, southern Germany, and the Low Countries. Some were found in coin hoards, indicating their owners considered them valuable. Most can be dated to the 2nd and 3rd century AD.
No mention of the dodecahedrons from Roman times has survived. Any theory as to their function is based solely on speculation. Some suggestions:
• A specific type of dice for a game since lost to history.
• A magical object, possibly from the Celtic religion. A similar small, hollow object with protrusions was recovered from Pompeii in a box with either jewellery or items for magic.
• A toy for children.
• A weight for fishing nets.
• The head of a chieftain’s scepter.
• A kind of musical instrument.
• A tool to estimate distances and survey land, especially for military purposes.
• An instrument to estimate the size of and distance to objects on the battlefield for the benefit of the artillery.
• A device for detecting counterfeit coins.
• A calendar for determining the spring and autumn equinoxes and/or the optimal date for sowing wheat.
• A candle holder. (Wax residue was found in one or two of the objects recovered.)
• A connector for metal or wooden poles.
• A knitting tool specifically for gloves. (That would explain why no dodecahedrons were found in the warmer regions of the Empire.)
• A gauge to calibrate water pipes.
• A base for eagle standards. (Each Roman legion carried a symbolic bird on a staff into battle.)
• An astrological device used for fortune-telling. (Inscribed on a dodecahedron found in Geneva in 1982 were the Latin names for the 12 signs of the zodiac.)
The geographic spread of the dodecahedrons we know of is particular: they were all found in territories administered by Rome, inhabited by Celts. That enhances the theory that they were specific to Gallo-Roman culture, which emerged from the contact between the Celtic peoples of Gaul and their Roman conquerors.
Intriguingly, archaeologists in the 1960s have found similar objects along the Maritime Silk Road in Southeast Asia, except smaller and made of gold. They do not appear to predate the Gallo-Roman artefacts and may be evidence of Roman influence on the ancient Indochinese kingdom of Funan…
The first of many was unearthed almost three centuries ago, and we still don’t know what they were for: “Mysterious dodecahedrons of the Roman Empire.”
* Jhumpa Lahiri
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As we ponder the puzzle, we might send compressed birthday greetings to Aaron “Bunny” Lapin; he was born on this date in 1914. In 1948, Lapin invented Reddi-Wip, the pioneering whipped cream dessert topping dispensed from a spray can. First sold by milkmen in St. Louis, the product rode the post-World War Two convenience craze to national success; in 1998, it was named by Time one of the century’s “100 great consumer items”– along with the pop-top can and Spam. Lapin became known as the Whipped Cream King; but his legacy is broader: in 1955, he patented a special valve to control the flow of Reddi-Wip from the can, and formed The Clayton Corporation to manufacture it. Reddi-Wip is now a Con-Agra brand; but Clayton goes strong, now making industrial valves, closures, caulk, adhesives and foamed plastic products (like insulation and cushioning materials).
“Dear Santa, before I submit my life to your scrutiny, I demand to know who made YOU the master of my fate?!*…
Father Christmas as pictured in Josiah King’s The Examination and Tryal of Father Christmas (1686)
Contrary to what many believe, Santa Claus as we know him today – sleigh riding, gift-giving, rotund and white bearded with his distinctive red suit trimmed with white fur – was not the creation of the Coca Cola Company. Although their Christmas advertising campaigns of the 1930s and 40s were key to popularising the image, Santa can be seen in his modern form decades before Coca Cola’s illustrator Haddon Sundblom got to work. Prior to settling on his famed red garb and jolly bearded countenance, throughout the latter half of the 19th century, Santa morphed through a variety of different looks. From the description given in Clement Moore’s A Visit from St Nicholas in 1822, through the vision of artist Thomas Nast, and later Norman Rockwell, Mr Claus gradually shed his various guises and became the jolly red-suited Santa we know today…
The illustrated story of St. Nick at “A Pictorial History of Santa Claus.”
* Calvin (Bill Watterson, Calvin and Hobbes)
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As we finish our letters, we might recall that it was on this date in 1913 that Arthur Wynne’s “word-cross,” the first crossword puzzle, was published in the New York World:
2-3. What bargain hunters enjoy. 6-22. What we all should be.
4-5. A written acknowledgment. 4-26. A day dream.
6-7. Such and nothing more. 2-11. A talon.
10-11. A bird. 19-28. A pigeon.
14-15. Opposed to less. F-7. Part of your head.
18-19. What this puzzle is. 23-30. A river in Russia.
22-23. An animal of prey. 1-32. To govern.
26-27. The close of a day. 33-34. An aromatic plant.
28-29. To elude. N-8. A fist.
30-31. The plural of is. 24-31. To agree with.
8-9. To cultivate. 3-12. Part of a ship.
12-13. A bar of wood or iron. 20-29. One.
16-17. What artists learn to do. 5-27. Exchanging.
20-21. Fastened. 9-25. To sink in mud.
24-25. Found on the seashore. 13-21. A boy.
10-18. The fibre of the gomuti palm.
“If it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.”*…
Your correspondent is headed into the chilly wilds for the Thanksgiving holiday, so this will be the last post until after the passing of the tryptophan haze. By way of keeping readers amused in the meantime, the puzzle above…
Find a step-by-step guide to its answer at “How to Solve the Hardest Logic Puzzle Ever.”
* Tweedledee, in Lewis Caroll’s Through the Looking-Glass, and What Alice Found There
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As we muddle in the excluded middle, we might recall that it was on this date in 1915 that Albert Einstein presented the Einstein Field Equations to the Prussian Academy of Sciences. Einstein developed what was elaborated into a set of 10 equations to account for gravitation in the curved spacetime described in his General Theory of Relativity; they are used to determine spacetime geometry.
(German mathematician David Hilbert reached the same conclusion, and actually published the equation before Einstein– though Hilbert, who was a correspondent of Einstein’s, never suggested that Einstein’s credit was inappropriate.)
On the right side of the equal sign, the distribution of matter and energy in space; on the left, the geometry of the space, the so-called metric, a prescription for how to compute the distance between two points.
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