Charlemagne's Puzzle?

What? Guess my education has not been as well-rounded as I thought, for I had no idea hat Charlemagne's Puzzle was until I read this article! Article from The New York Times: The Tierney Lab "Putting Ideas in Science to the Test" March 3, 2009, 2:12 pm — Updated: 4:25 pm --> A Prize for Solving Charlemagne’s Puzzle By John Tierney You might think that founding the Holy Roman Empire would be enough of a challenge for one man, but Charlemagne wanted more: to conquer mathematical puzzles! If you have the same ambition, you could win a prize here at the Lab. The emperor hired Alcuin, a renowned English scholar of the eighth century, to compile a collection of puzzles. Titled “Problems to Sharpen the Young,” the book was intended to get the youth of the day more interested in mathematics (a perennial challenge, obviously). Two of Alcuin’s puzzles are included in a new collection, “The Total Brain Workout,” compiled by Marcel Danesi, a professor of anthropology at the University of Toronto and an expert on puzzles. One of them is a river-crossing brainteaser that’s been found in other collections and cultures, but Dr. Danesi says that Alcuin’s may be the oldest known version: A traveler comes to a riverbank with a wolf, a goat and a head of cabbage. To his chagrin, he notes that there is only one boat for crossing over, which can carry no more than two passengers — the traveler and either one of the two animals or the cabbage. As the traveler knows, if left alone together, the goat will eat the cabbage and the wolf will eat the goat. The wolf does not eat cabbage. How does the traveler transport his animals and his cabbage to the other side intact in a minimum number of back-and-forth trips? Once you’ve solved that one, Dr. Danesi offers what he calls a modern classic devised by Boris Kordemsky: A detachment of soldiers must cross a river. The bridge is broken, and the river is deep. The officer in charge spots two boys playing in a rowboat by the shore. The boat is so tiny, however, that it can only hold two boys or one soldier. All the soldiers succeed in crossing the river in the boat. How? You submit answers to both puzzles as comments to this post, and you’re welcome to suggest another puzzle for Lab readers. If you get both correct and come up with most intriguing new challenge, you’ll win a prize of Dr. Danesi’s book, “The Total Brain Workout,” which has 450 puzzles designed to stimulate different parts of the brain. [UPDATE: If you're submitting a new puzzle, don't include the answer in the comment -- you can email it to me separately (tierneylab@nytimes.com). We've already gotten some intriguing new puzzles among the comments. You're welcome to try them and post answers, and to vote for any favorite. And, spoiler alert: In the comments you'll find lots of correct answers to Dr. Danesi's two puzzles.]

Pi and the Great Pyramid

An article or post written by Assem Deif is a professor of mathematics at Cairo University and Misr University for Science and Technology Pi, Phi and the Great Pyramid Assem Deif investigates the values -- not the symbols -- of the last of the Wonders of the Ancient World Al-Ahram Weekly Online March 27 - April 2, 2008 Issue No. 890 We can forget all the ideas crediting Atlanteans or space aliens with building the Great Pyramid of Giza, and instead imagine ourselves travelling back in time in H G Wells's time machine to try and work out not how the ancient Egyptians built this enormous edifice, because this lies beyond our present understanding, but rather what we can best judge to be its most appropriate proportions. Then, however, there were no electronic calculators, only ropes and rods. Constructing right angles at the four corners of a pyramid is easy. To do it, history tells us that the Egyptians were aware of the ratios 3:4:5 as the side-lengths of a right-angle triangle. Many old kingdom pyramids adhere to these ratios. The Egyptians also knew a rough value of Pi (the value, not the symbol) as the ratio between the circumference of any circle and its diameter. They worked out that 3 _ is less than Pi, and Pi is less than 3 1/7, i.e. Pi lies between the rational number 22/7 and the Babylonian value. This can be done by constructing a circle of diameter AB and laying the latter on its circumference, starting from A, once until C then D then E, to conclude that Pi is greater than 3. The remaining part EA from the circumference is laid down again on the diameter AB, so seven times EA is less than AB which in turn is less than eight times EA, or EA/AB is greater than 1/8 and less than 1/7. Rest of article. Leave it to a professor of mathematics to botch the explanation! I was drifting off into sleep just before I copied and posted the last paragraph here - snore... There has to be a better way of explaining the mathematical wonders of the pyramids and Pi, etc. For instance, WHY does he say it's easy to figure out how to do a 90 degree right angle by using the 3/4/5 method? We actually have NO FRICKING IDEA how the ancient Egyptians came up with this formula, all we know is that they used it to lay out square foundations and that it WORKED! The 3/4/5 method of laying out a 90 degree ("right") triangle was "proven" - much later - by Pythagoras and his "school" of followers in Greece. So, the ancient Egyptians knew it worked, but how did they figure it out to begin with? We don't know - we don't have a clue. Mathematics cannot speak to that quintessimal moment of discovery - when someone along the Nile River figured it out - had that "EUREKA" moment, some 5,000 years ago. For those of you (including yours truly, who made it all the way through college advanced mathematics without having a clue - and what does THAT say about the state of universities back in the 1980's, heh?) one of the few things I remember is that mathematical theory says that a RIGHT angle, that is, an angle that measures 90 degrees (1/4 of a full circle, which is 360 degrees), can be found by utilizing a triangle with the following formula: sides A, B and C of a triangle, with "A" being 3 "units" (whatever your units of measurement happen to be), side "B" being 4 units, and side "C" being five units. I'm sure I'm missing something here, LOL! Now you know why I'm not a mathematician. Using the classic Egyptian formula for figuring out how to make a square (90 degrees) corner of that triangle, the Sheshat Goddess (actually, a priestess representing Sheshat) had a length of rope knotted into twelve equal lengths. A stake was driven into the ground by her consort, the Anubis priest, at a predetermined sacred spot. The Sheshat priestess then looped the rope over the stake such that 3 knots formed one leg of a triangle, which was then staked, and 4 knots formed a second leg of the triangle, also staked. The remaining 5 knots linked together the two sides legs of the triangle previously staked out with the knotted rope, forming the - what I believe is called the hypotenus of the 90 degree right triangle. About all I remember from geometry is 3 squared (9) PLUS 4 squared (16), EQUALS 5 squared (25) - but that was just a Greek way of saying lay out a square corner by doing this...

Goddesschess' Showgirls wisdom: Brain Teasers, puzzles, inigmas, end-game chess problems, and play-time, are good for your mental health. The Mutilated Chess Board We have a chessboard with the two opposing corners removed,so that there are only 62 squares remaining. Now we take 31 dominoes shaped such that each domino covers exactly two squares. The question is: is it possible to arrange the 31 dominoes so that they cover all 62 squares on the chessboard? There are two approaches to the problem: To find the answer to this puzzle go to: FORTUNE CITY