Math Magic Squares

Mathnasium 'TriMathlon' winners announced

ALPHARETTA, Ga. – Mathnasium of Alpharetta recently held a "TriMathlon" math competition.

The competition for third- through sixth-graders was held in conjunction with Mathnasium Learning Center's National TriMathlon Day, created to generate excitement about math among kids. Students answered questions like, "A number that is the product of exactly two primes has exactly how many factors?" Answer: 4.

Scores of the local winners were ranked against those of other competitors nationwide, and the local winners have been announced.

Forty-five TriMathlon participants competed by completing three challenges, including the Counting Game (tests students' ability to count from any number, to any number, by any number), Magic Squares (students are awarded points for creativity in developing their own math problems) and Mental Math Workout (evaluates students' number sense by asking them to solve given problems the "smart" way without pencil and paper).

"Congratulations to the TriMathlon winners and all of the participants," said Giulio "G" Helmsdorff, the director of Mathnasium of Alpharetta. "We hope this competition was a fun and rewarding experience that continues to strengthen their passion for math.

The Math Mom: From Magic Squares to Sudoku

In 1415, the German renaissance painter and mathematician Albrecht Dürer created this busy copperplate engraving of a woman melancholically contemplating amongst a clutter that includes an hour glass, a balance scale, a sphere, a polyhedron (aka philosopher’s stone), a purse, and keys. Like his contemporary’s Mona Lisa, this mysterious painting has been extensively studied, speculated upon and written about. It is believed that it was planned to be the first in a series of paintings describing various temperaments: melancholic, phlegmatic, choleric, and sanguine. It is titled: “Melencolia I” Magic squares have been around for thousands of years. Magic squares of size 3x3 are mentioned in the Chinese literature dating 650 BC. Magic squares of size 5x5 and 6x6 are found in an encyclopedia from Baghdad written in the ten’s century. They were engraved in stone and metal, worn as talismans, their usage believed to ensure longevity and prevention of diseases (from Wikipedia). Magic squares can be spotted in art all around the globe. The Indian Parshva temple still contains a 4x4 magic square carved in the 10th century. The Passion facade of Gaudi’s Sagrada Família church in Barcelona, designed by sculptor Josep Subirachs, features a 4×4 magic square with a sum of 33 that is the age of Jesus at the time of Passion. While his squares are not truly magic squares because sum of each of the diagonals is not equal to the sum of numbers in every row or column, they are still pretty cool. To compensate for a lack of the diagonal property Franklin defined a broken diagonal or “bended rows” properties where the sum of numbers in each highlighted bended rows is the same. Magic squares could be considered the ancient relatives of the modern Sudoku game. In the late 19th century, French newspapers started publishing matrix puzzles – 9x9 magic squares with some numbers removed. Then the puzzle slowly evolved taking away the sum requirements and instead requiring that each row, column and diagonal have all the numbers from 1 to 9. And finally, the 3x3 sub-division was added producing the modern day Sudoku (you can click to play): Thousands of Sudoku are published in the world daily. You have likely seen someone doing Sudoku on his way to work, at the playground, laundromat or in the coffee shop. A good story attesting to Sudoku’s popularity was published in the Sydney Morning Herald .

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