## Magic square: the best way to have fun with logic and arithmetic!

A passion long millennia that unconsciously keeps on attracting us all

Fun with logic and arithmetic seems impossible to many of us, but it is actually an ancient, and still more widespread than one can think, activity! Take for example Magic Squares. These are squares, subdivided into smaller squares that contain all the numbers from 1 to n arranged in such a way that the sums on each row, column and diagonal give the same result, which is called the magic constant or magic sum. Legend has it that the first Magic Square mysteriously appeared to the Chinese Emperor Yu the Great (around 2000 BC) on the shell of a turtle coming out of the waters of the Yellow River. It was a magic square of order 3°, which means of 3 rows and 3 columns, containing numbers from 1 to 9.

This particular Magic Square, whose results of the total of each row, column and diagonal is the number 15, was named Luo Shu.
From that moment on Magic Squares have spread from China, India to all over the Arab world and have become an exciting game even for non- mathematicians, who amused themselves inventing variations always different and amazing . They were so greatly fascinating, that it was believed that some of them had real magical properties : printed on plates of silver or gold, they were used as a cure for diseases (from lovesickness , to plague) .

And now a question. Which game popular in Italy do Magic Squares remind you of? Think about it: squares, numbers … Precisely! Sudoku!

To be precise Sudoku is a Latin square, that is a square in which the only condition to be met is that the symbols chosen are present only once in each row and column. The Sudoku has symbols which are the numbers from 1 to 9, but in reality in Latin squares one can use symbols of any type, since there is no arithmetic condition to comply with. Instead inventing a magic square, compared to solving a Sudoku , also means practicing concepts of arithmetic (add numbers and compare amounts). It’s for this reason that Sudoku is a game of pure logic, while Magic Squares are also games of arithmetic!

Now tell the truth: you thought you were playing something very modern, isn’t it? The answer is: no! You too were infected with a passion, a challenge, born thousands of years ago. Inventing Magic Squares and solving Sudoku is your personal challenge with the mathematicians of the past: perhaps practicing hard you could become even better than Euler himself (a great Swiss mathematician and one of the fathers of Latin square)!

I can only wish good game to you all! And in case anyone of you discovers other wonders related to the magical world of Magic Squares, keep us posted!