NUMBER PUZZLES – MAGIC SQUARES

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Humans love to play games and do puzzles. Magic Squares are a difficult number puzzle and are not for the faint-hearted. You rearrange a set of digits to create rows, columns and diagonals that add to a given total.

The most famous Magic Square in the past is found on an engraving by Durer called Melancholia. Albrecht Durer was born on 21 May 1471 in Germany. He was one of 18 children and learnt to be a goldsmith and jeweller from his father and a woodcut designer from the leading craftsman at the time. But Albrecht was also a skilled painter at 13. Other artists taught him about the linked beauty of mathematics and art and he became a serious student of mathematics, perspective and proportion, studying Euclid in particular. Albrecht believed other artists might be jealous of him so he refused dinner invitations when travelling abroad in case someone tried to poison him. One of his most famous engravings is Melancholia, created in 1514.

This engraving famously shows a 4 x 4 Magic Square in the top right of the picture and the bottom row shows the date.

In a 4 x 4 Magic Square each row, column and diagonal add to the same total, in this case 34. Finding a solution is almost impossible so they are also known as Diabolical Squares.

You can try one for yourself using our Stage 3 (Grades 5/6/7) Addition and Subtraction Magic Squares activity by clicking here.

We provide a sample solution so that you can see it is possible to solve it.