It both blows my mind and delights me that a problem that I can investigate in full in an Ri Masterclass (how many magic squares of order 3 are there?) can in 3 straightforward steps become something so complex that no one (yet) knows how many answers there are. Statistical techniques indicate that there are probably of the order of 17,700,000,000,000,000,000 individual solutions.
MAGIC NUMBER MATHEMATICS SERIES
It is a subject of ongoing mathematical research. magic number, in physics, in the shell models of both atomic and nuclear structure, any of a series of numbers that connote stable structure. Now I know that you are asking what any self-respecting mathematician (=person) would want to know: how many solutions for a 6圆 magic square (numbers 1-36 and magic total 111)? The incredible fact is (although I do actually believe it) that is an unsolved problem. Go up again to a 5x5 magic square (numbers 1–25 and magic total 65) and research has proved there are no less than 275,305,224 different solutions. Another wonderful attribute of mathematics – the answers often surprise you, defying your first instinct. It is known that there are 880 distinct solutions for a 4x4, or order 4 magic square, containing the numbers 1-16, magic total 34.
Go up one degree of complexity, and what happens? Something very surprising! This constant, unchanging nature is one of the most satisfying aspects of mathematics for me-once something is proved true, it is eternally true. Multiply the magic number by your new number.
I really enjoy that people separated from me in time and space by thousands of years and thousands of miles enjoyed the same mathematical patterns as I do today. (This particular version is known as a Normal Magic Square, where the grid is n x n and contains each of the integers 1-n2). This arrangement is what we now know as the 3x3 magic square. No matter which way the 3 numbers in each row, each column and both diagonals of the square were added, the sum was always 15. The pattern was a 3x3 grid of nine squares, each containing one of the numbers between 1 and 9. In response a mystical turtle emerged to rescue them from the deluge, with a pattern inscribed on its back. Legend has it that when the Lo River was in flood, the people became increasingly desperate, and they asked the river gods to save them. The first recorded magic square is the Lo Shu Square, found in ancient China about 5000 years ago.
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