![]() ![]() Of course, you could just rotate and reflect the examples above, and you could multiply every number in the square by the same constant. The new squares would still be magic, and it is not difficult to see that the magic squares you create would again have the magic product property and the magic pairwise product property. You could also add the same number to each of the nine numbers in a magic square, and the result would clearly be a new magic square. ![]() In this case it is not at all clear that the new magic square will still have the magic product and the magic pairwise product properties. Try to make up your own magic squares by assigning a few numbers at random to some of the cells and then filling the other cells in so that the rows, columns and diagonals add up to the same number. Each time you succeed in making a magic square, you should check that the magic product and magic pairwise product properties also work.Īfter having worked out a few more examples, you may notice that the magic number is always three times the middle number of the magic square. In particular, it seems that the magic number is always a multiple of $3$. Now let's work out a systematic way of finding all $3\times 3$ magic squares. ![]()
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