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pythonmagic-square

Find all possible magic squares (3x3) python

I can find only one magic square how to find all please.

Solution

  • I'll leave finding out how to generate a magic square as an exercise. If you're still having trouble with it, you can find other questions on StackOverflow about how to generate a magic square of a given size in Python.

    Once you have your 3x3 magic square magic(3) (as a numpy ndarray), you can obtain all of the possible magic squares of that size by performing all of the possible rotations and reflections on it:

    rotations = [np.rot90(magic(3), x) for x in range(4)]
reflections = [np.flip(x, 1) for x in rotations]
all_magic_3x3 = rotations + reflections

    This produces a list containing the following 8 magic 3x3 matrices:

    [[8 1 6]
 [3 5 7]
 [4 9 2]]

[[6 7 2]
 [1 5 9]
 [8 3 4]]

[[2 9 4]
 [7 5 3]
 [6 1 8]]

[[4 3 8]
 [9 5 1]
 [2 7 6]]

[[6 1 8]
 [7 5 3]
 [2 9 4]]

[[2 7 6]
 [9 5 1]
 [4 3 8]]

[[4 9 2]
 [3 5 7]
 [8 1 6]]

[[8 3 4]
 [1 5 9]
 [6 7 2]]