3x3 (not pure) in 5x5 (pure) magic square
Use the row and column grids of the 3x3 magic square to construct the 3x3 inlay.
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To get the right numbers of the 3x3 inlay add 1 to all numbers.
Row grid 3x3 inlay Column grid 3x3 inlay
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Construct the row grid of the 5x5 border and take care that the sum of opposite numbers in the border is allways 4 and the sum of a row or a column is allways 10. Put the numbers as follows (n.b.: Put 2x the middle number from 0 up to 4 cross in the corners):
Row grid 5x5 border
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Construct the column grid of the 5x5 border and take care that all combinations of row coordinates and column coordinates are unique, so you get all the numbers from 1 up to 25 in the magic square.
Column grid 5x5 border
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Take 1x a number from the row grid, add 5x the number of the same cell from the column grid and add 1.
1x number from row grid + 5x number from column grid + 1 = 3x3 in 5x5 magic square
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Use this method to construct inlaid squares of odd order from 5x5 to infinity. See 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29 & 31x31
