### Panmagic inlay magic square in 7x7 magic square

Use the shift method to construct the 5x5 inlay magic square and take the middle 5 numbers from 0 uo to 6, that is 1 up to 5.

Column grid 5x5 inlay magic square           Row grid 5x5 inlay magic square

 1 2 3 4 5 1 2 3 4 5 4 5 1 2 3 3 4 5 1 2 2 3 4 5 1 5 1 2 3 4 5 1 2 3 4 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3

Construct the column grid of the border with the remaining numbers. The top row, the bottom row, the left column and the right column must sum to 15. Opposite numbers must sum to 6.

Column grid 7x7 border (around 5x5)

 3 0 3 1 2 4 5 6 0 0 6 0 6 6 0 6 0 0 6 0 6 6 0 6 0 0 6 0 6 6 3 6 5 4 2 1 0 3

Construct the row grid of the border. Take care that all combinations of column coordinate/row coordinate are unique, because all the numbers from 1 to 49 must be in the square to get a valid 7x7 magic square.

Row grid 7x7 border (around 5x5)

 0 6 0 0 6 6 3 1 5 2 4 5 1 4 2 6 0 3 0 6 6 0 0 6

Take 7x number from the column grid, add 1x number from the same cell of the row grid and add 1 to all cells.

7x number from column grid             +        1x number from row grid

 3 1 2 4 5 6 0 0 6 0 0 6 6 3 0 1 2 3 4 5 6 1 1 2 3 4 5 5 6 4 5 1 2 3 0 2 3 4 5 1 2 4 0 2 3 4 5 1 6 5 5 1 2 3 4 1 6 5 1 2 3 4 0 4 2 3 4 5 1 2 0 3 4 5 1 2 6 6 4 5 1 2 3 0 6 5 4 2 1 0 3 3 0 6 6 0 0 6

+1                                                   =     5x5 inlay in 7x7 magic square

 21 13 14 28 41 48 3 22 14 15 29 42 49 4 1 8 16 24 32 40 47 2 9 17 25 33 41 48 44 31 39 12 15 23 4 45 32 40 13 16 24 5 5 19 22 30 38 11 43 6 20 23 31 39 12 44 46 37 10 18 26 29 2 47 38 11 19 27 30 3 6 25 33 36 9 17 42 7 26 34 37 10 18 43 45 35 34 20 7 0 27 46 36 35 21 8 1 28

You can use this method to construct larger odd inlaid magic squares.

7x7, panmagic 5x5 in magic 7x7 square.xl