7x7 magic square

Lozenge method of John Horton Conway

 

With the Lozenge method of John Horton Conway you get magic squares of odd order and you find all odd numbers in the (white) 'diamond' and all even numbers outside the diamond (in the dark area). See for detailed explanation: Lozenge 5x5 magic square. 

 

 

Take 1x number from row grid +1

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

 

 

+ 7x number from column grid

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

 

 

= 7x7 Lozenge magic square

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

 

 

Use this method to construct magic squares of odd order (= 3x3, 5x5, 7x7, ... magic square).

 

See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27,   29x29 and 31x31

 

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7x7, Lozenge method.xls
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7x7 magic square