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).

 

Download
7x7, Lozenge method.xls
Microsoft Excel werkblad 29.5 KB