Lozenge method of John Horton Conway

 

With the Lozenge method of John Horton Conway you get a magic square 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

4 5 6 7 8 0 1 2 3
3 4 5 6 7 8 0 1 2
2 3 4 5 6 7 8 0 1
1 2 3 4 5 6 7 8 0
0 1 2 3 4 5 6 7 8
8 0 1 2 3 4 5 6 7
7 8 0 1 2 3 4 5 6
6 7 8 0 1 2 3 4 5
5 6 7 8 0 1 2 3 4

 

 

+ 9x number from column grid

5 6 7 8 0 1 2 3 4
6 7 8 0 1 2 3 4 5
7 8 0 1 2 3 4 5 6
8 0 1 2 3 4 5 6 7
0 1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8 0
2 3 4 5 6 7 8 0 1
3 4 5 6 7 8 0 1 2
4 5 6 7 8 0 1 2 3

 

 

= 9x9 Lozenge magic square

50 60 70 80 9 10 20 30 40
58 68 78 7 17 27 28 38 48
66 76 5 15 25 35 45 46 56
74 3 13 23 33 43 53 63 64
1 11 21 31 41 51 61 71 81
18 19 29 39 49 59 69 79 8
26 36 37 47 57 67 77 6 16
34 44 54 55 65 75 4 14 24
42 52 62 72 73 2 12 22 32

 

 

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

 

Download
9x9, Lozenge method.xls
Microsoft Excel werkblad 46.5 KB