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