Ultra magic 9x9 magic square
Use 2x the same of 2x different 3x3 magic square to construct an ultra magic 9x9 square.
1x number + 9x (number -/- 1) = Ultra magic 9x9 square
| 1 | 5 | 9 | 6 | 7 | 2 | 8 | 3 | 4 | 1 | 8 | 6 | 1 | 8 | 6 | 1 | 8 | 6 | 1 | 68 | 54 | 6 | 70 | 47 | 8 | 66 | 49 | ||||
| 8 | 3 | 4 | 1 | 5 | 9 | 6 | 7 | 2 | 5 | 3 | 7 | 5 | 3 | 7 | 5 | 3 | 7 | 44 | 21 | 58 | 37 | 23 | 63 | 42 | 25 | 56 | ||||
| 6 | 7 | 2 | 8 | 3 | 4 | 1 | 5 | 9 | 9 | 4 | 2 | 9 | 4 | 2 | 9 | 4 | 2 | 78 | 34 | 11 | 80 | 30 | 13 | 73 | 32 | 18 | ||||
| 1 | 5 | 9 | 6 | 7 | 2 | 8 | 3 | 4 | 6 | 1 | 8 | 6 | 1 | 8 | 6 | 1 | 8 | 46 | 5 | 72 | 51 | 7 | 65 | 53 | 3 | 67 | ||||
| 8 | 3 | 4 | 1 | 5 | 9 | 6 | 7 | 2 | 7 | 5 | 3 | 7 | 5 | 3 | 7 | 5 | 3 | 62 | 39 | 22 | 55 | 41 | 27 | 60 | 43 | 20 | ||||
| 6 | 7 | 2 | 8 | 3 | 4 | 1 | 5 | 9 | 2 | 9 | 4 | 2 | 9 | 4 | 2 | 9 | 4 | 15 | 79 | 29 | 17 | 75 | 31 | 10 | 77 | 36 | ||||
| 1 | 5 | 9 | 6 | 7 | 2 | 8 | 3 | 4 | 8 | 6 | 1 | 8 | 6 | 1 | 8 | 6 | 1 | 64 | 50 | 9 | 69 | 52 | 2 | 71 | 48 | 4 | ||||
| 8 | 3 | 4 | 1 | 5 | 9 | 6 | 7 | 2 | 3 | 7 | 5 | 3 | 7 | 5 | 3 | 7 | 5 | 26 | 57 | 40 | 19 | 59 | 45 | 24 | 61 | 38 | ||||
| 6 | 7 | 2 | 8 | 3 | 4 | 1 | 5 | 9 | 4 | 2 | 9 | 4 | 2 | 9 | 4 | 2 | 9 | 33 | 16 | 74 | 35 | 12 | 76 | 28 | 14 | 81 |
The ultra magic 9x9 square is panmagic, symmetric, 3x3 compact and each 1/3 row/ column gives 1/3 of the magic sum (extra magic feature that each 1/3 diagonal gives 1/3 of the magic sum it is not possible).
