Ultra magic 9x9 magic square

 

Use 2x the same of 2x different 3x3 magic square to construct an ultra magic 9x9 square.

 

 

1x digit                                            +     9x (digit -/- 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).

 

 

Download
9x9, Ultra magic.xls
Microsoft Excel werkblad 80.0 KB