Concentric

 

To construct a concentric magic square you can put each time a new border around the square to make it larger and larger and so you can construct a 4x4 in 6x6 in 8x8 in 10x10 in ... magic square.

 

 

number + 10  =    number + 14           =     number + 18                       =    4x4 in 6x6 in 8x8 in 10x10 MS

                                                92 2 98 4 14 18 84 16 86 91
                            57 12 52 14 1 3 63 58     88 75 30 70 32 19 21 81 76 13
            1 6 9 34 32 29     10 15 20 23 48 46 43 55     12 28 33 38 41 66 64 61 73 89
1 8 13 12     35 11 18 23 22 2     9 49 25 32 37 36 16 56     90 27 67 43 50 55 54 34 74 11
15 10 3 6     33 25 20 13 16 4     4 47 39 34 27 30 18 61     5 22 65 57 52 45 48 36 79 96
4 5 16 9     27 14 15 26 19 10     54 41 28 29 40 33 24 11     100 72 59 46 47 58 51 42 29 1
14 11 2 7     7 24 21 12 17 30     59 21 38 35 26 31 44 6     8 77 39 56 53 44 49 62 24 93
            8 31 28 3 5 36     60 22 45 42 17 19 50 5     94 78 40 63 60 35 37 68 23 7
                            7 53 13 51 64 62 2 8     6 25 71 31 69 82 80 20 26 95
                                                10 99 3 97 87 83 17 85 15 9

 

 

Take the 8x8 concentric magic square, add 18 to all numbers and construct the border [see webpage most perfect 8x8 in 10x10]

 

See how the concentric magic square on this website is growing bigger and bigger: 

3x34x45x56x67x78x89x910x1011x1112x1213x1314x1415x1516x1617x1718x1819x1920x2021x2122x2223x2324x2425x2526x2627x2728x2829x29,  30x3031x31 and 32x32

 

Download
10x10, concentric.xls
Microsoft Excel werkblad 57.5 KB