Bimagic Square Solutions 4x4 Nearly-Bimagic Square of Distinct Integers 5x5 Nearly-Bimagic Square of Distinct Integers 6x6 Bimagic Squares of Distinct Integers 7x7 Bimagic Squares of Distinct Integers 4x4 Nearly-Bimagic Square of Distinct Integers 18 of 20 Correct Sums (MaxNb = 95, S1 = 45, S2 = 11,487), bad sums are -27 and 6159 -6 83 29 -61 -49 -31 75 50 95 -46 11 -15 5 39 -70 71 5x5 Nearly-Bimagic Square of Distinct Integers 23 of 24 Correct Sums This solution is a magic square of squares and is also magic in all but one diagonal. (MaxNb = 394, S1 = 1485, S2 = 456,929), bad sum is 1505. 296 388 217 268 316 220 328 350 349 238 394 265 286 314 226 301 280 370 202 332 274 224 262 352 373 11 of 12 Bimagic Sums These all consist of an unsymmetrical set of numbers and therefore, the solutions come in complement pairs. One solution can be turned into its complement solution by subtracting each entry from the sum of the smallest and largest entries. This produces another solution with the same number range, but different magic sum and magic sum of squares, and with different translation characteristics. (MaxNb = 193, S1 = 480, S2 = 61,964) 95 187 115 16 67 19 127 37 149 148 73 23 172 61 151 193 64 25 85 113 100 79 131 169 1 (MaxNb = 193, S1 = 490, S2 = 63,904) 99 7 79 178 127 175 67 157 45 46 121 171 22 133 43 1 130 169 109 81 94 115 63 25 193 (MaxNb = 198, S1 = 465, S2 = 60,889) 112 60 20 196 77 1 188 96 98 82 110 80 49 28 198 62 13 194 102 94 180 124 106 41 14 (MaxNb = 198, S1 = 530, S2 = 73,824) 87 139 179 3 122 198 11 103 101 117 89 119 150 171 1 137 186 5 97 105 19 75 93 158 185 (MaxNb = 219, S1 = 530, S2 = 73,824) 107 77 49 78 219 135 61 206 39 89 182 171 45 85 47 105 38 99 215 73 1 183 131 113 102 (MaxNb = 219, S1 = 570, S2 = 82,624) 113 143 171 142 1 85 159 14 181 131 38 49 175 135 173 115 182 121 5 147 219 37 89 107 118 6x6 Bimagic Squares of Distinct Integers (MaxNb = 72, S1 = 219, S2 = 10,663) 72 18 17 16 49 47 13 52 36 5 50 63 38 35 7 66 15 58 20 53 34 39 69 4 55 1 57 56 26 24 21 60 68 37 10 23 (MaxNb = 109, S1 = 330, S2 = 26,432) 9 83 105 84 15 34 27 101 26 5 76 95 109 78 28 13 17 85 32 1 97 82 25 93 54 11 67 103 91 4 99 56 7 43 106 19 7x7 Bimagic Squares of Distinct Integers (MaxNb = 67, S1 = 238, S2 = 10,400) 26 50 51 21 19 10 61 18 42 49 47 17 7 58 57 41 1 22 54 38 25 15 53 31 34 37 62 6 27 11 14 46 67 43 30 66 39 48 5 24 33 23 29 2 44 63 20 45 35 (MaxNb = 67, S1 = 238, S2 = 10,616) 5 52 60 15 22 37 47 16 63 46 53 8 21 31 23 13 48 33 67 44 10 61 7 41 34 27 56 12 55 45 1 35 20 58 24 42 32 25 4 51 19 65 36 26 17 64 43 3 49 (MaxNb = 67, S1 = 238, S2 = 10,664) 1 52 63 44 30 23 25 16 67 38 24 5 43 45 54 31 20 49 11 61 12 29 39 15 34 53 4 64 37 14 57 19 48 56 7 41 8 9 65 32 33 50 60 27 36 3 59 18 35 (MaxNb = 67, S1 = 238, S2 = 11,024) 5 17 50 20 60 27 59 51 63 18 8 48 9 41 53 15 34 65 3 46 22 7 10 23 54 35 43 66 58 61 45 33 14 2 25 40 44 67 11 21 49 6 24 28 1 47 57 62 19 (MaxNb = 67, S1 = 238, S2 = 11,024) 5 17 50 60 20 27 59 51 63 18 48 8 9 41 53 15 34 3 65 46 22 58 61 45 14 33 2 25 7 10 23 35 54 43 66 40 44 67 21 11 49 6 24 28 1 57 47 62 19 (MaxNb = 69, S1 = 245, S2 = 11,483) 2 34 61 45 59 14 30 41 48 64 10 26 5 51 24 7 21 62 58 53 20 69 18 32 35 38 52 1 50 17 12 8 49 63 46 19 65 44 60 6 22 29 40 56 11 25 9 36 68 (MaxNb = 71, S1 = 252, S2 = 11,842) 63 47 15 31 58 33 5 25 9 14 41 57 67 39 71 45 52 8 18 28 30 21 51 34 36 38 2 70 27 1 54 64 20 42 44 19 46 17 60 6 56 48 26 53 66 12 55 24 16 (MaxNb = 71, S1 = 252, S2 = 11,980) 11 54 49 3 28 50 57 18 61 44 69 23 15 22 71 32 26 17 59 10 37 33 39 70 36 2 19 53 40 1 13 55 46 35 62 21 14 43 34 65 63 12 58 51 7 38 29 60 9