### Bimagic 8x8 square

A bimagic square is a simple magic square, but it is also a simple magic square if you fill in the squares of the numbers (= number x number) in each cell. The 8x8 bimagic square is the smallest bimagic square.

 260 260 260 260 260 260 260 260 11180 11180 11180 11180 11180 11180 11180 11180 260 260 11180 11180 260 56 34 8 57 18 47 9 31 11180 3136 1156 64 3249 324 2209 81 961 260 33 20 54 48 7 29 59 10 11180 1089 400 2916 2304 49 841 3481 100 260 26 43 13 23 64 38 4 49 11180 676 1849 169 529 4096 1444 16 2401 260 19 5 35 30 53 12 46 60 11180 361 25 1225 900 2809 144 2116 3600 260 15 25 63 2 41 24 50 40 11180 225 625 3969 4 1681 576 2500 1600 260 6 55 17 11 36 58 32 45 11180 36 3025 289 121 1296 3364 1024 2025 260 61 16 42 52 27 1 39 22 11180 3721 256 1764 2704 729 1 1521 484 260 44 62 28 37 14 51 21 3 11180 1936 3844 784 1369 196 2601 441 9

I have constructed a new 8x8 bimagic square by swapping 0 an 1 in the binary grids. I have constructed the inverse 8x8 bimagic square.

Original 8x8 bimagic square                              Inverse 8x8 bimagic square

 1x digit 1x digit 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 + 2x digit + 2x digit 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 + 4x digit + 4x digit 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 + 8x digit + 8x digit 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 + 16x digit + 16x digit 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 + 32x digit + 1 + 32x digit + 1 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0