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Office Applications and Entertainment, Magic Squares |
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Attachment 9.6.5 | About the Author |
Examples of four Ternary Squares, related Sudoku Comparable Squares,
Resulting Magic Square and Magic Square of Squares
John Hendricks (Bimagic Regular Subsquares)
G1
0 2 1 2 1 0 1 0 2 1 0 2 0 2 1 2 1 0 2 1 0 1 0 2 0 2 1 0 2 1 2 1 0 1 0 2 1 0 2 0 2 1 2 1 0 2 1 0 1 0 2 0 2 1 0 2 1 2 1 0 1 0 2 1 0 2 0 2 1 2 1 0 2 1 0 1 0 2 0 2 1 G2
2 1 0 0 2 1 1 0 2 2 1 0 0 2 1 1 0 2 2 1 0 0 2 1 1 0 2 1 0 2 2 1 0 0 2 1 1 0 2 2 1 0 0 2 1 1 0 2 2 1 0 0 2 1 0 2 1 1 0 2 2 1 0 0 2 1 1 0 2 2 1 0 0 2 1 1 0 2 2 1 0 G3
1 2 0 1 2 0 1 2 0 2 0 1 2 0 1 2 0 1 0 1 2 0 1 2 0 1 2 2 0 1 2 0 1 2 0 1 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 1 2 0 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 1 2 0 2 0 1 2 0 1 2 0 1 G4
1 1 1 2 2 2 0 0 0 0 0 0 1 1 1 2 2 2 2 2 2 0 0 0 1 1 1 2 2 2 0 0 0 1 1 1 1 1 1 2 2 2 0 0 0 0 0 0 1 1 1 2 2 2 0 0 0 1 1 1 2 2 2 2 2 2 0 0 0 1 1 1 1 1 1 2 2 2 0 0 0 B1
6 5 1 2 7 3 4 0 8 7 3 2 0 8 4 5 1 6 8 4 0 1 6 5 3 2 7 3 2 7 8 4 0 1 6 5 4 0 8 6 5 1 2 7 3 5 1 6 7 3 2 0 8 4 0 8 4 5 1 6 7 3 2 1 6 5 3 2 7 8 4 0 2 7 3 4 0 8 6 5 1 B2
4 5 3 7 8 6 1 2 0 2 0 1 5 3 4 8 6 7 6 7 8 0 1 2 3 4 5 8 6 7 2 0 1 5 3 4 3 4 5 6 7 8 0 1 2 1 2 0 4 5 3 7 8 6 0 1 2 3 4 5 6 7 8 7 8 6 1 2 0 4 5 3 5 3 4 8 6 7 2 0 1 M
43 51 29 66 80 58 14 19 9 26 4 12 46 36 41 78 56 70 63 68 73 2 16 24 31 39 53 76 57 71 27 5 10 47 34 42 32 37 54 61 69 74 3 17 22 15 20 7 44 49 30 64 81 59 1 18 23 33 38 52 62 67 75 65 79 60 13 21 8 45 50 28 48 35 40 77 55 72 25 6 11 M2
1849 2601 841 4356 6400 3364 196 361 81 676 16 144 2116 1296 1681 6084 3136 4900 3969 4624 5329 4 256 576 961 1521 2809 5776 3249 5041 729 25 100 2209 1156 1764 1024 1369 2916 3721 4761 5476 9 289 484 225 400 49 1936 2401 900 4096 6561 3481 1 324 529 1089 1444 2704 3844 4489 5625 4225 6241 3600 169 441 64 2025 2500 784 2304 1225 1600 5929 3025 5184 625 36 121
G1
0 0 2 1 2 0 2 1 1 1 1 0 2 0 1 0 2 2 1 1 0 2 0 1 0 2 2 2 2 1 0 1 2 1 0 0 2 2 1 0 1 2 1 0 0 2 2 1 0 1 2 1 0 0 0 0 2 1 2 0 2 1 1 0 0 2 1 2 0 2 1 1 1 1 0 2 0 1 0 2 2 G2
0 1 2 1 0 2 1 2 0 1 2 0 2 1 0 2 0 1 0 1 2 1 0 2 1 2 0 0 1 2 1 0 2 1 2 0 1 2 0 2 1 0 2 0 1 2 0 1 0 2 1 0 1 2 2 0 1 0 2 1 0 1 2 1 2 0 2 1 0 2 0 1 2 0 1 0 2 1 0 1 2 G3
0 1 0 0 1 2 2 1 2 2 0 2 2 0 1 1 0 1 1 2 1 1 2 0 0 2 0 2 0 2 2 0 1 1 0 1 0 1 0 0 1 2 2 1 2 1 2 1 1 2 0 0 2 0 2 0 2 2 0 1 1 0 1 1 2 1 1 2 0 0 2 0 0 1 0 0 1 2 2 1 2 G4
1 0 0 2 2 2 1 1 0 1 0 0 2 2 2 1 1 0 0 2 2 1 1 1 0 0 2 2 1 1 0 0 0 2 2 1 0 2 2 1 1 1 0 0 2 1 0 0 2 2 2 1 1 0 0 2 2 1 1 1 0 0 2 2 1 1 0 0 0 2 2 1 2 1 1 0 0 0 2 2 1 B1
0 3 8 4 2 6 5 7 1 4 7 0 8 3 1 6 2 5 1 4 6 5 0 7 3 8 2 2 5 7 3 1 8 4 6 0 5 8 1 6 4 2 7 0 3 8 2 4 0 7 5 1 3 6 6 0 5 1 8 3 2 4 7 3 6 2 7 5 0 8 1 4 7 1 3 2 6 4 0 5 8 B2
3 1 0 6 7 8 5 4 2 5 0 2 8 6 7 4 3 1 1 8 7 4 5 3 0 2 6 8 3 5 2 0 1 7 6 4 0 7 6 3 4 5 2 1 8 4 2 1 7 8 6 3 5 0 2 6 8 5 3 4 1 0 7 7 5 4 1 2 0 6 8 3 6 4 3 0 1 2 8 7 5 M
28 13 9 59 66 79 51 44 20 50 8 19 81 58 65 43 30 15 11 77 70 42 46 35 4 27 57 75 33 53 22 2 18 68 61 37 6 72 56 34 41 48 26 10 76 45 21 14 64 80 60 29 49 7 25 55 78 47 36 40 12 5 71 67 52 39 17 24 1 63 74 32 62 38 31 3 16 23 73 69 54 M2
784 169 81 3481 4356 6241 2601 1936 400 2500 64 361 6561 3364 4225 1849 900 225 121 5929 4900 1764 2116 1225 16 729 3249 5625 1089 2809 484 4 324 4624 3721 1369 36 5184 3136 1156 1681 2304 676 100 5776 2025 441 196 4096 6400 3600 841 2401 49 625 3025 6084 2209 1296 1600 144 25 5041 4489 2704 1521 289 576 1 3969 5476 1024 3844 1444 961 9 256 529 5329 4761 2916
Donald Keedwell (Partly Compact)
G1
1 1 1 0 0 0 2 2 2 0 0 0 2 2 2 1 1 1 2 2 2 1 1 1 0 0 0 1 1 1 0 0 0 2 2 2 0 0 0 2 2 2 1 1 1 2 2 2 1 1 1 0 0 0 1 1 1 0 0 0 2 2 2 0 0 0 2 2 2 1 1 1 2 2 2 1 1 1 0 0 0 G2
0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 G3
1 2 0 2 0 1 0 1 2 0 1 2 1 2 0 2 0 1 2 0 1 0 1 2 1 2 0 2 0 1 0 1 2 1 2 0 1 2 0 2 0 1 0 1 2 0 1 2 1 2 0 2 0 1 0 1 2 1 2 0 2 0 1 2 0 1 0 1 2 1 2 0 1 2 0 2 0 1 0 1 2 G4
0 2 1 1 0 2 2 1 0 2 1 0 0 2 1 1 0 2 1 0 2 2 1 0 0 2 1 2 1 0 0 2 1 1 0 2 1 0 2 2 1 0 0 2 1 0 2 1 1 0 2 2 1 0 1 0 2 2 1 0 0 2 1 0 2 1 1 0 2 2 1 0 2 1 0 0 2 1 1 0 2 B1 (Compact)
1 4 7 0 3 6 2 5 8 0 3 6 2 5 8 1 4 7 2 5 8 1 4 7 0 3 6 7 1 4 6 0 3 8 2 5 6 0 3 8 2 5 7 1 4 8 2 5 7 1 4 6 0 3 4 7 1 3 6 0 5 8 2 3 6 0 5 8 2 4 7 1 5 8 2 4 7 1 3 6 0 B2 (Partly Compact)
1 8 3 5 0 7 6 4 2 6 4 2 1 8 3 5 0 7 5 0 7 6 4 2 1 8 3 8 3 1 0 7 5 4 2 6 4 2 6 8 3 1 0 7 5 0 7 5 4 2 6 8 3 1 3 1 8 7 5 0 2 6 4 2 6 4 3 1 8 7 5 0 7 5 0 2 6 4 3 1 8 M (Partly Compact)
11 77 35 46 4 70 57 42 27 55 40 25 12 78 36 47 5 71 48 6 72 56 41 26 10 76 34 80 29 14 7 64 49 45 21 60 43 19 58 81 30 15 8 65 50 9 66 51 44 20 59 79 28 13 32 17 74 67 52 1 24 63 39 22 61 37 33 18 75 68 53 2 69 54 3 23 62 38 31 16 73 M2
121 5929 1225 2116 16 4900 3249 1764 729 3025 1600 625 144 6084 1296 2209 25 5041 2304 36 5184 3136 1681 676 100 5776 1156 6400 841 196 49 4096 2401 2025 441 3600 1849 361 3364 6561 900 225 64 4225 2500 81 4356 2601 1936 400 3481 6241 784 169 1024 289 5476 4489 2704 1 576 3969 1521 484 3721 1369 1089 324 5625 4624 2809 4 4761 2916 9 529 3844 1444 961 256 5329
Note: The elements of the nine regular subsquares of M2 sum to the Magic Sum (20049).
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About the Author |