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Intro. to Order-11 |
Cell designations & some of the features of Order-11 magic stars. |
Order 11A List of Basic Solutions |
A partial list of the 53,528 basic solutions with solution number, complement number, complement pair number, point totals, and special feature remarks. |
Order 11B List of Basic Solutions |
A partial list of the 75,940 basic solutions with complement number, complement pair number, point totals, and special feature remarks. |
Order 11C List of Basic Solutions |
A partial list of the 53,528 basic solutions. Same format as list A. |
Order 11D List of Basic Solutions |
A partial list of the 75,940 basic solutions. Same format as list A. |
Definitions |
Review magic star definitions and general features. Use Back button to return. |
Star Examples |
One example of each of 16 patterns, Orders 5 to 11. Use Back button to return |
Star Examples - 2 |
One example of each of 14 patterns, Orders 12 to 14. Use Back button to return |
Order-11 has 4 patterns and because 11 is a prime number, all the patterns are continuous.
| Number of basic solutions and search time Pattern A 53528 solutions, required approximately 62 DAYS. running time Pattern B 75940 solutions " " 33.5 hrs. running time Pattern C 53528 solutions " " 5.3 hrs. running time Pattern D 75940 solutions " " 20.2 hrs. running time Above are the running times are on a 200 Mhz Pentium Pro with 32 Megs. of RAM. Note the different times for 11A and 11C. Programs are written in QuickBasic 4.5 and compiled. Each solution contains the consecutive series of integers from 1 to 22. The sum of this series is 253, there are 6 lines with each cell appearing in 2 lines, so the magic constant (S) is (2 x 253)/11 = 46. |
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| Order-11A and 11C both contain the same number of solutions
even though the point names are different (as does order-8). 11B and 11D both have the
same number of solutions as expected, because the point names are the same. Value of cell a changes at the same solution number in 11B and 11D (as does order-10 A & C and 7 A & B). All these have the same point names, but so does 8 A & B and 9 B & C, but they do not have this feature. |
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Some complement pairs: |
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| The first solution | First with A = 2 | The last solution | |||||||||
| Solution numbers |
Pair # |
Solution numbers |
Pair # |
Solution numbers |
Pair # |
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| A | 1 | 115 | 1 | 27724 | 532 | 281 | 53528 | 25435 | 19998 | ||
| B | 1 | 126 | 1 | 41733 | 41865 | 31143 | 75940 | 32158 | 24052 | ||
| C | 1 | 17 | 1 | 26306 | 98 | 55 | 53528 | 20998 | 16874 | ||
| D | 1 | 106 | 1 | 41733 | 41950 | 31143 | 75940 | 31123 | 24738 | ||
| In each pair, the first solution is the one that meets the condition | |||||||||||
| Some solutions shown in diagram form. The four solutions shown here are the first one in each case with cell A = 3. .
Note that lines B and D (above)are the same. Point names are also the same. |
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Solut. | -------------Order11A ----- Cell Values -----upper case signifies points ----------| Comple- Pair Point
# A b c D e f G h i J k l M n o P q R S T U V ment # Total
1 1 2 21 22 3 4 17 10 12 7 11 13 15 9 6 16 20 8 14 18 5 19 115 1 142
2 1 2 21 22 3 4 17 11 10 8 12 19 7 5 14 20 15 9 13 18 6 16 409 2 137
3 1 2 21 22 3 4 17 11 10 8 12 19 7 5 14 20 18 6 16 15 9 13 253 3 134
4 1 2 21 22 3 4 17 15 9 5 7 16 18 6 12 10 20 14 8 19 11 13 48 4 138
5 1 2 21 22 3 5 16 7 11 12 6 15 13 4 10 19 17 8 14 20 9 18 324 5 152
6 1 2 21 22 3 5 16 7 11 12 6 18 10 4 13 19 17 8 14 20 9 15 302 6 146
7 1 2 21 22 3 5 16 9 7 14 8 18 6 4 17 19 15 10 12 20 11 13 396 7 144
8 1 2 21 22 3 5 16 14 4 12 7 8 19 6 10 11 20 13 9 18 17 15 75 8 153
9 1 2 21 22 3 5 16 20 4 6 19 8 13 11 10 12 17 15 7 14 9 18 316 9 133
10 1 2 21 22 3 5 16 20 4 6 19 8 13 12 10 11 18 15 7 14 9 17 275 10 131
769 1 2 22 21 15 7 3 18 12 13 11 14 8 10 9 19 20 5 4 17 6 16 27270 518 113
770 1 3 20 22 2 4 18 7 10 11 5 13 17 6 9 14 21 8 16 19 12 15 872 519 153
1616 1 3 22 20 15 9 2 19 13 12 8 10 16 7 6 17 21 5 4 14 11 18 39518 1104 120
1617 1 4 19 22 2 5 17 6 3 20 9 7 10 8 12 16 15 11 14 21 13 18 1888 1105 163
3044 1 4 22 19 16 9 2 17 14 13 11 12 10 8 7 21 18 3 5 15 6 20 29982 2354 115
3045 1 5 18 22 2 3 19 8 10 9 11 20 6 7 17 16 13 12 14 21 4 15 3369 2355 139
4635 1 5 22 18 16 8 4 17 15 10 9 20 7 12 13 14 21 6 2 19 3 11 47436 3713 95
4636 1 6 17 22 2 3 19 4 12 11 8 14 13 7 10 16 15 9 18 21 5 20 4815 3714 155
6490 1 6 22 17 16 11 2 10 13 21 4 14 7 8 12 19 18 3 5 20 9 15 34923 5342 119
6491 1 7 16 22 2 3 19 4 8 15 12 13 6 17 14 9 20 10 18 21 5 11 6535 5343 137
8558 1 7 22 16 17 10 3 21 4 18 9 8 11 6 14 15 19 5 2 13 20 12 45481 7118 116
8559 1 8 15 22 2 3 19 5 4 18 7 10 11 13 16 6 20 12 17 21 14 9 8593 7119 150
10617 1 8 22 15 19 5 7 21 12 6 13 18 9 10 11 16 20 2 3 17 4 14 51236 8819 94
10618 1 9 14 22 2 3 19 8 6 13 21 7 5 18 12 11 16 10 20 15 4 17 10781 8820 137
12967 1 9 22 14 19 8 5 20 11 10 12 18 6 4 15 21 13 3 2 16 7 17 33299 10705 102
12968 1 10 13 22 2 3 19 7 8 12 5 14 15 9 18 4 21 11 20 16 17 6 12979 10706 143
15093 1 10 22 13 19 6 8 20 4 14 15 5 12 11 7 16 17 3 2 18 9 21 36862 12358 117
15094 1 11 12 22 2 3 19 16 6 5 21 13 7 15 20 4 17 14 18 9 10 8 15126 12359 117
17048 1 11 22 12 19 10 5 21 6 14 9 16 7 4 20 15 17 3 2 13 18 8 50474 13916 98
17049 1 12 11 22 2 5 17 13 10 6 7 15 18 3 21 4 16 14 19 9 20 8 17081 13917 138
18651 1 12 22 11 19 10 6 14 9 17 4 7 18 5 8 15 16 3 2 20 13 21 38260 15146 127
18652 1 13 10 22 2 5 17 12 11 6 7 15 18 4 21 3 16 14 20 9 19 8 18673 15147 137
20290 1 13 22 10 19 12 5 17 9 15 7 18 6 8 21 11 20 2 3 14 16 4 52453 16407 87
20291 1 14 9 22 4 2 18 5 6 17 10 12 7 15 21 3 16 13 20 19 11 8 20315 16408 139
21772 1 14 22 9 19 11 7 17 6 16 4 8 18 5 13 10 20 2 3 15 21 12 38540 17484 114
21773 1 15 8 22 4 3 17 12 11 6 7 14 19 5 20 2 16 13 21 10 18 9 21778 17485 138
23543 1 15 22 8 19 14 5 13 16 12 4 20 10 11 18 7 21 3 2 17 9 6 51861 18707 80
23544 1 16 7 22 8 5 11 14 17 4 20 9 13 19 12 2 18 10 21 6 3 15 22770 18107 108
24729 1 16 22 7 19 12 8 18 9 11 13 17 5 15 20 6 21 3 2 14 10 4 53174 19524 71
24730 1 17 6 22 10 3 11 8 15 12 13 16 5 19 20 2 18 9 21 14 4 7 19832 16003 108
25781 1 17 22 6 19 16 5 14 18 9 4 12 21 8 10 7 20 2 3 13 11 15 36208 20289 93
25782 1 18 5 22 14 3 7 9 19 11 4 16 15 12 17 2 20 6 21 13 10 8 12364 10150 116
26569 1 18 22 5 19 16 6 15 17 8 7 11 20 12 10 4 21 3 2 13 9 14 44535 20815 85
26570 1 19 6 20 17 4 5 14 16 11 8 9 18 12 13 3 22 2 21 7 15 10 30886 20816 113
27068 1 19 22 4 16 18 8 7 10 21 9 3 13 17 11 5 20 2 6 15 12 14 37377 21176 101
27069 1 20 6 19 15 4 8 9 13 16 5 7 18 12 14 2 21 3 22 11 17 10 9136 7509 127
27223 1 20 19 6 18 17 5 10 22 9 8 15 14 16 13 3 21 2 7 12 4 11 53223 21259 74
27224 2 1 21 22 3 4 17 8 5 16 10 14 6 9 13 18 20 7 15 19 12 11 532 281 145
39470 2 19 17 8 15 9 14 5 16 11 1 21 13 12 18 3 20 4 10 22 7 6 8332 6892 100
39471 3 1 20 22 2 5 17 12 9 8 7 10 21 4 6 15 19 11 13 16 14 18 1411 899 158
45777 3 18 15 10 6 16 14 2 9 21 17 1 7 22 13 4 19 5 20 8 12 11 31510 22969 115
45778 4 1 19 22 2 5 17 20 3 6 21 9 10 7 11 18 15 12 13 8 14 16 2969 2279 140
49097 4 17 14 11 7 16 12 2 19 13 10 1 22 15 3 6 18 5 20 8 9 21 9970 8236 131
49098 5 1 18 22 2 3 19 11 7 9 6 21 10 4 17 15 16 14 12 20 13 8 4503 3581 147
50984 5 16 10 15 8 4 19 3 2 22 14 1 9 20 11 6 17 7 21 18 12 13 12775 10513 147
50985 6 1 17 22 2 3 19 4 10 13 7 12 14 11 5 16 20 9 18 21 8 15 6330 5182 161
52000 6 14 11 15 10 5 16 2 9 19 4 1 22 13 3 8 17 7 18 21 12 20 14557 11898 164
52001 6 15 12 13 9 4 20 3 1 22 5 2 17 11 10 8 16 7 18 21 19 14 26469 20722 165
52002 7 1 16 22 2 3 19 12 4 11 6 9 20 5 8 13 14 18 10 21 15 17 8478 7038 173
52653 7 13 10 16 5 3 22 2 4 18 12 1 15 17 6 8 14 11 20 21 9 19 27193 21244 166
52654 8 1 15 22 2 3 19 5 4 18 7 10 11 6 9 20 13 12 17 21 14 16 10565 8767 178
53028 8 10 16 12 2 11 21 1 7 17 4 3 22 5 6 13 14 9 19 15 20 18 26221 20541 174
53029 9 1 14 22 2 5 17 10 4 15 3 7 21 6 8 11 16 18 12 19 20 13 12866 10604 177
53241 9 8 19 10 1 15 20 3 5 18 4 2 22 6 7 11 13 14 12 16 21 17 25225 19842 170
53242 10 1 13 22 2 3 19 8 5 14 9 6 17 7 4 18 11 16 15 20 12 21 15062 12327 184
53364 10 9 8 19 6 3 18 2 4 22 7 1 16 13 5 12 14 11 21 20 15 17 24680 19475 181
53365 11 1 12 22 2 3 19 6 5 16 7 10 13 4 8 21 9 15 17 20 14 18 17009 13877 186
53444 11 8 14 13 3 9 21 5 2 18 7 1 20 4 6 16 10 12 17 15 22 19 24632 19431 184
53445 12 2 10 22 1 3 20 4 5 17 7 9 13 6 8 19 11 14 21 18 16 15 20028 16160 187
53518 12 7 9 18 2 6 20 1 11 14 3 8 21 4 5 16 10 13 22 17 15 19 25739 20247 187
53519 12 7 9 18 4 3 21 5 1 19 10 2 15 11 6 14 8 17 16 22 13 20 26425 20683 187
53520 12 7 9 18 6 3 19 5 2 20 1 8 17 4 11 14 10 15 16 22 21 13 26422 20681 187
53521 12 7 9 18 8 3 17 5 4 20 6 1 19 10 2 15 11 13 16 22 14 21 26406 20671 187
53522 12 7 9 18 10 2 16 8 3 19 1 5 21 4 6 15 11 13 14 22 20 17 23323 18510 187
53523 12 7 10 17 2 5 22 1 3 20 4 6 16 8 9 13 11 15 19 21 18 14 26477 20729 187
53524 12 8 6 20 4 1 21 7 3 15 10 2 19 9 5 13 11 14 22 16 17 18 26852 20999 187
53525 12 8 6 20 10 1 15 7 3 21 4 2 19 9 5 13 11 14 16 22 17 18 24703 19498 187
53526 12 8 7 19 10 1 16 9 3 18 2 4 22 5 6 13 11 14 15 21 20 17 26229 20548 187
53527 12 9 5 20 7 2 17 4 3 22 8 1 15 11 6 14 10 13 21 19 16 18 23484 18648 187
53528 12 9 7 18 5 8 15 1 11 19 2 3 22 6 4 14 10 13 21 16 17 20 25435 19998 187
Solut. | -------------Order11B ----- Cell Values -----upper case signifies points ----------| Comple- Pair Point
# A b c D e f G h i J k L m N o P q R s T U V ment # Total
1 1 2 21 22 3 5 16 7 6 17 9 18 10 15 13 11 14 12 20 4 8 19 126 1 143
2 1 2 21 22 3 5 16 9 6 15 11 18 12 13 7 17 8 10 20 4 14 19 139 2 149
3 1 2 21 22 3 5 16 9 6 15 11 18 12 13 7 17 14 4 20 10 8 19 132 3 143
4 1 2 21 22 3 5 16 9 6 15 11 18 12 13 14 10 17 8 19 7 4 20 240 4 134
5 1 2 21 22 3 5 16 9 6 15 11 18 13 12 8 17 14 4 19 10 7 20 243 5 142
6 1 2 21 22 3 5 16 9 6 15 17 12 13 18 8 11 14 4 19 10 7 20 242 6 136
7 1 2 21 22 3 5 16 13 6 11 15 18 8 17 9 7 10 14 20 4 12 19 137 7 141
8 1 2 21 22 3 5 16 15 6 9 17 18 12 13 7 11 8 10 20 4 14 19 138 8 137
9 1 2 21 22 3 5 16 15 6 9 17 18 12 13 7 11 14 4 20 10 8 19 131 9 131
10 1 2 21 22 3 5 16 15 6 9 17 18 13 12 8 11 14 4 19 10 7 20 241 10 130
620 1 2 21 22 15 6 3 19 7 17 14 13 8 10 12 5 16 11 18 9 4 20 304 229 115
621 1 3 20 22 2 6 16 7 8 15 11 17 13 14 4 21 9 5 18 10 12 19 899 311 152
1402 1 3 20 22 16 6 2 21 8 15 17 11 14 5 13 7 12 10 18 4 9 19 889 531 105
1403 1 4 19 22 2 5 17 11 8 10 12 20 9 15 6 14 7 13 21 3 18 16 1447 702 149
3577 1 4 21 20 17 7 2 22 8 14 15 13 11 5 3 16 9 6 19 10 12 18 57910 2561 117
3578 1 5 18 22 2 3 19 11 7 9 12 20 10 14 8 13 6 15 17 4 16 21 3856 2562 154
5458 1 5 21 19 18 7 2 22 8 14 15 12 13 3 10 11 16 4 20 9 6 17 66307 4102 98
5459 1 6 17 22 2 3 19 7 8 12 13 15 9 20 14 5 18 10 16 11 4 21 5714 4103 140
8129 1 6 21 18 19 7 2 20 8 16 14 10 5 12 3 11 4 17 15 9 13 22 30213 6399 131
8130 1 7 16 22 2 3 19 4 9 14 5 20 11 13 12 17 18 6 21 8 10 15 8155 6400 145
10886 1 7 21 17 19 8 2 20 9 15 18 6 16 5 10 11 13 4 14 12 3 22 17118 8698 98
10887 1 8 15 22 2 3 19 4 10 13 14 11 12 21 16 5 20 7 18 9 6 17 10982 8699 131
13757 1 8 21 16 20 3 7 18 4 17 12 9 6 11 2 15 14 5 22 13 10 19 68236 11079 123
13758 1 9 14 22 2 3 19 4 11 12 5 20 6 18 8 16 15 10 13 17 7 21 13905 11080 163
16337 1 9 21 15 22 7 2 16 8 20 12 5 13 6 10 14 17 3 19 11 4 18 62588 13106 99
16338 1 10 13 22 2 3 19 6 12 9 11 16 7 21 5 14 17 4 15 20 8 18 16494 13107 152
19351 1 10 21 14 22 8 2 18 9 17 4 15 6 3 13 12 11 19 16 5 7 20 63029 15366 115
19352 1 11 12 22 2 3 19 4 13 10 9 16 7 21 6 15 5 17 14 8 20 18 19464 15367 167
22159 1 11 21 13 22 9 2 19 10 15 8 12 5 7 16 4 14 20 18 3 6 17 59127 17399 100
22160 1 12 11 22 2 3 19 4 14 9 8 17 6 21 5 16 15 7 13 20 10 18 22319 17400 160
24937 1 12 20 13 22 9 2 16 11 17 7 10 8 6 3 21 4 14 19 5 18 15 46357 19345 122
24938 1 13 10 22 2 3 19 4 15 8 5 20 7 17 14 11 18 12 21 6 16 9 24951 19346 141
27581 1 13 21 11 22 9 4 20 10 12 19 2 15 7 14 5 16 6 17 8 3 18 71105 21040 77
27582 1 14 9 22 2 3 19 5 16 6 18 8 15 21 7 13 11 4 17 10 20 12 27625 21041 136
30117 1 14 21 10 22 11 3 13 12 18 6 8 7 9 19 5 15 20 17 2 4 16 59541 22723 96
30118 1 15 8 22 2 3 19 4 17 6 5 20 14 10 11 21 13 7 16 9 18 12 30160 22724 145
32581 1 15 21 9 22 13 2 10 14 20 6 5 8 11 18 7 17 16 19 3 4 12 61356 24337 90
32582 1 16 7 22 2 3 19 5 18 4 11 15 8 21 14 6 20 9 17 12 13 10 32599 24338 132
34998 1 16 21 8 22 14 2 12 15 17 7 6 13 5 18 11 19 9 20 4 3 10 73548 26018 76
34999 1 17 6 22 5 3 16 9 19 2 7 20 11 10 15 12 14 13 18 4 21 8 35000 26019 129
37079 1 17 21 7 22 15 2 19 16 9 14 6 5 13 10 4 8 20 18 3 12 11 59135 27391 88
37080 1 18 5 22 7 2 15 3 19 9 8 11 12 16 14 13 21 4 20 10 17 6 34951 25977 124
38759 1 18 21 6 22 16 2 14 17 13 11 4 5 15 10 7 19 9 20 12 3 8 74847 28581 80
38760 1 19 8 18 4 2 22 3 16 5 10 12 13 17 11 15 14 7 20 6 21 9 40044 28582 133
40039 1 19 21 5 22 17 2 16 18 10 14 3 6 15 4 11 13 8 20 12 9 7 74836 29562 83
40040 1 20 7 18 8 4 16 2 19 9 6 11 10 17 14 13 15 12 21 3 22 5 14637 11680 127
41103 1 20 21 4 19 17 6 15 18 7 16 3 14 10 12 9 13 8 22 2 11 5 75904 30513 66
41104 1 21 8 16 7 4 19 6 18 3 9 13 12 14 11 15 20 2 22 10 17 5 69655 30514 115
41732 1 21 20 4 19 16 7 15 18 6 17 2 13 12 9 10 11 8 22 3 14 5 75490 31142 72
41733 2 1 22 21 3 6 16 7 5 18 15 12 14 17 9 13 10 8 20 4 11 19 41865 31143 141
57546 2 21 20 3 19 14 10 17 15 4 13 8 1 18 6 5 16 12 22 11 9 7 70842 36815 89
57547 3 1 22 20 2 8 16 9 6 15 17 13 10 21 12 4 14 11 18 7 5 19 50233 34059 134
65841 3 21 18 4 20 12 10 5 14 17 2 6 1 19 9 13 16 15 22 8 11 7 66785 37854 113
65842 4 1 20 21 2 6 17 8 5 16 14 15 7 22 3 13 9 10 18 11 12 19 40422 29883 160
69881 4 21 16 5 20 3 18 7 6 15 2 8 1 17 9 13 19 12 22 11 10 14 72461 37956 127
69882 5 1 19 21 2 8 15 4 7 20 12 13 9 22 3 17 6 11 16 10 14 18 40878 30290 166
72568 5 21 14 6 16 7 17 3 11 15 1 9 2 19 4 20 13 12 22 10 18 8 62369 37370 139
72569 6 1 18 21 2 4 19 8 3 16 12 17 7 20 5 13 11 10 15 14 9 22 24387 18945 167
74076 6 20 9 11 15 2 18 5 10 13 1 12 3 16 4 21 17 7 22 14 19 8 45443 32433 145
74077 7 1 17 21 2 13 10 5 12 19 6 20 8 16 3 22 4 14 9 15 11 18 38529 28407 173
74820 7 20 11 8 15 1 22 5 6 13 3 10 2 19 4 18 16 9 21 14 17 12 38091 28080 149
74821 8 1 16 21 2 4 19 6 3 18 10 17 5 22 7 11 13 12 15 14 9 20 33691 25073 171
75283 8 16 7 15 6 3 22 4 11 9 1 20 2 18 5 19 12 14 17 13 21 10 39143 28877 169
75284 9 1 15 21 2 13 10 5 12 19 6 20 8 16 3 22 4 14 7 17 11 18 38530 28408 177
75570 9 13 7 17 6 1 22 5 8 11 4 18 3 19 2 20 10 12 15 16 21 14 37763 27849 179
75571 10 1 14 21 3 6 16 8 5 17 9 19 2 22 4 12 7 18 11 15 13 20 39293 28981 183
75742 10 12 8 16 9 1 20 2 6 18 5 11 4 22 3 19 7 15 13 14 21 17 29177 22118 183
75743 11 1 13 21 3 10 12 8 9 17 6 22 5 16 4 18 2 20 7 14 15 19 38508 28389 185
75847 11 10 7 18 6 3 19 5 8 14 1 21 2 17 4 20 9 16 15 13 22 12 39447 29103 183
75848 12 2 10 22 1 3 20 5 4 17 6 21 8 16 7 18 9 13 11 14 15 19 27305 20864 187
75931 12 8 9 17 10 5 14 6 7 19 4 15 1 20 2 18 3 21 11 13 22 16 38455 28338 187
75932 12 8 10 16 6 3 21 7 4 14 9 15 5 20 1 18 2 17 11 13 22 19 41088 30498 187
75933 12 9 4 21 7 3 15 5 10 16 1 20 2 17 6 18 8 19 11 14 22 13 36413 26931 187
75934 12 9 4 21 11 1 13 5 8 20 2 15 3 17 6 18 7 19 10 14 22 16 36385 26904 187
75935 12 9 10 15 7 2 22 8 3 13 5 19 4 16 1 21 6 14 11 17 18 20 32227 24100 187
75936 12 9 10 15 7 5 19 1 6 20 3 14 4 21 2 22 8 13 11 18 16 17 32097 24004 187
75937 12 9 10 15 8 1 22 4 2 18 6 13 5 20 3 19 7 14 11 16 17 21 40000 29523 187
75938 12 9 10 15 8 1 22 6 2 16 7 14 5 19 3 18 4 17 11 13 20 21 36919 27281 187
75939 12 9 10 15 8 6 17 4 7 18 5 14 3 21 1 20 2 19 11 13 22 16 36912 27275 187
75940 12 10 7 17 9 1 19 8 5 14 2 20 4 13 3 22 6 16 11 15 21 18 32158 24052 187
Solut. | -------------Order11C ----- Cell Values -----upper case signifies points ----------| Comple- Pair Point
# A b c D e f G h I j K l M n O p Q r S t U V ment # Total
1 1 2 21 22 3 9 12 13 19 6 18 7 8 17 15 10 14 4 11 20 5 16 17 1 141
2 1 2 21 22 3 9 12 13 19 7 17 6 10 18 11 14 15 5 8 20 4 16 16 2 135
3 1 2 21 22 3 9 12 15 17 19 7 14 10 11 6 8 18 4 13 20 5 16 19 3 127
4 1 2 21 22 3 10 11 16 17 8 18 7 5 19 14 13 12 6 9 20 4 15 14 4 128
5 1 2 21 22 3 10 11 20 13 18 12 8 6 15 7 14 17 5 9 19 4 16 44 5 118
6 1 2 21 22 3 11 10 16 18 12 13 8 9 19 6 17 15 7 5 20 4 14 9 6 117
7 1 2 21 22 3 11 10 18 16 12 15 5 8 17 9 13 19 4 6 20 7 14 11 7 127
8 1 2 21 22 3 12 9 15 20 7 16 11 4 18 17 8 10 5 13 19 6 14 41 8 132
9 1 2 21 22 3 12 9 16 19 6 18 4 8 15 17 11 14 7 10 20 5 13 6 6 136
10 1 2 21 22 3 12 9 18 17 16 10 5 13 11 6 15 20 7 8 19 4 14 40 9 124
153 1 2 22 21 9 10 6 20 18 15 4 14 8 11 12 7 13 5 17 19 3 16 26340 110 119
154 1 3 20 22 2 7 15 9 19 11 14 10 13 16 6 12 18 4 8 21 5 17 178 111 138
375 1 3 22 20 13 9 4 21 18 7 8 6 11 12 16 10 14 5 15 19 2 17 38701 290 126
376 1 4 19 22 2 8 14 10 18 11 15 12 9 21 5 13 16 3 6 20 7 17 433 291 130
759 1 4 22 19 15 9 3 21 18 5 8 7 10 17 14 13 12 6 11 20 2 16 44938 612 114
760 1 5 18 22 2 7 15 6 20 8 16 14 10 19 9 12 11 3 13 17 4 21 861 613 142
1322 1 5 22 18 16 10 2 20 19 3 8 7 11 15 17 9 13 6 12 21 4 14 48121 1101 119
1323 1 6 17 22 2 4 18 7 15 10 19 8 12 11 13 9 16 5 14 20 3 21 1420 1102 154
2366 1 6 22 17 16 11 2 20 18 3 9 7 10 21 12 14 13 4 8 19 5 15 50347 2029 110
2367 1 7 16 22 2 4 18 8 13 12 19 10 9 11 14 5 17 3 15 20 6 21 2426 2030 155
3389 1 7 22 16 18 8 4 21 14 11 3 12 10 19 6 15 13 5 9 20 2 17 51600 2950 95
3390 1 8 15 22 2 5 17 7 14 18 12 16 11 13 4 6 20 3 10 21 9 19 3435 2951 139
4739 1 8 22 15 19 10 2 20 16 6 5 14 7 21 12 11 9 3 13 18 4 17 51486 4173 101
4740 1 9 14 22 2 5 17 4 16 18 10 20 12 13 3 8 15 7 11 21 6 19 4760 4174 132
6111 1 9 22 14 20 7 5 19 13 11 2 10 15 8 12 6 18 4 16 21 3 17 50032 5401 116
6112 1 10 13 22 2 4 18 7 11 14 19 8 12 15 5 17 16 9 6 20 3 21 6189 5402 134
7628 1 10 22 13 21 9 3 18 15 6 4 16 8 20 12 11 7 5 14 19 2 17 51545 6734 96
7629 1 11 12 22 2 4 18 7 10 19 15 16 8 6 13 3 14 9 17 21 5 20 7667 6735 143
9326 1 11 22 12 21 10 3 19 13 5 7 14 6 20 15 9 8 2 16 17 4 18 49946 8204 103
9327 1 12 11 22 2 4 18 3 13 15 16 19 8 17 6 7 14 5 10 20 9 21 9420 8205 138
10989 1 12 22 11 21 10 4 17 13 3 9 14 6 18 19 8 5 7 16 20 2 15 47662 9505 101
10990 1 13 10 22 2 6 16 9 8 17 19 7 11 14 4 20 15 12 5 18 3 21 11095 9506 125
12785 1 13 22 10 21 11 4 17 12 6 7 3 19 5 16 9 18 8 15 20 2 14 45677 10956 118
12786 1 14 9 22 2 5 17 4 11 13 20 15 7 8 18 3 10 12 16 21 6 19 12817 10957 147
14859 1 14 22 9 21 12 4 18 10 13 2 20 6 19 8 11 7 5 15 17 3 16 52306 12511 81
14860 1 15 8 22 2 5 17 4 10 18 16 14 12 7 9 3 20 6 13 19 11 21 14932 12512 152
17125 1 15 22 8 21 14 3 19 9 12 4 18 5 13 16 2 10 6 17 20 7 11 50800 14190 91
17126 1 16 7 22 2 5 17 3 10 14 20 15 8 18 6 12 13 11 4 21 9 19 17163 14191 129
19197 1 16 22 7 21 15 3 19 8 5 12 4 11 20 10 14 18 2 6 17 9 13 50502 15642 98
19198 1 17 6 22 2 7 15 10 4 19 21 12 3 8 16 5 13 11 14 18 9 20 19251 15643 138
21080 1 17 22 6 21 16 3 19 7 8 10 12 5 15 18 2 14 4 13 20 11 9 50189 16956 97
21081 1 18 5 22 2 7 15 3 10 14 20 19 4 16 12 6 9 13 8 21 11 1 21100 16957 129
22914 1 18 22 5 21 17 3 15 10 8 7 4 20 6 12 14 16 13 11 19 2 9 40400 18183 96
22915 1 19 4 22 2 14 8 10 9 18 17 7 12 3 13 5 21 16 6 20 15 11 22919 18184 135
24465 1 19 22 4 21 18 3 15 9 2 14 6 11 16 17 13 10 12 8 20 5 7 51352 19293 89
24466 1 20 3 22 2 9 13 5 8 17 19 18 4 14 11 7 10 16 6 21 12 15 24469 19294 121
25649 1 20 22 3 18 19 6 13 7 12 9 10 14 16 4 15 17 11 2 21 8 5 51428 20144 76
25650 1 21 4 20 2 13 11 5 9 19 16 18 7 12 8 6 14 17 3 22 15 10 44365 20145 114
26305 1 21 20 4 18 17 7 16 2 14 12 15 3 19 10 8 13 9 5 22 11 6 53301 20800 74
26306 2 1 21 22 3 9 12 14 19 8 16 5 11 17 10 13 18 4 7 20 6 15 98 55 138
38651 2 21 20 3 19 18 6 14 5 15 7 17 8 11 12 1 16 9 10 22 13 4 52162 25901 86
38652 3 1 20 22 2 8 14 10 21 11 12 17 7 13 15 5 9 6 18 19 4 16 274 189 141
44914 3 21 18 4 20 7 15 2 8 1 17 11 16 19 10 13 12 9 6 22 5 14 50818 26652 110
44915 4 1 19 22 2 8 14 16 15 12 17 7 6 18 10 9 20 3 5 21 11 13 648 501 137
48436 4 21 15 6 11 12 17 3 5 10 20 7 16 1 19 2 18 14 13 22 9 8 41840 26283 135
48437 5 1 18 22 2 6 16 12 17 8 19 4 11 13 14 7 21 3 9 20 10 15 1197 976 159
50551 5 21 13 7 19 4 16 1 8 2 17 18 10 20 14 3 11 6 9 22 12 15 50910 26763 124
50552 6 1 17 22 2 4 18 14 13 12 19 3 10 9 15 7 21 5 11 20 8 16 2242 1905 159
51762 6 21 2 17 16 4 9 1 15 8 7 18 20 5 13 3 12 19 10 22 11 14 44287 26522 134
51763 7 1 16 22 2 4 18 10 17 8 19 6 11 13 14 5 21 3 9 20 12 15 3242 2803 165
52553 7 20 5 14 13 8 11 3 12 2 19 6 18 4 22 1 17 16 9 21 15 10 26249 20744 154
52554 8 1 15 22 2 5 17 10 18 7 19 6 11 12 16 3 21 4 9 20 14 13 4602 4036 168
52981 8 20 6 12 14 5 15 2 9 4 19 7 18 3 21 1 17 16 10 22 13 11 37775 25419 153
52982 9 1 14 22 5 2 17 12 16 6 19 4 11 8 21 3 18 7 13 20 10 15 5949 5239 171
53192 9 16 7 14 8 5 19 1 10 6 22 3 20 2 18 4 21 11 12 17 13 15 16113 13341 173
53193 10 1 14 21 2 6 17 8 20 9 15 4 19 5 13 7 22 3 16 12 11 18 23912 18811 182
53324 10 12 5 19 3 6 18 1 15 7 21 8 16 9 14 2 22 4 11 13 20 17 16867 13937 183
53325 11 2 12 21 6 5 14 8 22 3 15 7 16 9 18 4 17 1 19 10 13 20 25367 19886 186
53444 11 10 9 16 6 5 19 2 15 3 22 1 21 4 18 7 20 8 14 13 12 17 20732 16641 185
53445 12 2 11 21 4 8 13 9 22 3 17 1 19 6 18 7 20 5 15 10 14 16 25553 20048 187
53518 12 9 6 19 7 3 17 4 16 10 13 8 21 1 14 2 22 5 18 11 15 20 16848 13929 187
53519 12 9 7 18 4 2 22 1 14 8 20 10 15 6 17 3 16 5 19 11 13 21 26237 20732 187
53520 12 9 8 17 3 11 15 2 20 5 18 7 19 6 16 1 22 4 14 10 21 13 19156 15601 187
53521 12 9 8 17 4 5 20 2 15 6 21 7 16 10 14 3 22 1 13 11 19 18 18869 15341 187
53522 12 9 8 17 7 3 19 2 16 5 18 11 15 6 20 1 14 4 22 10 13 21 12692 10863 187
53523 12 9 8 17 11 3 15 6 16 5 14 7 19 2 20 1 18 4 22 10 13 21 12691 10862 187
53524 12 10 3 21 7 4 14 5 17 2 20 8 13 9 22 1 15 6 16 11 18 19 26020 20515 187
53525 12 10 3 21 7 4 14 5 17 9 13 8 20 2 15 1 22 6 16 11 18 19 17039 14104 187
53526 12 10 5 19 3 6 18 4 14 8 21 1 20 2 16 7 22 9 13 11 15 17 14558 12224 187
53527 12 10 8 16 5 3 22 1 13 7 21 9 15 6 18 2 17 4 19 11 14 20 25453 19960 187
53528 12 10 8 16 6 9 15 4 17 1 22 2 18 7 20 3 21 5 13 11 19 14 20998 16874 187
Solut. | -------------Order11D ----- Cell Values -----upper case signifies points ----------| Comple- Pair Point
# A b c D e f G h i J k L m N o P q R s T U V ment # Total
1 1 3 20 22 2 6 16 21 4 5 8 13 9 18 17 7 19 12 10 15 11 14 106 1 134
2 1 3 20 22 2 6 16 21 4 5 8 13 9 18 17 7 19 12 14 11 15 10 54 2 130
3 1 3 20 22 2 6 16 21 4 5 8 13 15 12 11 19 9 10 7 14 18 17 159 3 147
4 1 3 20 22 2 6 16 21 4 5 9 12 18 10 17 15 14 8 13 7 19 11 83 4 126
5 1 3 20 22 2 6 16 21 4 5 12 9 13 18 17 7 19 8 10 15 11 14 104 5 126
6 1 3 20 22 2 6 16 21 4 5 12 9 13 18 17 7 19 8 14 11 15 10 52 6 122
7 1 3 20 22 2 6 16 21 4 5 12 9 18 13 14 15 8 11 7 10 19 17 162 7 138
8 1 3 20 22 2 6 16 21 4 5 13 8 18 14 17 11 10 12 9 7 19 15 130 8 130
9 1 3 20 22 2 6 16 21 5 4 8 14 7 19 12 10 11 17 9 13 18 15 125 9 149
10 1 3 20 22 2 6 16 21 5 4 8 14 7 19 12 10 17 11 15 13 18 9 45 10 137
618 1 3 22 20 2 19 5 21 16 4 14 6 13 8 10 12 9 11 7 15 18 17 57789 494 117
619 1 4 19 22 2 5 17 20 3 6 7 14 9 18 15 10 21 8 13 16 11 12 920 495 135
1553 1 4 22 19 3 18 6 21 17 2 15 7 16 5 14 10 12 9 13 8 20 11 62964 1196 98
1554 1 5 18 22 2 6 16 19 3 8 11 9 21 10 20 13 15 7 14 4 17 12 1869 1197 119
2636 1 5 22 18 4 17 7 21 16 2 19 3 15 11 13 6 12 9 14 8 20 10 62907 2068 95
2637 1 6 17 22 2 3 19 18 4 5 8 16 7 20 9 13 11 14 15 10 21 12 2999 2069 153
4363 1 6 22 17 5 20 4 21 19 2 15 7 16 3 14 10 12 9 13 8 18 11 71915 3557 90
4364 1 7 16 22 2 3 19 17 6 4 5 21 14 8 12 20 11 10 13 9 18 15 4800 3558 147
6297 1 7 22 16 6 20 4 21 19 2 17 5 11 10 14 3 18 8 15 12 13 9 74077 5238 83
6298 1 8 15 22 2 3 19 16 4 7 6 18 5 20 13 9 21 10 17 14 11 12 6664 5239 143
9392 1 8 22 15 7 20 4 21 19 2 17 5 10 11 13 3 12 14 6 16 9 18 72432 8046 98
9393 1 9 14 22 2 3 19 15 5 7 4 21 6 16 8 17 13 12 10 18 11 20 9786 8047 164
12109 1 9 22 14 8 20 4 21 19 2 12 10 13 3 6 18 5 11 7 15 16 17 71921 10417 111
12110 1 10 13 22 2 3 19 14 6 7 21 5 18 20 11 9 12 4 16 8 17 15 12610 10418 127
15870 1 10 22 13 9 20 4 21 19 2 17 5 15 6 18 3 14 12 8 11 7 16 74800 13661 80
15871 1 11 12 22 2 3 19 13 4 10 8 16 20 7 21 14 18 6 15 5 9 17 16328 13662 126
19585 1 11 22 12 10 20 4 21 19 2 17 5 18 3 16 8 14 7 15 6 13 9 75733 16716 70
19586 1 12 11 22 3 2 19 13 4 10 9 16 7 21 6 15 5 17 14 8 20 18 19918 16717 167
22987 1 12 22 11 10 21 4 20 16 6 15 3 13 9 2 19 5 7 8 18 14 17 67737 19368 109
22988 1 13 10 22 5 2 17 14 3 12 6 18 7 19 8 16 9 15 20 4 21 11 23155 19369 156
25770 1 13 22 10 12 20 4 21 19 2 17 5 18 3 16 8 14 7 15 6 11 9 75929 21331 66
25771 1 14 9 22 7 5 12 15 3 16 2 19 4 18 8 17 6 21 10 11 13 20 25823 21332 170
28397 1 14 22 9 13 20 4 21 19 2 17 5 15 6 11 10 7 12 16 3 18 8 71443 23101 78
28398 1 15 8 22 9 3 12 16 7 11 21 6 20 17 4 18 5 2 10 14 13 19 27683 22519 135
31126 1 15 22 8 14 20 4 21 19 2 16 6 9 11 3 13 5 12 7 18 10 17 72450 24741 102
31127 1 16 7 22 11 3 10 17 4 15 6 18 12 13 8 21 14 5 9 20 2 19 22378 18796 146
33842 1 16 22 7 15 20 4 21 19 2 17 5 18 3 13 11 12 6 14 8 9 10 75904 26372 66
33843 1 17 6 22 13 2 9 18 3 16 4 20 5 19 10 14 7 21 12 8 11 15 15302 13110 156
36271 1 17 22 6 16 20 4 21 19 2 15 7 5 14 3 10 9 12 11 18 8 13 72069 27799 95
36272 1 18 5 22 15 2 7 19 3 17 4 20 8 16 6 21 10 11 14 13 9 12 8836 7496 149
38817 1 18 22 5 17 20 4 21 19 2 16 6 11 9 3 15 7 8 14 13 12 10 75119 29337 85
38818 1 19 4 22 17 2 5 20 3 18 9 15 8 21 6 16 7 14 13 11 10 12 3794 2988 145
40461 1 19 22 4 18 17 7 21 16 2 12 10 6 13 14 3 11 20 15 5 8 9 63222 30279 82
40462 1 20 7 18 19 3 6 21 5 14 8 17 4 22 9 10 12 16 11 15 2 13 37464 28384 134
41732 1 20 22 3 19 18 6 21 17 2 15 7 16 5 14 10 12 9 13 8 4 11 75878 31142 66
41733 2 3 20 21 1 6 18 19 4 5 7 14 10 16 17 9 22 8 13 15 11 12 41950 31143 131
57546 2 20 19 5 21 17 3 22 14 7 8 12 4 13 1 18 9 11 16 15 10 6 72369 36815 102
57547 3 1 20 22 2 6 16 21 4 5 7 14 8 18 9 15 13 11 10 17 19 12 383 259 152
65841 3 19 20 4 21 16 5 22 13 6 9 11 2 17 1 15 10 12 14 18 8 7 71566 37854 106
65842 4 1 19 22 2 5 17 20 3 6 7 14 11 16 9 18 13 8 12 15 21 10 1439 1082 151
69881 4 20 17 5 22 13 6 21 11 8 9 12 3 18 1 16 2 19 14 10 15 7 69861 37949 120
69882 5 1 18 22 2 10 12 19 4 11 3 14 6 16 17 9 21 13 7 20 8 15 2620 2052 145
72568 5 19 15 7 22 3 14 21 1 10 9 12 11 20 8 17 2 18 4 13 6 16 63464 37629 138
72569 6 1 17 22 2 7 15 18 5 8 9 12 16 11 10 20 4 13 3 14 21 19 4361 3555 161
74076 6 19 12 9 22 1 14 20 4 8 10 16 11 18 3 21 2 13 5 17 7 15 52405 35109 144
74077 7 1 16 22 2 8 14 17 5 10 9 11 12 15 6 20 4 13 3 18 21 19 6297 5238 170
74820 7 18 13 8 21 5 12 19 1 14 2 17 4 20 3 22 6 16 11 15 10 9 41670 31080 150
74821 8 1 15 22 5 7 12 19 4 11 3 17 2 20 6 16 13 14 9 21 18 10 9115 7769 169
75283 8 17 12 9 20 7 10 18 5 13 2 19 4 16 3 22 1 21 6 15 11 1 41387 30806 158
75284 9 1 14 22 2 5 17 15 3 11 8 13 12 16 6 21 7 10 4 20 19 1 12079 10387 176
75570 9 17 6 14 21 1 10 18 5 13 8 19 4 22 3 16 2 20 7 15 11 12 38081 28696 161
75571 10 1 13 22 4 6 14 16 5 11 3 19 9 12 8 21 7 15 2 20 17 18 15714 13505 179
75742 10 9 15 12 7 8 19 11 2 14 1 16 5 17 6 21 4 20 3 18 13 22 32964 25680 182
75743 11 3 10 22 4 6 14 13 2 17 7 12 8 20 9 15 5 19 1 18 16 21 25006 20644 185
75847 11 9 14 12 7 8 19 10 2 15 1 16 5 17 6 21 4 20 3 18 13 22 32965 25681 184
75848 12 2 11 21 1 4 20 10 3 13 5 17 7 18 6 19 8 14 9 16 22 15 31056 24671 187
75930 12 9 11 14 8 2 22 10 1 13 3 19 5 20 4 21 6 16 7 18 15 17 25766 21327 187
75931 12 9 11 14 8 2 22 10 1 13 6 16 7 21 5 19 3 18 4 17 15 20 25692 21253 187
75932 12 9 11 14 8 4 20 10 3 13 1 21 2 19 6 18 5 22 7 15 16 17 38808 29328 187
75933 12 9 11 14 8 4 20 10 3 13 5 17 7 18 6 19 1 21 2 16 15 22 31062 24677 187
75934 12 9 11 14 8 5 19 10 1 16 2 17 4 20 3 22 7 15 6 21 13 18 41687 31097 187
75935 12 9 11 14 8 5 19 10 1 16 4 15 6 20 7 18 3 21 2 17 13 22 30618 24306 187
75936 12 9 11 14 8 5 19 10 2 15 7 13 6 22 4 18 1 20 3 17 16 21 35336 27100 187
75937 12 9 11 14 8 5 19 10 4 13 6 16 3 22 2 18 1 21 7 15 20 17 40262 30080 187
75938 12 9 11 14 8 7 17 10 1 18 2 15 4 20 3 22 6 16 5 21 13 19 41613 31023 187
75939 12 9 11 14 8 7 17 10 6 13 2 20 4 15 3 22 1 21 5 16 18 19 41290 30739 187
75940 12 9 11 14 8 7 17 10 6 13 4 18 5 16 3 21 1 20 2 19 15 22 31123 24738 187
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