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. |
|
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. |
Some complement pairs: |
|||||||||||
The first solution | First with A = 2 | The last solution | |||||||||
Solution numbers |
Pair # |
Solution numbers |
Pair # |
Solution numbers |
Pair # |
||||||
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. |
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
Please send me Feedback about my Web site!
Harvey Heinz harveyheinz@shaw.ca
This page last updated
September 09, 2003
Copyright © 1998, 1999 by Harvey D. Heinz