Introduction to Order-10 |
Cell designations & some of the features of Order-10 magic stars. |
Characteristics - Order-10 |
Adjacent complement pairs, numbers at points, solutions with each point total, etc. |
Order 10A List of Basic Solutions |
A partial list of the 10,882 basic solutions with solution number,
complement number, complement pair number, and point totals. I show the first and last 10 solutions. In addition, while A = 1, I show the first solution for each value of B. Finally, I show the first solution for each value of A above 1. |
Order 10B List of Basic Solutions |
A partial list of the 115,552 basic solutions for this pattern. Same information as for pattern A. |
Order 10C List of Basic Solutions |
A partial list of the 10,882 basic solutions for this pattern. Same information as for pattern 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 |
Pattern A consists of two super-imposed pentagons, pattern B is continuous, and pattern C is two super-imposed pentagrams. (2 and 5 are the factors of 10).
As expected, patterns A and C have the same number of basic solutions because point names are the same. However, it seems odd that B has over ten times as many as A and C. Are there equivalents in the list? I used the same algorithm for all three patterns (in fact, for all orders). If so, it is very coincidental that all matched up into complement pairs.
Pattern A 10882 solutions
approx. 24 hrs. to run
Pattern B 115552 solutions
approx. 6.5 hrs. to run
Pattern C 10882 solutions
approx. 24 hrs. to run
Running times are on a 200 Mhz Pentium Pro with 32 Megs. of RAM.
Each solution contains the consecutive series of integers from 1 to 20. The sum of this series is 210, there are 6 lines with each cell appearing in 2 lines, so the magic constant (S) is (2 x 210)/10 = 42.
Characteristics - Order-10Some adjacent complement pairs:
10A 1 & 26
5304 &
186 10882 &
5128
10B 1 & 254 54777 & 2432
115552 & 40180
10C 1 & 6
5304 & 27
10882 &
4823
In each case, the first solution shown here is the first, the first for a = 2, and
the last solution in the list.
Number of complement pairs for 10B is 57,776 (115,552/2).
Number of solutions with a equal to 1 is 57,776 !
Order 10B has exactly 27,000 solutions with a = 2. They start at index number
57,777. It also has more solutions then order-11 just as order-6 has more solutions then
order-7.
The first solutions with A = 3
Feature | Pattern 10A |
Pattern 10B |
Pattern 10C |
Comments |
Number of basic solutions | 10882 |
115552 |
10882 |
B over 10 times as many as A & C |
Adjacent Complement Pairs | 27 |
26 |
50 |
B has a small percentage of A & C |
Solutions with numbers 1 to 10 at the points (See note below) |
0 |
0 |
0 |
No, same as Order-6 & Order-8. It follows that no solutions exist with numbers 11 to 20 (these would be the complement solutions). |
Solutions with all odd numbers at the points | 0 |
0 |
0 |
No, same as Order-6 & Order-8. It follows that no solutions exist with even numbers at the points (these would be the complement solutions). |
Point total of pentagon or pentagram equal | Pentagon Yes |
Not applicable | Pentagram Yes |
NOTE: Order 8A has 2 squares and the corners of these always
sum the same. Order-6 has two triangles, and the corners of these always sum the same. |
Two features that may be present in any order,always appear together.
Of course, in each case, there will be the same number of solutions with the opposite
condition.
There will always be the same number of solutions of each feature (for a
given order and pattern).
All odd orders have these types of solutions.
Singly-even (6, 10, 14) orders cannot have these types of solutions
because of parity.
Doubly-even orders may have these types although order-8 does not.
Order-12 does, and presumably orders 16 , 20, etc do also.
Summary of Point Totals - Low Range | |||||||||||||
Point | |------ Pattern ------| | Point | |------ Pattern ------| | Point | |------ Pattern ------| | ||||||||
Total | A | B | C | Total | A | B | C | Total | A | B | C | ||
56 | 10 | 54 | 10 | 74 | 118 | 1141 | 118 | 90 | 387 | 4218 | 387 | ||
58 | 17 | 354 | 17 | 76 | 166 | 1376 | 166 | 92 | 387 | 3956 | 387 | ||
60 | 30 | 530 | 30 | 78 | 176 | 1726 | 176 | 94 | 351 | 4177 | 351 | ||
62 | 16 | 260 | 16 | 80 | 174 | 1783 | 174 | 96 | 448 | 4478 | 448 | ||
64 | 36 | 388 | 36 | 82 | 185 | 1757 | 185 | 98 | 458 | 4123 | 458 | ||
66 | 33 | 468 | 33 | 84 | 254 | 1881 | 254 | 100 | 449 | 4311 | 449 | ||
68 | 62 | 672 | 62 | 86 | 223 | 3887 | 223 | 102 | 513 | 5415 | 513 | ||
70 | 71 | 736 | 71 | 88 | 306 | 4020 | 306 | 104 | 454 | 4939 | 454 | ||
72 | 117 | 1153 | 117 |
Above is the low range of point totals. The arrangement of point totals from 106 to 154 is a mirror image of this i.e. 106 is the same as 104, 108 is the same as 102, , 154 is the same as 56. Solutions in this high bank are the complements of the solutions in the low bank. Note that the point total distribution for patterns A and C are exactly the same. This is because the point names are exactly the same.
Solut. |---- Order-10A ----- 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 ment # Total 1 1 2 19 20 3 4 15 10 5 12 6 8 16 7 18 9 11 17 14 13 26 1 128 2 1 2 19 20 3 4 15 12 5 10 6 8 18 7 16 11 9 17 14 13 76 2 128 3 1 2 19 20 3 4 15 13 5 9 6 11 16 7 18 12 8 17 14 10 25 3 122 4 1 2 19 20 3 5 14 15 7 6 18 10 8 16 17 11 9 13 4 12 35 4 98 5 1 2 19 20 3 5 14 18 4 6 11 9 16 8 17 13 7 12 15 10 54 5 114 6 1 2 19 20 3 5 14 18 4 6 13 7 16 8 17 11 9 10 15 12 55 6 114 7 1 2 19 20 3 6 13 14 5 10 11 12 9 15 17 16 4 18 8 7 37 7 106 8 1 2 19 20 3 6 13 17 7 5 8 11 18 9 14 16 4 15 12 10 91 8 114 9 1 2 19 20 3 7 12 4 11 15 9 8 10 13 18 6 14 17 5 16 14 9 116 10 1 2 19 20 3 7 12 6 8 16 9 4 13 10 18 5 15 14 11 17 23 10 124 201 1 2 20 19 13 7 3 16 12 11 9 8 14 10 17 5 4 15 6 18 5341 148 96 202 1 3 18 20 2 4 16 8 6 12 5 10 15 7 19 9 13 17 14 11 222 149 128 434 1 3 20 18 13 5 6 16 8 12 11 9 10 14 17 7 2 19 4 15 6002 324 94 435 1 4 17 20 2 5 15 3 10 14 8 11 9 13 19 7 16 18 6 12 445 325 118 778 1 4 20 17 12 2 11 15 10 6 9 13 14 8 19 3 7 18 5 16 8687 629 98 779 1 5 16 20 2 7 13 10 11 8 3 17 14 12 15 18 6 19 9 4 822 630 112 1214 1 5 20 16 13 9 4 17 15 6 10 8 18 12 11 7 2 14 3 19 7079 1014 90 1215 1 6 15 20 2 3 17 16 4 5 19 8 10 18 13 14 11 12 7 9 1254 1015 106 1645 1 6 20 15 13 11 3 10 17 12 2 9 19 8 14 4 5 16 7 18 7652 1391 100 1646 1 7 14 20 2 3 17 9 10 6 5 18 13 12 16 15 11 19 8 4 1682 1392 114 2126 1 7 20 14 15 8 5 12 16 9 6 10 17 11 13 3 4 18 2 19 6809 1787 92 2127 1 8 13 20 2 3 17 5 9 11 10 14 7 18 16 12 15 19 4 6 2139 1788 112 2601 1 8 20 13 17 5 7 19 6 10 12 4 16 11 14 2 3 15 9 18 8738 2187 94 2602 1 9 12 20 2 4 16 7 11 8 15 14 5 19 17 10 18 13 3 6 2624 2188 100 3132 1 9 20 12 17 7 6 18 10 8 13 5 16 14 11 3 2 15 4 19 6578 2609 86 3133 1 10 11 20 2 4 16 14 3 9 19 6 8 18 15 12 17 7 13 5 3139 2610 108 3518 1 10 20 11 17 8 6 14 15 7 4 12 19 9 13 3 2 18 5 16 7154 2917 88 3519 1 11 10 20 2 7 13 8 4 17 14 5 6 19 16 12 18 9 15 3 3525 2918 114 3862 1 11 20 10 17 6 9 16 12 5 4 14 19 7 15 3 2 18 8 13 6618 3196 88 3863 1 12 9 20 3 5 14 8 4 16 13 7 6 18 17 11 19 10 15 2 3864 3197 114 4149 1 12 20 9 17 6 10 15 4 13 14 8 7 18 16 3 2 19 5 11 6224 3411 80 4150 1 13 8 20 3 5 14 7 4 17 9 6 10 16 15 12 19 11 18 2 4152 3412 124 4483 1 13 20 8 17 6 11 15 4 12 14 9 7 18 16 3 2 19 5 10 6223 3675 78 4484 1 14 7 20 9 2 11 12 13 6 15 16 5 19 17 8 18 10 4 3 4103 3370 86 4698 1 14 20 7 15 12 8 11 6 17 2 10 13 9 19 4 3 16 18 5 9186 3838 92 4699 1 15 6 20 12 2 8 13 18 3 9 19 11 14 16 7 17 10 5 4 3034 2518 86 4929 1 15 20 6 17 11 8 16 4 14 7 9 12 10 19 3 2 13 18 5 9252 4021 82 4930 1 16 6 19 11 2 10 13 15 4 12 17 9 14 18 5 20 7 8 3 3285 2731 86 5131 1 16 20 5 17 14 6 18 7 11 12 10 9 13 19 3 2 8 15 4 10670 4164 64 5132 1 17 8 16 9 3 14 6 7 15 12 11 4 19 18 5 20 13 10 2 3964 3264 100 5258 1 17 20 4 14 16 8 13 6 15 7 9 11 12 18 5 3 10 19 2 7573 4253 78 5259 1 18 7 16 12 8 6 10 11 15 13 9 5 17 19 3 20 4 14 2 2738 2270 86 5303 1 18 17 6 15 16 5 14 11 12 7 10 13 9 19 2 8 4 20 3 3555 2925 74 5304 2 1 19 20 3 5 14 15 7 6 8 11 17 10 13 16 4 18 9 12 186 133 118 7975 2 17 13 10 20 1 11 19 5 7 12 15 8 14 18 3 6 16 9 4 10265 5217 76 7976 3 1 18 20 2 4 16 11 6 9 5 13 15 7 17 14 8 19 12 10 363 253 126 9376 3 16 13 10 19 2 11 14 9 8 1 18 15 7 17 4 6 20 12 5 1999 1662 94 9377 4 1 17 20 2 5 15 18 3 6 13 11 12 7 19 14 9 10 16 8 722 573 114 10121 4 15 11 12 19 2 9 13 3 17 1 10 14 8 16 5 7 20 18 6 2486 2077 112 10122 5 1 16 20 2 3 17 6 4 15 7 9 11 8 18 10 14 19 12 13 1135 935 136 10511 5 13 4 20 11 2 9 3 16 14 1 17 10 12 15 8 19 18 7 6 3470 2869 116 10512 6 1 15 20 2 4 16 5 3 18 8 7 9 10 17 11 14 19 12 13 1610 1356 138 10677 6 10 18 8 3 16 15 1 9 17 2 4 19 5 12 7 14 11 20 13 5217 4215 130 10678 7 1 14 20 2 3 17 9 6 10 4 16 12 5 18 15 11 19 13 8 2083 1744 132 10794 7 10 16 9 4 12 17 1 5 19 2 3 18 6 11 8 14 15 20 13 5284 4265 140 10795 8 1 13 20 2 3 17 9 4 12 5 7 18 6 10 16 11 19 14 15 2584 2170 150 10847 8 7 17 10 2 14 16 3 5 18 4 1 19 6 9 11 12 13 20 15 5226 4223 142 10848 9 1 12 20 3 5 14 2 7 19 4 8 11 6 16 10 17 18 13 15 3095 2572 146 10866 9 6 13 14 2 8 18 4 1 19 5 3 15 11 7 17 10 20 16 12 5184 4190 150 10867 10 1 11 20 2 4 16 7 6 13 3 8 18 5 9 17 12 19 14 15 3498 2897 154 10873 10 3 13 16 4 7 15 1 8 18 2 5 17 6 9 11 14 20 12 19 4434 3626 152 10874 10 4 8 20 3 7 12 2 9 19 1 6 16 5 11 13 18 15 17 14 4352 3563 154 10875 10 4 9 19 1 5 17 7 2 16 8 3 15 6 11 14 18 12 20 13 4429 3622 154 10876 10 4 13 15 3 8 16 1 7 18 5 2 17 9 6 12 14 19 11 20 4112 3374 152 10877 10 5 7 20 8 1 13 9 4 16 2 6 18 3 11 12 15 17 19 14 4476 3668 154 10878 10 5 11 16 4 2 20 9 1 12 8 3 19 7 6 14 13 18 15 17 4142 3404 154 10879 10 5 13 14 2 6 20 1 4 17 7 3 15 9 8 11 16 19 12 18 4889 3982 152 10880 10 5 13 14 2 8 18 6 3 15 7 1 19 4 9 11 16 12 20 17 4647 3795 152 10881 10 6 8 18 3 5 16 4 7 15 1 9 17 2 13 12 19 14 20 11 4102 3369 152 10882 10 6 9 17 2 3 20 5 1 16 8 4 14 7 11 12 19 15 18 13 5128 4161 154
Solution |-----Order-10B----- 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 ment # Total 1 1 2 19 20 3 4 15 5 10 12 17 7 6 8 9 13 16 14 18 11 254 1 122 2 1 2 19 20 3 4 15 6 7 14 11 9 8 5 10 12 16 17 13 18 975 2 132 3 1 2 19 20 3 4 15 7 6 14 11 9 8 10 5 17 16 18 12 13 906 3 122 4 1 2 19 20 3 4 15 8 6 13 10 12 7 11 5 17 16 18 9 14 1044 4 118 5 1 2 19 20 3 4 15 9 6 12 10 13 7 11 5 17 16 18 8 14 1042 5 116 6 1 2 19 20 3 4 15 9 6 12 13 7 10 8 5 17 16 18 14 11 752 6 122 7 1 2 19 20 3 4 15 9 7 11 18 8 5 6 1 10 16 17 14 13 107 7 124 8 1 2 19 20 3 4 15 11 7 9 13 14 6 5 1 10 16 17 8 18 826 8 122 9 1 2 19 20 3 4 15 12 6 9 11 14 8 10 5 17 16 18 7 13 904 9 112 10 1 2 19 20 3 4 15 12 6 9 14 8 11 7 5 17 16 18 13 10 594 10 118 2960 1 2 20 19 16 4 3 18 13 8 14 11 9 7 6 15 17 10 5 12 58639 2320 90 2961 1 3 18 20 2 4 16 5 7 14 9 11 8 6 10 13 15 17 12 19 3679 2321 132 5476 1 3 20 18 17 5 2 19 13 8 14 11 9 7 6 15 16 10 4 12 85272 4404 86 5477 1 4 17 20 2 5 15 9 7 11 12 16 3 8 14 10 13 18 6 19 5765 4405 120 8904 1 4 20 17 18 5 2 13 19 8 15 10 9 6 7 14 16 3 11 12 99243 7622 86 8905 1 5 16 20 2 3 17 4 12 9 8 19 6 13 7 18 14 11 10 15 9510 7623 110 12194 1 5 20 16 19 4 3 13 18 8 15 10 9 6 7 14 17 2 11 12 101055 10544 86 12195 1 6 15 20 2 3 17 5 4 16 9 10 7 8 12 14 13 19 11 18 12405 10545 134 16086 1 6 20 15 19 5 3 14 18 7 13 12 10 8 4 17 16 2 9 11 107378 14223 78 16087 1 7 14 20 2 3 17 6 10 9 18 11 4 5 19 8 12 13 16 15 16151 14224 126 20186 1 7 20 14 19 6 3 18 11 10 17 2 13 4 5 16 15 9 12 8 111963 17979 90 20187 1 8 13 20 2 9 11 3 10 18 14 4 6 7 16 12 5 19 17 15 20230 17980 128 24364 1 8 20 13 19 7 3 17 18 4 15 12 11 6 5 16 14 2 9 10 113247 21857 72 24365 1 9 12 20 2 3 17 4 8 13 16 6 7 5 18 11 10 15 19 14 24500 21858 134 28544 1 9 20 12 19 8 3 18 5 16 17 2 7 4 11 10 13 15 6 14 108356 25515 98 28545 1 10 11 20 2 3 17 4 8 13 18 6 5 12 14 16 9 15 19 7 28590 25516 120 32882 1 10 20 11 19 9 3 18 14 7 16 15 4 5 13 8 12 6 2 17 100986 29381 76 32883 1 11 10 20 2 3 17 4 5 16 13 7 6 14 12 19 8 18 15 9 33122 29382 122 36396 1 11 20 10 19 9 4 18 13 7 17 15 3 14 5 16 12 6 2 8 115171 32202 58 36397 1 12 9 20 2 4 16 14 7 5 18 8 11 3 19 13 6 17 15 10 36408 32203 120 40402 1 12 20 9 19 11 3 18 14 7 16 15 4 5 13 8 10 6 2 17 100985 35622 72 40403 1 13 8 20 2 3 17 9 5 11 15 12 4 16 14 19 6 18 10 7 40440 35623 108 43972 1 13 20 8 19 12 3 18 5 16 17 2 7 4 11 10 9 15 6 14 108353 38412 90 43973 1 14 7 20 2 3 17 6 10 9 18 11 4 12 19 15 5 13 16 8 43982 38413 112 47360 1 14 20 7 19 13 3 17 18 4 15 12 11 6 5 16 8 2 9 10 115347 41075 60 47361 1 15 6 20 7 2 13 8 10 11 19 9 3 16 17 18 5 12 14 4 46423 40173 100 50558 1 15 20 6 19 14 3 18 11 10 17 2 13 4 5 16 7 9 12 8 114366 43295 74 50559 1 16 5 20 7 4 11 8 14 9 18 12 3 15 19 17 2 10 13 6 45640 39598 94 53392 1 16 20 5 19 14 4 18 8 12 17 10 3 13 6 15 7 11 2 9 115134 45333 60 53393 1 17 5 19 6 2 15 8 9 10 18 11 3 14 20 16 4 12 13 7 17190 15089 104 55488 1 17 20 4 19 14 5 15 16 6 18 8 10 3 9 12 7 2 13 11 114403 46915 68 55489 1 18 6 17 7 4 14 9 11 8 20 12 2 15 19 16 3 10 13 5 66529 46916 92 57082 1 18 20 3 17 16 6 15 9 12 19 4 7 2 13 8 5 10 11 14 114078 48138 82 57083 1 19 6 16 7 5 14 11 8 9 20 10 3 15 18 17 2 13 12 4 90254 48139 92 57776 1 19 18 4 17 16 5 15 14 8 20 12 2 9 13 10 3 6 7 11 114738 48832 60 57777 2 1 19 20 3 4 15 7 6 14 11 9 8 10 5 16 17 18 12 13 2432 1792 124 84776 2 19 18 3 17 9 13 15 4 10 20 5 7 1 16 6 11 8 12 14 109994 56858 96 84777 3 1 18 20 2 4 16 7 5 14 11 9 8 10 6 15 17 19 12 13 5033 3961 128 99124 3 19 16 4 18 14 6 17 11 8 20 2 12 1 13 10 5 7 15 9 111360 57715 82 99125 4 1 17 20 2 6 14 3 7 18 9 10 5 12 8 13 15 19 11 16 8533 7251 130 106020 4 19 14 5 16 12 9 18 2 13 20 1 8 3 17 7 6 15 10 11 103673 57734 98 106021 5 1 16 20 2 3 17 4 8 13 14 6 9 7 10 11 18 15 19 12 11383 9733 138 110486 5 19 12 6 18 4 14 15 3 10 20 1 11 2 17 8 13 7 16 9 105974 57773 108 110487 6 1 15 20 2 3 17 4 7 14 5 13 10 8 9 12 18 16 11 19 15949 14086 140 112758 6 18 11 7 17 3 15 16 2 9 19 4 10 1 20 5 14 8 13 12 56660 47735 114 112759 7 1 14 20 2 3 17 5 4 16 12 6 8 9 11 10 18 19 15 13 19645 17438 144 114302 7 15 11 9 10 5 18 6 2 16 17 1 8 3 20 4 13 12 19 14 52303 44401 136 114303 8 1 13 20 2 3 17 11 4 10 16 7 9 5 15 6 18 19 14 12 23556 21049 142 114944 8 13 5 16 4 3 19 6 2 15 14 1 12 7 18 11 10 17 20 9 44943 39162 144 114945 9 1 12 20 2 3 17 5 7 13 8 10 11 4 15 6 18 16 14 19 28168 25139 152 115276 9 11 8 14 4 7 17 6 3 16 13 1 12 2 20 5 10 18 19 15 45408 39479 150 115277 10 1 11 20 2 5 15 3 7 17 4 8 13 6 12 9 16 18 14 19 32785 29284 154 115543 10 8 7 17 4 2 19 9 1 13 11 6 12 3 20 5 15 18 14 16 56309 47500 154 115544 10 8 7 17 6 1 18 9 4 11 15 3 13 2 20 5 16 14 19 12 57394 48450 150 115545 10 8 7 17 9 2 14 4 6 18 11 1 12 3 20 5 15 13 19 16 56358 47549 154 115546 10 8 7 17 11 1 13 6 4 19 9 2 12 3 20 5 16 14 15 18 56346 47537 154 115547 10 8 9 15 3 5 19 4 2 17 13 1 11 6 16 7 14 18 20 12 49153 42059 152 115548 10 8 13 11 6 5 20 4 1 17 9 2 14 3 12 7 18 15 19 16 51975 44250 152 115549 10 9 5 18 6 3 15 8 2 17 11 1 13 4 20 7 12 19 16 14 54824 46308 154 115550 10 9 6 17 5 1 19 7 4 12 11 3 16 2 18 8 15 14 20 13 52479 44518 154 115551 10 9 8 15 3 4 20 5 1 16 13 2 11 6 17 7 14 18 19 12 52988 44929 152 115552 10 9 8 15 3 6 18 7 1 16 13 2 11 4 19 5 12 20 17 14 40180 35400 152
Solut. |---- Order-10C ----- 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 ment # Total 1 1 2 19 20 3 11 8 10 9 15 6 5 16 7 18 17 13 14 4 12 6 1 120 2 1 2 19 20 3 12 7 10 9 16 6 5 15 8 18 17 13 14 4 11 5 2 118 3 1 2 19 20 3 12 7 14 16 5 10 9 18 6 17 15 8 11 4 13 12 3 102 4 1 2 19 20 3 12 7 14 16 5 10 9 18 8 15 17 6 13 4 12 18 4 102 5 1 2 19 20 3 13 6 16 15 5 12 11 14 9 18 17 7 8 4 10 2 2 92 6 1 2 19 20 3 14 5 16 15 6 12 11 13 10 18 17 7 8 4 9 1 1 90 7 1 2 19 20 3 15 4 14 16 8 9 7 18 6 17 13 10 11 5 12 13 5 102 8 1 2 19 20 4 12 6 15 7 14 9 3 16 8 17 18 13 11 5 10 11 6 114 9 1 2 19 20 4 13 5 10 12 15 6 7 14 11 16 18 8 17 3 9 15 7 110 10 1 2 19 20 4 13 5 12 15 10 8 6 18 9 14 16 7 17 3 11 20 8 108 31 1 2 20 19 7 11 5 15 10 12 8 4 18 6 17 16 9 14 3 13 5311 21 110 32 1 3 18 20 2 8 12 9 10 11 7 5 19 6 16 17 13 15 4 14 43 22 126 55 1 3 20 18 8 10 6 13 11 12 7 4 19 5 17 14 9 16 2 15 7470 38 112 56 1 4 17 20 2 9 11 10 18 3 8 12 19 6 16 15 7 13 5 14 66 39 108 128 1 4 20 17 11 12 2 15 7 18 6 5 13 9 19 16 8 14 3 10 8999 100 102 129 1 5 16 20 2 9 11 6 17 8 3 12 19 4 18 13 10 14 7 15 144 101 118 229 1 5 20 16 11 8 7 10 12 13 3 9 17 6 18 15 4 19 2 14 5339 185 108 230 1 6 15 20 2 9 11 7 5 19 8 3 12 13 16 17 18 14 4 10 248 186 126 414 1 6 20 15 12 10 5 16 3 18 9 4 11 13 17 19 8 14 2 7 7314 351 100 415 1 7 14 20 2 4 16 6 5 15 9 8 10 12 19 18 17 11 3 13 417 352 124 649 1 7 20 14 13 11 4 10 12 16 3 6 17 5 19 9 8 18 2 15 8000 567 104 650 1 8 13 20 2 5 15 7 4 16 11 6 9 14 18 17 19 10 3 12 662 568 122 993 1 8 20 13 14 9 6 16 2 18 4 3 17 5 19 15 11 12 7 10 9284 886 110 994 1 9 12 20 2 5 15 3 11 13 7 6 16 8 17 10 19 14 4 18 1022 887 130 1316 1 9 20 12 17 5 8 19 4 11 10 3 18 7 16 15 6 14 2 13 8990 1167 100 1317 1 10 11 20 2 3 17 4 9 12 5 6 19 7 15 13 18 14 8 16 1359 1168 138 1788 1 10 20 11 17 12 2 16 6 18 7 9 8 14 19 15 4 13 3 5 9027 1571 80 1789 1 11 10 20 2 5 15 6 17 4 3 19 16 7 18 14 9 8 13 12 1795 1572 112 2091 1 11 20 10 17 13 2 16 6 18 8 9 7 15 19 14 5 12 3 4 8930 1815 76 2092 1 12 9 20 2 3 17 6 5 14 13 7 8 18 15 16 19 10 4 11 2135 1816 120 2626 1 12 20 9 18 7 8 16 3 15 6 10 11 13 17 19 2 14 5 4 6059 2256 88 2627 1 13 8 20 3 2 17 9 5 11 14 10 7 16 18 15 19 4 6 12 2628 2257 112 3047 1 13 20 8 19 12 3 14 15 10 5 9 18 7 16 6 2 17 4 11 8824 2575 80 3048 1 14 7 20 2 9 11 8 6 17 3 10 12 13 16 15 19 5 18 4 3060 2576 122 3550 1 14 20 7 19 13 3 17 16 6 9 12 15 8 18 5 2 11 4 10 10624 2933 64 3551 1 15 6 20 2 12 8 7 11 16 4 13 9 14 18 10 19 3 17 5 3555 2934 108 3973 1 15 20 6 19 14 3 17 13 9 10 5 18 7 16 2 8 12 4 11 8987 3226 74 3974 1 16 5 20 2 7 13 3 17 9 8 14 11 12 18 4 19 6 10 15 3979 3227 108 4435 1 16 20 5 19 12 6 14 4 18 2 7 15 9 17 11 8 13 10 3 9223 3560 90 4436 1 17 4 20 2 6 14 5 11 12 8 15 7 16 18 10 19 3 13 9 4437 3561 108 4831 1 17 20 4 19 16 3 15 11 13 8 12 9 14 18 7 5 10 6 2 10843 3858 60 4832 1 18 3 20 9 6 7 5 17 13 4 15 10 12 19 2 14 8 11 16 2417 2067 102 5135 1 18 20 3 17 12 10 14 2 16 11 6 9 13 19 8 15 7 5 4 10371 4104 78 5136 1 19 4 18 7 2 15 6 9 12 5 17 8 13 20 10 16 3 14 11 9055 4105 108 5303 1 19 18 4 17 15 6 11 9 16 2 10 14 7 20 3 13 8 12 5 10415 4272 82 5304 2 1 19 20 3 11 8 14 15 5 10 9 18 6 16 17 7 12 4 13 27 17 106 7975 2 19 18 3 16 11 12 9 4 17 1 10 14 6 20 7 15 8 13 5 10058 5217 96 7976 3 1 18 20 2 8 12 15 10 5 13 7 17 6 16 19 11 9 4 14 53 36 114 9376 3 19 16 4 17 7 14 2 8 18 1 13 10 9 20 5 12 15 6 11 8974 5323 98 9377 4 1 17 20 2 9 11 10 15 6 5 12 19 3 16 18 7 13 8 14 118 90 120 10121 4 19 14 5 16 3 18 6 1 17 2 15 8 10 20 13 12 9 11 7 9142 5345 104 10122 5 1 16 20 2 9 11 6 13 12 3 8 19 4 14 17 10 18 7 15 225 181 134 10511 5 18 13 6 16 1 19 4 2 17 3 12 10 7 20 9 15 11 8 14 7758 5061 114 10512 6 1 16 19 3 9 11 5 8 18 2 10 12 4 20 17 14 13 7 15 5491 4329 132 10677 6 17 10 9 14 3 16 4 2 20 1 8 13 5 18 7 19 11 12 15 5279 4248 128 10678 7 1 14 20 2 9 11 8 6 17 4 3 18 5 12 19 15 16 10 13 641 559 146 10794 7 14 3 18 5 4 15 2 6 19 1 12 10 9 16 11 20 8 17 13 1266 1118 138 10795 8 1 16 17 2 9 14 6 7 15 3 5 19 4 11 20 13 18 10 12 3491 2877 146 10847 8 12 4 18 9 2 13 6 3 20 1 7 14 5 15 11 19 10 16 17 5026 4015 146 10848 9 1 15 17 3 8 14 5 7 16 2 6 18 4 11 20 12 19 10 13 3438 2838 148 10866 9 11 7 15 5 3 19 4 1 18 2 8 14 6 13 16 20 10 17 12 2875 2428 150 10867 10 2 13 17 1 9 15 4 7 16 3 5 18 6 8 20 14 19 12 11 3537 2920 152 10873 10 5 11 16 1 6 19 2 9 12 3 7 20 4 8 17 15 18 13 14 3430 2834 154 10874 10 6 9 17 2 5 18 1 8 15 4 7 16 3 13 12 20 14 11 19 3512 2895 152 10875 10 6 11 15 8 3 16 7 2 17 1 5 19 4 9 20 12 18 14 13 3859 3134 154 10876 10 7 6 19 8 3 12 9 1 20 4 2 16 5 11 15 18 13 14 17 4797 3824 154 10877 10 7 11 14 4 6 18 1 8 15 2 5 20 3 9 13 17 19 12 16 4379 3508 154 10878 10 7 11 14 8 4 16 5 1 20 2 3 17 6 9 18 15 19 12 13 5287 4256 154 10879 10 8 9 15 3 7 17 4 5 16 1 6 19 2 11 14 20 12 18 13 3815 3103 154 10880 10 9 6 17 5 2 18 1 7 16 3 8 15 4 13 11 19 14 12 20 4717 3761 152 10881 10 9 7 16 5 1 20 4 6 12 3 8 19 2 11 14 17 13 15 18 4718 3762 154 10882 10 9 8 15 7 3 17 1 4 20 2 6 14 5 13 12 19 16 11 18 4823 3850 152
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September 09, 2003
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