 |
 |
 |
 |
 |
|
|
|
|
|
|
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.
Some 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
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