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Introduction to Order-8 |
Cell designations & some of the features of Order-8 magic stars. |
Adjacent Complement Pairs |
Pairs that are complements of each other and appear nest to each other in the solutions list. |
Values at the points |
Characteristics of point values and point total distribution. |
Order 8A List of Basic Solutions |
The list of 112 basic solutions, complement number, complement pair number, point totals, and special feature remarks. |
Order 8B List of Basic Solutions |
The 112 basic solutions for this pattern. Same information as for pattern A. |
Definitions |
Review magic star definitions and general features. Use Back button to return. |
Examples |
One example of each of 16 patterns, Orders 5 to 11. Back button to return. |
Examples -2 |
One example of each of 14 patterns, Orders 12, 13 and 14. Back button to return. |
The order-8 magic star has 112 basic solutions for each of the two patterns. This despite the fact that the two patterns have points with different names. Order- 7 has the same number of solutions for the two patterns, but the point names are the same. .Both order-9 and order-10 have the same number of solutions for patterns with similar point names and different solution totals for dissimilar patterns. However, order-11 has two patterns with similar cell names and similar total solutions. It also has two patterns with different cell names and similar total solutions
Pattern A consists of two superimposed squares (2 and 4 are the factors of 8). Pattern B is continuous.
Each solution contains the consecutive series of integers from 1 to 16. The sum of this series is 136, there are 8 lines with each cell appearing in 2 lines, so the magic constant (S) is 2 x 136/8 = 34.
Order-8A has four times as many Adjacent Complement Pairs (8) as order-8B (2).
Order-8a Order-8b
Solution # Pair Solution # Pair
1 2 1 4 5 4
6 7 5 26 27 23
9 10 6
16 17 12
29 30 24
50 51 43
78 79 55
97 98 56
Fig. 1A. Index # 1 Fig. 1B. complement of fig.A Fig. 1C. fig.B. normalized = #2
Above is a graphic example of the first adjacent complement pair.
The middle star is obtained by subtracting each number in star A from 17.Figure 1C is then
obtained by rotating B one position to the left and then reflecting it. C is now in the
normalized position and by checking the solutions list below (pattern A) we see that it is
index number 2.
No solutions in either pattern have the points all even or all odd. (If a solution existed with all even points, another one would exist with all odd points because of the complement feature of all magic stars.)
No solutions in either pattern have the points with numbers 1 to 8 or numbers 9 to 16. Again, if a solution exists with numbers 1 to 8 at the points, another must exist with numbers 9 to 16.
In both patterns the sum of the points range from 38 to 98 with no solution having a point sum of 40 or its complement, 96.
Order-8A The corners of the two squares always have the same sum. Because the valleys
are common to both squares, the sum of the 12 cells in each square is always the same.
Order-8B The opposite small triangles, such as a, b, n and e, k, l always
sum to the same value.
Point Pattern Point Pattern Point Pattern
Total A B Total A B Total A B
38 2 2 48 1 1 58 6 6
40 0 0 50 4 4 60 7 7
42 2 2 52 5 5 62 5 5
44 1 1 54 3 3 64 1 1
46 5 5 56 2 2 66 3 3
68 18 18
90 5 5 80 2 2 70 3 3
92 1 1 82 3 3 72 1 1
94 2 2 84 5 5 74 5 5
96 0 0 86 4 4 76 7 7
98 2 2 88 1 1 78 6 6
Order-8 is different then most orders in that the solutions that have
a point total of 68, have a complement that also has a point total of 68.
The point totals that are lower then 68 have complements that are
higher then 68, thus the high range is a mirror image of the low range.
All solutions of pattern A, with point total of 68 have the corners of each of the two squares summing to the constant (S).
Sol.# |------- Cell value ---- Upper case indicates points -------| Comple Pair Point Remarks # A b c D e f G h i J k l M N O P ment # total 1 1 3 14 16 2 7 9 4 8 13 5 15 6 12 11 10 2 1 78 Adjacent complement pair 2 1 3 14 16 2 12 4 9 13 8 10 15 11 7 6 5 1 1 58 3 1 3 16 14 2 11 7 4 8 15 5 13 6 10 9 12 72 2 74 4 1 3 16 14 6 12 2 13 11 8 10 15 7 5 4 9 77 3 50 5 1 4 13 16 2 10 6 9 5 14 11 8 7 12 3 15 8 4 74 6 1 4 13 16 6 5 7 11 2 14 9 10 12 3 15 8 7 5 76 Adjacent complement pair 7 1 4 13 16 7 8 3 15 6 10 12 11 5 9 2 14 6 5 60 8 1 4 13 16 9 6 3 12 8 11 7 15 10 2 14 5 5 4 62 9 1 5 12 16 3 8 7 2 10 15 4 14 6 13 11 9 10 6 78 Adjacent complement pair 10 1 5 12 16 3 13 2 7 15 10 9 14 11 8 6 4 9 6 58 11 1 5 15 13 8 11 2 6 12 14 3 16 4 7 10 9 82 7 60 12 1 5 15 13 12 7 2 16 6 10 9 14 4 3 8 11 95 8 52 13 1 5 16 12 6 13 3 15 7 9 14 10 8 4 2 11 102 9 50 14 1 6 15 12 2 16 4 5 14 11 9 13 7 10 3 8 105 10 56 15 1 6 15 12 2 16 4 7 10 13 11 9 14 3 8 5 81 11 60 16 1 7 10 16 4 11 3 2 14 15 5 13 8 12 9 6 17 12 70 Adjacent complement pair 17 1 7 10 16 4 12 2 3 15 14 6 13 9 11 8 5 16 12 66 18 1 7 11 15 8 5 6 4 10 14 3 16 2 13 12 9 60 13 72 19 1 7 16 10 2 13 9 6 5 14 11 8 4 12 3 15 62 14 68 Corners of each square = S 20 1 8 11 14 6 12 2 3 16 13 5 15 7 10 9 4 84 15 60 21 1 8 16 9 5 13 7 12 11 4 15 14 10 3 6 2 110 16 42 22 1 8 16 9 6 7 12 3 4 15 5 13 2 10 14 11 75 17 74 23 1 8 16 9 10 4 11 15 2 6 13 14 5 3 12 7 106 18 54 24 1 8 16 9 10 13 2 6 11 15 4 14 5 3 12 7 61 19 54 25 1 9 11 13 2 7 12 8 10 4 15 14 5 16 3 6 31 20 60 26 1 9 11 13 8 7 6 2 12 14 3 16 5 10 15 4 57 21 68 27 1 9 11 13 8 7 6 14 12 2 15 16 5 10 3 4 99 22 44 28 1 9 16 8 6 15 5 4 11 14 7 12 10 2 13 3 87 23 56 29 1 10 7 16 4 2 12 3 6 13 9 11 8 15 14 5 30 24 84 Adjacent complement pair 30 1 10 7 16 6 8 4 11 14 5 15 13 9 12 3 2 29 24 52 31 1 10 9 14 7 2 11 3 8 12 6 15 5 13 16 4 25 20 76 32 1 10 9 14 7 5 8 13 11 2 16 15 6 12 4 3 93 25 50 33 1 10 9 14 8 5 7 11 12 4 13 16 2 15 3 6 69 26 52 34 1 10 11 12 14 2 6 13 7 8 9 16 5 4 15 3 56 27 54 35 1 10 14 9 5 7 13 11 8 2 16 15 3 12 4 6 100 28 50 36 1 11 12 10 6 3 15 4 7 8 9 16 2 14 13 5 76 29 68 37 1 11 12 10 6 3 15 8 7 4 13 16 2 14 9 5 71 30 60 38 1 11 13 9 6 5 14 2 8 10 7 16 3 12 15 4 70 31 68 39 1 11 13 9 6 5 14 10 8 2 15 16 3 12 7 4 91 32 52 40 1 11 13 9 8 15 2 4 16 12 7 14 3 10 5 6 103 33 48 41 1 11 13 9 12 7 6 15 10 3 14 16 5 4 8 2 112 34 38 42 1 11 15 7 13 8 6 14 9 5 12 16 4 2 10 3 111 35 38 43 1 12 13 8 5 6 15 3 9 7 10 16 2 14 11 4 74 36 62 44 1 12 13 8 9 14 3 4 16 11 7 15 2 10 6 5 109 37 46 45 1 12 14 7 6 8 13 10 9 2 16 15 3 11 5 4 101 38 46 46 1 12 16 5 13 7 9 11 6 8 10 15 3 2 14 4 86 39 46 47 1 12 16 5 13 10 6 8 9 11 7 15 3 2 14 4 94 40 46 48 1 13 9 11 16 5 2 15 10 7 12 14 3 6 8 4 108 41 42 49 1 13 11 9 7 10 8 6 15 5 12 16 2 14 4 3 92 42 46 50 2 1 16 15 3 9 7 8 5 14 6 12 11 4 13 10 51 43 76 Adjacent complement pair 51 2 1 16 15 5 11 3 12 9 10 8 14 6 7 4 13 50 43 60 52 2 3 15 14 6 4 10 16 1 7 13 12 8 5 9 11 80 44 66 53 2 3 16 13 1 15 5 4 11 14 6 12 9 8 7 10 90 45 68 54 2 3 16 13 1 15 5 4 11 14 6 12 10 7 8 9 89 46 68 55 2 3 16 13 6 5 10 14 1 9 11 12 4 8 7 15 58 47 68 56 2 4 15 13 3 6 12 7 1 14 8 10 11 5 16 9 34 27 82 57 2 5 14 13 1 8 12 6 9 7 10 15 3 16 4 11 26 21 68 58 2 5 14 13 1 11 9 12 3 10 16 6 15 4 7 8 55 47 68 59 2 5 16 11 1 13 9 6 4 15 10 7 14 3 12 8 66 48 74 60 2 6 10 16 1 14 3 7 13 11 12 9 15 8 5 4 18 13 64 61 2 6 11 15 4 7 8 1 9 16 3 13 5 14 12 10 24 19 82 62 2 6 12 14 11 4 5 15 1 13 10 9 3 8 7 16 19 14 68 63 2 6 14 12 1 16 5 4 15 10 9 13 8 11 3 7 107 49 58 64 2 6 16 10 3 12 9 1 11 13 4 15 8 7 14 5 88 50 68 65 2 6 16 10 4 13 7 1 12 14 3 15 5 9 11 8 83 51 66 66 2 7 10 15 12 1 6 16 4 8 11 13 9 3 14 5 59 48 62 67 2 7 11 14 10 1 9 15 6 4 12 16 8 5 13 3 85 52 58 68 2 7 15 10 9 3 12 16 1 5 14 13 6 4 11 8 104 53 58 69 2 9 8 15 7 1 11 4 5 14 6 12 3 16 13 10 33 26 84 70 2 9 10 13 1 6 14 4 11 5 12 15 7 16 8 3 38 31 68 71 2 9 10 13 4 1 16 6 5 7 11 14 8 12 15 3 37 30 76 72 2 9 13 10 6 15 3 1 14 16 4 12 8 7 11 5 3 2 62 73 2 11 8 13 15 1 5 14 9 6 10 16 4 7 12 3 96 54 52 74 2 11 12 9 4 5 16 1 7 10 8 14 3 15 13 6 43 36 74 75 2 12 4 16 9 1 8 11 10 5 14 13 6 15 7 3 22 17 62 76 2 13 10 9 8 1 16 6 5 7 11 14 4 12 15 3 36 29 68 77 3 1 14 16 2 7 9 6 4 15 5 11 10 8 13 12 4 3 86 78 3 1 16 14 2 5 13 8 4 9 7 15 6 10 11 12 79 55 78 Adjacent complement pair 79 3 1 16 14 2 10 8 13 9 4 12 15 11 5 6 7 78 55 58 80 3 2 14 15 5 4 10 16 1 7 13 11 9 6 8 12 52 44 70 81 3 2 15 14 1 10 9 7 6 12 8 11 5 13 4 16 15 11 76 82 3 5 11 15 6 9 4 2 12 16 1 14 7 10 13 8 11 7 76 83 3 5 16 10 4 13 7 1 11 15 2 14 6 8 12 9 65 51 70 84 3 6 9 16 2 12 4 1 14 15 5 11 10 13 8 7 20 15 76 85 3 6 10 15 1 5 13 11 2 8 16 7 9 14 4 12 67 52 78 86 3 6 10 15 4 1 14 5 2 13 7 11 8 12 16 9 46 39 90 87 3 6 13 12 2 11 9 1 8 16 5 10 4 15 7 14 28 23 80 88 3 6 13 12 2 11 9 1 14 10 5 16 4 15 7 8 64 50 68 89 3 6 13 12 2 16 4 1 14 15 5 11 9 10 7 8 54 46 68 90 3 6 13 12 2 16 4 1 14 15 5 11 10 9 8 7 53 45 68 91 3 7 9 15 2 1 16 6 4 8 11 12 10 13 14 5 39 32 84 92 3 7 11 13 2 5 14 1 4 15 6 10 9 12 16 8 49 42 90 93 3 8 7 16 2 1 15 6 4 9 12 10 11 14 13 5 32 25 86 94 3 8 10 13 2 5 14 1 4 15 7 9 6 16 12 11 47 40 90 95 4 2 12 16 3 8 7 11 1 15 10 5 13 6 9 14 12 8 84 96 4 2 16 12 3 8 11 7 1 15 6 9 10 5 14 13 73 54 84 97 4 2 16 12 3 8 11 15 1 7 14 9 10 5 6 13 98 56 68 Adjacent complement pair 98 4 3 16 11 2 9 12 14 1 7 15 8 10 6 5 13 97 56 68 99 4 6 8 16 1 2 15 5 3 11 10 9 12 13 14 7 27 22 92 100 4 6 9 15 1 2 16 7 3 8 12 10 13 11 14 5 35 28 86 101 4 7 8 15 1 2 16 5 3 10 11 9 12 13 14 6 45 38 90 102 5 1 12 16 7 3 8 10 2 14 4 11 9 6 15 13 13 9 86 103 5 1 13 15 2 9 8 4 6 16 3 10 12 7 14 11 40 33 88 104 5 1 16 12 3 4 15 10 2 7 8 14 6 9 11 13 68 53 78 105 5 2 11 16 4 8 6 3 12 13 1 15 10 9 14 7 14 10 80 106 5 2 13 14 7 1 12 9 3 10 4 15 6 8 16 11 23 18 82 107 5 3 11 15 4 8 7 2 13 12 1 16 9 10 14 6 63 49 78 108 6 1 12 15 2 7 10 5 3 16 4 8 11 9 13 14 48 41 94 109 6 1 13 14 3 8 9 4 5 16 2 10 11 7 15 12 44 37 90 110 7 1 12 14 4 5 11 6 2 15 3 9 8 10 13 16 21 16 94 111 7 3 9 15 4 2 13 6 1 14 5 8 11 10 16 12 42 35 98 112 8 4 6 16 1 3 14 7 2 11 10 5 12 15 9 13 41 34 98
Sol.# |------- Cell value ---- Upper case indicates points -------| Comple Pair Point Remarks # A b c D e f G h I j K l M n O P ment # total 1 1 3 16 14 2 13 5 11 15 7 10 4 9 12 6 8 75 1 68 2 1 3 16 14 5 8 7 11 13 4 12 2 9 15 6 10 81 2 72 3 1 3 16 14 7 8 5 15 11 10 6 4 9 13 2 12 82 3 60 4 1 5 12 16 3 11 4 10 15 7 9 2 13 8 6 14 5 4 78 Adjacent complement pair 5 1 5 12 16 9 6 3 15 11 10 4 7 8 14 2 13 4 4 58 6 1 5 13 15 3 14 2 16 11 12 8 4 6 9 7 10 66 5 60 7 1 5 13 15 7 8 4 14 11 10 6 2 12 9 3 16 19 6 68 8 1 5 13 15 8 7 4 14 11 3 12 2 6 16 9 10 64 7 68 9 1 5 13 15 8 7 4 14 11 9 6 2 12 10 3 16 28 8 68 10 1 5 13 15 10 7 2 16 11 9 4 6 8 14 3 12 65 9 56 11 1 7 11 15 4 3 12 6 9 8 13 5 10 14 2 16 37 10 78 12 1 7 11 15 10 3 6 8 13 2 9 5 12 16 4 14 69 11 74 13 1 7 14 12 10 9 3 8 16 2 6 5 15 13 4 11 29 12 68 14 1 7 15 11 5 8 10 3 14 2 13 6 12 16 4 9 88 13 74 15 1 7 15 11 6 9 8 16 3 13 12 4 2 14 5 10 103 14 52 16 1 7 16 10 2 13 9 3 15 5 12 8 11 14 4 6 74 15 68 17 1 8 11 14 2 5 13 6 7 10 15 4 9 12 3 16 36 16 78 18 1 8 12 13 10 7 4 6 16 3 5 9 14 15 2 11 20 17 66 19 1 9 8 16 12 4 2 10 13 3 6 7 11 15 5 14 7 6 68 20 1 9 11 13 10 7 4 5 16 2 6 8 15 14 3 12 18 17 70 21 1 9 11 13 12 3 6 15 4 8 10 2 7 14 5 16 55 18 62 22 1 9 13 11 7 4 12 10 3 8 16 2 6 15 5 14 30 19 68 23 1 9 14 10 3 15 6 12 7 8 16 4 2 13 11 5 47 20 58 24 1 9 16 8 2 14 10 11 4 13 15 5 3 12 6 7 76 21 54 25 1 9 16 8 4 12 10 2 13 3 14 7 11 15 5 6 89 22 68 26 1 10 7 16 5 9 4 14 6 8 15 2 3 11 12 13 27 23 70 Adjacent complement pair 27 1 10 7 16 6 8 4 15 5 9 14 3 2 12 11 13 26 23 66 28 1 10 7 16 12 4 2 9 13 3 6 8 11 15 5 14 9 8 68 29 1 10 9 14 8 7 5 3 16 4 6 12 13 15 2 11 13 12 68 30 1 10 9 14 8 7 5 13 6 4 16 2 3 15 12 11 22 19 68 31 1 10 11 12 14 2 6 13 5 7 8 4 9 15 3 16 48 24 60 32 1 10 16 7 6 13 8 2 14 3 11 9 12 15 4 5 84 25 62 33 1 11 7 15 5 6 8 12 3 10 16 4 2 13 9 14 39 26 68 34 1 11 12 10 16 5 3 14 6 8 4 7 9 15 2 13 94 27 48 35 1 11 15 7 5 14 8 12 3 10 16 4 2 13 9 6 38 28 52 36 1 12 5 16 9 6 3 15 4 11 10 7 2 13 8 14 17 16 58 37 1 12 6 15 9 3 7 11 4 13 8 10 5 14 2 16 11 10 58 38 1 12 7 14 6 5 9 3 10 2 16 4 11 13 8 15 35 28 84 39 1 12 7 14 6 5 9 11 2 10 16 4 3 13 8 15 33 26 68 40 1 12 10 11 15 3 5 13 4 9 6 8 7 16 2 14 85 29 50 41 1 12 11 10 16 6 2 15 5 9 4 7 8 14 3 13 95 30 46 42 1 12 13 8 4 15 7 6 9 10 11 14 3 16 5 2 105 31 46 43 1 12 13 8 4 16 6 7 9 11 10 14 3 15 5 2 110 32 44 44 1 12 15 6 8 16 4 13 5 11 10 9 2 14 7 3 111 33 38 45 1 12 16 5 7 14 8 11 3 15 9 10 4 13 2 6 112 34 38 46 1 12 16 5 13 14 2 9 11 3 7 8 10 15 6 4 108 35 46 47 1 13 5 15 4 9 6 3 12 2 16 8 7 14 11 10 23 20 78 48 1 13 6 14 10 2 8 4 9 3 12 7 11 15 5 16 31 24 76 49 1 13 8 12 16 4 2 10 9 3 6 7 11 15 5 14 87 36 60 50 1 13 9 11 14 5 4 15 2 8 10 6 3 16 7 12 104 37 50 51 1 13 11 9 4 15 6 5 10 8 12 14 3 16 7 2 97 38 50 52 1 13 14 6 9 15 4 5 12 3 10 11 8 16 7 2 99 39 50 53 1 13 16 4 8 12 10 2 9 3 14 7 11 15 5 6 86 40 60 54 1 13 16 4 14 11 5 10 6 2 12 3 9 15 8 7 98 41 52 55 1 14 3 16 8 6 4 5 11 2 13 9 7 15 10 12 21 18 74 56 1 14 7 12 10 8 4 11 5 13 6 15 2 16 3 9 100 42 42 57 1 14 11 8 16 6 4 13 3 10 5 9 7 15 2 12 102 43 42 58 1 14 12 7 6 8 13 5 2 11 15 10 4 16 3 9 72 44 54 59 1 14 12 7 15 8 4 5 11 2 6 10 13 16 3 9 91 45 54 60 1 14 13 6 8 16 4 5 11 3 12 10 7 15 9 2 101 46 52 61 1 15 7 11 12 9 2 4 13 3 6 14 10 16 5 8 92 47 56 62 1 15 14 4 8 12 10 3 6 9 11 13 7 16 2 5 106 48 46 63 1 15 14 4 11 12 7 3 9 6 8 13 10 16 2 5 109 49 46 64 2 4 12 16 1 10 7 15 8 14 11 3 5 9 6 13 8 7 68 65 2 4 12 16 3 10 5 11 14 8 9 1 13 7 6 15 10 9 80 66 2 4 12 16 8 3 7 13 10 5 11 1 9 14 6 15 6 5 76 67 2 4 16 12 6 7 9 8 13 5 10 1 15 11 3 14 70 50 78 68 2 5 16 11 1 13 9 6 14 4 15 3 10 12 8 7 79 51 76 69 2 6 10 16 1 14 3 12 13 15 5 9 8 7 4 11 12 11 62 70 2 6 12 14 1 16 3 10 15 13 5 11 8 9 4 7 67 50 58 71 2 6 16 10 3 12 9 14 5 15 11 1 8 7 4 13 93 52 62 72 2 7 12 13 1 6 14 5 8 9 16 3 10 11 4 15 58 44 82 73 2 7 14 11 3 15 5 16 6 12 13 1 4 8 10 9 96 53 60 74 2 10 14 8 4 15 7 1 16 3 11 9 13 12 6 5 16 15 68 75 2 10 15 7 13 6 8 5 11 1 9 4 16 14 3 12 1 1 68 76 2 12 6 14 5 4 11 1 10 3 16 8 9 15 7 13 24 21 82 77 2 12 9 11 16 3 4 8 10 1 7 6 13 15 5 14 90 54 66 78 2 13 11 8 16 7 3 6 12 1 5 9 14 15 4 10 83 55 58 79 2 14 11 7 5 13 9 1 10 4 15 12 6 16 8 3 68 51 60 80 2 14 15 3 13 12 6 5 9 1 11 8 10 16 7 4 107 56 52 81 3 1 14 16 2 9 7 15 11 13 8 6 5 12 4 10 2 2 64 82 3 1 14 16 4 9 5 13 15 7 8 2 11 10 6 12 3 3 76 83 3 2 16 13 6 8 7 10 15 4 9 1 14 11 5 12 78 55 78 84 3 7 15 9 4 11 10 1 16 2 12 8 13 14 5 6 32 25 74 85 3 9 7 15 8 1 10 4 11 2 13 5 12 14 6 16 40 29 86 86 3 9 14 8 4 15 7 5 13 1 16 2 11 10 12 6 53 40 76 87 3 10 9 12 14 2 6 7 11 1 8 4 15 13 5 16 49 36 76 88 3 10 14 7 9 12 6 2 16 1 8 11 13 15 5 4 14 13 62 89 3 10 15 6 2 14 12 1 11 5 16 8 9 13 7 4 25 22 68 90 3 11 8 12 16 2 4 9 10 1 7 5 13 14 6 15 77 54 70 91 4 1 15 14 5 7 8 9 16 3 10 2 13 12 6 11 59 45 82 92 4 2 13 15 8 5 6 10 16 1 9 3 12 14 7 11 61 47 80 93 4 5 10 15 11 1 7 14 8 3 12 2 6 16 9 13 71 52 74 94 4 10 5 15 9 2 8 3 13 1 11 6 14 12 7 16 34 27 88 95 4 10 6 14 8 3 9 2 13 1 12 5 15 11 7 16 41 30 90 96 4 14 5 11 10 1 12 2 6 3 15 9 8 16 7 13 73 53 76 97 5 3 12 14 1 9 10 6 15 2 16 4 8 13 11 7 51 38 86 98 5 3 15 11 4 7 12 6 13 1 16 2 10 14 9 8 54 41 84 99 5 4 12 13 2 8 11 3 16 1 15 6 10 14 9 7 52 39 86 100 5 7 9 13 6 3 12 4 11 2 15 1 14 10 8 16 56 42 94 101 5 7 12 10 2 14 8 4 15 1 16 3 11 9 13 6 60 46 84 102 5 8 6 15 7 2 10 4 12 1 14 3 13 11 9 16 57 43 94 103 5 11 4 14 10 1 9 8 6 2 16 3 7 13 12 15 15 14 84 104 5 11 8 10 9 1 14 2 7 3 15 4 13 12 6 16 50 37 86 105 6 3 11 14 1 7 12 4 15 2 16 5 9 13 10 8 42 31 90 106 6 4 14 10 1 8 15 3 12 5 16 2 13 9 7 11 62 48 90 107 6 4 16 8 3 12 11 5 14 2 15 1 13 9 10 7 80 56 84 108 6 5 8 15 3 4 12 1 16 2 13 9 11 14 7 10 46 35 90 109 7 1 11 15 3 4 12 5 16 2 13 6 10 14 8 9 63 49 90 110 7 3 10 14 2 6 12 4 15 1 16 5 9 13 11 8 43 32 92 111 7 8 4 15 3 6 10 2 14 1 16 5 11 9 13 12 44 33 98 112 8 7 6 13 4 2 15 1 11 3 16 5 12 10 9 14 45 34 98
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August 25, 2009
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