Order-11 Magic Stars

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Introduction to Order-10 Cell designations & some of the features of Order-11 magic stars.
Order-11A List A partial list of the 53,528 basic solutions with solution #,
complement #, complement pair #, and point totals.
Order-11B List A partial list of the 75,940 basic solutions for this pattern.
Same information as for pattern A.
Order-11C List A partial list of the 53,528 basic solutions for this pattern.
Same information as for pattern A.
Order-11D List A partial list of the 75,940 basic solutions for this pattern.
Same information as for pattern A.
Related pages on this site Use the browser 'back' button to return here if you wish.
Definitions Review magic star definitions and general features.
Examples One example of each of 16 patterns, Orders 5 to 11.
Examples-2 One example of each of 14 patterns, Orders 12,13,14.

Introduction to Order-10

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 on a 200 Mhz Pentium Pro with 32 Megs. of  RAM.
Note the different times for 11A and 11C.
Programs were 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, which 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.
.

The first solutions for cell A equal to 2 to 12

  A=2 A=3 A=4 A=5 A=6 A=7 A=8 A=9 A=10 A=11 A=12
A 27224 39471 45778 49098 50985 52002 52654 53029 53242 53365 53445
B 41733 57547 65842 69882 72569 74077 74821 75284 75571 75743 75848
C 26306 38652 44915 48437 50552 51763 52554 52982 53193 53325 53445
D 41733 57547 65842 69882 72569 74077 74821 75284 75571 75743 75848

Note that lines B and D (above) are the same. Point names are also the same.

 

                     

Order-11A Partial List of Basic Solutions

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

                    

Order-11B Partial List of Basic Solutions

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  

                    

Order-11C Partial List of Basic Solutions

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  

                    

Order-11D Partial List of Basic Solutions

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  

This page was originally posted November 1998
It was last updated March 27, 2010
Harvey Heinz   harveyheinz@shaw.ca
Copyright 1998-2009 by Harvey D. Heinz