Order-6 -- List of Basic Solutions

Star-6 Notes re: Basic Solutions List

 Solution number The 80 basic solutions appear in order, sorted by position A, then position B, then C, etc. Mutsumi Suzuki Set The 80 solutions are divided into 20 subsets of four. Each of the four solutions are related to the other three by simple translations. See 20 sets of 4. In general, these subsets are scattered throughout the range of 80 solutions. But one coincidence worth noting: 8D, 7D, 6D and 5D appear as index numbers 58 to 61. Solutions Value of each cell. Upper case cell names (in heading) indicate points. Complement # Complement pair # The solution number of the complement of each basic solution. And also the complement pair number . Note that solutions 1 and 2 form the first complement pair. There are 5 other adjacent pairs . Total sum of the 6 Points The total number of solutions with the points numbering to each value themselves form a palindromic pattern. Large triangle point sum The points of each large triangle (a, d, g & i, j, k) sum to the same value which is one-half the value of the total points. Pairs of points totaling 13 Every solution has one or two pairs of points, which sum to the same value. However, there are never three such pairs. H.E.Dudeney classes H.E.Dudeney classified the solutions on the basis of which sets of 2 or 3 pairs of cells sum to 13. However, most require rotation and/or reflection to normalize to my list of basic solutions. Lower case letters indicate degree of rotation required, Upper case R indicates reflection is required. Review classes (return here with your back button). H Groups Similar to Dudeney’s classification but involves all 12 cells and requires only 3 simple rules. Review H groups (return here with your back button). Last column A.c. = adjacent complement pair members, M.p. = Magic points, M.v. = Magic valleys.

Star-6 Basic Solutions, Sub-sets, Complements,

```                                                          Comple.    Pnts.Totl  Pnt
Sol. M.S. |---- Basic Solutions (Upper case = peaks)----| Sol. Pair  All  Each  Prs  H.E.D.  H
#    Set   A   b   c   D   e   f   G   h   i   J   K   L   #    #    Pnts Tri.  =13  Class  Group
1    1A    1   2  11  12   3   5   6  10   9   8   4   7   2    1    38    19    2   IIIbR  H-2  A.c.
2    2A    1   2  11  12   4   3   7   8  10   5   6   9   1    1    40    20    2   IIId   H-2  A.c.
3    3A    1   2  12  11   3   4   8   7  10   5   6   9  41    2    40    20    1   Ic     H-1
4    4A    1   2  12  11   4   5   6  10   9   7   3   8  42    3    36    18    1   Ic     H-1
5    5A    1   3  10  12   2   4   8   6  11   5   9   7   6    4    42    21    2   Ic     H-3  A.c.
6    6A    1   3  10  12   2   7   5   9  11   8   6   4   5    4    36    18    2   Ic     H-3  A.c.
7    7A    1   3  12  10   4   7   5  11   9   8   2   6  59    5    32    16    1   Ic     H-1
8    8A    1   4  10  11   5   3   7   6  12   2   9   8  45    6    38    19    1   IIeR   H-2
9    9A    1   4  11  10   2   9   5   8  12   7   6   3  62    7    32    16    2   Ib     H-2
10  10A    1   4  12   9   5   2  10   7   8   3   6  11  50    8    40    20    1   Ic     H-1
11  11A    1   5   8  12   3   2   9   6  10   4  11   7  12    9    44    22    2   Ic     H-3  A.c.
12   9B    1   5   8  12   3   7   4  11  10   9   6   2  11    9    34    17    2   Ic     H-3  A.c.
13   6B    1   5   9  11   4   8   3  10  12   7   6   2  49   10    30    15    2   Ib     H-2
14  12A    1   5  11   9   3   2  12   6   7   4   8  10  24   11    44    22    2   IIIb   H-2
15  13A    1   5  11   9   3   8   6  12   7  10   2   4  64   12    32    16    1   Ib     H-2
16   7B    1   5  11   9   6   8   3  12  10   7   2   4  73   13    26    13    1   Ib     H-2  M.p.
17  14A    1   5  12   8   2   6  10   4  11   3   9   7  71   14    38    19    1   Ic     H-1
18  15A    1   5  12   8   7   2   9  10   6   4   3  11  47   15    36    18    1   Ic     H-1
19   1B    1   6  10   9   7   8   2  11  12   5   4   3  74   16    24    12    1   IIa    H-2
20   4B    1   6  10   9   8   7   2  12  11   5   3   4  75   17    24    12    1   Ib     H-2
21  16A    1   6  11   8   2   7   9   4  12   3  10   5  70   18    36    18    2   Ib     H-2
22  17A    1   6  12   7   3   5  11   4  10   2   9   8  57   19    38    19    1   Ic     H-1
23  13B    1   6  12   7   4  10   5  11   9   8   2   3  77   20    26    13    1   Ic     H-1  M.p.
24   8B    1   7   6  12   8   2   4  10  11   3   9   5  14   11    34    17    2   IIId   H-2
25  18A    1   7   8  10   2   3  11   5   9   4  12   6  40   21    44    22    1   Ia     H-2
26  19A    1   7   8  10   4   3   9   5  11   2  12   6  36   22    40    20    1   Ia     H-2
27   2B    1   7   8  10   9   5   2  11  12   3   6   4  67   23    26    13    1   IIeR   H-2  M.p.
28  20A    1   7  10   8   3   6   9   4  12   2  11   5  56   24    36    18    2   Ib     H-2
29  17B    1   7  12   6   2   8  10   4  11   3   9   5  68   25    34    17    1   Ic     H-1
30   5B    1   8   6  11   7   5   3  10  12   4   9   2  53   26    30    15    2   Ib     H-2
31   3B    1   8   7  10   9   5   2  12  11   4   6   3  66   27    26    13    1   Ib     H-2  M.p.
32  20B    1   8  10   7   2   5  12   4   9   3  11   6  33   28    40    20    2   Ib     H-2  A.c.
33  16B    1   8  11   6   3   5  12   4   9   2  10   7  32   28    38    19    2   Ib     H-2  A.c.
34  14B    1   8  12   5   3   7  11   4  10   2   9   6  54   29    34    17    1   Ic     H-1
35  15B    1   8  12   5   4  11   6  10   9   7   3   2  80   30    24    12    1   Ic     H-1
36  19B    1   9   5  11   6   2   7   8  10   3  12   4  26   22    38    19    1   Ia     H-2
37  11B    1   9   6  10   7   4   5   8  12   2  11   3  52   31    32    16    2   Ib     H-2
38  12B    1   9  11   5   4  10   7   6  12   3   8   2  79   32    26    13    1   IIa    H-2  M.p.
39  10B    1   9  12   4   3  11   8   7  10   5   6   2  78   33    26    13    1   Ic     H-1  M.p.
40  18B    1  10   8   7   4   6   9   5  11   2  12   3  25   21    34    17    1   Ia     H-2
41   3D    2   1  11  12   3   6   5   9  10   8   4   7   3    2    38    19    1   Ic     H-1
42   4D    2   1  11  12   4   3   7   8   9   6   5  10   4    3    42    21    1   Ic     H-1
43   1D    2   1  12  11   3   4   8   7   9   6   5  10  44   34    42    21    2   IIId   H-2  A.c.
44   2D    2   1  12  11   4   6   5   9  10   7   3   8  43   34    36    18    2   IIIbR  H-2  A.c.
45  12D    2   3   9  12   1   7   6  10   8  11   5   4   8    6    40    20    1   IIc    H-2
46  18C    2   3  11  10   1   7   8   4  12   5   9   6  63   35    40    20    1   Ic     H-1
47  15D    2   3  11  10   6   1   9   8   7   4   5  12  18   15    42    21    1   Ic     H-1
48  11D    2   3  12   9   1  10   6   7  11   8   5   4  72   36    34    17    2   Ib     H-2
49   5C    2   4   8  12   1   3  10   5   9   6  11   7  13   10    48    24    2   Ia     H-2
50  10D    2   5   9  10   1   8   7  11   6  12   4   3  10    8    38    19    1   Ib     H-2
51  20D    2   5  12   7   1   8  10   3  11   4   9   6  69   37    38    19    2   Ib     H-2
52   9C    2   6   7  11   4   1  10   5   9   3  12   8  37   31    46    23    2   Ic     H-3
53   6C    2   6   8  10   3   1  12   5   7   4  11   9  30   26    48    24    2   Ia     H-2
54  14C    2   6  10   8   1   5  12   3   9   4  11   7  34   29    44    22    1   Ia     H-2
55  19C    2   6  11   7   1  10   8   4  12   5   9   3  76   38    34    17    1   Ic     H-1
56  16C    2   7   9   8   1   6  11   3  10   4  12   5  28   24    42    21    2   Ib     H-2
57  17D    2   8  10   6   1   7  12   3   9   4  11   5  22   19    40    20    1   Ia     H-2
58   8D    2   8  12   4   1  11  10   5   9   6   7   3  65   39    32    16    2   IIIe   H-2
59   7D    3   1  10  12   4   2   8   6   9   5   7  11   7    5    46    23    1   Ic     H-1
60   6D    3   1  12  10   2   6   8   4  11   5   7   9  61   40    42    21    2   Ic     H-3  A.c.
61   5D    3   1  12  10   2   9   5   7  11   8   4   6  60   40    36    18    2   Ic     H-3  A.c.
62  11C    3   2   9  12   1   5   8   4  11   6  10   7   9    7    46    23    2   Ia     H-2
63  18D    3   2  10  11   1   9   5   6  12   8   7   4  46   35    38    19    1   Ic     H-1
64  13C    3   2  10  11   5   1   9   6   8   4   7  12  15   12    46    23    1   Ic     H-1
65  12C    3   2  12   9   1   5  11   4   8   6   7  10  58   39    46    23    2   IIIaR  H-2
66   3C    3   4   8  11   1   2  12   5   6   7  10   9  31   27    52    26    1   Ia     H-2  M.v.
67   1C    3   4   8  11   2   1  12   6   5   7   9  10  27   23    52    26    1   IIaR   H-2  M.v.
68  17C    3   5  11   7   1   6  12   2   9   4  10   8  29   25    44    22    1   Ia     H-2
69  16D    3   5  12   6   1   8  11   2  10   4   9   7  51   37    40    20    2   Ib     H-2
70  20C    3   6   9   8   1   7  10   2  11   4  12   5  21   18    42    21    2   Ib     H-2
71  14D    3   7  11   5   1   8  12   2   9   4  10   6  17   14    40    20    1   Ia     H-2
72   9D    4   1  10  11   2   6   7   3  12   5   9   8  48   36    44    22    2   Ia     H-2
73   7C    4   2   8  12   3   1  10   5   7   6   9  11  16   13    52    26    1   Ia     H-2  M.v.
74   2C    4   3   7  12   1   2  11   5   6   8  10   9  19   16    54    27    1   IIaR   H-2
75   4C    4   3   7  12   2   1  11   6   5   8   9  10  20   17    54    27    1   Ia     H-2
76  19C    4   3   9  10   1   7   8   2  12   5  11   6  55   38    44    22    1   Ic     H-1
77  13D    5   1   9  11   3   2  10   4   7   6   8  12  23   20    52    26    1   Ia     H-2  M.v.
78  10C    5   2  10   9   1   4  12   3   6   7   8  11  39   33    52    26    1   Ia     H-2  M.v.
79   8C    5   3   7  11   1   4  10   2   9   6  12   8  38   32    52    26    1   IIf    H-2  M.v.
80  15C    6   1   9  10   2   3  11   4   5   8   7  12  35   30    54    27    1   Ia     H-2

M.p. = Magic points      M.v. = Magic valleys      A.c. = Adjacent complements```

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Last updated December 19, 2007
Harvey Heinz   harveyheinz@shaw.ca
Copyright © 1998 by Harvey D. Heinz