18DEC98B.TXT
9 Jan 1999 by Marc Kummel aka Treebeard.
Contact mkummel@rain.org, http://www.treebeard.org/
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The stumper is problem 400 from Henry Ernest Dudeney _536 Puzzles & Curious 
Problems_.  The puzzle is to place all the numbers 1 to 12 on the pattern 
below, with one number on each character, so they add up to 26 in these 
seven different ways:

  * each of the two center columns ($@@$)
  * each of the two center rows    (#@@#)
  * the four $ (trees)   together
  * the four # (stars)   together
  * the four @ (wreaths) together

          $ $
        # @ @ #
        # @ @ #
          $ $

The first line of each group gives the tetrads that make up the solutions.
Then there are 0-3 solutions with different tetrads in the center position.
Each of these solutions is actually a family of 128 or 256 solutions since
the numbers can be rotated and exchanged in various ways.  For details, see
<http://www.rain.org/~mkummel/stumpers/18dec98.html>.

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< 1 >     12  11  2  1      10  9  4  3      8  7  6  5 

               10            9 
 7             11            2             6 
 8             1             12            5 
               4             3 


               12            11 
 7             9             4             6 
 8             3             10            5 
               2             1 


               12            11 
 9             7             6             4 
 10            5             8             3 
               2             1 

------------------------------------------------------------
< 2 >     12  11  2  1      10  8  5  3      9  7  6  4 

               11            12 
 9             8             3             6 
 7             5             10            4 
               2             1 


               11            12 
 10            7             4             5 
 8             6             9             3 
               2             1 

------------------------------------------------------------
< 3 >     12  11  2  1      10  7  6  3      9  8  5  4 

               7             10 
 9             11            1             5 
 8             2             12            4 
               6             3 


               11            12 
 9             6             3             8 
 5             7             10            4 
               2             1 


               12            11 
 7             8             5             6 
 10            4             9             3 
               2             1 

------------------------------------------------------------
< 4 >     12  11  2  1      10  7  5  4      9  8  6  3 

               12            11 
 9             7             4             6 
 8             5             10            3 
               2             1 


               12            11 
 10            3             8             5 
 7             9             6             4 
               2             1 

------------------------------------------------------------
< 5 >     12  10  3  1      11  9  4  2      8  7  6  5 

               11            9 
 7             10            3             6 
 8             1             12            5 
               4             2 


               12            10 
 7             9             4             6 
 8             2             11            5 
               3             1 


               12            10 
 9             6             7             4 
 11            5             8             2 
               3             1 

------------------------------------------------------------
< 6 >     12  10  3  1      11  8  5  2      9  7  6  4 

               8             11 
 9             10            1             6 
 7             3             12            4 
               5             2 


               10            12 
 9             8             2             7 
 6             5             11            4 
               3             1 


               12            10 
 11            4             6             5 
 8             7             9             2 
               3             1 

------------------------------------------------------------
< 7 >     12  10  3  1      11  7  6  2      9  8  5  4 

               10            12 
 9             7             2             8 
 5             6             11            4 
               3             1 


               10            12 
 11            5             4             6 
 7             8             9             2 
               3             1 

------------------------------------------------------------
< 8 >     12  10  3  1      11  6  5  4      9  8  7  2 

               12            10 
 9             6             4             7 
 8             5             11            2 
               3             1 


               12            10 
 11            2             8             5 
 6             9             7             4 
               3             1 

------------------------------------------------------------
< 9 >     12  9  4  1      11  10  3  2      8  7  6  5 

               11            3 
 7             4             9             6 
 8             1             12            5 
               10            2 


               9             12 
 8             10            2             6 
 7             3             11            5 
               4             1 


               9             12 
 11            7             5             3 
 10            6             8             2 
               4             1 

------------------------------------------------------------
< 10 >     12  9  4  1      11  8  5  2      10  7  6  3 

               11            8 
 7             9             4             6 
 10            1             12            3 
               5             2 


               12            9 
 7             8             5             6 
 10            2             11            3 
               4             1 


               12            9 
 8             7             6             5 
 11            3             10            2 
               4             1 

------------------------------------------------------------
< 11 >     12  9  4  1      11  7  6  2      10  8  5  3 

               9             12 
 10            6             2             8 
 5             7             11            3 
               4             1 


               9             12 
 11            5             3             7 
 6             8             10            2 
               4             1 

------------------------------------------------------------
< 12 >     12  9  4  1      11  7  5  3      10  8  6  2 

               12            9 
 8             7             5             6 
 10            3             11            2 
               4             1 


               12            9 
 7             8             6             5 
 11            2             10            3 
               4             1 

------------------------------------------------------------
< 13 >     12  9  3  2      11  10  4  1      8  7  6  5 

               11            10 
 8             9             3             6 
 7             2             12            5 
               4             1 


               12            9 
 8             1             11            6 
 7             10            4             5 
               3             2 


               12            9 
 10            5             7             4 
 11            6             8             1 
               3             2 

------------------------------------------------------------
< 14 >     12  9  3  2      11  8  6  1      10  7  5  4 

               8             11 
 10            9             2             5 
 7             3             12            4 
               6             1 


               9             12 
 10            8             1             7 
 5             6             11            4 
               3             2 


               12            9 
 11            4             5             6 
 8             7             10            1 
               3             2 

------------------------------------------------------------
< 15 >     12  9  3  2      11  6  5  4      10  8  7  1 

               12            9 
 10            5             4             7 
 8             6             11            1 
               3             2 


               12            9 
 11            1             8             6 
 5             10            7             4 
               3             2 

------------------------------------------------------------
< 16 >     12  8  5  1      11  10  3  2      9  7  6  4 
------------------------------------------------------------
< 17 >     12  8  5  1      11  9  4  2      10  7  6  3 

               9             11 
 10            8             1             7 
 6             5             12            3 
               4             2 


               12            5 
 7             4             9             6 
 10            2             11            3 
               8             1 


               12            8 
 9             6             7             4 
 11            3             10            2 
               5             1 

------------------------------------------------------------
< 18 >     12  8  5  1      11  7  6  2      10  9  4  3 

               11            7 
 9             8             5             4 
 10            1             12            3 
               6             2 


               12            8 
 9             7             6             4 
 10            2             11            3 
               5             1 

------------------------------------------------------------
< 19 >     12  8  4  2      11  9  5  1      10  7  6  3 

               9             11 
 10            8             2             6 
 7             4             12            3 
               5             1 


               8             12 
 10            9             1             6 
 7             5             11            3 
               4             2 

------------------------------------------------------------
< 20 >     12  8  4  2      11  7  5  3      10  9  6  1 

               7             11 
 10            2             8             6 
 9             12            4             1 
               5             3 


               8             12 
 10            3             7             6 
 9             11            5             1 
               4             2 

------------------------------------------------------------
< 21 >     12  7  6  1      11  10  3  2      9  8  5  4 

               7             12 
 9             10            2             5 
 8             3             11            4 
               6             1 


               7             12 
 11            8             4             3 
 10            5             9             2 
               6             1 

------------------------------------------------------------
< 22 >     12  7  6  1      11  9  4  2      10  8  5  3 

               9             11 
 10            7             1             8 
 5             6             12            3 
               4             2 


               7             12 
 10            9             2             5 
 8             4             11            3 
               6             1 


               12            7 
 11            3             8             4 
 9             5             10            2 
               6             1 

------------------------------------------------------------
< 23 >     12  7  6  1      11  8  5  2      10  9  4  3 

               8             11 
 10            6             1             9 
 4             7             12            3 
               5             2 


               7             12 
 10            5             2             9 
 4             8             11            3 
               6             1 


               7             12 
 11            4             3             8 
 5             9             10            2 
               6             1 

------------------------------------------------------------
< 24 >     12  7  6  1      11  8  4  3      10  9  5  2 

               12            6 
 10            3             8             5 
 9             4             11            2 
               7             1 


               12            6 
 11            2             9             4 
 8             5             10            3 
               7             1 

------------------------------------------------------------
< 25 >     12  7  5  2      11  10  4  1      9  8  6  3 

               10            11 
 9             7             2             8 
 6             5             12            3 
               4             1 


               7             12 
 9             10            1             6 
 8             4             11            3 
               5             2 


               12            7 
 11            3             8             4 
 10            6             9             1 
               5             2 

------------------------------------------------------------
< 26 >     12  7  5  2      11  8  6  1      10  9  4  3 

               11            8 
 10            7             5             4 
 9             2             12            3 
               6             1 


               12            7 
 10            1             11            4 
 9             8             6             3 
               5             2 


               7             12 
 11            4             3             8 
 6             10            9             1 
               5             2 

------------------------------------------------------------
< 27 >     12  7  5  2      11  8  4  3      10  9  6  1 

               8             11 
 10            2             5             9 
 6             12            7             1 
               4             3 


               7             12 
 9             3             8             6 
 10            11            4             1 
               5             2 

------------------------------------------------------------
< 28 >     12  7  4  3      11  9  5  1      10  8  6  2 

               12            7 
 8             1             11            6 
 10            9             5             2 
               4             3 


               12            7 
 9             2             10            5 
 11            8             6             1 
               4             3 

------------------------------------------------------------
< 29 >     12  7  4  3      11  8  6  1      10  9  5  2 

               11            6 
 10            4             7             5 
 9             3             12            2 
               8             1 


               7             12 
 8             10            2             6 
 11            5             9             1 
               4             3 

------------------------------------------------------------
< 30 >     12  7  4  3      11  8  5  2      10  9  6  1 

               11            8 
 9             7             4             6 
 10            3             12            1 
               5             2 


               12            7 
 10            2             5             9 
 6             8             11            1 
               4             3 


               12            7 
 11            1             6             8 
 5             9             10            2 
               4             3 

------------------------------------------------------------
< 31 >     12  6  5  3      11  10  4  1      9  8  7  2 

               11            10 
 9             6             3             8 
 7             5             12            2 
               4             1 

------------------------------------------------------------
< 32 >     12  6  5  3      11  9  4  2      10  8  7  1 

               11            9 
 10            6             3             7 
 8             5             12            1 
               4             2 


               12            6 
 11            1             10            4 
 9             8             7             2 
               5             3 

------------------------------------------------------------
75 groups total!