or has this been mentioned elsewhere ?
I wonder why I didn't already read about it or found it
earlier by myself.
It's so clear,obvious,beautiful,general,easy to implement,...
e.g. sudoku:
given a {1,2,3}^6 binary hypercubegrid with exactly
c ones (clues).
Place 81c further ones such that each of the 2dimensional planes
of varying (x1,x2),(x3,x4),(x5,x6),(x2,x4) contains
exactly 1 one.
this can be illustrated by a constraintdiagram,
the xi are the coordinates, edges are constraints=
planes spanned by two coordinates :
 Code: Select all
x1x2


x5  x3
\  /
\  /
x6 x4
sudoku,{1,2,3}^6={1,2,3,4,5,6,7,8,9}^3
(x1,x2):rows
(x3,x4):columns
(x5,x6):symbols
(x2,x4):blocks
each in base 3, with x2,x4,x6 being the less significant digits
in their twodigit base3numbers
Now see the diagrams of these variants:
(of course, when the graphs are isomorphic then the
problems are equivalent and vice versa)
 Code: Select all
x2x1
\ \
\ \
x5 \ x3
\ \ /
\ \ /
x6 x4
4sudoku,{1,2,3}^6
http://www.setbb.com/phpbb/viewtopic.php?t=57&mforum=sudoku
 Code: Select all
x1x2
x3 x6
\ /
\ /
x4 x5
latin squares,QCP,QWH {1,2,3}^6
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x1x2
/
/ 
x3/  x6
\  /
 \  /
x4 \x5
3doku,{1,2,3}^6
http://forum.enjoysudoku.com/viewtopic.php?t=44&postdays=0&postorder=asc&highlight=3doku+coloin&start=393&sid=e1a32d25184f22650f08704f608b2889
 Code: Select all
x5x6
 \ / 
 / \ 
x1x2x4x3
magic sudoku,{1,2,3}^6
http://forum.enjoysudoku.com/viewtopic.php?t=2082&sid=e2f5ec28e9ee56b4b9dbded15f47db87
 Code: Select all
x1x2 x5
 \ /  
 / \  
x3x4 x6
4dim sudoku,sudoku6{1,2,3}^6
http://magictour.free.fr/sudoku6
 Code: Select all
x4 x1
/  \
/  \
x5  x2
 /
 /
x3
minicube,{1,2,3}^5
 Code: Select all
x1 x2
/ 
/ 
x3  x6
 /
 /
x5
3*9 sudokuband,{1,2,3}^5
 Code: Select all
x1x2
 \
 \
x3  x6
\  /
\  /
x4 x5
3*3*9tower,{1,2,3}^6
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x1x2 x7
/ 
/  
x3/  x6 x8
\  /
 \  /
x4 \x5
9*9*9  Dioncube, {1,2,3}^8
http://forum.enjoysudoku.com/viewtopic.php?t=532&sid=8c16e3605e25c8a8629020087e87f683
this shows also that the 3*3 blocks are not just a puzzlespecific
creation but can be naturally interpreted as an additional dimension
which makes it more mathematical and maybe even applicable
to molecules or such.
Guenter
edit 2010/06/05
 Code: Select all
x1x2
/
/
x5 /  x3
\ /  /
\ /  /
x6x4
3ersudoku
(x1,x2):rows
(x3,x4):columns
(x5,x6):symbols
(x2,x4):blocks
write symbols in base 3, or 3 symbols only but in 3 colors,
different symbols and colors in minirows and minicolumns
81 nonattacking sudokurunners (moves inside 9*1*1 or 3*3*1 boxes) on a 9*9*9 board