possible different 2x2 sudoku

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possible different 2x2 sudoku

Postby qwerty » Thu Jan 26, 2006 4:04 am

i was trying to find the number of possible 2x2 sudoku, but i dont know where to start. would someone help me out and tell me how this is done? thanks
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Postby kjellfp » Thu Jan 26, 2006 8:52 am

Simplify, then multiply.

Fix only one choice for the first box. All others contribute equally, and only corresponds to symbol permutation, 24 in total.

Then assume the elements in the first column in box 3 are sorted. That is because swapping them corresponds to swapping the two bottom rows, and gives equally many solutions.

Do the same with the top row in box 2. Hence, you only work with the grid

Code: Select all
+--+--+
|12|34|
|34|..|
+--+--+
|2.|..|
|4.|..|
+--+--+


Count all solutions to this, then multiply by 24*2*2.
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Postby coloin » Thu Jan 26, 2006 11:04 am

I suggessted "mortals" could do it here

http://forum.enjoysudoku.com/viewtopic.php?t=170&start=0&postdays=0&postorder=asc&highlight=
note I failed.
geoff wrote:A neat way of counting.

Consider grids of the type

AB | xx
Cx | xx
--------
xx | Dx
xx | x E

where A,B,C are different, D and E are different. There are 288 of these and each gives a unique solution. Therefore 288 solutions.


But there are only 2 essentially different grids !

http://www.setbb.com/phpbb/viewtopic.php?p=227&highlight=&mforum=sudoku#227
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