3 posts
• Page **1** of **1**

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

- qwerty
**Posts:**4**Joined:**06 December 2005

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

Count all solutions to this, then multiply by 24*2*2.

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.

- kjellfp
**Posts:**140**Joined:**04 October 2005

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.

But there are only 2 essentially different grids !

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

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

- coloin
**Posts:**1638**Joined:**05 May 2005

3 posts
• Page **1** of **1**