|
So instead of the full 3x3 Sudoku, let's examine the smaller and more tractable 2x2 sudoku, and start with the base solution and adopt a 0-based index labeling:
0 1 2 3 <- columns
a b c d <- internal labels
w 0 1 2 | 3 4
x 1 3 4 | 1 2
----+----
y 2 2 3 | 4 1
z 3 4 1 | 2 3
^ ^
| rows
internal labels
|
The set of operations are listed as the following where the operations are also assigned a 'bit' and the order of operations are performed from top to bottom (or from least value to greatest). This then gives each generated solution a "value" and permutation, where the permutation is of the symbols "1234".
| Operation | Bit Value | Explanation |
|---|---|---|
| swapRwx | 0x01 | swap rows 0 and 1 |
| swapRyz | 0x02 | swap rows 2 and 3 |
| swapCab | 0x04 | swap columns 0 and 1 |
| swapCcd | 0x08 | swap columns 2 and 3 |
| swapBR | 0x10 | swap block rows |
| swapBC | 0x20 | swap block columns |
| swapT | 0x40 | transpose around main diagonal |
The number of different combinations becomes:
(2 x 2 x 2) x (2 x 2 x 2) x 2 x 4!
= 27 x 4! = 3072
However, we shall find that this overcounts the number of solutions that can be generated by these operations by a factor of 16, and does not generate solutions that include the Christian Baune "flip".
Brought to you by: R.K. Owen,Ph.D.
This page is http://rkowen.owentrek.com/howto/sudoku2x2bad.html