|
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 labelsThe 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! = 3072However, 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".
Last Modified: 2008/04/19 08:20:15
Brought to you by: R.K. Owen,Ph.D.
This page is http://owen.sj.ca.us/rkowen/howto/sudoku2x2bad.html
