It involves distilling the puzzle into nine separate binary puzzles, so that the state of play for each number can be seen with clarity. Each grid deals with a particular digit and is concerned simply with whether each cell is or is not that number. The grids are binary in the sense that each cell is marked with a true/false value showing whether or not that digit is in that cell (or blank for "don't know yet"). I use a cross to mark false and a large dot for true.
The first negative aspect is that to do this entirely by hand is an awful lot of effort to prepare the nine grids and mark off all the initial possibilities. However, it is a mindless job easily carried out by a spreadsheet. Below is The Sunday Times Su Doku 6 distilled into its nine constituent binary puzzles:
The dots and crosses that have been added so far are by the application of basic sudoku assumptions alone, namely no repeats in a block, row, or column, coupled with the fact that a cell obviously cannot be a given digit if it is already known to be another digit.
Hidden Singles are very obvious using this notation. There is a glaringly obvious one in the centre block of grid 6, another in row 1 of grid 2, and yet another in grid 4.
X-Wing configurations are also very easily spotted. There is one in grid 6 (rows 1 and 3, columns 2 and 4).
Swordfish and Turbot configurations are relatively simple to find with the puzzle laid out like this as well.
Another technique that is particularly easy to implement with this notation is the elimination of candidates when a given digit can only occur in a particular row or column of a given block.
With a little effort some naked pairs can be located, but because these require cross-referencing between the grids they cannot be spotted with great ease. Naked triples are tougher to find, generally.
That is one of the interesting things I have found about this approach to solving sudokus. Some of the techniques considered to be higher-level (such as X-Wing and Swordfish) are actually much easier to implement than lower-level techniques (like naked pairs) that are more easily found using conventional notation.
This makes it of limited use as a solution method alone. (I eventually got stuck on the above sudoku on a very hard-to-spot triple.) But when solving tough puzzles, it would be an interesting approach to use this method in parallel with a conventional grid of candidates.
Does anyone use anything along these lines already?
