Sudoku Assistant - The Sudoku Trainer and Solver

Row and Column Limits

Sometimes known as Block and Row / Column Interaction

This is the first of several techniques that effect the possible values (pencil-marks or candidates) for cells, rather than resulting in filling a cell value in.

Now, sometimes when looking at the possible placement of a value in a subgrid, you may notice that the value can only exist in just one row or column. If you find this circumstance, then you can remove that number from possible values from all other cells in that row or column (but outside the particular subgrid of course).

Let's look at an example:

The positioning of the 2 in the top-left subgrid, in addition to the placement of other values in the top-right subgrid, means that 2 can only be placed in the first column of that grid (column 7 of the puzzle). As the 2 must be in column 7 in subgrid 3, we know that it can not be in column 7 on any other subgrid. We've indicated that 2 can therefore be removed from candidate values in the green cells marked with an x.

            2 1 3
            2 4 5
  2              
            x    
            x    
            x    
            x    
            x    
            x    

The grid below shows another couple of situations that you might look for:

  3              
            7 8 9
      x x x 3 3 3
                 
                 
                 
1 2 3            
                 
4 5 6            

The first example with a 3 as the significant value shows how cause and effect can 'loop-back' - with the green cells marked x being able to have 3 removed from the possible values. The green cells are not shown in the top-left subgrid as there is already a 3 in there, so by implication it is already not possible for them to take that value.

The example in the bottom-left subgrid shows a scenario in which 7,8,9 values can only exist in row 8 simply by action of cells that have already been set in the subgrid. By now, we hope that you understand what the impact of this is likely to be!

Implications for Manual vs. Automated Solving

When using automated pencil-mark generation such as that available with Sudoku Assistant, these kinds of techniques are 'easy' in the sense that all cells that have not had a value set on them have a complete list of pencil marks of candidate values for the cell. Hence, it is very clear what the impact is and which cells need to have values removed from the pencil-marks. Sudoku Assistant has been programmed to identify such features of a puzzle, but only brings them to the attention of the user as hints if there is a consequence to it (i.e. you need to remove a possible value from one or more cells)!

But, when manually solving a puzzle, it is less likely that you will have exhaustively listed the possible values for each cell; so you may not have as good an idea of what the impact is. Sometimes, you will spot a row or column limit that has no impact at all, and sometimes you may simply need to keep a mental note that such a limit exists for possible use later.

 

If you are unsure of any of the terminology we use, you may find it helpful to refer to our Glossary.

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