Sudoku Assistant - The Sudoku Trainer and Solver

Cell Colouring

The technique that has become known as Cell Colouring is about making connections between cells that can take a particular value, and the potential consequences that might be found in a Sudoku puzzle.

The 'chain' is made up from cells that can take a particular value, where there are only two cells in that region (row, column or subgrid) that can take the value. We assign each cell in the chain one of two colours by alternating them... the idea is that when there are only two possible locations for a value in a region, only one of them can take the value... here's an example for symbol 3:

We start with the cell near the top-left, and colour it red. There are three possible locations for the value in the row and the subgrid, so we can not continue the chain in those regions... but there is only one other candidate cell for 3 on the column, so the chain can continue there. We move down to that cell, and colour it blue. In this example, our next step is within the subgrid, then along the row, and so on. We continue until we find a key indicator; the two red flags on the same row.

Remember, we don't know if reds are 3 or blues are 3 - but one or the other must be true. Now, if we have two cells with the same colour in a region, we know that they can't both be the value we are interested in. So, in this example, Blue cells must be 3, and Red cells can not.

3   3   3        
    3     3      
    3   3        
3         3      

Suggested Exercise: Using the grid above, find an alternative chain of cells for 3 that has the same (or a very similar) result.

In addition to examples like the one above, where the result of finding the chain leads to the ability to set one or more cells; there are chains that can result in the ability to remove a candidate value:

    2       2    
  2         2    

The chain of cells for value 2 does not contain any direct inconsistencies as before, but you may notice that the candidate cell [2,5], whilst not in the chain itself, is on the same column as a red-flagged cell, and the same row as a blue-flagged cell. Even though we don't know which colour flag will take the value 2, we know that one of them has to be... so whichever way, 2 can be removed from the candidates for the cell (or cells) that are in the intersection of the influence regions of the red and blue cells.


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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