Sudoku Assistant - The Sudoku Trainer and Solver

Cross-Hatching

Also known as Hidden Single

The Sudoku grid below demonstrates a classic example of the solving technique known as 'scanning'. For a particular value, in this case 8, we look at the cells that already have that value placed in them:

        8        
            8    
Y 2              
                 
    8            
                8
                 
                 
                 

We know that the rows and columns can not have another 8 on them, as this is the fundamental rule of Sudoku. We are concentrating on the top-left grid for this example, and to keep things as simple as possible, we only highlight these rows and columns in towards that subgrid. We look for subgrids where the cells that can not have the value on them (the cells coloured in pink), in conjunction with other cells that are already taken (like the cell marked with a 2) leaves only one possible cell that the value can exist on. In this case, the value 8 can only be placed in the green cell marked with a Y.

It is also worth noting that the 8 placed in the middle-right subgrid has no impact on the top-left corner grid.

Reminder: We have only highlighted the arrows and pink cells in the subgrid that we are demonstrating here. In practice, these arrows could be drawn left-and-right and up-and-down from each marked 8.

Suggested Exercise: Print-out this grid, and considering all the current 8's, work out which cells in the other subgrids might be able to have an 8 in them. If you prefer to, you could shade-in all the cells that can not be 8 to help you isolate the cells that might be.

Why Hidden Single?

This technique is known as a 'Hidden Single' because, if we were to write down all the places that each number is possible for each cell, in our example the list of possible values for cell Y would be {1,3,4,5,6,7,8,9}. However, all the other cells in that subgrid (excepting the cell with the 2 already set on it) have possible values of {1,3,4,5,6,7,9}. So, there is only one possible placement for value 8, but we have to find it by specifically considering that value. Compare and contrast this to the Counting / Naked Single technique that comes next!

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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