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Solving Mosaic Puzzles

The table side

0-s and 9-ers are obvious, but 4-s in a corner, or 6-es at the table side are easier to miss. Look for them.

4             0
               
4     6     0  
4             0
               
4     6     0  

What a difference a difference makes

While a hard GraphiLogic puzzle is mostly about addition: calculating sums, a difficult Mosaic puzzle is more about subtraction. When numbers in two adjacent cells are having a difference of 3, it means something. It isn't obvious at first (well, not after second... :) ), but as 6 of their cells are common, the difference of 3 means that the cells adjacent to the bigger number only must be all set, while the cells adjacent to the smaller number only must be all clear.

               
    5 2        
               
               
    5 2        
               

The same goes for adjacent numbers with a difference of 2 at the table sides, or bordered by empty cells or already set cells:

  4 2          
          7 5  
               
  4 2          
          7 5  
               

This difference calculation goes on, depending on the number of undetermined cells on the two sides of the adjacent numbers, the proper difference sets and clears them, respectively. This rule can be applied to numbers adjacent on corners only, but less common circumstances must be met for those to make a conclusion:

       
    6  
  2    
      0
       
    6  
  2    
      0
This case, the difference between "6" and "2" is 4. The "6" has 5 cells, which is not common with the "2", but one of them is already cleared. All its remaining 4 undetermined cells must be set, to make the difference. After setting these, we have 4 set cells. The remaining 2 to set are common with the "2", which means that "2" has no private set cells, so we can clear them.


  

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