SUDOKU #2  
 

I'm going to repeat the info at the top of Sudoku #1, just in case you haven't seen that one yet.
 
I've been doing Sudoku for a while. There are a lot of people like me who have figured out some tricks or techniques that help them complete the puzzles. This page is not really for them. I met a woman recently who was just starting to try to do Sudoku. This page is for people like her. I'm not saying that I know every single trick, but I know enough to complete most puzzles.
 
The basic rules of Sudoku are that there is only one of each number in each row, column, and 9 square grid. There isn't any mathematics or arithmetic. If you know how to count from 1 to 9, then you can do these puzzles. All of the techniques are based on this rule.
 
Here is a sample Sudoku puzzle.
 
    1       9 6 2   5  
            8     6    
        6 3     4 7    
    6   8   5       4  
            2          
    2       3   7   6  
      1 4     9 3      
      5     4          
    3   9 2 7       1  
 
This is a medium difficulty puzzle, and it will allow me to show some examples of a few of the tricks that I've uncovered. I've added the letters below to the rows and columns in order to talk about each of the 81 squares. As a convention, I will talk about squares and boxes. There are 81 squares, but there are 9 boxes of 9 squares.
     
  A 1       9 6 2   5  
  B         8     6    
  C     6 3     4 7    
  D 6   8   5       4  
  E         2          
  F 2       3   7   6  
  G   1 4     9 3      
  H   5     4          
  I 3   9 2 7       1  
  J K L M N O P Q R  
                         
The first technique that I will use is the lines of influence concept. This is what I mean. There is a 1 at AJ and another at IR, so there can't be another 1 in row A or column R. So there has to be a 1 at BP.
         
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3     4 7      
  D 6   8   5       4    
  E         2            
  F 2       3   7   6    
  G   1 4     9 3        
  H   5     4            
  I 3   9 2 7       1    
    J K L M N O P Q R    
                             
There is a 4 in columns P and R, and there are 4s in rows G and H, so there has to be a 4 at IQ.
             
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3     4 7      
  D 6   8   5       4    
  E         2            
  F 2       3   7   6    
  G   1 4     9 3        
  H   5     4            
  I 3   9 2 7     4 1    
    J K L M N O P Q R    
                         
There is a 2 in column J and another in row I, so there has to be a 2 in HL.
         
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3     4 7      
  D 6   8   5       4    
  E         2            
  F 2       3   7   6    
  G   1 4     9 3        
  H   5 2   4            
  I 3   9 2 7     4 1    
    J K L M N O P Q R    
                         
There is a 3 in columns M and N, and there is a 3 in row I, so there has to be a 3 at HO.
         
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3     4 7      
  D 6   8   5       4    
  E         2            
  F 2       3   7   6    
  G   1 4     9 3        
  H   5 2   4 3          
  I 3   9 2 7     4 1    
    J K L M N O P Q R    
                         
There is a 6 in columns J and L, so there has to be a 6 in IK. There is a 6 in columns Q and R, and now there is a 6 in row I, so there has to be a 6 in HP. There is a 6 in column O, so there has to be a 6 in EM. The final 6 goes in GN. So there has to be a 1 in CN.
         
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3 1   4 7      
  D 6   8   5       4    
  E       6 2            
  F 2       3   7   6    
  G   1 4   6 9 3        
  H   5 2   4 3 6        
  I 3 6 9 2 7     4 1    
    J K L M N O P Q R    
                         
There is a 2 in rows E and F, and there is a 2 in column P, so there has to be a 2 in DQ. There is a 2 in columns P and Q, and there is a 2 in row H, so there has to be a 2 in GR.
         
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3 1   4 7      
  D 6   8   5     2 4    
  E       6 2            
  F 2       3   7   6    
  G   1 4   6 9 3   2    
  H   5 2   4 3 6        
  I 3 6 9 2 7     4 1    
    J K L M N O P Q R    
                         
There is a 3 in row F and in column P, so the 3 in box DP-FR is either in EQ or ER. That means that there can't be a 3 in row E in the other two boxes to the left. There already is one in the center box in row F, so the one in box DJ-FL has to be in row D at square DK.
         
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3 1   4 7      
  D 6 3 8   5     2 4    
  E       6 2            
  F 2       3   7   6    
  G   1 4   6 9 3   2    
  H   5 2   4 3 6        
  I 3 6 9 2 7     4 1    
    J K L M N O P Q R    
                         
There is a 7 in row I and one in column Q, so there has to be a 7 in HR. That means that there is a 7 in GJ, which leaves the 8 in HJ.
         
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3 1   4 7      
  D 6 3 8   5     2 4    
  E       6 2            
  F 2       3   7   6    
  G 7 1 4   6 9 3   2    
  H 8 5 2   4 3 6   7    
  I 3 6 9 2 7     4 1    
    J K L M N O P Q R    
                         
There is a 9 in rows G and I, so there has to be a 9 in HQ and therefore a 1 in HM.
         
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3 1   4 7      
  D 6 3 8   5     2 4    
  E       6 2            
  F 2       3   7   6    
  G 7 1 4   6 9 3   2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7     4 1    
    J K L M N O P Q R    
                         
Now look at row D. The numbers missing are 1, 7 and 9. There is a 1 in column M and P, so the 1 has to be in DO.
         
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3 1   4 7      
  D 6 3 8   5 1   2 4    
  E       6 2            
  F 2       3   7   6    
  G 7 1 4   6 9 3   2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7     4 1    
    J K L M N O P Q R    
                         
So there are two squares left in row D. One is a 7, and the other is a 9. One of the basic rules of Sudoku is that there can be only one of each number in each 9-square box. Do you see the 7 in square FP? That makes it impossible for the 7 to be in DP, so it has to be in DM, and the 9 has to be in DP.
         
  A 1       9 6 2   5    
  B         8   1 6      
  C     6 3 1   4 7      
  D 6 3 8 7 5 1 9 2 4    
  E       6 2            
  F 2       3   7   6    
  G 7 1 4   6 9 3   2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7     4 1    
    J K L M N O P Q R    
                         
There is a 7 in column M and row C, so there has to be a 7 in BO. There is a 2 in column M, so the 2 that's missing from box AM-CO has to be in CO.
         
  A 1       9 6 2   5    
  B         8 7 1 6      
  C     6 3 1 2 4 7      
  D 6 3 8 7 5 1 9 2 4    
  E       6 2            
  F 2       3   7   6    
  G 7 1 4   6 9 3   2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7     4 1    
    J K L M N O P Q R    
                         
That leaves the 4 and 5 missing from box AM-CO. That means there can't be a 4 or a 5 in any other square in column M. Now look at box GM-IO. The two missing numbers there are 5 and 8. So based on our knowledge of column M, the 5 has to be in IO. That means that there has to be an 8 in IP and GM, and there has to be a 5 in GQ.
         
  A 1       9 6 2   5    
  B         8 7 1 6      
  C     6 3 1 2 4 7      
  D 6 3 8 7 5 1 9 2 4    
  E       6 2            
  F 2       3   7   6    
  G 7 1 4 8 6 9 3 5 2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7 5 8 4 1    
    J K L M N O P Q R    
                         
We already know that the 4 and 5 missing from column M would be in rows A and B, so there has to be a 9 in FM. Another way to see this is to notice that there is a 9 in columns N and O. There is only one other square in column M where the 9 could be. A third way to see this is that there are 3 open squares in column M. The missing numbers are 4, 5 and 9. The 9 is already in box AM-CO, so it has to go in FM. This is a good thing to do while you are working on a puzzle. Use multiple techniques to confirm that you haven't made a mistake.
         
  A 1       9 6 2   5    
  B         8 7 1 6      
  C     6 3 1 2 4 7      
  D 6 3 8 7 5 1 9 2 4    
  E       6 2            
  F 2     9 3   7   6    
  G 7 1 4 8 6 9 3 5 2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7 5 8 4 1    
    J K L M N O P Q R    
                         
But there is a 5 in AR, so the 5 in column M has to be in BM -- which means the 4 is in AM. There is a 5 missing from row C, but there is a 5 in column K, so there must be a 5 in CJ. There is a 5 in EP (the only missing number in column P). That means that there is a 5 in FL (because there is a 5 in HK).
         
  A 1     4 9 6 2   5    
  B       5 8 7 1 6      
  C 5   6 3 1 2 4 7      
  D 6 3 8 7 5 1 9 2 4    
  E       6 2   5        
  F 2   5 9 3   7   6    
  G 7 1 4 8 6 9 3 5 2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7 5 8 4 1    
    J K L M N O P Q R    
                         
There are 1s in column A (AJ) and column K (GK), so there has to be a 1 in EL. That means that there has to be a 1 in FQ.
         
  A 1     4 9 6 2   5    
  B       5 8 7 1 6      
  C 5   6 3 1 2 4 7      
  D 6 3 8 7 5 1 9 2 4    
  E     1 6 2   5        
  F 2   5 9 3   7 1 6    
  G 7 1 4 8 6 9 3 5 2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7 5 8 4 1    
    J K L M N O P Q R    
                         
The numbers missing from box DP-FR are 3 and 8, and the ones missing from DM-FO are 4 and 8, so there has to be an 8 in FO, which means that there is a 4 in EO and FK.
         
  A 1     4 9 6 2   5    
  B       5 8 7 1 6      
  C 5   6 3 1 2 4 7      
  D 6 3 8 7 5 1 9 2 4    
  E     1 6 2 5 5        
  F 2 5 5 9 3 8 7 1 6    
  G 7 1 4 8 6 9 3 5 2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7 5 8 4 1    
    J K L M N O P Q R    
                         
The numbers missing from column L are the 3 and 7, but there is a 7 in row B, so there must be a 7 in AL, and the 3 is in BL. That means that a 3 is in AQ, which means that there is an 8 in EQ and a 3 in ER.
         
  A 1   7 4 9 6 2 3 5    
  B     3 5 8 7 1 6      
  C 5   6 3 1 2 4 7      
  D 6 3 8 7 5 1 9 2 4    
  E     1 6 2 5 5 8 3    
  F 2 5 5 9 3 8 7 1 6    
  G 7 1 4 8 6 9 3 5 2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7 5 8 4 1    
    J K L M N O P Q R    
                         
The only number missing from row A is an 8 which is in AK, but there is an 8 in BN, so there has to be an 8 in CR, which means that a 9 is in BR, which means that a 9 is in CK, which means that a 9 is in EJ, which means that a 7 is in EK. There has to be a 2 in BK, and a 4 has to be in BJ.
         
  A 1 8 7 4 9 6 2 3 5    
  B 4 2 3 5 8 7 1 6 9    
  C 5 9 6 3 1 2 4 7 8    
  D 6 3 8 7 5 1 9 2 4    
  E 9 7 1 6 2 5 5 8 3    
  F 2 5 5 9 3 8 7 1 6    
  G 7 1 4 8 6 9 3 5 2    
  H 8 5 2 1 4 3 6 9 7    
  I 3 6 9 2 7 5 8 4 1    
    J K L M N O P Q R    
                             
 
 
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