SUDOKU #9  
 

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.
 
    3 1       7 8      
              1   9    
    4     9         6  
    6       9       8  
      7           6    
    5       4       1  
    1         5     9  
      2   6            
        8 3       5 2  
 
This is a Evil difficulty puzzle (harder than Hard), 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 3 1       7 8      
  B           1   9    
  C 4     9         6  
  D 6       9       8  
  E   7           6    
  F 5       4       1  
  G 1         5     9  
  H   2   6            
  I     8 3       5 2  
  J K L M N O P Q R  
                         
There is a 9 in AL (because of CM and BQ). There is a 5 in HL (because of GO and IQ). There is a 6 in FO (because of DJ, EQ, and HM) and another 6 in AN (because of CR and HM).
         
  A 3 1 9   6 7 8        
  B           1   9      
  C 4     9         6    
  D 6       9       8    
  E   7           6      
  F 5       4 6     1    
  G 1         5     9    
  H   2 5 6              
  I     8 3       5 2    
    J K L M N O P Q R    
                             
There has to be a 4 in either AM or BM (because of CJ and FN). There has to be a 4 or 9 in HO and IO (because of the 4 in AM-BM and FN, and because of the 9s in CM and DN). There's an 8 and 9 in EJ and FK (because of AL, DN, DR, and IL).
             
  A 3 1 9   6 7 8        
  B           1   9      
  C 4     9         6    
  D 6       9       8    
  E 89 7           6      
  F 5 89     4 6     1    
  G 1         5     9    
  H   2 5 6   49          
  I     8 3   49   5 2    
    J K L M N O P Q R    
                         
There's a 2 in BJ (because of HK). So there is a 5 or 8 in BK and CK (because of HL and IL). That means that there is an 8 in EJ and a 9 in FK. And there's a 6 and 7 in BL and CL, which means there is a 6 in BL (because of CR) and a 7 in CL. The missing numbers in column J are the 7 and 9.
         
  A 3 1 9   6 7 8        
  B 2 58 6     1   9      
  C 4 58 7 9         6    
  D 6       9       8    
  E 8 7           6      
  F 5 9     4 6     1    
  G 1         5     9    
  H 79 2 5 6   49          
  I 79   8 3   49   5 2    
    J K L M N O P Q R    
                         
There is a 9 in EP (because of FK, DN, and GR). There's an 8 in FM (because of DR and EJ) and another one in CO (because of FM). That means there is an 8 in BK and a 5 in CK. There's a 2 and a 3 in DO and EO. There's a 7 in DM (because of AO and EK).
         
  A 3 1 9   6 7 8        
  B 2 8 6     1   9      
  C 4 5 7 9   8     6    
  D 6     7 9 23     8    
  E 8 7       23 9 6      
  F 5 9   8 4 6     1    
  G 1         5     9    
  H 79 2 5 6   49          
  I 79   8 3   49   5 2    
    J K L M N O P Q R    
                         
There's a 1 and a 5 in EM and EN. Therefore, there's a 5 in DP (because of EM/EN, FJ, and IQ), and there's a 1 in DL (because of EM/EN, FR, and AK).
         
  A 3 1 9   6 7 8          
  B 2 8 6     1   9        
  C 4 5 7 9   8     6      
  D 6   1 7 9 23 5   8      
  E 8 7   15 15 23 9 6        
  F 5 9   8 4 6     1      
  G 1         5     9      
  H 79 2 5 6   49            
  I 79   8 3   49   5 2      
    J K L M N O P Q R    
                         
The numbers missing from box GM-IO are 1, 2, 7, 8. There is a 1 in GJ and a 7 and 8 in column M, so there has to be a 2 in GM. That means that there has to be a 2 in CN (because of GM and DO/EO) and another 2 in AQ (because of IR, BJ, and CN).
         
  A 3 1 9   6 7 8 2      
  B 2 8 6     1   9      
  C 4 5 7 9 2 8     6    
  D 6   1 7 9 23 5   8    
  E 8 7   15 15 23 9 6      
  F 5 9   8 4 6     1    
  G 1     2   5     9    
  H 79 2 5 6   49          
  I 79   8 3   49   5 2    
    J K L M N O P Q R    
                         
There's a 3 in BN (because of AJ and IM). That means that there is a 4 and a 5 in AM and BM -- and AR, which means EM has to be a 1 and EN has to be a 5.
         
  A 3 1 9 45 6 7 8 2 45    
  B 2 8 6 45 3 1   9      
  C 4 5 7 9 2 8     6    
  D 6   1 7 9 23 5   8    
  E 8 7   1 5 23 9 6      
  F 5 9   8 4 6     1    
  G 1     2   5     9    
  H 79 2 5 6   49          
  I 79   8 3   49   5 2    
    J K L M N O P Q R    
                         
The numbers missing from row D are the 2, 3, and 4, but there is a 2 in HK and AQ, so the 2 has to be in DO -- which means the 3 is in EO. There's another 2 in FP (because of IR and AQ). So there is a 2 in EL and a 4 in ER. That means there is a 4 in DK, a 3 in DQ, a 4 in ER, a 7 in FQ, a 3 in FL, and a 4 in GL.
         
  A 3 1 9 45 6 7 8 2 45    
  B 2 8 6 45 3 1   9      
  C 4 5 7 9 2 8     6    
  D 6 4 1 7 9 2 5 3 8    
  E 8 7 2 1 5 3 9 6 4    
  F 5 9 3 8 4 6 2 7 1    
  G 1   4 2   5     9    
  H 79 2 5 6   49          
  I 79   8 3   49   5 2    
    J K L M N O P Q R    
                         
Wow! There is a 3 in IM, so a 3 has to be in GK. That means a 6 is in IK, which means a 6 is in GP (because of HM and EQ).
         
  A 3 1 9 45 6 7 8 2 45    
  B 2 8 6 45 3 1   9      
  C 4 5 7 9 2 8     6    
  D 6 4 1 7 9 2 5 3 8    
  E 8 7 2 1 5 3 9 6 4    
  F 5 9 3 8 4 6 2 7 1    
  G 1 3 4 2   5 6   9    
  H 79 2 5 6   49          
  I 79 6 8 3   49   5 2    
    J K L M N O P Q R    
                         
There's a 4 in ER, so there has to be a 5 in AR, a 4 in AM, and a 5 in BM. There is a 5 in BP (because of CJ and ER), so there is a 7 in BR and a 3 in HR.
         
  A 3 1 9 4 6 7 8 2 5    
  B 2 8 6 5 3 1 4 9 7    
  C 4 5 7 9 2 8     6    
  D 6 4 1 7 9 2 5 3 8    
  E 8 7 2 1 5 3 9 6 4    
  F 5 9 3 8 4 6 2 7 1    
  G 1 3 4 2   5 6   9    
  H 79 2 5 6   49     3    
  I 79 6 8 3   49   5 2    
    J K L M N O P Q R    
                         
There is a 3 in CP (because of DQ) and a 1 in CQ. There's a 7 in GN (because of FQ), an 8 in GQ, and a 4 in HQ. That means there is a 4 in IO, a 9 in HO, a 7 in HJ, and a 9 in IJ.
         
  A 3 1 9 4 6 7 8 2 5    
  B 2 8 6 5 3 1 4 9 7    
  C 4 5 7 9 2 8 3 1 6    
  D 6 4 1 7 9 2 5 3 8    
  E 8 7 2 1 5 3 9 6 4    
  F 5 9 3 8 4 6 2 7 1    
  G 1 3 4 2 7 5 6 8 9    
  H 7 2 5 6   9   4 3    
  I 9 6 8 3   4   5 2    
    J K L M N O P Q R    
                         
That means there is a 7 in IP, a 1 in HP, a 1 in IN, and an 8 in HN.
         
  A 3 1 9 4 6 7 8 2 5    
  B 2 8 6 5 3 1 4 9 7    
  C 4 5 7 9 2 8 3 1 6    
  D 6 4 1 7 9 2 5 3 8    
  E 8 7 2 1 5 3 9 6 4    
  F 5 9 3 8 4 6 2 7 1    
  G 1 3 4 2 7 5 6 8 9    
  H 7 2 5 6 8 9 1 4 3    
  I 9 6 8 3 1 4 7 5 2    
    J K L M N O P Q R    
 
 
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