SUDOKU #10  
 

 
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       5          
              3 4   6  
    2   9         7    
                7 3    
    4 1     8     9 5  
      5 2              
      2         9   7  
    6   5 1            
            9       3  
 
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 1       5          
  B           3 4   6  
  C 2   9         7    
  D             7 3    
  E 4 1     8     9 5  
  F   5 2              
  G   2         9   7  
  H 6   5 1            
  I         9       3  
  J K L M N O P Q R  
                         
There's a 9 in AR (because of GP, EQ, and CL), another 9 in BM (because of AR, CL, and IN). There's a 5 in BJ (because of HL and FK) and another 5 in CP (because of BJ, AN, and ER).
         
  A 1       5       9    
  B 5     9   3 4   6    
  C 2   9       5 7      
  D             7 3      
  E 4 1     8     9 5    
  F   5 2                
  G   2         9   7    
  H 6   5 1              
  I         9       3    
    J K L M N O P Q R    
                             
There's a 3 in AP (because of DQ and IR) and another one in CK (because of AP and BO). The 3s in CK and IR mean there has to be a 3 in either GJ or GL, so there has to be a 3 in HN (because of IR, CK, and BO). There has to be a 9 in HK (because of GP and IN).
             
  A 1       5   3   9    
  B 5     9   3 4   6    
  C 2 3 9       5 7      
  D             7 3      
  E 4 1     8     9 5    
  F   5 2                
  G   2         9   7    
  H 6 9 5 1 3            
  I         9       3    
    J K L M N O P Q R    
                         
There is a 7 in HO. You can see that in two ways. First, the 7 in GR means the 7 in box GJ-IL has to be in row I. Second, the numbers missing in row H are 2, 4, 7, and 8. All but one of the squares of row H are in box GP-IR, but there is a 7 in GR, so the 7 has to be in HO.
         
  A 1       5   3   9    
  B 5     9   3 4   6    
  C 2 3 9       5 7      
  D             7 3      
  E 4 1     8     9 5    
  F   5 2                
  G   2         9   7    
  H 6 9 5 1 3 7          
  I         9       3    
    J K L M N O P Q R    
                         
The 4 in BP and the 6 in BR mean that there has to be a 4 and 6 in AK and AL, which means that a 7 and an 8 have to be in BK and BL. The 3 in DQ and 7 in DP mean that there has to be a 3 and 7 in EL and FJ. There is a 6, 8, and 9 in squares DJ-DL, so the 9 has to be in DJ (because of CL and HK).
         
  A 1 46 46   5   3   9    
  B 5 78 78 9   3 4   6    
  C 2 3 9       5 7      
  D 9 68 68       7 3      
  E 4 1 37   8     9 5    
  F 37 5 2                
  G   2         9   7    
  H 6 9 5 1 3 7          
  I         9       3    
    J K L M N O P Q R    
                         
There is a 9 in FO (because of BM, DJ, EQ, and IN). There's a 7 in AM (because of BK-BL, CQ, and HO) and another one in FN (because of AM, HO, and DP).
         
  A 1 46 46 7 5   3   9      
  B 5 78 78 9   3 4   6      
  C 2 3 9       5 7        
  D 9 68 68       7 3        
  E 4 1 37   8     9 5      
  F 37 5 2   7 9            
  G   2         9   7      
  H 6 9 5 1 3 7            
  I         9       3      
    J K L M N O P Q R    
                         
The 7 in FN means there is a 3 in FJ and a 7 in EL. The numbers missing from column J are a 7 and 8. The 7 in GR means there is a 7 in IJ and an 8 in GJ. The 7 in EL means there is a 7 in BK, an 8 in BL and DK, a 6 in DL and AK, and a 4 in AL.
         
  A 1 6 4 7 5   3   9    
  B 5 7 8 9   3 4   6    
  C 2 3 9       5 7      
  D 9 8 6       7 3      
  E 4 1 7   8     9 5    
  F 3 5 2   7 9          
  G 8 2         9   7    
  H 6 9 5 1 3 7          
  I 7       9       3    
    J K L M N O P Q R    
                         
There's a 4 in IK. There's a 3 in EM (because of DQ, FJ, and BO). There's a 3 in GL (because of IR) and a 1 in IL, a 1 in GQ (because of IL and HM), a 1 in CR (because of GQ), a 1 in FP (because of CR, HQ, and EK), a 1 in BN (because of AJ and CR), and a 1 in DO (because of EK, HM, and BN). That's all the 1s.
         
  A 1 6 4 7 5   3   9    
  B 5 7 8 9 1 3 4   6    
  C 2 3 9       5 7 1    
  D 9 8 6     1 7 3      
  E 4 1 7 3 8     9 5    
  F 3 5 2   7 9 1        
  G 8 2 3       9 1 7    
  H 6 9 5 1 3 7          
  I 7 4 1   9       3    
    J K L M N O P Q R    
                         
There's a 2 in AO, because the numbers missing from row C are the 4, 6, and 8. So there's an 8 in AQ, a 2 in BQ. The numbers missing from row E are a 2 and 6, but the 2 in AO means the 2 is in EP and the 6 is in EO.
         
  A 1 6 4 7 5 2 3 8 9    
  B 5 7 8 9 1 3 4 2 6    
  C 2 3 9       5 7 1    
  D 9 8 6     1 7 3      
  E 4 1 7 3 8 6 2 9 5    
  F 3 5 2   7 9 1        
  G 8 2 3       9 1 7    
  H 6 9 5 1 3 7          
  I 7 4 1   9       3    
    J K L M N O P Q R    
                         
The numbers missing from row G are 4, 5, and 6, so the numbers in IM and IO are the 2 and 8. The 2 has to be in IM (because of AO), and the 8 is in IO. There is an 8 in FR (because of DK and AQ).
         
  A 1 6 4 7 5 2 3 8 9    
  B 5 7 8 9 1 3 4 2 6    
  C 2 3 9       5 7 1    
  D 9 8 6     1 7 3      
  E 4 1 7 3 8 6 2 9 5    
  F 3 5 2   7 9 1   8    
  G 8 2 3       9 1 7    
  H 6 9 5 1 3 7          
  I 7 4 1 2 9 8     3    
    J K L M N O P Q R    
                         
There's an 8 in HP (because of IO, AQ, and FR), an 8 in CM (in EN and IO). There's a 6 in IP, and a 5 in IQ.
         
  A 1 6 4 7 5 2 3 8 9    
  B 5 7 8 9 1 3 4 2 6    
  C 2 3 9 8     5 7 1    
  D 9 8 6     1 7 3      
  E 4 1 7 3 8 6 2 9 5    
  F 3 5 2   7 9 1   8    
  G 8 2 3       9 1 7    
  H 6 9 5 1 3 7 8        
  I 7 4 1 2 9 8 6 5 3    
    J K L M N O P Q R    
                         
There's a 2 in DN (because of IM), a 6 in CN (because of EO), a 4 in CO. There's a 4 in GM, a 5 in GO, and a 6 in GM.
         
  A 1 6 4 7 5 2 3 8 9    
  B 5 7 8 9 1 3 4 2 6    
  C 2 3 9 8 6 4 5 7 1    
  D 9 8 6   2 1 7 3      
  E 4 1 7 3 8 6 2 9 5    
  F 3 5 2   7 9 1   8    
  G 8 2 3 6 4 5 9 1 7    
  H 6 9 5 1 3 7 8        
  I 7 4 1 2 9 8 6 5 3    
    J K L M N O P Q R    
                         
There's a 5 in DM (because of ER), a 4 in FM, a 6 in FQ, a 4 in DR, a 4 in HQ, and a 2 in HR.
         
  A 1 6 4 7 5 2 3 8 9    
  B 5 7 8 9 1 3 4 2 6    
  C 2 3 9 8 6 4 5 7 1    
  D 9 8 6 5 2 1 7 3 4    
  E 4 1 7 3 8 6 2 9 5    
  F 3 5 2 4 7 9 1 6 8    
  G 8 2 3 6 4 5 9 1 7    
  H 6 9 5 1 3 7 8 4 2    
  I 7 4 1 2 9 8 6 5 3    
    J K L M N O P Q R    
                         
 
 
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