SUDOKU #11  
 
 

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.
 
          8       6 2  
            6       4  
                9   3  
        2 9     6 4    
      9   1   2   5    
      4 7     3 8      
    9   5              
    3       7          
    7 2       1        
 
This is a Hard 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       8       6 2  
  B         6       4  
  C             9   3  
  D     2 9     6 4    
  E   9   1   2   5    
  F   4 7     3 8      
  G 9   5              
  H 3       7          
  I 7 2       1        
  J K L M N O P Q R  
                         
There is a 2 in FQ (because of DL, EO, and AR), and a 9 in FR (because of EK and DM). There's a 3 in EP (because of CR), a 1 in DR (because of EM), and a 7 in ER.
         
  A       8       6 2    
  B         6       4    
  C             9   3    
  D     2 9     6 4 1    
  E   9   1   2 3 5 7    
  F   4 7     3 8 2 9    
  G 9   5                
  H 3       7            
  I 7 2       1          
    J K L M N O P Q R    
                             
There's a 7 in DO (because of FL, ER, and HN), and a 4 in EN (because of DQ and FK). There's an 8 in DN (because of FP). There's a 3 in DK (because of EP and HJ), so there's a 5 in DJ and a 1 in FJ (because of EM). There's a 6 in FM (because of BN) and a 5 in FN.
             
  A       8       6 2    
  B         6       4    
  C             9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5                
  H 3       7            
  I 7 2       1          
    J K L M N O P Q R    
                         
AL and BL have to be a 3 or a 9 (because of GJ/GJ, DK/EK, and CR/CP). GO and HO have to be the 6 and 8 (because of FM/AM and BN/DN).
         
  A     39 8       6 2    
  B     39   6       4    
  C             9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5     68          
  H 3       7 68          
  I 7 2       1          
    J K L M N O P Q R    
                         
So AO-CO are 4, 5, or 9. Therefore, AN, BM, CM, and CN have to be 1, 2, 3, and 7.
         
  A     39 8       6 2    
  B     39   6       4    
  C             9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5     68          
  H 3       7 68          
  I 7 2       1          
    J K L M N O P Q R    
                         
There's a 9 in IN (because of DM and GJ) and another 9 at HQ (because of GJ, IN, CP, and FR).
         
  A     39 8       6 2      
  B     39   6       4      
  C             9   3      
  D 5 3 2 9 8 7 6 4 1      
  E   9   1 4 2 3 5 7      
  F 1 4 7 6 5 3 8 2 9      
  G 9   5     68            
  H 3       7 68   9        
  I 7 2     9 1            
    J K L M N O P Q R    
                         
The numbers missing from column P are a 1, 2, 4, 5, and 7, but there's a 1, 2, and 7 in row I. So there's either a 4 or a 5 in IP, but the 5 in EQ means there is a 5 in either AP or BP. Therefore, the 4 is in IP.
         
  A     39 8       6 2    
  B     39   6       4    
  C             9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5     68          
  H 3       7 68   9      
  I 7 2     9 1 4        
    J K L M N O P Q R    
                         
There is a 4 in HL (because of FK and IP). There's a 4 in AO-CO, so there's a 4 in GM-IM, but the 4s in HL and IP force a 4 in GM. The 1 in IO means there has to be a 1 in GK/IK, so there is a 1 in CL (because of FJ and GK/IK).
         
  A     39 8       6 2    
  B     39   6       4    
  C     1       9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5 4   68          
  H 3   4   7 68   9      
  I 7 2     9 1 4        
    J K L M N O P Q R    
                         
The numbers missing from column N are 1, 2, and 3. There's a 1 in AN (because of EM, IO, and CL). The 3 in CR forces the 2 into CN, so the 3 goes into GN.
         
  A     39 8 1     6 2    
  B     39   6       4    
  C     1   2   9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5 4 3 68          
  H 3   4   7 68   9      
  I 7 2     9 1 4        
    J K L M N O P Q R    
                         
The numbers missing from HM and IM are a 2 and a 5, and the 2 in IK means the 5 is in IM and the 2 is in HM.
         
  A     39 8 1     6 2    
  B     39   6       4    
  C     1   2   9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5 4 3 68          
  H 3   4 2 7 68   9      
  I 7 2   5 9 1 4        
    J K L M N O P Q R    
                         
The numbers missing from column M are a 3 and a 7, but the 3 in CR means the 3 in column M has to be in BM, which means the 7 is in CM. So there is a 3 in AL and a 9 in BL.
         
  A     3 8 1     6 2    
  B     9 3 6       4    
  C     1 7 2   9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5 4 3 68          
  H 3   4 2 7 68   9      
  I 7 2   5 9 1 4        
    J K L M N O P Q R    
                         
There's a 9 in AO (because of BL and CP), a 4 in CO (because of BR), and a 5 in BO.
         
  A     3 8 1 9   6 2    
  B     9 3 6 5     4    
  C     1 7 2 4 9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5 4 3 68          
  H 3   4 2 7 68   9      
  I 7 2   5 9 1 4        
    J K L M N O P Q R    
                         
There's a 4 in AJ (because of BR, CO, and FK) a 2 in BJ (because of CN and IK).
         
  A 4   3 8 1 9   6 2    
  B 2   9 3 6 5     4    
  C     1 7 2 4 9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5 4 3 68          
  H 3   4 2 7 68   9      
  I 7 2   5 9 1 4        
    J K L M N O P Q R    
                         
The numbers missing from column R are a 5, 6, and 8. The 5s in GL and IM mean that the 5 in column R is in HR. The numbers missing from row I are a 3, 6, and 8, but there is a 3 in AL and CR. So the 3 has to be in IQ.
 
  A 4   3 8 1 9   6 2    
  B 2   9 3 6 5     4    
  C     1 7 2 4 9   3    
  D 5 3 2 9 8 7 6 4 1    
  E   9   1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5 4 3 68          
  H 3   4 2 7 68   9 5    
  I 7 2   5 9 1 4 3      
    J K L M N O P Q R    
                         
There are a series of squares where the only numbers that could be in them are a 6 or 8: CJ, EJ, EL, IL, IR, and GR -- along with GO and HO. So there should be a flood of numbers to put in soon.
 
  A 4   3 8 1 9   6 2    
  B 2   9 3 6 5     4    
  C 68   1 7 2 4 9   3    
  D 5 3 2 9 8 7 6 4 1    
  E 68 9 68 1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9   5 4 3 68     68    
  H 3   4 2 7 68   9 5    
  I 7 2 68 5 9 1 4 3 68    
    J K L M N O P Q R    
                         
The numbers missing from row H are a 1, 6, and 8, but the 6 in DP and the 8 in FP mean that the 1 has to be in HP. So HK has to be a 6 or an 8. HK and IL have to be the 6 or 8, so a 1 has to be in GK.
 
  A 4   3 8 1 9   6 2    
  B 2   9 3 6 5     4    
  C 68   1 7 2 4 9   3    
  D 5 3 2 9 8 7 6 4 1    
  E 68 9 68 1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9 1 5 4 3 68     68    
  H 3 68 4 2 7 68 1 9 5    
  I 7 2 68 5 9 1 4 3 68    
    J K L M N O P Q R    
                         
The numbers missing from column Q are a 1, 7, and 8. There's a 1 in BQ (because of HP and CL). There is a 7 in CM, so the 7 is in GQ and the 8 is in CQ.
 
  A 4   3 8 1 9   6 2    
  B 2   9 3 6 5   1 4    
  C 68   1 7 2 4 9 8 3    
  D 5 3 2 9 8 7 6 4 1    
  E 68 9 68 1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9 1 5 4 3 68   7 68    
  H 3 68 4 2 7 68 1 9 5    
  I 7 2 68 5 9 1 4 3 68    
    J K L M N O P Q R    
                         
Now we're cooking. The 8 in row C is in CQ, so there's a 6 in CJ, an 8 in EJ, a 6 in EL, an 8 in IL, a 6 in IR, an 8 in GR, a 6 in GO, and an 8 in HO.
 
  A 4   3 8 1 9   6 2    
  B 2   9 3 6 5   1 4    
  C 6   1 7 2 4 9 8 3    
  D 5 3 2 9 8 7 6 4 1    
  E 8 9 6 1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9 1 5 4 3 6   7 8    
  H 3   4 2 7 8 1 9 5    
  I 7 2 8 5 9 1 4 3 6    
    J K L M N O P Q R    
                         
There's a 6 in HK, a 2 in GP, and a 5 in CK.
 
  A 4   3 8 1 9   6 2    
  B 2   9 3 6 5   1 4    
  C 6 5 1 7 2 4 9 8 3    
  D 5 3 2 9 8 7 6 4 1    
  E 8 9 6 1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9 1 5 4 3 6 2 7 8    
  H 3 6 4 2 7 8 1 9 5    
  I 7 2 8 5 9 1 4 3 6    
    J K L M N O P Q R    
                         
There's an 8 in BK (because of AM), a 7 in AK, a 7 in BP (because of AK), and a 5 in AP.
 
  A 4 7 3 8 1 9 5 6 2    
  B 2 8 9 3 6 5 7 1 4    
  C 6 5 1 7 2 4 9 8 3    
  D 5 3 2 9 8 7 6 4 1    
  E 8 9 6 1 4 2 3 5 7    
  F 1 4 7 6 5 3 8 2 9    
  G 9 1 5 4 3 6 2 7 8    
  H 3 6 4 2 7 8 1 9 5    
  I 7 2 8 5 9 1 4 3 6    
    J K L M N O P Q R    
                         
 
 
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