SUDOKU #14  
 

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. It might be good to just print out this grid and write in the numbers as I go. There may be times when I do more numbers in one step than can be followed just by looking at the webpage.
 
                       
                9 2    
      9     6 4   5    
        8 4   3 6      
        4 6   5 2      
        2 1   7 5      
      6   2 5     8    
      7 1              
                       
 
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                    
  B             9 2    
  C   9     6 4   5    
  D     8 4   3 6      
  E     4 6   5 2      
  F     2 1   7 5      
  G   6   2 5     8    
  H   7 1              
  I                    
  J K L M N O P Q R  
                         
There is a 6 in FJ (because of DP, EM, and GK). The numbers missing from box DM-FO are 2, 8, and 9. There is a 2 in DN (because of FL and EP). There is a 2 in AO (because of GM, DN, and BQ). There is another 2 in CJ (because of AO, BQ, and FL), and another one in IK (because of CJ and FL). The final 2 is in HR (because of BQ, EP, GM, and IK).
         
  A           2          
  B             9 2      
  C 2 9     6 4   5      
  D     8 4 2 3 6        
  E     4 6 89 5 2        
  F 6   2 1 89 7 5        
  G   6   2 5     8      
  H   7 1           2    
  I   2                  
    J K L M N O P Q R    
                             
There is a 7 and a 9 in DJ and EJ (because of CK and HK), so the numbers missing from column K in box DJ-FL are a 1, 3, and 5. But there is a 1 in FM and a 5 in FP, so there is a 3 in FK, a 1 in EK (because of EO), and the 5 goes in DK.
             
  A           2          
  B             9 2      
  C 2 9     6 4   5      
  D 79 5 8 4 2 3 6        
  E 79 1 4 6 89 5 2        
  F 6 3 2 1 89 7 5        
  G   6   2 5     8      
  H   7 1           2    
  I   2                  
    J K L M N O P Q R    
                         
There is a 9 in AM (because of CK, BP, and EN-FN). There is a 5 in BM (because of CQ, EO, and GN). There is another 5 in IR (because of CQ, FP, and GN). So there is a 5 in HJ (because of GN and IR) and another 5 in AL (because of BM, CQ, DK, and HJ).
         
  A     5 9   2          
  B       5     9 2      
  C 2 9     6 4   5      
  D 79 5 8 4 2 3 6        
  E 79 1 4 6 89 5 2        
  F 6 3 2 1 89 7 5        
  G   6   2 5     8      
  H 5 7 1           2    
  I   2             5    
    J K L M N O P Q R    
                         
There is an 8 in IJ (because of GQ and DL). There is a 6 in BL (because of CN, GK, and FJ). There is another 6 in AR (because of GK, DP, BL, and CN). There is a 4 in GJ (because of EL).
         
  A     5 9   2     6    
  B     6 5     9 2      
  C 2 9     6 4   5      
  D 79 5 8 4 2 3 6        
  E 79 1 4 6 89 5 2        
  F 6 3 2 1 89 7 5        
  G 4 6   2 5     8      
  H 5 7 1           2    
  I 8 2             5    
    J K L M N O P Q R    
                         
There is a 7 in CL (because of HK and DJ-EJ), and there is another 7 in IM (because of CL, FO, and AN-BN).
         
  A     5 9   2     6      
  B     6 5     9 2        
  C 2 9 7   6 4   5        
  D 79 5 8 4 2 3 6          
  E 79 1 4 6 89 5 2          
  F 6 3 2 1 89 7 5          
  G 4 6   2 5     8        
  H 5 7 1           2      
  I 8 2   7         5      
    J K L M N O P Q R    
                         
The number missing from column N are 1, 3, 4, and 7, but there is a 1 and 7 in row H. So there is either a 3 or a 4 in HN. The numbers missing from column P are 1, 3, 4, 7, and 8, but there is a 1 and a 7 in row H, and there is an 8 in GQ. So HP has to be either a 3 or a 4. So there cannot be a 3 in HM. Therefore, an 8 has to be in HM and a 3 in CM.
         
  A     5 9   2     6    
  B     6 5     9 2      
  C 2 9 7 3 6 4   5      
  D 79 5 8 4 2 3 6        
  E 79 1 4 6 89 5 2        
  F 6 3 2 1 89 7 5        
  G 4 6   2 5     8      
  H 5 7 1 8 34   34   2    
  I 8 2   7         5    
    J K L M N O P Q R    
                         
There has to be either a 3 or a 4 in IN (because of CM and CO), so there has to be a 1 or a 7 in AN and BN. Therefore, there is an 8 in BO.
         
  A     5 9 17 2     6    
  B     6 5 17 8 9 2      
  C 2 9 7 3 6 4   5      
  D 79 5 8 4 2 3 6        
  E 79 1 4 6 89 5 2        
  F 6 3 2 1 89 7 5        
  G 4 6   2 5     8      
  H 5 7 1 8 34   34   2    
  I 8 2   7 34       5    
    J K L M N O P Q R    
                         
There is an 8 in AK (because of IJ and BO), and a 4 is in BK. There is an 8 in CP (because of GQ), and a 1 is in CR.
         
  A   8 5 9 17 2     6    
  B   4 6 5 17 8 9 2      
  C 2 9 7 3 6 4 8 5 1    
  D 79 5 8 4 2 3 6        
  E 79 1 4 6 89 5 2        
  F 6 3 2 1 89 7 5        
  G 4 6   2 5     8      
  H 5 7 1 8 34   34   2    
  I 8 2   7 34       5    
    J K L M N O P Q R    
                         
There is a 1 in DQ (because of CR, EK, and FM). There is a 4 in FR (because of BK, GR, EL, and DM). There is an 8 in FN (because of GQ), a 9 in EN and FQ). So there is a 7 in EJ and a 9 in DJ, and there is a 7 in DR.
         
  A   8 5 9 17 2     6    
  B   4 6 5 17 8 9 2      
  C 2 9 7 3 6 4 8 5 1    
  D 9 5 8 4 2 3 6 1 7    
  E 7 1 4 6 9 5 2        
  F 6 3 2 1 8 7 5 9 4    
  G 4 6   2 5     8      
  H 5 7 1 8 34   34   2    
  I 8 2   7 34       5    
    J K L M N O P Q R    
                         
The number missing from row E are a 3 and an 8. There is an 8 in ER and a 3 in EQ. The numbers missing from row H are a 6 and a 9, so the 9 is in HO (because of FQ), and the 6 is in HQ.
         
  A   8 5 9 17 2     6    
  B   4 6 5 17 8 9 2      
  C 2 9 7 3 6 4 8 5 1    
  D 9 5 8 4 2 3 6 1 7    
  E 7 1 4 6 9 5 2 3 8    
  F 6 3 2 1 8 7 5 9 4    
  G 4 6   2 5     8      
  H 5 7 1 8 34 9 34 6 2    
  I 8 2   7 34       5    
    J K L M N O P Q R    
                         
There is a 9 in GR (because of BP and FQ) and a 3 in BR. There is a 9 in IL (because of GR and HO) and a 3 in GL.
         
  A   8 5 9 17 2     6    
  B   4 6 5 17 8 9 2 3    
  C 2 9 7 3 6 4 8 5 1    
  D 9 5 8 4 2 3 6 1 7    
  E 7 1 4 6 9 5 2 3 8    
  F 6 3 2 1 8 7 5 9 4    
  G 4 6 3 2 5     8 9    
  H 5 7 1 8 34 9 34 6 2    
  I 8 2 9 7 34       5    
    J K L M N O P Q R    
                         
The numbers missing from box AP-CR are the 4 and the 7, so there has to be a 7 in BN and a 1 in AN. So there is a 1 in BJ (because of AN) and a 3 in AJ.
         
  A 3 8 5 9 1 2     6    
  B 1 4 6 5 7 8 9 2 3    
  C 2 9 7 3 6 4 8 5 1    
  D 9 5 8 4 2 3 6 1 7    
  E 7 1 4 6 9 5 2 3 8    
  F 6 3 2 1 8 7 5 9 4    
  G 4 6 3 2 5     8 9    
  H 5 7 1 8 34 9 34 6 2    
  I 8 2 9 7 34       5    
    J K L M N O P Q R    
                         
The numbers missing from column O are a 1 and a 6, but there is a 6 in GK. So the 6 is in IO and the 1 is in GO. Therefore, there is a 1 in IP.
         
  A 3 8 5 9 1 2     6    
  B 1 4 6 5 7 8 9 2 3    
  C 2 9 7 3 6 4 8 5 1    
  D 9 5 8 4 2 3 6 1 7    
  E 7 1 4 6 9 5 2 3 8    
  F 6 3 2 1 8 7 5 9 4    
  G 4 6 3 2 5 1   8 9    
  H 5 7 1 8 34 9 34 6 2    
  I 8 2 9 7 34 6 1   5    
    J K L M N O P Q R    
                         
The numbers missing from row I are a 3 and a 4, but there is a 3 in EQ. So there is a 4 in IQ, a 3 in IN, a 4 in HN, and a 3 in HP. There is a 7 in GP, a 4 in AP, a 7 in AQ.
         
  A 3 8 5 9 1 2 4 7 6    
  B 1 4 6 5 7 8 9 2 3    
  C 2 9 7 3 6 4 8 5 1    
  D 9 5 8 4 2 3 6 1 7    
  E 7 1 4 6 9 5 2 3 8    
  F 6 3 2 1 8 7 5 9 4    
  G 4 6 3 2 5 1 7 8 9    
  H 5 7 1 8 4 9 3 6 2    
  I 8 2 9 7 3 6 1 4 5    
    J K L M N O P Q R    
 
 
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