SUDOKU #12  
 

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.
 
    9   7           6  
      2   1         8  
    1       7   4 9    
        9 4            
      3           7    
              8 3      
      1 5   6       9  
    3         5   1    
    2           6   3  
 
This is an 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 9   7           6  
  B   2   1         8  
  C 1       7   4 9    
  D     9 4            
  E   3           7    
  F           8 3      
  G   1 5   6       9  
  H 3         5   1    
  I 2           6   3  
  J K L M N O P Q R  
                         
There is a 7 in BP (because of AL, CN, and EQ). So there is a 7 in HR.
         
  A 9   7           6    
  B   2   1     7   8    
  C 1       7   4 9      
  D     9 4              
  E   3           7      
  F           8 3        
  G   1 5   6       9    
  H 3         5   1 7    
  I 2           6   3    
    J K L M N O P Q R    
                             
There is a 9 in EP (because of CQ, GR, and DL). There is a 1 in AP (because of CJ, BM, and HQ).
             
  A 9   7       1   6    
  B   2   1     7   8    
  C 1       7   4 9      
  D     9 4              
  E   3         9 7      
  F           8 3        
  G   1 5   6       9    
  H 3         5   1 7    
  I 2           6   3    
    J K L M N O P Q R    
                         
There is a 5 in IQ (because of GL and HO), a 5 in CR (because of IQ), and a 5 in DP (because of CR and IQ).
         
  A 9   7       1   6    
  B   2   1     7   8    
  C 1       7   4 9 5    
  D     9 4     5        
  E   3         9 7      
  F           8 3        
  G   1 5   6       9    
  H 3         5   1 7    
  I 2           6 5 3    
    J K L M N O P Q R    
                         
There is a 2 in AQ (because of BK), so there is a 3 in BQ.
         
  A 9   7       1 2 6    
  B   2   1     7 3 8    
  C 1       7   4 9 5    
  D     9 4     5        
  E   3         9 7      
  F           8 3        
  G   1 5   6       9    
  H 3         5   1 7    
  I 2           6 5 3    
    J K L M N O P Q R    
                         
There is an 8 in DQ (because of BR and FO). The numbers missing from column Q are a 4 and 6, but there is a 6 in GN. So the 6 is in FQ, and the 4 is in GQ. There is a 3 in CL (because of HJ, EK, and BQ).
         
  A 9   7       1 2 6      
  B   2   1     7 3 8      
  C 1   3   7   4 9 5      
  D     9 4     5 8        
  E   3         9 7        
  F           8 3 6        
  G   1 5   6     4 9      
  H 3         5   1 7      
  I 2           6 5 3      
    J K L M N O P Q R    
                         
There is a 1 and a 2 in EL and FL (because of CJ, GK, IJ, and BK). So there is an 8 in EJ (because of DQ and FO).
         
  A 9   7       1 2 6    
  B   2   1     7 3 8    
  C 1   3   7   4 9 5    
  D     9 4     5 8      
  E 8 3 12       9 7      
  F     12     8 3 6      
  G   1 5   6     4 9    
  H 3         5   1 7    
  I 2           6 5 3    
    J K L M N O P Q R    
                         
There is a 4 and a 5 in FJ and FK (because of DM and DP), so there is a 6 and a 7 in DJ and DK.
         
  A 9   7       1 2 6    
  B   2   1     7 3 8    
  C 1   3   7   4 9 5    
  D 67 67 9 4     5 8      
  E 8 3 12       9 7      
  F 45 45 12     8 3 6      
  G   1 5   6     4 9    
  H 3         5   1 7    
  I 2           6 5 3    
    J K L M N O P Q R    
                         
There is a 4 in ER (because of DM and FJ-FK).
         
  A 9   7       1 2 6    
  B   2   1     7 3 8    
  C 1   3   7   4 9 5    
  D 67 67 9 4     5 8      
  E 8 3 12       9 7 4    
  F 45 45 12     8 3 6      
  G   1 5   6     4 9    
  H 3         5   1 7    
  I 2           6 5 3    
    J K L M N O P Q R    
                         
We can treat FJ and FK as solved even though we don't know which square the 4 and 5 are actually in, so the number missing from row F are the 1, 2, 7, and 9. There has to be a 7 in FM (because of EQ-HR, DJ-DK, and CN), and there is a 9 in FN (because of DL and GR). There is a 1 and a 2 in EL and FL (which we've already established), but now we know that there is a 1 and a 2 in DR and FR.
         
  A 9   7       1 2 6    
  B   2   1     7 3 8    
  C 1   3   7   4 9 5    
  D 67 67 9 4     5 8 12    
  E 8 3 12       9 7 4    
  F 45 45 12 7 9 8 3 6 12    
  G   1 5   6     4 9    
  H 3         5   1 7    
  I 2           6 5 3    
    J K L M N O P Q R    
                         
There is a 9 in BO (because of AJ, CQ, and FN).
         
  A 9   7       1 2 6    
  B   2   1   9 7 3 8    
  C 1   3   7   4 9 5    
  D 67 67 9 4     5 8 12    
  E 8 3 12       9 7 4    
  F 45 45 12 7 9 8 3 6 12    
  G   1 5   6     4 9    
  H 3         5   1 7    
  I 2           6 5 3    
    J K L M N O P Q R    
                         
The numbers missing from row G are 2, 3, 7, and 8, but there is a 2, 3, and 8 in column J. So a 7 has to be in GJ. That means that there has to be a 7 in IO, a 7 in DK, and a 6 in DJ.
         
  A 9   7       1 2 6    
  B   2   1   9 7 3 8    
  C 1   3   7   4 9 5    
  D 6 7 9 4     5 8 12    
  E 8 3 12       9 7 4    
  F 45 45 12 7 9 8 3 6 12    
  G 7 1 5   6     4 9    
  H 3         5   1 7    
  I 2         7 6 5 3    
    J K L M N O P Q R    
                         
The 6s in AR and GN mean that there has to be a 6 in either CM or CO, which means there has to be a 6 in BL (because of AR, CM-CO, and DJ). And there has to be a 6 in HK (because of BL and IP).
         
  A 9   7       1 2 6    
  B   2 6 1   9 7 3 8    
  C 1   3   7   4 9 5    
  D 6 7 9 4     5 8 12    
  E 8 3 12       9 7 4    
  F 45 45 12 7 9 8 3 6 12    
  G 7 1 5   6     4 9    
  H 3 6       5   1 7    
  I 2         7 6 5 3    
    J K L M N O P Q R    
                         
The numbers missing from column L are a 4 and an 8 (assuming the 1 and 2 in EL and FL). So there has to be a 9 in IK. Therefore, there is a 9 in HM (because of IK, FN, and GR).
 
  A 9   7       1 2 6    
  B   2 6 1   9 7 3 8    
  C 1   3   7   4 9 5    
  D 6 7 9 4     5 8 12    
  E 8 3 12       9 7 4    
  F 45 45 12 7 9 8 3 6 12    
  G 7 1 5   6     4 9    
  H 3 6   9   5   1 7    
  I 2 9       7 6 5 3    
    J K L M N O P Q R    
                         
There is a 4 and a 5 in AK and BJ (because of CP and CR), so there is an 8 in CK.
 
  A 9 45 7       1 2 6    
  B 45 2 6 1   9 7 3 8    
  C 1 8 3   7   4 9 5    
  D 6 7 9 4     5 8 12    
  E 8 3 12       9 7 4    
  F 45 45 12 7 9 8 3 6 12    
  G 7 1 5   6     4 9    
  H 3 6   9   5   1 7    
  I 2 9       7 6 5 3    
    J K L M N O P Q R    
                         
Now we can see that there is a 4 or a 5 in BN, and there is a 2 or a 6 in CM and CO.
 
  A 9 45 7       1 2 6    
  B 45 2 6 1 45 9 7 3 8    
  C 1 8 3 26 7 26 4 9 5    
  D 6 7 9 4     5 8 12    
  E 8 3 12       9 7 4    
  F 45 45 12 7 9 8 3 6 12    
  G 7 1 5   6     4 9    
  H 3 6 48 9   5   1 7    
  I 2 9 48     7 6 5 3    
    J K L M N O P Q R    
                         
The numbers missing from row I are a 1, 4 and 8, but there is a 1 in BM and a 4 in DM. So there is an 8 in IM. Therefore, there is an 8 in HL and a 4 in IL, and there is a 1 in IN.
 
  A 9 45 7       1 2 6    
  B 45 2 6 1 45 9 7 3 8    
  C 1 8 3 26 7 26 4 9 5    
  D 6 7 9 4     5 8 12    
  E 8 3 12       9 7 4    
  F 45 45 12 7 9 8 3 6 12    
  G 7 1 5   6     4 9    
  H 3 6 8 9   5   1 7    
  I 2 9 4 8 1 7 6 5 3    
    J K L M N O P Q R    
                         
There is a 4 in HN (because of GP), so there is a 5 in BN, a 4 in BJ, a 5 in AK, a 4 in FK, and a 5 in FJ. There is a 4 in AO (because of HN and DM).
 
  A 9 5 7     4 1 2 6    
  B 4 2 6 1 5 9 7 3 8    
  C 1 8 3 26 7 26 4 9 5    
  D 6 7 9 4     5 8 12    
  E 8 3 12       9 7 4    
  F 5 4 12 7 9 8 3 6 12    
  G 7 1 5   6     4 9    
  H 3 6 8 9 4 5   1 7    
  I 2 9 4 8 1 7 6 5 3    
    J K L M N O P Q R    
                         
There is a 5 in EM (because of HO and BN). There's a 6 in EO (because of DJ and GN), so there is a 6 in CM and a 2 in CO.
 
  A 9 5 7     4 1 2 6    
  B 4 2 6 1 5 9 7 3 8    
  C 1 8 3 6 7 2 4 9 5    
  D 6 7 9 4     5 8 12    
  E 8 3 12 5   6 9 7 4    
  F 5 4 12 7 9 8 3 6 12    
  G 7 1 5   6     4 9    
  H 3 6 8 9 4 5   1 7    
  I 2 9 4 8 1 7 6 5 3    
    J K L M N O P Q R    
                         
The numbers missing from row E are a 1 and a 2, but there is a 1 in IN, so the 2 has to be in EN and the 1 in EL. So there is a 2 in FL, a 1 in FR, and a 2 in DR.
 
  A 9 5 7     4 1 2 6    
  B 4 2 6 1 5 9 7 3 8    
  C 1 8 3 6 7 2 4 9 5    
  D 6 7 9 4     5 8 2    
  E 8 3 1 5 2 6 9 7 4    
  F 5 4 2 7 9 8 3 6 1    
  G 7 1 5   6     4 9    
  H 3 6 8 9 4 5   1 7    
  I 2 9 4 8 1 7 6 5 3    
    J K L M N O P Q R    
                         
There is a 2 in GM and a 3 in GO, so there is a 3 in DN and AM. Therefore, there is an 8 in AN and a 1 in DO. And there is an 8 in GP and a 2 in HP.
 
  A 9 5 7 3 8 4 1 2 6    
  B 4 2 6 1 5 9 7 3 8    
  C 1 8 3 6 7 2 4 9 5    
  D 6 7 9 4 3 1 5 8 2    
  E 8 3 1 5 2 6 9 7 4    
  F 5 4 2 7 9 8 3 6 1    
  G 7 1 5 2 6 3 8 4 9    
  H 3 6 8 9 4 5 2 1 7    
  I 2 9 4 8 1 7 6 5 3    
    J K L M N O P Q R    
                         
 
 
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