SUDOKU #13  
 

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.
 
              6 9      
          1 5 7   8    
        8       7      
    9 6   5         7  
      5           3    
    8         9   4 1  
        6       2      
      1   3 7 8        
        3 2            
 
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           6 9      
  B       1 5 7   8    
  C     8       7      
  D 9 6   5         7  
  E   5           3    
  F 8         9   4 1  
  G     6       2      
  H   1   3 7 8        
  I     3 2            
  J K L M N O P Q R  
                         
There is a 5 in FP (because of EK and DM). There is a 1 in AQ or CQ (because of BM and FR), so there is a 1 in IP (because of AQ-CQ, FR, and HK). There is a 3 in GR (because of IL, HM, and EQ). That means there is a 3 in BP (because of GR and EQ).
         
  A           6 9        
  B       1 5 7 3 8      
  C     8       7        
  D 9 6   5         7    
  E   5           3      
  F 8         9 5 4 1    
  G     6       2   3    
  H   1   3 7 8          
  I     3 2     1        
    J K L M N O P Q R    
                             
There is a 9 in ER (because of DJ, FO, and AP). There's a 4 in HP (because of FQ). There's a 6 in EP (because of DK), and the 8 is in EP. There's a 2 in DQ.
             
  A           6 9        
  B       1 5 7 3 8      
  C     8       7        
  D 9 6   5     8 2 7    
  E   5         6 3 9    
  F 8         9 5 4 1    
  G     6       2   3    
  H   1   3 7 8 4        
  I     3 2     1        
    J K L M N O P Q R    
                         
There's a 3 in FK (because of IL and EQ). There's a 6 in IN (because of GL and AO), so there's a 6 in FM (because of IN, AO, DK, and EP).
         
  A           6 9        
  B       1 5 7 3 8      
  C     8       7        
  D 9 6   5     8 2 7    
  E   5         6 3 9    
  F 8 3   6   9 5 4 1    
  G     6       2   3    
  H   1   3 7 8 4        
  I     3 2 6   1        
    J K L M N O P Q R    
                         
There is a 7 in EM (because of BO and HN) and another 7 in FL (because of DR and EM), so there is a 2 in FN (the last number missing from row F) and CO (because of FN and IM). There's an 8 in EN (because of DP and HO). There is an 8 in AM (because of EN and CL).
         
  A       8   6 9        
  B       1 5 7 3 8      
  C     8     2 7        
  D 9 6   5     8 2 7    
  E   5   7 8   6 3 9    
  F 8 3 7 6 2 9 5 4 1    
  G     6       2   3    
  H   1   3 7 8 4        
  I     3 2 6   1        
    J K L M N O P Q R    
                         
This is where I got stuck for a while. Then I noticed that there is a 1, 3, and 5 in row B and another set in column K. That means that squares AJ, CJ, and AL have to be the 1, 3, and 5 in box AJ-CK. So there has to be a 7 in AK (because of BO and CP, and because the AJ-AL-CJ are the 1,3,5). Similar logic can be used to see that there is a 6 in BJ (because of DK and GL).
         
  A   7   8   6 9          
  B 6     1 5 7 3 8        
  C     8     2 7          
  D 9 6   5     8 2 7      
  E   5   7 8   6 3 9      
  F 8 3 7 6 2 9 5 4 1      
  G     6       2   3      
  H   1   3 7 8 4          
  I     3 2 6   1          
    J K L M N O P Q R    
                         
The 2 in row H is in either HJ or HL (because of GP and IM), and there is a 2 in either EJ or EL (because of DQ). So there is a 2 in BK (because of CO), which means there is a 2 in AR (because of BK, CO, and DQ).
         
  A   7   8   6 9   2    
  B 6 2   1 5 7 3 8      
  C     8     2 7        
  D 9 6   5     8 2 7    
  E   5   7 8   6 3 9    
  F 8 3 7 6 2 9 5 4 1    
  G     6       2   3    
  H   1   3 7 8 4        
  I     3 2 6   1        
    J K L M N O P Q R    
                         
There is a 9 in BL (because of AP and CM-CN), so there is a 4 in BR. The 9 in FO means there is a 9 in either GM or GN, so there is a 9 in IK (because of GM-GN, DJ, and BL).
         
  A   7   8   6 9   2    
  B 6 2 9 1 5 7 3 8 4    
  C     8     2 7        
  D 9 6   5     8 2 7    
  E   5   7 8   6 3 9    
  F 8 3 7 6 2 9 5 4 1    
  G     6       2   3    
  H   1   3 7 8 4        
  I   9 3 2 6   1        
    J K L M N O P Q R    
                         
The numbers missing from column K are a 4 and an 8. There is an 8 in CL, so the 8 is in GK and the 4 is in CK. There is a 4 in AN (because of CK), and therefore there is a 4 in GM and a 9 in CM and another 9 in GN (because of FO). There is a 3 in CN and a 1 in DN. There is an 8 in IR (because of GK, HO, and BQ).
         
  A   7   8 4 6 9   2    
  B 6 2 9 1 5 7 3 8 4    
  C   4 8 9 3 2 7        
  D 9 6   5 1   8 2 7    
  E   5   7 8   6 3 9    
  F 8 3 7 6 2 9 5 4 1    
  G   8 6 4 9   2   3    
  H   1   3 7 8 4        
  I   9 3 2 6   1   8    
    J K L M N O P Q R    
                         
There is a 3 in AJ (because of IL and CN) and another 3 in DO (because of EQ). So there is a 4 in CO and another 4 in DL.
         
  A 3 7   8 4 6 9   2    
  B 6 2 9 1 5 7 3 8 4    
  C   4 8 9 3 2 7        
  D 9 6 4 5 1 3 8 2 7    
  E   5   7 8 4 6 3 9    
  F 8 3 7 6 2 9 5 4 1    
  G   8 6 4 9   2   3    
  H   1   3 7 8 4        
  I   9 3 2 6   1   8    
    J K L M N O P Q R    
                         
There is a 4 in IJ (because of GM and HP). There's a 1 in GO (because of HK and IP), which means there is a 5 in IO and a 7 in IQ. There is a 7 in GJ (because of IQ and HN). There is a 5 in GQ.
         
  A 3 7   8 4 6 9   2    
  B 6 2 9 1 5 7 3 8 4    
  C   4 8 9 3 2 7        
  D 9 6 4 5 1 3 8 2 7    
  E   5   7 8 4 6 3 9    
  F 8 3 7 6 2 9 5 4 1    
  G 7 8 6 4 9 1 2 5 3    
  H   1   3 7 8 4        
  I 4 9 3 2 6 5 1 7 8    
    J K L M N O P Q R    
                         
There is a 5 in CR (because of GQ). This means that there is a 5 in AL, a 1 in CJ, a 1 in AQ, a 6 into CQ. There is a 9 in HQ and a 6 in HR.
         
  A 3 7 5 8 4 6 9 1 2    
  B 6 2 9 1 5 7 3 8 4    
  C 1 4 8 9 3 2 7 6 5    
  D 9 6 4 5 1 3 8 2 7    
  E   5   7 8 4 6 3 9    
  F 8 3 7 6 2 9 5 4 1    
  G 7 8 6 4 9 1 2 5 3    
  H   1   3 7 8 4 9 6    
  I 4 9 3 2 6 5 1 7 8    
    J K L M N O P Q R    
                         
There is a 1 in EL, a 2 in EJ, a 2 in HL, and a 5 in HJ.
         
  A 3 7 5 8 4 6 9 1 2    
  B 6 2 9 1 5 7 3 8 4    
  C 1 4 8 9 3 2 7 6 5    
  D 9 6 4 5 1 3 8 2 7    
  E 2 5 1 7 8 4 6 3 9    
  F 8 3 7 6 2 9 5 4 1    
  G 7 8 6 4 9 1 2 5 3    
  H 5 1 2 3 7 8 4 9 6    
  I 4 9 3 2 6 5 1 7 8    
 
 
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