SUDOKU #5  
 

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.
 
    7   8 9       2    
      1   7            
        6   5   1      
    2   4 1            
      6           3    
              8 4   9  
        3   6   5      
              5   8    
      5       3 9   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 7   8 9       2    
  B   1   7            
  C     6   5   1      
  D 2   4 1            
  E   6           3    
  F           8 4   9  
  G     3   6   5      
  H           5   8    
  I   5       3 9   1  
  J K L M N O P Q R  
                         
There is a 1 in FQ (because of CP, IR, and DM).
         
  A 7   8 9       2      
  B   1   7              
  C     6   5   1        
  D 2   4 1              
  E   6           3      
  F           8 4 1 9    
  G     3   6   5        
  H           5   8      
  I   5       3 9   1    
    J K L M N O P Q R    
                             
Notice that there is a 1 and a 9 in row I and column M. That means that HN and GO have to be the 1 and 9 in the box GM-IO. That leaves 4 open squares in that box. One of those squares is IN. Sometimes when there are a lot of numbers filled in in a column, you can find the number in a square like IN. The 7 in BM does that for us. It forces a 7 to be in IN.
             
  A 7   8 9       2      
  B   1   7              
  C     6   5   1        
  D 2   4 1              
  E   6           3      
  F           8 4 1 9    
  G     3   6   5        
  H           5   8      
  I   5     7 3 9   1    
    J K L M N O P Q R    
                         
Since there is a 1 and a 9 in HN and GO, the missing numbers in box GM-IO are 2, 4, 8. There is also an 8 in FO and AL. That means that there has to be an 8 in BN.
 
Notice the 2 in DJ. It means that there is a 2 in either EP or ER, which means that there is a 2 in either FM or FN. But there is a 2 somewhere in GM-IM, so there has to be a 2 in FN. Now notice the 6 in EK. It means that there is a 6 in DP-DR, so there has to be a 6 in FM.
         
  A 7   8 9       2      
  B   1   7 8            
  C     6   5   1        
  D 2   4 1              
  E   6           3      
  F       6 2 8 4 1 9    
  G     3   6   5        
  H           5   8      
  I   5     7 3 9   1    
    J K L M N O P Q R    
                         
There is a 5 in EM (because of CN and HO). Since the 2, 4, and 8 are in GM-IM, there has to be a 3 in CM. So there is a 3 in DN (because of IO and EQ).
         
  A 7   8 9       2      
  B   1   7 8            
  C     6 3 5   1        
  D 2   4 1 3            
  E   6   5       3      
  F       6 2 8 4 1 9    
  G     3   6   5        
  H           5   8      
  I   5     7 3 9   1    
    J K L M N O P Q R    
                         
There is an 8 in CR (because of AL, BN, and HQ), and there is a 7 in CQ (because of AJ and BM). There is a 9 in BQ (because of IP and FR).
         
  A 7   8 9       2      
  B   1   7 8     9      
  C     6 3 5   1 7 8    
  D 2   4 1 3            
  E   6   5       3      
  F       6 2 8 4 1 9    
  G     3   6   5        
  H           5   8      
  I   5     7 3 9   1    
    J K L M N O P Q R    
                         
The missing numbers from column Q are 4, 5, and 6, but there is a 6 and 5 in row G. So there is a 4 in GQ, a 6 in IQ (because of IK), and a 5 in DQ.
         
  A 7   8 9       2      
  B   1   7 8     9      
  C     6 3 5   1 7 8    
  D 2   4 1 3     5      
  E   6   5       3      
  F       6 2 8 4 1 9    
  G     3   6   5 4      
  H           5   8      
  I   5     7 3 9 6 1    
    J K L M N O P Q R    
                         
There is a 6 in HJ (because of CL, EK, GN, and IQ).
         
  A 7   8 9       2      
  B   1   7 8     9      
  C     6 3 5   1 7 8    
  D 2   4 1 3     5      
  E   6   5       3      
  F       6 2 8 4 1 9    
  G     3   6   5 4      
  H 6         5   8      
  I   5     7 3 9 6 1    
    J K L M N O P Q R    
                         
The 5 in IK and the 5 in CN mean that the 5 in box AJ-CL has to be in row B. So the 5 in box AP-CR has to be in row A, but there is a 5 in GP, so there has to be a 5 in AR. There has to be a 4 in BR (because of FP and GQ).
         
  A 7   8 9       2 5    
  B   1   7 8     9 4    
  C     6 3 5   1 7 8    
  D 2   4 1 3     5      
  E   6   5       3      
  F       6 2 8 4 1 9    
  G     3   6   5 4      
  H 6         5   8      
  I   5     7 3 9 6 1    
    J K L M N O P Q R    
                         
There has to be a 6 in DR (because of a 6 in either AP or BP, and because of EK).
         
  A 7   8 9       2 5    
  B   1   7 8     9 4    
  C     6 3 5   1 7 8    
  D 2   4 1 3     5 6    
  E   6   5       3      
  F       6 2 8 4 1 9    
  G     3   6   5 4      
  H 6         5   8      
  I   5     7 3 9 6 1    
    J K L M N O P Q R    
                         
The missing numbers in column R are 2, 3, and 7, but there is a 3 in EQ and another in GL. So there is a 3 in HR.
         
  A 7   8 9       2 5    
  B   1   7 8     9 4    
  C     6 3 5   1 7 8    
  D 2   4 1 3     5 6    
  E   6   5       3      
  F       6 2 8 4 1 9    
  G     3   6   5 4      
  H 6         5   8 3    
  I   5     7 3 9 6 1    
    J K L M N O P Q R    
                         
The missing numbers from row I are 2, 4, 8, but there is a 4 and 8 in column L. So the 2 has to be at IL. That means that there has to be a 2 in CK and BO.
         
  A 7   8 9       2 5    
  B   1   7 8 2   9 4    
  C   2 6 3 5   1 7 8    
  D 2   4 1 3     5 6    
  E   6   5       3      
  F       6 2 8 4 1 9    
  G     3   6   5 4      
  H 6         5   8 3    
  I   5 2   7 3 9 6 1    
    J K L M N O P Q R    
                         
The numbers missing from row C is a 4 and 9, but there is a 9 in AM. So the 9 has to be in CJ, and the 4 is in CO.
         
  A 7   8 9       2 5    
  B   1   7 8 2   9 4    
  C 9 2 6 3 5 4 1 7 8    
  D 2   4 1 3     5 6    
  E   6   5       3      
  F       6 2 8 4 1 9    
  G     3   6   5 4      
  H 6         5   8 3    
  I   5 2   7 3 9 6 1    
    J K L M N O P Q R    
                         
There is a 6 in AO (because of GN) and a 1 in AN. Remember that a 1 and a 9 have to be in HN and GO? The 1 in AN means that there is a 1 in GO, and the 9 is in HN. So there has to be a 4 in EN.
         
  A 7   8 9 1 6   2 5    
  B   1   7 8 2   9 4    
  C 9 2 6 3 5 4 1 7 8    
  D 2   4 1 3     5 6    
  E   6   5 4     3      
  F       6 2 8 4 1 9    
  G     3   6 1 5 4      
  H 6       9 5   8 3    
  I   5 2   7 3 9 6 1    
    J K L M N O P Q R    
                         
There is a 9 in HN and another in CJ. That means that there has to be a 9 in GK -- and therefore in EL and in DO. And therefore a 7 is in EO.
         
  A 7   8 9 1 6   2 5    
  B   1   7 8 2   9 4    
  C 9 2 6 3 5 4 1 7 8    
  D 2   4 1 3 9   5 6    
  E   6 9 5 4 7   3      
  F       6 2 8 4 1 9    
  G   9 3   6 1 5 4      
  H 6       9 5   8 3    
  I   5 2   7 3 9 6 1    
    J K L M N O P Q R    
                         
The 7 in EO forces a 7 into DP, so an 8 is in DK. The 7 in DP means that there is a 7 in GR, and therefore a 2 is in HP. There is a 2 in ER, an 8 in EP, and a 1 in EJ.
         
  A 7   8 9 1 6   2 5    
  B   1   7 8 2   9 4    
  C 9 2 6 3 5 4 1 7 8    
  D 2 8 4 1 3 9 7 5 6    
  E 1 6 9 5 4 7 8 3 2    
  F       6 2 8 4 1 9    
  G   9 3   6 1 5 4 7    
  H 6       9 5 2 8 3    
  I   5 2   7 3 9 6 1    
    J K L M N O P Q R    
                         
There is a 2 in GM (because of IL and HP), an 8 in IM (because of HQ), and a 4 in HM.
                             
    A 7   8 9 1 6   2 5      
    B   1   7 8 2   9 4      
    C 9 2 6 3 5 4 1 7 8      
    D 2 8 4 1 3 9 7 5 6      
    E 1 6 9 5 4 7 8 3 2      
    F       6 2 8 4 1 9      
    G   9 3 2 6 1 5 4 7      
    H 6     4 9 5 2 8 3      
    I   5 2 8 7 3 9 6 1      
      J K L M N O P Q R      
                             
There is a 1 in HL (because of GO, IR, and BK).
                             
    A 7   8 9 1 6   2 5      
    B   1   7 8 2   9 4      
    C 9 2 6 3 5 4 1 7 8      
    D 2 8 4 1 3 9 7 5 6      
    E 1 6 9 5 4 7 8 3 2      
    F       6 2 8 4 1 9      
    G   9 3 2 6 1 5 4 7      
    H 6   1 4 9 5 2 8 3      
    I   5 2 8 7 3 9 6 1      
      J K L M N O P Q R      
                             
The numbers missing from column L are a 5 and 7. There is a 7 at AJ, so the 7 is in FL, and the 5 is in BL. There is a 5 in FJ (because of IK), and therefore a 3 in FK.
                             
  A 7   8 9 1 6   2 5    
  B   1 5 7 8 2   9 4    
  C 9 2 6 3 5 4 1 7 8    
  D 2 8 4 1 3 9 7 5 6    
  E 1 6 9 5 4 7 8 3 2    
  F 5 3 7 6 2 8 4 1 9    
  G   9 3 2 6 1 5 4 7    
  H 6   1 4 9 5 2 8 3    
  I   5 2 8 7 3 9 6 1    
    J K L M N O P Q R    
                             
There is a 3 in BJ (because of FK) and another in AP. Therefore, there is a 4 in AK and a 6 in BP. There is a 4 in IJ, a 7 in HK, and an 8 in GJ.
                             
  A 7 4 8 9 1 6 3 2 5    
  B 3 1 5 7 8 2 6 9 4    
  C 9 2 6 3 5 4 1 7 8    
  D 2 8 4 1 3 9 7 5 6    
  E 1 6 9 5 4 7 8 3 2    
  F 5 3 7 6 2 8 4 1 9    
  G 8 9 3 2 6 1 5 4 7    
  H 6 7 1 4 9 5 2 8 3    
  I 4 5 2 8 7 3 9 6 1    
    J K L M N O P Q R    
                             
                             
 
 
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