SUDOKU #4  
 

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.
 
    2 8       1 4      
      1             5  
    5     2 9     8    
      5   9 7          
                       
            3 5   9    
      7     8 6     2  
    3             5    
        2 3       7 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 2 8       1 4      
  B   1             5  
  C 5     2 9     8    
  D   5   9 7          
  E                    
  F         3 5   9    
  G   7     8 6     2  
  H 3             5    
  I     2 3       7 1  
  J K L M N O P Q R  
                         
There is a 5 in GL (because of CJ, DK, and HQ), IN (because of HQ, FO, and GL), AM (because of IN, BR, and CJ), and EP (because of DK, FO, HQ, and BR). The 5s are done. Now the fun starts.
         
  A 2 8   5   1 4        
  B   1             5    
  C 5     2 9     8      
  D   5   9 7            
  E             5        
  F         3 5   9      
  G   7 5   8 6     2    
  H 3             5      
  I     2 3 5     7 1    
    J K L M N O P Q R    
                             
There is a 1 in CP (because of AO, BK, and IR).
             
  A 2 8   5   1 4        
  B   1             5    
  C 5     2 9   1 8      
  D   5   9 7            
  E             5        
  F         3 5   9      
  G   7 5   8 6     2    
  H 3             5      
  I     2 3 5     7 1    
    J K L M N O P Q R    
                         
Look at column N, and compare it to box AM-CO. There is a 5 at AM and IN, but the 3 (FN), 7 (DN), and 8 (GN) are not in box AM-CO. Those numbers cannot be in squares AN and BN. That leaves three open squares in box AM-CO where the 3, 7, and 8 fit. That means that the 4 and 6 have to be in AN and BN. But there is a 4 in AP, so the 6 is in AN and the 4 is in BN.
         
  A 2 8   5 6 1 4        
  B   1     4       5    
  C 5     2 9   1 8      
  D   5   9 7            
  E             5        
  F         3 5   9      
  G   7 5   8 6     2    
  H 3             5      
  I     2 3 5     7 1    
    J K L M N O P Q R    
                         
The numbers missing from row A are the 3, 7, and 9, but the 7 and 9 are in column Q, so a 3 is in AQ. The numbers missing now from column Q are the 1, 2, 4, and 6, but the 1 and 2 are in box GP-IR, and the 6 is in GO, so the 4 has to be in GQ.
         
  A 2 8   5 6 1 4 3      
  B   1     4       5    
  C 5     2 9   1 8      
  D   5   9 7            
  E             5        
  F         3 5   9      
  G   7 5   8 6   4 2    
  H 3             5      
  I     2 3 5     7 1    
    J K L M N O P Q R    
                         
The numbers missing from row G are 1, 3, and 9, but the 3 and 9 are in column M, so the 1 is in GM. That means that a 1 is in EN, which means a 2 is in HN.
         
  A 2 8   5 6 1 4 3      
  B   1     4       5    
  C 5     2 9   1 8      
  D   5   9 7            
  E         1   5        
  F         3 5   9      
  G   7 5 1 8 6   4 2    
  H 3       2     5      
  I     2 3 5     7 1    
    J K L M N O P Q R    
                         
The numbers missing from row G are the 3 and 9, but a 3 is in HJ, so the 3 is in GP and the 9 is in GJ. There is a 1 at HL (because of BK and IR), and there is a 1 at DQ (because of CP, IR, and EN).
         
  A 2 8   5 6 1 4 3      
  B   1     4       5    
  C 5     2 9   1 8      
  D   5   9 7     1      
  E         1   5        
  F         3 5   9      
  G 9 7 5 1 8 6 3 4 2    
  H 3   1   2     5      
  I     2 3 5     7 1    
    J K L M N O P Q R    
                         
There is an 8 in IJ (because of AK). There is a 1 in FJ (because of BK, HL, DQ, and EN).
         
  A 2 8   5 6 1 4 3      
  B   1     4       5    
  C 5     2 9   1 8      
  D   5   9 7     1      
  E         1   5        
  F 1       3 5   9      
  G 9 7 5 1 8 6 3 4 2    
  H 3   1   2     5      
  I 8   2 3 5     7 1    
    J K L M N O P Q R    
                         
The numbers missing from box GJ-IL are the 4 and 6. This helps us place a 4 in CL (because of BN and AP). The 4 and 6 in HK-IJ help us get another square filled in: CR. The 6 in HK-IK and the 6 in AN mean that the 6 in box AJ-CL have to be in either BJ or BL, so the 6 in BJ/BL and the 6 in AN mean that there's a 6 in CR.
         
  A 2 8   5 6 1 4 3      
  B   1     4       5    
  C 5   4 2 9   1 8 6    
  D   5   9 7     1      
  E         1   5        
  F 1       3 5   9      
  G 9 7 5 1 8 6 3 4 2    
  H 3   1   2     5      
  I 8   2 3 5     7 1    
    J K L M N O P Q R    
                         
The numbers missing in row C are the 3 and 7, but there's a 7 in GK. So the 3 is in CK and the 7 is in CO, which means that there is a 7 in HM.
         
  A 2 8   5 6 1 4 3      
  B   1     4       5    
  C 5 3 4 2 9 7 1 8 6    
  D   5   9 7     1      
  E         1   5        
  F 1       3 5   9      
  G 9 7 5 1 8 6 3 4 2    
  H 3   1 7 2     5      
  I 8   2 3 5     7 1    
    J K L M N O P Q R    
                         
The numbers missing from box GM-IO are the 4 and 9. The 4 and the 6 in GO indicate that there is a 4 and 6 in EM and FM. That means that the numbers in DO and EO are a 2 and an 8. The 4 and 9 in HO-IO and the 2 and 8 in DO and EO mean that a 3 is in BO, which means that an 8 is in BM.
         
  A 2 8   5 6 1 4 3      
  B   1   8 4 3     5    
  C 5 3 4 2 9 7 1 8 6    
  D   5   9 7     1      
  E         1   5        
  F 1       3 5   9      
  G 9 7 5 1 8 6 3 4 2    
  H 3   1 7 2     5      
  I 8   2 3 5     7 1    
    J K L M N O P Q R    
                         
The missing numbers in box GJ-IL are 4 and 6, which means that a 2 and a 9 have to be in EK and FK. There is a 9 in FQ, so the 9 has to be in EK, and the 2 has to be in FK.
         
  A 2 8   5 6 1 4 3      
  B   1   8 4 3     5    
  C 5 3 4 2 9 7 1 8 6    
  D   5   9 7     1      
  E   9     1   5        
  F 1 2     3 5   9      
  G 9 7 5 1 8 6 3 4 2    
  H 3   1 7 2     5      
  I 8   2 3 5     7 1    
    J K L M N O P Q R    
                         
The numbers missing from column Q are the 2 and 6, but there is a 6 in CR. So the 6 must be in EQ, and the 2 must be in BQ. That means that a 6 must be in FM, which puts a 4 in EM.
         
  A 2 8   5 6 1 4 3      
  B   1   8 4 3   2 5    
  C 5 3 4 2 9 7 1 8 6    
  D   5   9 7     1      
  E   9   4 1   5 6      
  F 1 2   6 3 5   9      
  G 9 7 5 1 8 6 3 4 2    
  H 3   1 7 2     5      
  I 8   2 3 5     7 1    
    J K L M N O P Q R    
                         
There is a 4 in DJ (because of CL and EM) and another 4 in FR (because of DJ, EM, and AP).
         
  A 2 8   5 6 1 4 3      
  B   1   8 4 3   2 5    
  C 5 3 4 2 9 7 1 8 6    
  D 4 5   9 7     1      
  E   9   4 1   5 6      
  F 1 2   6 3 5   9 4    
  G 9 7 5 1 8 6 3 4 2    
  H 3   1 7 2     5      
  I 8   2 3 5     7 1    
    J K L M N O P Q R    
                         
There's a 2 in DP (because of GR and FK) and another 2 in EO. That means that there is an 8 in DO.
         
  A 2 8   5 6 1 4 3      
  B   1   8 4 3   2 5    
  C 5 3 4 2 9 7 1 8 6    
  D 4 5   9 7 8 2 1      
  E   9   4 1 2 5 6      
  F 1 2   6 3 5   9 4    
  G 9 7 5 1 8 6 3 4 2    
  H 3   1 7 2     5      
  I 8   2 3 5     7 1    
    J K L M N O P Q R    
                         
There is a 6 in DL (because of FM and EQ), and there is one in BJ (because of DL). That means that there is a 3 in DR. There is another 3 in EL (because of HJ and FN). And there is a 7 in EJ, which means there is an 8 in ER and a 7 in FP and an 8 in FL
         
  A 2 8   5 6 1 4 3      
  B 6 1   8 4 3   2 5    
  C 5 3 4 2 9 7 1 8 6    
  D 4 5 6 9 7 8 2 1 3    
  E 7 9 3 4 1 2 5 6 8    
  F 1 2 8 6 3 5 7 9 4    
  G 9 7 5 1 8 6 3 4 2    
  H 3   1 7 2     5      
  I 8   2 3 5     7 1    
    J K L M N O P Q R    
                         
The missing numbers in box AP-CR are 7 and 9, but there is a 7 in FP. So there is a 9 in BP, a 7 in AR, a 9 in HR, a 9 in AL, and a 7 in BL.
                             
    A 2 8 9 5 6 1 4 3 7      
    B 6 1 7 8 4 3 9 2 5      
    C 5 3 4 2 9 7 1 8 6      
    D 4 5 6 9 7 8 2 1 3      
    E 7 9 3 4 1 2 5 6 8      
    F 1 2 8 6 3 5 7 9 4      
    G 9 7 5 1 8 6 3 4 2      
    H 3   1 7 2     5 9      
    I 8   2 3 5     7 1      
      J K L M N O P Q R      
                             
There is a 9 in IO (because of HR), which means that there is a 4 in HO and in IK, and there is a 6 in HK and IP, and there is an 8 in HP.
                             
    A 2 8 9 5 6 1 4 3 7      
    B 6 1 7 8 4 3 9 2 5      
    C 5 3 4 2 9 7 1 8 6      
    D 4 5 6 9 7 8 2 1 3      
    E 7 9 3 4 1 2 5 6 8      
    F 1 2 8 6 3 5 7 9 4      
    G 9 7 5 1 8 6 3 4 2      
    H 3 6 1 7 2 4 8 5 9      
    I 8 4 2 3 5 9 6 7 1      
      J K L M N O P Q R      
                             
 
 
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