SUDOKU #8  
 

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.
 
              1        
          4   9 3 2    
    4 1     7          
        1     8     7  
      6           9    
    2     3     4      
            4     8 5  
      3 9 7   2        
          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           1        
  B       4   9 3 2    
  C 4 1     7          
  D     1     8     7  
  E   6           9    
  F 2     3     4      
  G         4     8 5  
  H   3 9 7   2        
  I       1            
  J K L M N O P Q R  
                         
There is a 1 in BR (because of CK and AO). There is a 4 in EO (because of BM, GN, and FP) and a 7 in FO (because of HM and CN). There is a 4 in DK (because of CJ, EO, and FP) and one in IL (because of CJ, DK, and GN).
         
  A           1          
  B       4   9 3 2 1    
  C 4 1     7            
  D   4 1     8     7    
  E   6       4   9      
  F 2     3   7 4        
  G         4     8 5    
  H   3 9 7   2          
  I     4 1              
    J K L M N O P Q R    
                             
The 3 in HK and BP means that there has to be a 3 in either IQ or IR, so the 3 in box GM-IO has to be in GO. There is a 3 in AN (because of FM, GO, and BP). There is another 3 in CL (because of AN and BP).
             
  A         3 1          
  B       4   9 3 2 1    
  C 4 1 3   7            
  D   4 1     8     7    
  E   6       4   9      
  F 2     3   7 4        
  G         4 3   8 5    
  H   3 9 7   2          
  I     4 1              
    J K L M N O P Q R    
                         
There is an 8 in GQ and one in DO, so the 8 in column M has to be in either AM or CM. There is a 2 in BQ and another in HO, so there has to be a 2 in either AM or CM. That means that the 5 and 6 in box AM-CO have to be in BN and CO. The 2 in BQ means that the 2 in box AJ-CL has to be in for A, so the 2 has to be in CM and the 8 has to be in AM.
         
  A       8 3 1          
  B       4   9 3 2 1    
  C 4 1 3 2 7            
  D   4 1     8     7    
  E   6       4   9      
  F 2     3   7 4        
  G         4 3   8 5    
  H   3 9 7   2          
  I     4 1              
    J K L M N O P Q R    
                         
The missing numbers from column M are 5, 6, and 9. But there are a 6 and 9 in row E, so a 5 is in EM.
         
  A       8 3 1          
  B       4   9 3 2 1    
  C 4 1 3 2 7            
  D   4 1     8     7    
  E   6   5   4   9      
  F 2     3   7 4        
  G         4 3   8 5    
  H   3 9 7   2          
  I     4 1              
    J K L M N O P Q R    
                         
The numbers missing from box AM-CO are the 5 and 6. The numbers missing from row C are 5, 6, 8, and 9. But there is an 8 and a 9 in column Q, so the possible numbers in CQ are 5 and 6 -- the same as in CO. So the possible numbers in CP and CR are the 8 and 9. The numbers missing from column O are a 5 and 6, and the numbers missing from column M are a 6 and 9.
         
  A       8 3 1          
  B       4 56 9 3 2 1    
  C 4 1 3 2 7 56 89 56 89    
  D   4 1 69   8     7    
  E   6   5   4   9      
  F 2     3   7 4        
  G       69 4 3   8 5    
  H   3 9 7   2          
  I     4 1   56          
    J K L M N O P Q R    
                         
This puzzle is hard enough that I am trying to see patterns. Are there a couple squares in a row, column or box that have to be one of two numbers, so we can get more information about other squares?
 
The numbers missing from row B are 5, 6, 7, 8. The numbers missing from row C are 5, 6, 8, 9. The numbers in row F are 1, 5, 6, 8, 9. There are a 1 and 5 in column R and a 9 in box DP-FR, so the possible numbers in FR are a 6 or 8.
         
  A       8 3 1          
  B       4 56 9 3 2 1 5678  
  C 4 1 3 2 7 56 89 56 89 5689  
  D   4 1 69   8     7    
  E   6   5   4   9      
  F 2     3   7 4   68 15689  
  G       69 4 3   8 5 12679  
  H   3 9 7   2       14568  
  I     4 1   56          
    J K L M N O P Q R    
                         
The numbers missing from box AP-CR (aside from the 8 and 9) are 4, 5, 6, and 7, but there is a 5 and a 7 in column R. So the possible numbers in AR would be 4 and 6. The numbers missing from row H are 1, 4, 5, 6, and 8, but there are a 1 and 5 in column R and an 8 in box FP-IR. So the possible numbers in HR would be a 4 and a 6. So the 4 and 6 have to be in AR or HR. That means that there cannot be a 6 in FR, which means that the 8 has to be in FR. That means there has to be a 9 in CR and an 8 in CP.
         
  A       8 3 1     46    
  B       4 56 9 3 2 1 5678  
  C 4 1 3 2 7 56 8 56 9 5689  
  D   4 1 69   8     7    
  E   6   5   4   9 23    
  F 2     3   7 4   8 15689  
  G       69 4 3   8 5 12679  
  H   3 9 7   2     46 14568  
  I     4 1   56     23    
    J K L M N O P Q R    
                         
There is a 2 and a 3 in ER and IR. There is a 1, 2, or 3 in EN, EP, and ER, but there is a 3 in AN and in BP. So the 3 has to be in ER, and that means the 2 is in IR. There has to be a 3 in DJ (because of ER and FM). There has to be a 7 and 8 in EJ and EL (because of DO, FR, FO, and DR).
         
  A       8 3 1     46    
  B       4 56 9 3 2 1 5678  
  C 4 1 3 2 7 56 8 56 9 56  
  D 3 4 1 69   8     7    
  E 78 6 78 5   4   9 3    
  F 2     3   7 4   8 1569  
  G       69 4 3   8 5 12679  
  H   3 9 7   2     46 14568  
  I     4 1   56     2    
    J K L M N O P Q R    
                         
The numbers missing from box DJ-FL are a 5 and 9, but there is a 9 in HL. So the 9 is in FK, and the 5 is in FL. The missing numbers from row F are a 1 and a 6, and the numbers missing from row E are a 1 and 2.
         
  A       8 3 1     46    
  B       4 56 9 3 2 1 5678  
  C 4 1 3 2 7 56 8 56 9 56  
  D 3 4 1 69   8     7    
  E 78 6 78 5 12 4 12 9 3    
  F 2 9 5 3 16 7 4 16 8 1569  
  G       69 4 3   8 5 12679  
  H   3 9 7   2     46 14568  
  I     4 1   56     2    
    J K L M N O P Q R    
                         
A 9 is in AJ (because of BO, HL, and FK), a 3 is in IQ (because of HK and BP), and a 4 is in HQ (because of FP). The 7 in box GP-IR has to be in either GP or IP (because of HM), so there has to be a 7 in AQ.
         
  A 9     8 3 1   7 46    
  B       4 56 9 3 2 1 5678  
  C 4 1 3 2 7 56 8 56 9 56  
  D 3 4 1 69   8     7    
  E 78 6 78 5 12 4 12 9 3    
  F 2 9 5 3 16 7 4 16 8 16  
  G       69 4 3   8 5 12679  
  H   3 9 7   2   4 46 1568  
  I     4 1   56   3 2    
    J K L M N O P Q R    
                         
There has to be a 4 in AR (because of CJ, BM, and FP), so a 6 is in HR. The numbers missing from row H are 1, 5, and 8, but there is a 5 and an 8 in box GP-IR, so a 1 has to be in HP. That means that a 2 has to be in EP, and a 1 is in EN.
         
  A 9     8 3 1 56 7 4    
  B       4 56 9 3 2 1 5678  
  C 4 1 3 2 7 56 8 56 9 56  
  D 3 4 1 69   8   56 7    
  E 78 6 78 5 1 4 2 9 3    
  F 2 9 5 3 16 7 4 16 8 1569  
  G       69 4 3   8 5 12679  
  H   3 9 7   2 1 4 6 1568  
  I     4 1   56   3 2    
    J K L M N O P Q R    
                         
A 6 has to be in FN, a 1 is in FQ. There has to be a 9 in DM, a 6 in GM, and a 2 in DN.
         
  A 9     8 3 1 56 7 4    
  B       4 56 9 3 2 1 5678  
  C 4 1 3 2 7 56 8 56 9    
  D 3 4 1 9 2 8 56 56 7    
  E 78 6 78 5 1 4 2 9 3    
  F 2 9 5 3 6 7 4 1 8    
  G       6 4 3 79 8 5 1279  
  H   3 9 7   2 1 4 6 58  
  I     4 1   56 79 3 2    
    J K L M N O P Q R    
                         
The numbers missing from row G are 1, 2, 7, and 9. But there is a 9 in HL, so the 9 has to be in GP. Another way to look at it is that there is a 1 and a 9 in columns K and L, so the 2 and 7 have to be in GK and GL. So there can't be a 7 in row G, and that means that square GP has to contain a 9. So there is a 7 in IP, and there is a 1 in GJ.
         
  A 9     8 3 1 56 7 4    
  B       4 56 9 3 2 1 5678  
  C 4 1 3 2 7 56 8 56 9    
  D 3 4 1 9 2 8 56 56 7    
  E 78 6 78 5 1 4 2 9 3    
  F 2 9 5 3 6 7 4 1 8    
  G 1 27 27 6 4 3 9 8 5 1279  
  H   3 9 7   2 1 4 6 58  
  I     4 1   56 7 3 2    
    J K L M N O P Q R    
         
The number in IO has to be a 5 (since it can't be a 6), so there is a 6 in CO, a 5 in BN, a 5 in CQ, a 6 in AP, a 5 in DP, and a 6 in DQ.
         
  A 9     8 3 1 6 7 4    
  B       4 5 9 3 2 1    
  C 4 1 3 2 7 6 8 5 9    
  D 3 4 1 9 2 8 5 6 7    
  E 78 6 78 5 1 4 2 9 3    
  F 2 9 5 3 6 7 4 1 8    
  G 1 27 27 6 4 3 9 8 5    
  H   3 9 7   2 1 4 6    
  I     4 1   5 7 3 2    
    J K L M N O P Q R    
         
There is a 5 in HJ (because of IO) and another 5 in AK (because of HJ, FL, and BN). So there is a 2 in AL.
         
  A 9 5 2 8 3 1 6 7 4    
  B       4 5 9 3 2 1    
  C 4 1 3 2 7 6 8 5 9    
  D 3 4 1 9 2 8 5 6 7    
  E 78 6 78 5 1 4 2 9 3    
  F 2 9 5 3 6 7 4 1 8    
  G 1 27 27 6 4 3 9 8 5    
  H 5 3 9 7   2 1 4 6    
  I     4 1   5 7 3 2    
    J K L M N O P Q R    
         
The two in AL means there is a 7 in GL and a 2 in GK. The 7 in GL means there is an 8 in AL and a 7 in EJ.
         
  A 9 5 2 8 3 1 6 7 4    
  B       4 5 9 3 2 1    
  C 4 1 3 2 7 6 8 5 9    
  D 3 4 1 9 2 8 5 6 7    
  E 7 6 8 5 1 4 2 9 3    
  F 2 9 5 3 6 7 4 1 8    
  G 1 2 7 6 4 3 9 8 5    
  H 5 3 9 7   2 1 4 6    
  I     4 1   5 7 3 2    
    J K L M N O P Q R    
         
There is a 7 in BK (because of EJ and GL), an 8 in BJ (because of EL), and a 6 in BL.
         
  A 9 5 2 8 3 1 6 7 4    
  B 8 7 6 4 5 9 3 2 1    
  C 4 1 3 2 7 6 8 5 9    
  D 3 4 1 9 2 8 5 6 7    
  E 7 6 8 5 1 4 2 9 3    
  F 2 9 5 3 6 7 4 1 8    
  G 1 2 7 6 4 3 9 8 5    
  H 5 3 9 7   2 1 4 6    
  I     4 1   5 7 3 2    
    J K L M N O P Q R    
         
There is an 8 in HN, a 9 in IN, an 8 in IK, and a 6 in IJ.
         
  A 9 5 2 8 3 1 6 7 4    
  B 8 7 6 4 5 9 3 2 1    
  C 4 1 3 2 7 6 8 5 9    
  D 3 4 1 9 2 8 5 6 7    
  E 7 6 8 5 1 4 2 9 3    
  F 2 9 5 3 6 7 4 1 8    
  G 1 2 7 6 4 3 9 8 5    
  H 5 3 9 7 8 2 1 4 6    
  I 6 8 4 1 9 5 7 3 2    
    J K L M N O P Q R    
 
 
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