SUDOKU #3  
 

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   1 2     6  
    5         3   2    
      1 7              
      5     8     3    
        3   4   9      
      9     5     7    
                8 6    
      8   1         3  
    4     6 2   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     9   1 2     6  
  B 5         3   2    
  C   1 7              
  D   5     8     3    
  E     3   4   9      
  F   9     5     7    
  G             8 6    
  H   8   1         3  
  I 4     6 2   1      
  J K L M N O P Q R  
                         
There are 2s in row A and row B, so the 2 in row C has to be in CJ. That's because sets of 3 boxes are linked when you combine the two rules: (1) one of each number is in each row or column, and (2) there is one of each number in each box.
         
  A     9   1 2     6    
  B 5         3   2      
  C 2 1 7                
  D   5     8     3      
  E     3   4   9        
  F   9     5     7      
  G             8 6      
  H   8   1         3    
  I 4     6 2   1        
    J K L M N O P Q R    
                             
There is a 3 in column O and in rows D and E, so there has to be a 3 in FM. So there are 3s in columns M and O and in row H, so another 3 is in GN. There is another 3 in IK (because of HR and GN and EL), there is another 3 in AJ (because of BO and IK), and the final 3 is in CP (because of AJ, BO, DQ, and HR).
             
  A 3   9   1 2     6    
  B 5         3   2      
  C 2 1 7       3        
  D   5     8     3      
  E     3   4   9        
  F   9   3 5     7      
  G         3   8 6      
  H   8   1         3    
  I 4 3   6 2   1        
    J K L M N O P Q R    
                         
There is a 1 in BR (because of CK, AN, and IP) and another 1 in EQ, and there is an 8 inn IO (because of GP and HK) and another 8 in BL (because of HK).
         
  A 3   9   1 2     6    
  B 5   8     3   2 1    
  C 2 1 7       3        
  D   5     8     3      
  E     3   4   9 1      
  F   9   3 5     7      
  G         3   8 6      
  H   8   1         3    
  I 4 3   6 2 8 1        
    J K L M N O P Q R    
                         
Box AJ-CL has two numbers missing -- a 4 and a 6, but there is a 6 in AR, so the 6 is in BK and the 4 is in AK
         
  A 3 4 9   1 2     6    
  B 5 6 8     3   2 1    
  C 2 1 7       3        
  D   5     8     3      
  E     3   4   9 1      
  F   9   3 5     7      
  G         3   8 6      
  H   8   1         3    
  I 4 3   6 2 8 1        
    J K L M N O P Q R    
                         
There is a 6 in IM, which means that there has to be a 6 in column O in box DM-FO, and there is a 6 in BK. All of this put together means that there is a 6 in CN.
         
  A 3 4 9   1 2     6    
  B 5 6 8     3   2 1    
  C 2 1 7   6   3        
  D   5     8     3      
  E     3   4   9 1      
  F   9   3 5     7      
  G         3   8 6      
  H   8   1         3    
  I 4 3   6 2 8 1        
    J K L M N O P Q R    
                         
There is a 5 in ER (because of DK and FN).
         
  A 3 4 9   1 2     6    
  B 5 6 8     3   2 1    
  C 2 1 7   6   3        
  D   5     8     3      
  E     3   4   9 1 5    
  F   9   3 5     7      
  G         3   8 6      
  H   8   1         3    
  I 4 3   6 2 8 1        
    J K L M N O P Q R    
                         
The missing numbers from row I are the 5, 7, and 9, but there is a 7 in columns L and Q. So the 7 has to be in IR. There is an 8 in FR (because DN and GP), and there is an 8 in EJ (because of DN, FR, and HK).
         
  A 3 4 9   1 2     6    
  B 5 6 8     3   2 1    
  C 2 1 7   6   3        
  D   5     8     3      
  E 8   3   4   9 1 5    
  F   9   3 5     7 8    
  G         3   8 6      
  H   8   1         3    
  I 4 3   6 2 8 1   7    
    J K L M N O P Q R    
                         
The missing numbers in row E are 2, 6, and 7. There is a 6 in columns K and M, so the 6 has to be in EO. The missing numbers in row I are 5 and 9, but there is a 9 in column L, so the 5 is in IL and the 9 is in IQ.
         
  A 3 4 9   1 2     6    
  B 5 6 8     3   2 1    
  C 2 1 7   6   3        
  D   5     8     3      
  E 8   3   4 6 9 1 5    
  F   9   3 5     7 8    
  G         3   8 6      
  H   8   1         3    
  I 4 3 5 6 2 8 1 9 7    
    J K L M N O P Q R    
                         
There is a 9 in CR (because of EP and IQ). The missing numbers in row F are 1, 2, 4, and 6, but there is a 2 in column O and the 4 and 6 in box DM-FO. So there is a 1 in FO. That leaves the 2, 4, and 6. There is a 2 and a 4 in column J, so the 6 is in FJ.
         
  A 3 4 9   1 2     6    
  B 5 6 8     3   2 1    
  C 2 1 7   6   3   9    
  D   5     8     3      
  E 8   3   4 6 9 1 5    
  F 6 9   3 5 1   7 8    
  G         3   8 6      
  H   8   1         3    
  I 4 3 5 6 2 8 1 9 7    
    J K L M N O P Q R    
                         
There is a 6 in HL (because of BK, FJ, and GQ) and another one in DP (because of FJ and AR).
         
  A 3 4 9   1 2     6    
  B 5 6 8     3   2 1    
  C 2 1 7   6   3   9    
  D   5     8   6 3      
  E 8   3   4 6 9 1 5    
  F 6 9   3 5 1   7 8    
  G         3   8 6      
  H   8 6 1         3    
  I 4 3 5 6 2 8 1 9 7    
    J K L M N O P Q R    
                         
There is a 2 in column J which means that the 2 in box GJ-IL is in either GK or GL. So there cannot be a 2 in any of the other squares in row G. That means that there is a 2 in either HP or HQ, but the 2 in BQ means that the 2 has to be in HP. So there is a 2 in DR, a 4 in FP and GR, and a 5 in HQ.
         
  A 3 4 9   1 2     6    
  B 5 6 8     3   2 1    
  C 2 1 7   6   3   9    
  D   5     8   6 3 2    
  E 8   3   4 6 9 1 5    
  F 6 9   3 5 1 4 7 8    
  G         3   8 6 4    
  H   8 6 1     2 5 3    
  I 4 3 5 6 2 8 1 9 7    
    J K L M N O P Q R    
                         
There is a 5 in AP (because of HQ and BJ). There is a 4 in CQ (because of AK and FP). That means that there is an 8 in AQ, a 7 in BP, and a 7 in AM.
         
  A 3 4 9 7 1 2 5 8 6    
  B 5 6 8     3 7 2 1    
  C 2 1 7   6   3 4 9    
  D   5     8   6 3 2    
  E 8   3   4 6 9 1 5    
  F 6 9   3 5 1 4 7 8    
  G         3   8 6 4    
  H   8 6 1     2 5 3    
  I 4 3 5 6 2 8 1 9 7    
    J K L M N O P Q R    
                         
There is a 4 in BM (because of AK, CQ, and EN), so there is a 9 in BN. There is a 4 in HO (because of GR and EN), and another one is in DL (because of IJ, AK, and FP). Now there is a 2 in FL and a 1 in GL.
         
  A 3 4 9 7 1 2 5 8 6    
  B 5 6 8 4 9 3 7 2 1    
  C 2 1 7   6   3 4 9    
  D   5 4   8   6 3 2    
  E 8   3   4 6 9 1 5    
  F 6 9 2 3 5 1 4 7 8    
  G     1   3   8 6 4    
  H   8 6 1   4 2 5 3    
  I 4 3 5 6 2 8 1 9 7    
    J K L M N O P Q R    
                         
There is a 1 in DJ (because of CK), which means the 7 is in EK. Another 7 is in DO (because of AM). Now we can fill in DM with a 9 and EM with a 2.
         
  A 3 4 9 7 1 2 5 8 6    
  B 5 6 8 4 9 3 7 2 1    
  C 2 1 7   6   3 4 9    
  D 1 5 4 9 8 7 6 3 2    
  E 8 7 3 2 4 6 9 1 5    
  F 6 9 2 3 5 1 4 7 8    
  G     1   3   8 6 4    
  H   8 6 1   4 2 5 3    
  I 4 3 5 6 2 8 1 9 7    
    J K L M N O P Q R    
                         
There isa 9 in GO (because of BN and DM) and another 9 in HJ. So a 7 is in HN, a 5 is in CO, an 8 is in CM, a 5 is in GM, a 7 is in HN, a 9 is in HJ, a 7 is in GJ, and a 2 is in GK.
         
  A 3 4 9 7 1 2 5 8 6    
  B 5 6 8 4 9 3 7 2 1    
  C 2 1 7 8 6 5 3 4 9    
  D 1 5 4 9 8 7 6 3 2    
  E 8 7 3 2 4 6 9 1 5    
  F 6 9 2 3 5 1 4 7 8    
  G 7 2 1 5 3 9 8 6 4    
  H 9 8 6 1 7 4 2 5 3    
  I 4 3 5 6 2 8 1 9 7    
    J K L M N O P Q R    
                         
 
 
HOME