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