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 AJCL 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 DMFO, 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 DMFO. 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 GJIL 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  
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