SUDOKU #15  
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. You won't need to do 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 these rules.  
Here is a sample Sudoku puzzle. It might be good to just print out this grid and write in the numbers as I go. There may be times when I do more numbers in one step than can be followed just by looking at the webpage.  
3  5  7  
1  7  6  
5  6  8  
9  4  7  
2  5  
3  6  4  
7  9  2  
2  8  1  
3  6  1  
This is a common pattern of the Hard category of Sudoku puzzles. You can see that the upper left box and the lower right box are empty. 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  3  5  7  
B  1  7  6  
C  5  6  8  
D  9  4  7  
E  2  5  
F  3  6  4  
G  7  9  2  
H  2  8  1  
I  3  6  1  
J  K  L  M  N  O  P  Q  R  
There is a 3, a 6, and a 1 in row I, but there isn't a 3 or a 6 in box GMIO. So the 3 and 6 have to be in squares GN and HM. But there is a 3 in FM, so the 3 is in GN, and the 6 is in HM. There is a 3 in BO (because of FM, GN, and AP).  
A  3  5  7  
B  1  7  3  6  
C  5  6  8  
D  9  4  7  
E  2  5  
F  3  6  4  
G  7  9  3  2  
H  2  6  8  1  
I  3  6  1  
J  K  L  M  N  O  P  Q  R  
There is a 2 and a 5 in row E, but there isn't a 2 or 5 in box DMFO. So the 2 and 5 have to be in squares DM and FO. But there is a 2 in GO and a 5 in CM. So the 5 is in FO, and the 2 is in DM. There is a 5 in IM (becase of CM and FO).  
A  3  5  7  
B  1  7  3  6  
C  5  6  8  
D  9  2  4  7  
E  2  5  
F  3  6  5  4  
G  7  9  3  2  
H  2  6  8  1  
I  3  6  1  5  
J  K  L  M  N  O  P  Q  R  
There is a 7 in IM (because of BN and DO), and a 4 has to be in IO. So there is a 4 in AM (because of IO and DN), which means an 8 is in EM. There is an 8 in AO (because of EM and HO), so there is a 9 in EO, which means there is a 1 in EN. Now it gets a little more challenging.  
A  4  8  3  5  7  
B  1  7  3  6  
C  5  6  8  
D  9  2  4  7  
E  2  8  1  9  5  
F  3  6  5  4  
G  7  9  3  2  
H  2  6  8  1  
I  3  6  1  7  5  4  
J  K  L  M  N  O  P  Q  R  
Row A still needs a 1, 2, 6, and a 9. There is a 2, a 6, and a 9 in column K. So the 1 goes in AK. There is a 3 and a 7 in Row A in box APCR, and there is a 3 and a 7 in row B in box AMCO, so there has to be a 3 and a 7 in box AJCL. But there is a 3 and a 7 in column J. So there is a 3 and a 7 in CK and CL.  
A  1  4  8  3  5  7  
B  1  7  3  6  
C  37  37  5  6  8  
D  9  2  4  7  
E  2  8  1  9  5  
F  3  6  5  4  
G  7  9  3  2  
H  2  6  8  1  
I  3  6  1  7  5  4  
J  K  L  M  N  O  P  Q  R  
There is a 2 and a 9 in row D, and another 2 and 9 in row E, so there has to be a 2 and a 9 in row F in box DPFR in squares FP and FR.  
A  1  4  8  3  5  7  
B  1  7  3  6  
C  37  37  5  6  8  
D  9  2  4  7  
E  2  8  1  9  5  
F  3  6  5  29  4  29  
G  7  9  3  2  
H  2  6  8  1  
I  3  6  1  7  5  4  
J  K  L  M  N  O  P  Q  R  
The numbers missing from row F are the 1, 7, and 8. The 1 has to be in FJ (because of AK and IL).  
A  1  4  8  3  5  7  
B  1  7  3  6  
C  37  37  5  6  8  
D  9  2  4  7  
E  2  8  1  9  5  
F  1  3  6  5  29  4  29  
G  7  9  3  2  
H  2  6  8  1  
I  3  6  1  7  5  4  
J  K  L  M  N  O  P  Q  R  
There is an 8 in either GK or GL (because of HN). There has to be an 8 in row D in box DPFR, and that means that an 8 has to be in either FK or FL. The 8 in FKFL and the 8 in GKGL mean that there has to be 8 in BJ (because of AO and CR).  
A  1  4  8  3  5  7  
B  8  1  7  3  6  
C  37  37  5  6  8  
D  9  2  4  7  
E  2  8  1  9  5  
F  1  78  78  3  6  5  29  4  29  
G  7  9  3  2  
H  2  6  8  1  
I  3  6  1  7  5  4  
J  K  L  M  N  O  P  Q  R  
There is a 7 in EQ (because of DO and AR), and there is a 7 in HP (because of EQ, AR, GJ, and IM).  
A  1  4  8  3  5  7  
B  8  1  7  3  6  
C  37  37  5  6  8  
D  9  2  4  7  
E  2  8  1  9  5  7  
F  1  78  78  3  6  5  29  4  29  
G  7  9  3  2  
H  2  6  8  1  7  
I  3  6  1  7  5  4  
J  K  L  M  N  O  P  Q  R  
There is a 2 in either AJ or CJ (because of EL and HK). There is a 2 in either AN or CN. Therefore, there has to be a 2 in BP or BR. There is a 2 in either FP or FR, so there has to be a 2 in column Q in box GPIR. So the 2 in box GPIR has to be in IQ. There is an 8 in IP (because of CR) and a 9 in IR.  
A  1  4  8  3  5  7  
B  8  1  7  3  6  
C  37  37  5  6  8  
D  9  2  4  7  
E  2  8  1  9  5  7  
F  1  78  78  3  6  5  29  4  29  
G  7  9  3  2  
H  2  6  8  1  7  
I  3  6  1  7  5  4  8  2  9  
J  K  L  M  N  O  P  Q  R  
There is a 9 in FP or FR and in IP or IR, so there has to be a 9 in CQ. Therefore there has to be a 9 in AN, a 2 in CN, a 9 in BL (because of DK), and another 9 in HJ. There isa 9 in FP and a 2 in FR.  
A  1  4  9  8  3  5  7  
B  8  9  1  7  3  6  
C  37  37  5  2  6  9  8  
D  9  2  4  7  
E  2  8  1  9  5  7  
F  1  78  78  3  6  5  9  4  2  
G  7  9  3  2  
H  9  2  6  8  1  7  
I  3  6  1  7  5  4  8  2  9  
J  K  L  M  N  O  P  Q  R  
The numbers missing from row A are a 2 and a 6. The 2 has to be in AJ (because of EL), and the 6 is in AL. There is a 5 in BK (because of CM) and a 4 in CJ. There is a 4 in EK (because of CJ and DN).  
A  2  1  6  4  9  8  3  5  7  
B  8  5  9  1  7  3  6  
C  4  37  37  5  2  6  9  8  
D  9  2  4  7  
E  4  2  8  1  9  5  7  
F  1  78  78  3  6  5  9  4  2  
G  7  9  3  2  
H  9  2  6  8  1  7  
I  3  6  1  7  5  4  8  2  9  
J  K  L  M  N  O  P  Q  R  
The numbers missing from Row E are a 3 and a 6. The 6 has to be in EJ (because of IJ), and the 3 is in ER. There is a 3 in HQ (because of GN, ER, and AP). There is a 1 in CP.  
A  2  1  6  4  9  8  3  5  7  
B  8  5  9  1  7  3  6  
C  4  37  37  5  2  6  1  9  8  
D  9  2  4  7  
E  6  4  2  8  1  9  5  7  3  
F  1  78  78  3  6  5  9  4  2  
G  7  9  3  2  
H  9  2  6  8  1  7  3  
I  3  6  1  7  5  4  8  2  9  
J  K  L  M  N  O  P  Q  R  
The numbers missing from box DJFL are a 3 and a 5 in DJ and DL. The 3 is in DL (because of IJ), and the 5 is in DJ. So there is a 7 in CL, a 3 in CK, a 7 in FK, and an 8 in FL. There is an 8 in GK.  
A  2  1  6  4  9  8  3  5  7  
B  8  5  9  1  7  3  6  
C  4  3  7  5  2  6  1  9  8  
D  5  9  3  2  4  7  
E  6  4  2  8  1  9  5  7  3  
F  1  7  8  3  6  5  9  4  2  
G  7  8  9  3  2  
H  9  2  6  8  1  7  3  
I  3  6  1  7  5  4  8  2  9  
J  K  L  M  N  O  P  Q  R  
The numbers missing from row B are a 2 and a 4. There is a 2 in BP (because of FR) and a 4 in BR. There is a 4 in GP (because of BR and FQ), and a 4 in HL (because of GP). So there is a 5 in GL.  
A  2  1  6  4  9  8  3  5  7  
B  8  5  9  1  7  3  2  6  4  
C  4  3  7  5  2  6  1  9  8  
D  5  9  3  2  4  7  
E  6  4  2  8  1  9  5  7  3  
F  1  7  8  3  6  5  9  4  2  
G  7  8  5  9  3  2  4  
H  9  2  4  6  8  1  7  3  
I  3  6  1  7  5  4  8  2  9  
J  K  L  M  N  O  P  Q  R  
There is a 5 in HR (because of GL). There is a 6 in GR (because of BQ) and a 1 in GQ. There is a 1 in DR (because of CP and GQ), an 8 in DQ (because of IP), and a 6 in DP.  
A  2  1  6  4  9  8  3  5  7  
B  8  5  9  1  7  3  2  6  4  
C  4  3  7  5  2  6  1  9  8  
D  5  9  3  2  4  7  6  8  1  
E  6  4  2  8  1  9  5  7  3  
F  1  7  8  3  6  5  9  4  2  
G  7  8  5  9  3  2  4  1  6  
H  9  2  4  6  8  1  7  3  5  
I  3  6  1  7  5  4  8  2  9  
J  K  L  M  N  O  P  Q  R  
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