SUDOKU #10  
 
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  5  
3  4  6  
2  9  7  
7  3  
4  1  8  9  5  
5  2  
2  9  7  
6  5  1  
9  3  
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  5  
B  3  4  6  
C  2  9  7  
D  7  3  
E  4  1  8  9  5  
F  5  2  
G  2  9  7  
H  6  5  1  
I  9  3  
J  K  L  M  N  O  P  Q  R  
There's a 9 in AR (because of GP, EQ, and CL), another 9 in BM (because of AR, CL, and IN). There's a 5 in BJ (because of HL and FK) and another 5 in CP (because of BJ, AN, and ER).  
A  1  5  9  
B  5  9  3  4  6  
C  2  9  5  7  
D  7  3  
E  4  1  8  9  5  
F  5  2  
G  2  9  7  
H  6  5  1  
I  9  3  
J  K  L  M  N  O  P  Q  R  
There's a 3 in AP (because of DQ and IR) and another one in CK (because of AP and BO). The 3s in CK and IR mean there has to be a 3 in either GJ or GL, so there has to be a 3 in HN (because of IR, CK, and BO). There has to be a 9 in HK (because of GP and IN).  
A  1  5  3  9  
B  5  9  3  4  6  
C  2  3  9  5  7  
D  7  3  
E  4  1  8  9  5  
F  5  2  
G  2  9  7  
H  6  9  5  1  3  
I  9  3  
J  K  L  M  N  O  P  Q  R  
There is a 7 in HO. You can see that in two ways. First, the 7 in GR means the 7 in box GJIL has to be in row I. Second, the numbers missing in row H are 2, 4, 7, and 8. All but one of the squares of row H are in box GPIR, but there is a 7 in GR, so the 7 has to be in HO.  
A  1  5  3  9  
B  5  9  3  4  6  
C  2  3  9  5  7  
D  7  3  
E  4  1  8  9  5  
F  5  2  
G  2  9  7  
H  6  9  5  1  3  7  
I  9  3  
J  K  L  M  N  O  P  Q  R  
The 4 in BP and the 6 in BR mean that there has to be a 4 and 6 in AK and AL, which means that a 7 and an 8 have to be in BK and BL. The 3 in DQ and 7 in DP mean that there has to be a 3 and 7 in EL and FJ. There is a 6, 8, and 9 in squares DJDL, so the 9 has to be in DJ (because of CL and HK).  
A  1  46  46  5  3  9  
B  5  78  78  9  3  4  6  
C  2  3  9  5  7  
D  9  68  68  7  3  
E  4  1  37  8  9  5  
F  37  5  2  
G  2  9  7  
H  6  9  5  1  3  7  
I  9  3  
J  K  L  M  N  O  P  Q  R  
There is a 9 in FO (because of BM, DJ, EQ, and IN). There's a 7 in AM (because of BKBL, CQ, and HO) and another one in FN (because of AM, HO, and DP).  
A  1  46  46  7  5  3  9  
B  5  78  78  9  3  4  6  
C  2  3  9  5  7  
D  9  68  68  7  3  
E  4  1  37  8  9  5  
F  37  5  2  7  9  
G  2  9  7  
H  6  9  5  1  3  7  
I  9  3  
J  K  L  M  N  O  P  Q  R  
The 7 in FN means there is a 3 in FJ and a 7 in EL. The numbers missing from column J are a 7 and 8. The 7 in GR means there is a 7 in IJ and an 8 in GJ. The 7 in EL means there is a 7 in BK, an 8 in BL and DK, a 6 in DL and AK, and a 4 in AL.  
A  1  6  4  7  5  3  9  
B  5  7  8  9  3  4  6  
C  2  3  9  5  7  
D  9  8  6  7  3  
E  4  1  7  8  9  5  
F  3  5  2  7  9  
G  8  2  9  7  
H  6  9  5  1  3  7  
I  7  9  3  
J  K  L  M  N  O  P  Q  R  
There's a 4 in IK. There's a 3 in EM (because of DQ, FJ, and BO). There's a 3 in GL (because of IR) and a 1 in IL, a 1 in GQ (because of IL and HM), a 1 in CR (because of GQ), a 1 in FP (because of CR, HQ, and EK), a 1 in BN (because of AJ and CR), and a 1 in DO (because of EK, HM, and BN). That's all the 1s.  
A  1  6  4  7  5  3  9  
B  5  7  8  9  1  3  4  6  
C  2  3  9  5  7  1  
D  9  8  6  1  7  3  
E  4  1  7  3  8  9  5  
F  3  5  2  7  9  1  
G  8  2  3  9  1  7  
H  6  9  5  1  3  7  
I  7  4  1  9  3  
J  K  L  M  N  O  P  Q  R  
There's a 2 in AO, because the numbers missing from row C are the 4, 6, and 8. So there's an 8 in AQ, a 2 in BQ. The numbers missing from row E are a 2 and 6, but the 2 in AO means the 2 is in EP and the 6 is in EO.  
A  1  6  4  7  5  2  3  8  9  
B  5  7  8  9  1  3  4  2  6  
C  2  3  9  5  7  1  
D  9  8  6  1  7  3  
E  4  1  7  3  8  6  2  9  5  
F  3  5  2  7  9  1  
G  8  2  3  9  1  7  
H  6  9  5  1  3  7  
I  7  4  1  9  3  
J  K  L  M  N  O  P  Q  R  
The numbers missing from row G are 4, 5, and 6, so the numbers in IM and IO are the 2 and 8. The 2 has to be in IM (because of AO), and the 8 is in IO. There is an 8 in FR (because of DK and AQ).  
A  1  6  4  7  5  2  3  8  9  
B  5  7  8  9  1  3  4  2  6  
C  2  3  9  5  7  1  
D  9  8  6  1  7  3  
E  4  1  7  3  8  6  2  9  5  
F  3  5  2  7  9  1  8  
G  8  2  3  9  1  7  
H  6  9  5  1  3  7  
I  7  4  1  2  9  8  3  
J  K  L  M  N  O  P  Q  R  
There's an 8 in HP (because of IO, AQ, and FR), an 8 in CM (in EN and IO). There's a 6 in IP, and a 5 in IQ.  
A  1  6  4  7  5  2  3  8  9  
B  5  7  8  9  1  3  4  2  6  
C  2  3  9  8  5  7  1  
D  9  8  6  1  7  3  
E  4  1  7  3  8  6  2  9  5  
F  3  5  2  7  9  1  8  
G  8  2  3  9  1  7  
H  6  9  5  1  3  7  8  
I  7  4  1  2  9  8  6  5  3  
J  K  L  M  N  O  P  Q  R  
There's a 2 in DN (because of IM), a 6 in CN (because of EO), a 4 in CO. There's a 4 in GM, a 5 in GO, and a 6 in GM.  
A  1  6  4  7  5  2  3  8  9  
B  5  7  8  9  1  3  4  2  6  
C  2  3  9  8  6  4  5  7  1  
D  9  8  6  2  1  7  3  
E  4  1  7  3  8  6  2  9  5  
F  3  5  2  7  9  1  8  
G  8  2  3  6  4  5  9  1  7  
H  6  9  5  1  3  7  8  
I  7  4  1  2  9  8  6  5  3  
J  K  L  M  N  O  P  Q  R  
There's a 5 in DM (because of ER), a 4 in FM, a 6 in FQ, a 4 in DR, a 4 in HQ, and a 2 in HR.  
A  1  6  4  7  5  2  3  8  9  
B  5  7  8  9  1  3  4  2  6  
C  2  3  9  8  6  4  5  7  1  
D  9  8  6  5  2  1  7  3  4  
E  4  1  7  3  8  6  2  9  5  
F  3  5  2  4  7  9  1  6  8  
G  8  2  3  6  4  5  9  1  7  
H  6  9  5  1  3  7  8  4  2  
I  7  4  1  2  9  8  6  5  3  
J  K  L  M  N  O  P  Q  R  
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