SUDOKU #8  
 
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  
4  9  3  2  
4  1  7  
1  8  7  
6  9  
2  3  4  
4  8  5  
3  9  7  2  
1  
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  
B  4  9  3  2  
C  4  1  7  
D  1  8  7  
E  6  9  
F  2  3  4  
G  4  8  5  
H  3  9  7  2  
I  1  
J  K  L  M  N  O  P  Q  R  
There is a 1 in BR (because of CK and AO). There is a 4 in EO (because of BM, GN, and FP) and a 7 in FO (because of HM and CN). There is a 4 in DK (because of CJ, EO, and FP) and one in IL (because of CJ, DK, and GN).  
A  1  
B  4  9  3  2  1  
C  4  1  7  
D  4  1  8  7  
E  6  4  9  
F  2  3  7  4  
G  4  8  5  
H  3  9  7  2  
I  4  1  
J  K  L  M  N  O  P  Q  R  
The 3 in HK and BP means that there has to be a 3 in either IQ or IR, so the 3 in box GMIO has to be in GO. There is a 3 in AN (because of FM, GO, and BP). There is another 3 in CL (because of AN and BP).  
A  3  1  
B  4  9  3  2  1  
C  4  1  3  7  
D  4  1  8  7  
E  6  4  9  
F  2  3  7  4  
G  4  3  8  5  
H  3  9  7  2  
I  4  1  
J  K  L  M  N  O  P  Q  R  
There is an 8 in GQ and one in DO, so the 8 in column M has to be in either AM or CM. There is a 2 in BQ and another in HO, so there has to be a 2 in either AM or CM. That means that the 5 and 6 in box AMCO have to be in BN and CO. The 2 in BQ means that the 2 in box AJCL has to be in for A, so the 2 has to be in CM and the 8 has to be in AM.  
A  8  3  1  
B  4  9  3  2  1  
C  4  1  3  2  7  
D  4  1  8  7  
E  6  4  9  
F  2  3  7  4  
G  4  3  8  5  
H  3  9  7  2  
I  4  1  
J  K  L  M  N  O  P  Q  R  
The missing numbers from column M are 5, 6, and 9. But there are a 6 and 9 in row E, so a 5 is in EM.  
A  8  3  1  
B  4  9  3  2  1  
C  4  1  3  2  7  
D  4  1  8  7  
E  6  5  4  9  
F  2  3  7  4  
G  4  3  8  5  
H  3  9  7  2  
I  4  1  
J  K  L  M  N  O  P  Q  R  
The numbers missing from box AMCO are the 5 and 6. The numbers missing from row C are 5, 6, 8, and 9. But there is an 8 and a 9 in column Q, so the possible numbers in CQ are 5 and 6  the same as in CO. So the possible numbers in CP and CR are the 8 and 9. The numbers missing from column O are a 5 and 6, and the numbers missing from column M are a 6 and 9.  
A  8  3  1  
B  4  56  9  3  2  1  
C  4  1  3  2  7  56  89  56  89  
D  4  1  69  8  7  
E  6  5  4  9  
F  2  3  7  4  
G  69  4  3  8  5  
H  3  9  7  2  
I  4  1  56  
J  K  L  M  N  O  P  Q  R  
This puzzle is hard enough that I am trying to see patterns. Are there a couple squares in a row, column or box that have to be one of two numbers, so we can get more information about other squares?  
The numbers missing from row B are 5, 6, 7, 8. The numbers missing from row C are 5, 6, 8, 9. The numbers in row F are 1, 5, 6, 8, 9. There are a 1 and 5 in column R and a 9 in box DPFR, so the possible numbers in FR are a 6 or 8.  
A  8  3  1  
B  4  56  9  3  2  1  5678  
C  4  1  3  2  7  56  89  56  89  5689  
D  4  1  69  8  7  
E  6  5  4  9  
F  2  3  7  4  68  15689  
G  69  4  3  8  5  12679  
H  3  9  7  2  14568  
I  4  1  56  
J  K  L  M  N  O  P  Q  R  
The numbers missing from box APCR (aside from the 8 and 9) are 4, 5, 6, and 7, but there is a 5 and a 7 in column R. So the possible numbers in AR would be 4 and 6. The numbers missing from row H are 1, 4, 5, 6, and 8, but there are a 1 and 5 in column R and an 8 in box FPIR. So the possible numbers in HR would be a 4 and a 6. So the 4 and 6 have to be in AR or HR. That means that there cannot be a 6 in FR, which means that the 8 has to be in FR. That means there has to be a 9 in CR and an 8 in CP.  
A  8  3  1  46  
B  4  56  9  3  2  1  5678  
C  4  1  3  2  7  56  8  56  9  5689  
D  4  1  69  8  7  
E  6  5  4  9  23  
F  2  3  7  4  8  15689  
G  69  4  3  8  5  12679  
H  3  9  7  2  46  14568  
I  4  1  56  23  
J  K  L  M  N  O  P  Q  R  
There is a 2 and a 3 in ER and IR. There is a 1, 2, or 3 in EN, EP, and ER, but there is a 3 in AN and in BP. So the 3 has to be in ER, and that means the 2 is in IR. There has to be a 3 in DJ (because of ER and FM). There has to be a 7 and 8 in EJ and EL (because of DO, FR, FO, and DR).  
A  8  3  1  46  
B  4  56  9  3  2  1  5678  
C  4  1  3  2  7  56  8  56  9  56  
D  3  4  1  69  8  7  
E  78  6  78  5  4  9  3  
F  2  3  7  4  8  1569  
G  69  4  3  8  5  12679  
H  3  9  7  2  46  14568  
I  4  1  56  2  
J  K  L  M  N  O  P  Q  R  
The numbers missing from box DJFL are a 5 and 9, but there is a 9 in HL. So the 9 is in FK, and the 5 is in FL. The missing numbers from row F are a 1 and a 6, and the numbers missing from row E are a 1 and 2.  
A  8  3  1  46  
B  4  56  9  3  2  1  5678  
C  4  1  3  2  7  56  8  56  9  56  
D  3  4  1  69  8  7  
E  78  6  78  5  12  4  12  9  3  
F  2  9  5  3  16  7  4  16  8  1569  
G  69  4  3  8  5  12679  
H  3  9  7  2  46  14568  
I  4  1  56  2  
J  K  L  M  N  O  P  Q  R  
A 9 is in AJ (because of BO, HL, and FK), a 3 is in IQ (because of HK and BP), and a 4 is in HQ (because of FP). The 7 in box GPIR has to be in either GP or IP (because of HM), so there has to be a 7 in AQ.  
A  9  8  3  1  7  46  
B  4  56  9  3  2  1  5678  
C  4  1  3  2  7  56  8  56  9  56  
D  3  4  1  69  8  7  
E  78  6  78  5  12  4  12  9  3  
F  2  9  5  3  16  7  4  16  8  16  
G  69  4  3  8  5  12679  
H  3  9  7  2  4  46  1568  
I  4  1  56  3  2  
J  K  L  M  N  O  P  Q  R  
There has to be a 4 in AR (because of CJ, BM, and FP), so a 6 is in HR. The numbers missing from row H are 1, 5, and 8, but there is a 5 and an 8 in box GPIR, so a 1 has to be in HP. That means that a 2 has to be in EP, and a 1 is in EN.  
A  9  8  3  1  56  7  4  
B  4  56  9  3  2  1  5678  
C  4  1  3  2  7  56  8  56  9  56  
D  3  4  1  69  8  56  7  
E  78  6  78  5  1  4  2  9  3  
F  2  9  5  3  16  7  4  16  8  1569  
G  69  4  3  8  5  12679  
H  3  9  7  2  1  4  6  1568  
I  4  1  56  3  2  
J  K  L  M  N  O  P  Q  R  
A 6 has to be in FN, a 1 is in FQ. There has to be a 9 in DM, a 6 in GM, and a 2 in DN.  
A  9  8  3  1  56  7  4  
B  4  56  9  3  2  1  5678  
C  4  1  3  2  7  56  8  56  9  
D  3  4  1  9  2  8  56  56  7  
E  78  6  78  5  1  4  2  9  3  
F  2  9  5  3  6  7  4  1  8  
G  6  4  3  79  8  5  1279  
H  3  9  7  2  1  4  6  58  
I  4  1  56  79  3  2  
J  K  L  M  N  O  P  Q  R  
The numbers missing from row G are 1, 2, 7, and 9. But there is a 9 in HL, so the 9 has to be in GP. Another way to look at it is that there is a 1 and a 9 in columns K and L, so the 2 and 7 have to be in GK and GL. So there can't be a 7 in row G, and that means that square GP has to contain a 9. So there is a 7 in IP, and there is a 1 in GJ.  
A  9  8  3  1  56  7  4  
B  4  56  9  3  2  1  5678  
C  4  1  3  2  7  56  8  56  9  
D  3  4  1  9  2  8  56  56  7  
E  78  6  78  5  1  4  2  9  3  
F  2  9  5  3  6  7  4  1  8  
G  1  27  27  6  4  3  9  8  5  1279  
H  3  9  7  2  1  4  6  58  
I  4  1  56  7  3  2  
J  K  L  M  N  O  P  Q  R  
The number in IO has to be a 5 (since it can't be a 6), so there is a 6 in CO, a 5 in BN, a 5 in CQ, a 6 in AP, a 5 in DP, and a 6 in DQ.  
A  9  8  3  1  6  7  4  
B  4  5  9  3  2  1  
C  4  1  3  2  7  6  8  5  9  
D  3  4  1  9  2  8  5  6  7  
E  78  6  78  5  1  4  2  9  3  
F  2  9  5  3  6  7  4  1  8  
G  1  27  27  6  4  3  9  8  5  
H  3  9  7  2  1  4  6  
I  4  1  5  7  3  2  
J  K  L  M  N  O  P  Q  R  
There is a 5 in HJ (because of IO) and another 5 in AK (because of HJ, FL, and BN). So there is a 2 in AL.  
A  9  5  2  8  3  1  6  7  4  
B  4  5  9  3  2  1  
C  4  1  3  2  7  6  8  5  9  
D  3  4  1  9  2  8  5  6  7  
E  78  6  78  5  1  4  2  9  3  
F  2  9  5  3  6  7  4  1  8  
G  1  27  27  6  4  3  9  8  5  
H  5  3  9  7  2  1  4  6  
I  4  1  5  7  3  2  
J  K  L  M  N  O  P  Q  R  
The two in AL means there is a 7 in GL and a 2 in GK. The 7 in GL means there is an 8 in AL and a 7 in EJ.  
A  9  5  2  8  3  1  6  7  4  
B  4  5  9  3  2  1  
C  4  1  3  2  7  6  8  5  9  
D  3  4  1  9  2  8  5  6  7  
E  7  6  8  5  1  4  2  9  3  
F  2  9  5  3  6  7  4  1  8  
G  1  2  7  6  4  3  9  8  5  
H  5  3  9  7  2  1  4  6  
I  4  1  5  7  3  2  
J  K  L  M  N  O  P  Q  R  
There is a 7 in BK (because of EJ and GL), an 8 in BJ (because of EL), and a 6 in BL.  
A  9  5  2  8  3  1  6  7  4  
B  8  7  6  4  5  9  3  2  1  
C  4  1  3  2  7  6  8  5  9  
D  3  4  1  9  2  8  5  6  7  
E  7  6  8  5  1  4  2  9  3  
F  2  9  5  3  6  7  4  1  8  
G  1  2  7  6  4  3  9  8  5  
H  5  3  9  7  2  1  4  6  
I  4  1  5  7  3  2  
J  K  L  M  N  O  P  Q  R  
There is an 8 in HN, a 9 in IN, an 8 in IK, and a 6 in IJ.  
A  9  5  2  8  3  1  6  7  4  
B  8  7  6  4  5  9  3  2  1  
C  4  1  3  2  7  6  8  5  9  
D  3  4  1  9  2  8  5  6  7  
E  7  6  8  5  1  4  2  9  3  
F  2  9  5  3  6  7  4  1  8  
G  1  2  7  6  4  3  9  8  5  
H  5  3  9  7  8  2  1  4  6  
I  6  8  4  1  9  5  7  3  2  
J  K  L  M  N  O  P  Q  R  
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