SUDOKU #17        
             
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 16 square grid. You won't need to do mathematics or arithmetic. If you know how to count from 1 to 16, then you can do these puzzles. All of the techniques are based on these rules. Each puzzle starts with some boxes filled in. As you solve the puzzle, make one mistake, and many of the boxes filled in later may be wrong. So Sudoku is like a house of cards.  
             
I've been working on 16x16 puzzles for quite a while. 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.  
             
  A 7   4   16 15   12 2 10       6 9 11      
  B 12     9     3 10               8      
  C   15 8         9 5     6 16     3      
  D             11     8   9 14 15          
  E     3       14 2   15 10 7     11        
  F     9   6 12   16     14   7 10 3        
  G               13 3 16 11 8 6     1      
  H 14   10       7 15               9      
  I 16               15 3       9   2      
  J 9     3 7 1 4 5 8                    
  K   7 15 8   14     16   4 13   5          
  L   13     15 8 16   7 1       3          
  M     5 7 9   15     12                  
  N 15     11 10     14 13         4 1        
  O 3               10 6     15     7      
  P 4 8 1       6 7 14   15 5   2   10      
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
         
This is an evil version of a Sudoku puzzle. I've added the letters below to the rows and columns in order to talk about each of the 256 squares. As a convention, I will talk about squares and boxes. There are 256 squares, but there are 16 boxes of 16 squares.  
   
        1
3
4
6
8
11
1
4
6
9
11
12
             
  A 7   4   16 15   12 2 10       6 9 11 1,3,5,8,13,14  
  B 12     9     3 10       15       8    
  C   15 8         9 5     6 16     3    
  D             11     8   9 14 15        
  E     3       14 2   15 10 7     11      
  F     9   6 12   16     14   7 10 3      
  G               13 3 16 11 8 6     1    
  H 14   10   3 3 7 15               9    
  I 16               15 3       9   2    
  J 9     3 7 1 4 5 8                  
  K   7 15 8 3 14   3 16   4 13   5        
  L   13     15 8 16   7 1       3        
  M     5 7 9   15     12                
  N 15     11 10     14 13         4 1      
  O 3               10 6     15     7    
  P 4 8 1       6 7 14   15 5   2   10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
                                 
The 15s in C2, D14, and A6 mean that the 15 in Box A9-D12 has to be in Row B, and the 15s in I9, E10, and P11 mean that the 15 in Box A9-D12 has to be in B12. There is a 3 in either H5 or H6 (E3, F15, and G9). There is a 3 in either K5 or K8 (I10, L14, B7). One thing I like to do is look for rows or columns that have 6 or less missing numbers. Row A is missing the 1,3,5,8,13,and 14; Row P is missing 3,9,11,12,13,and 16; Column 8 is missing 1,3,4,6,8, and 11; Column 9 is missing 1,4,6,9,11, and 12.  
   
        1
3
4
6
8
11
1
4
6
9
11
12
             
  A 7   4   16 15   12 2 10       6 9 11 1,3,5,8,13,14  
  B 12     9     3 10       15   7   8    
  C   15 8         9 5     6 16 7   3    
  D             11     8   9 14 15        
  E     3     9 14 2 9 15 10 7     11      
  F     9   6 12   16     14   7 10 3      
  G     7     9   13 3 16 11 8 6     1    
  H 14   10   3 3 7 15               9    
  I 16               15 3       9 7 2    
  J 9     3 7 1 4 5 8                  
  K   7 15 8 3 14 9 3 16   4 13   5        
  L   13     15 8 16   7 1 9     3        
  M     5 7 9   15     12                
  N 15     11 10     14 13 7,9 7     4 1      
  O 3               10 6     15     7    
  P 4 8 1       6 7 14 9 15 5   2   10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
                     
There is a 7 in I15 (K2, J5, L9, F13), and there is a 7 in G3 (A1,K2,M4). There is a 7 in either B14 or C14 (F13,I15,O16), and there is a 7 in either N10 or N11 (M4,P8,O16,E12). There has to be a 9 in K7 (M5, C8, I14). The 9 in Box E5-H8 is either in E6 or G6 (M5,K7,H16). There is a 9 in L11 (J1,K7,I14,D12). There is a 9 in either N10 or P10 (D12,L11,M5). So there is a 9 in E9 (D12,L11,N10/P10,F3,H16), and there is a 9 in G6.  
         
         
        1
3
4
6
8
11
1
4
6
9
11
12
             
  A 7 3 4   16 15   12 2 10       6 9 11 1,3,5,8,13,14  
  B 12     9     3 10       15   7   8    
  C   15 8         9 5     6 16 7,12 12 3    
  D   3         11   12 8   9 14 15        
  E     3       14 2 9 15 10 7     11      
  F     9   6 12   16     14   7 10 3      
  G     7     9   13 3 16 11 8 6     1    
  H 14   10   3 3 7 15 6   12 12       9    
  I 16               15 3 6     9 7 2    
  J 9     3 7 1 4 5 8   6              
  K   7 15 8 2 14 9 3 16   4 13   5        
  L   13     15 8 16   7 1 9     3        
  M     5 7 9   15     12                
  N 15     11 10     14 13 7,9 7     4 1      
  O 3               10 6     15     7    
  P 4 8 1       6 7 14 9 15 5   2   10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
                   
There is a 3 in either A2 or D2 (O1,E3,J4,C7). There is a 2 in K5 (I16,E8), so there is a 3 in K8. There is a 6 in either I11 or J11 (O10,C12), so there is a 6 in H9 (F5). There is a 12 in D9 (M10,F6,B1), so there is a 12 in either C14 or D14 - and either H11 or H12.  
   
      1
3
4
6
8
11
1
4
6
9
11
12
             
  A 7 3 4   16 15   12 2 10       6 9 11 1,3,5,8,13,14  
  B 12     9     3 10       15   7   8    
  C   15 8         9 5     6 16 7,12 12 3    
  D   3         11   12 8   9 14 15        
  E     3       14 2 9 15 10 7     11      
  F 11 11 9   6 12   16     14   7 10 3      
  G     7     9 10 13 3 16 11 8 6 14 14 1    
  H 14   10   3,11 3,11 7 15 6   12 12       9    
  I 16         10     15 3 6     9 7 2    
  J 9     3 7 1 4 5 8   6              
  K   7 15 8 2 14 9 3 16   4 13   5        
  L   13     15 8 16   7 1 9     3        
  M     5 7 9   15     12                
  N 15     11 10     14 13 7,9 7   9 4 1      
  O 3 9             10 6     15     7    
  P 4 8 1       6 7 14 9 15 5 9 2   10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
      -
1,4,5,8,
10
6,
10,11,12,13
-
         
                       
There is an 11 in either H5 or H6 (D7,E15,G11), so there is an 11 in either F1 or F2 (N4,E15,G11,H5/H6). There is a 9 in either N13 or P13 (A15,H16,I14,M5). The 9s in N10/P10 and N13/P13 cancel themselves out for Rows N and P, and since there is a 9 in M5, the 9 in Box M1-P4 has to be in Row O - and since there is a 9 in B4 and F3, the 9 in Box M1-P4 has to be in O2. There is a 14 in either G14 or G15 (H1,E7,F11). There is a 10 in G7 (N5,E11,G14), and another 10 is in I6 (N5,B8,G7).  
                   
      1
3
4
6
8
11
1
4
6
9
11
12
             
  A 7 3 4   16 15 8 12 2 10       6 9 11 1,3,5,8,13,14  
  B 12     9     3 10       15   7   8    
  C   15 8         9 5     6 16 7,12 12 3    
  D   3         11 1,4 12 8   9 14 15        
  E     3   8 4,5 14 2 9 15 10 7     11      
  F 11 11 9   6 12 1 16     14   7 10 3      
  G     7   4,5 9 10 13 3 16 11 8 6 14 14 1    
  H 14   10   3,11 3,11 7 15 6   1,12 1,12       9    
  I 16       12,13 10 12,13 6,11 15 3 6     9 7 2    
  J 9     3 7 1 4 5 8   6              
  K   7 15 8 2 14 9 3 16   4 13   5        
  L   13     15 8 16 6,11 7 1 9     3        
  M 10 10 5 7 9   15 8   12                
  N 15     11 10     14 13 7,9 7   9 4 1      
  O 3 9           8 10 6     15     7    
  P 4 8 1       6 7 14 9 15 5 9 2   10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
      -
1,4,5,8,10
6,
10,11,12,13
-
-
2,4,5,13
-
-
       
The 12 and 13 of Box I5-L8 are in I5 and I7 (A8,G8), so the 6 and 11 are in I8 and L8. There is an 8 in A7 (B16,C3,D10). The 8 in Column 8 is in M8 or O8 (D10). There is an 8 in E5 (M8/O8,A7,L6,G12). There is a 1 in F7 (G16,J6). The 1 in Box E9-H12 is either in H11 or H12 (F7,G16,L10). The numbers missing from Box E5-H8 are the 4 and 5 in E6 and G5. There is a 4 in F9, since the missing number from Column 9 are 1,4,11, and the 1 in F7 and 11 in G11 means the 4 has to be in F9. The numbers missing from Box E9-H12 are 2,4,5,13.  
                               
      2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
             
  A 7 3 4   16 15 8 12 2 10       6 9 11 1,3,5,8,13,14  
  B 12     9     3 10 11     15   1,7   8    
  C 11 15 8         9 5     6 16 1,7 12 3    
  D   3         11 1,4 12 8   9 14 15        
  E     3   8 4,5 14 2 9 15 10 7     11      
  F   11 9   6 12 1 16 4 5 14   7 10 3   2,5,8,13,15  
  G     7   4,5 9 10 13 3 16 11 8 6 14 14 1 2,4,5,12,14,15  
  H 14   10   3,11 3,11 7 15 6 5 1,12 1,12       9 2,4,5,8,13,16  
  I 16       12,13 10 12,13 6,11 15 3 5     9 7 2    
  J 9     3 7 1 4 5 8   6              
  K   7 15 8 2 14 9 3 16 11 4 13   5     1,6,10,12  
  L 5 13   5 15 8 16 6,11 7 1 9     3        
  M 10 10 5 7 9   15 8 1 12                
  N 15     11 10     14 13 7,9 7   9 4 1      
  O 3 9           8 10 6     15     7    
  P 4 8 1       6 7 14 9 15 5 9 2   10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
      -
1,4,5,8,10
6,10,11,12,13
-
-
2,
4,5,13
2,10,
11,12,14
-
       
The 5 in Box E9-H12 is either in F10 or H10 (C9,P12), so there is a 5 in I11 (J8) and the 6 is in J11. The 5 in Box I1-L4 is either in L1 or L4. There is a 4 in F9 (F7,G11). The missing numbers in Box I9-L12 are 2,10,11,12,14, so there is an 11 in K10 (M10,A10,K5,K6). There is an 11 in B9 (K10,G11,A16), so the 1 is in M9. There has to be a 1 in either B14 or C14 (J6,N15,G16), and since there also has to be a 7 in B14 or C14, then there has to be a 12 in C15. There is an 11 in C1 (A16,B9,D7,N4), and another 11 in F2.  
                       
      2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
             
  A 7 3,14 4 14 16 15 8 12 2 10       6 9 11 1,3,5,8,13,14  
  B 12     9 14   3 10 11 14   15   1,7   8    
  C 11 15 8 10 14   2,13 9 5 14   6 16 1,7 12 3    
  D   3         11 1,4 12 8   9 14 15 10      
  E     3   8 4,5 14 2 9 15 10 7     11      
  F   11 9   6 12 1 16 4 5 14   7 10 3   2,5,8,13,15  
  G     7   4,5 9 10 13 3 16 11 8 6 14 14 1 2,4,5,12,14,15  
  H 14   10   3,11 3,11 7 15 6 5 12 1       9 2,4,5,8,13,16  
  I 16       12,13 10 12,13 6,11 15 3 5 14 8 9 7 2 1,4,6,8,11,14  
  J 9     3 7 1 4 5 8 2 6 10,12            
  K   7 15 8 2 14 9 3 16 11 4 13 1 5     1,6,10,12  
  L 5 13   5 15 8 16 6,11 7 1 9 10,12   3        
  M 10 10 5 7 9   15 8 1 12                
  N 15     11 10     14 13 7,9 7   9 4 1      
  O 3 9           8 10 6     15     7    
  P 4 8 1       6 7 14 9 15 5 9 2   10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
      -
1,4,5,8,10
6,10,11,12,13
-
-
2,
4,5,13
2,10,11,12,14
-
2,4,5,13
-
-
-
     
There is a 10 in D15 (P16,A10,B8), so there is a 10 in C4 (A10,B8,D15). There is a 1 in H12 (M10) and a 12 in H11. The missing numbers in Box I9-L12 are 2,10,12,14. There is a 2 in I16, a 10 in I6, and a 12 in either I5 or I7, so there is a 14 in I12. And because there is a 10 in A10 and a 12 in M10, there is a 2 in J10. That means the 14 in Box A9-D12 is either in B10 or C10. Because there is a 14 in D13 and 14s in F11 and I12, the 14 in Box A1-D4 is either in A2 or A4. There has to be an 8 in I13 (K4,L6), which means there is a 1 in K13.  
                           
    2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
4
7
9
14
           
  A 7 3,14 4 14 16 15 8 12 2 10     5,13 6 9 11 1,3,5,8,13,14  
  B 12     9 14   3 10 11 4,14   15 2 1,7 2 8    
  C 11 15 8 10 14 2 2,13 9 5 4,14   6 16 1,7 12 3    
  D   3         11 1,4 12 8   9 14 15 10      
  E     3   8 4,5 14 2 9 15 10 7     11      
  F   11 9   6 12 1 16 4 5,13 14 2 7 10 3   2,5,8,13,15  
  G     7   4,5 9 10 13 3 16 11 8 6 14 14 1 2,4,5,12,14,15  
  H 14   10   3,11 3,11 7 15 6 5,13 12 1       9 2,4,5,8,13,16  
  I 16 1,4 6,11 1,4 12,13 10 12,13 6,11 15 3 5 14 8 9 7 2 1,4,6,8,11,14  
  J 9     3 7 1 4 5 8 2 6 10,12            
  K 10 7 15 8 2 14 9 3 16 11 4 13 1 5 6 12 1,6,10,12  
  L 5 13   5 15 8 16 6,11 7 1 9 10,12   3        
  M   10 5 7 9   15 8 1 12           6    
  N 15     11 10     14 13 7     9 4 1 6    
  O 3 9           8 10 6     15     7    
  P 4 8 1       6 7 14 9 15 5   2   10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
      -
1,4,5,8,10
6,10,11,12,13
-
-
2,4,5,13
2,10,11,12,14
-
2,4,5,13
-
-
-
     
                       
The missing numbers from Row I are 1,4,6,11. The 4 in A3 and the 1 in P3 means there is either a 6 or 11 in I3 - which means the 1 and 4 are in I2 and I4. The missing numbers from Row K are 6,10,12, so there is a 10 in K1 (C15,P16), a 6 in K15 (C15,D15), and a 12 in K16. So there is a 10 in M2. The 2 in Box A13-D16 is in either B13 or B15 (A9,P14,I16). Therefore the 2 in Box A1-D4 is in Row D (A9,B13/B15), and the 2 in Box A5-D8 has to be either in C6 or C7. There has to be a 2 in F12 (J10). The missing numbers from Column 10 are 4,7,9,14. The 4s in N14 and P1, and the 14 in P9, mean that the 7 and 9 have to be in N10 and P10. But the 7 in P8 means that the 9 is in P10, and the 7 is in N10. So the 4 and 14 have to be in B10 and C10. And there is a 9 in N13.  
                       
    2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
4
7
9
14
  3
4
11
16
           
  A 7 14 4 14 16 15 8 12 2 10 1,13 3 5,13 6 9 11 1,3,5,8,13,14  
  B 12     9 14   3 10 11 4,14   15 2 1,7 2 8    
  C 11 15 8 10 14 2 2,13 9 5 4,14   6 16 1,7 12 3    
  D   3         11 1,4 12 8   9 14 15 10      
  E     3   8 4,5 14 2 9 15 10 7     11      
  F 8 11 9   6 12 1 16 4 5,13 14 2 7 10 3   2,5,8,13,15  
  G     7   4,5 9 10 13 3 16 11 8 6 14 14 1 2,4,5,12,14,15  
  H 14   10   3,11 3,11 7 15 6 5,13 12 1   8 8 9 2,4,5,8,13,16  
  I 16 1,4 6,11 1,4 12,13 10 12,13 6,11 15 3 5 14 8 9 7 2 1,4,6,8,11,14  
  J 9     3 7 1 4 5 8 2 6 10,12            
  K 10 7 15 8 2 14 9 3 16 11 4 13 1 5 6 12 1,6,10,12  
  L 5 13   5 15 8 16 6,11 7 1 9 10,12   3        
  M   10 5 7 9   15 8 1 12 3 4,11       6    
  N 15     11 10     14 13 7 8 16 9 4 1 6    
  O 3 9           8 10 6 2 4,11 15     7    
  P 4 8 1       6 7 14 9 15 5   2   10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
      -
1,4,5,8,10
6,10,11,12,13
-
1,7,13,16
2,4,5,13
2,10,11,12,14
2,3,
8 - 4,11,16
2,4,5,13
-
-
-
     
                   
The numbers missing from Column 12 are 3,4,11,16, so the 3 is in A12 (A3,A5,A16). And there is a 3 in D2. The missing numbers from Box M9-P12 are 2,3,8 in Column 11 and the 4,11,16 in Column 12. So the 16 is in N12 (N4,N14). There is an 8 in F1 (P2,C3,K4,E5,G12). The 8 in Box M5-P8 is either in Row M or O, and the 8 in Box M13-P16 is also either in Row M or O (I13,P2,B16). So the third 8 of Rows M-P has to be in Row N - that is in N11, which means that there is a 3 in M11 (O1) and a 2 in O11.  
                   
    2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
4
7
9
14
  3
4
11
16
           
  A 7 14 4 14 16 15 8 12 2 10 1,13 3 5,13 6 9 11 1,3,5,8,13,14  
  B 12     9 14   3 10 11 4,14   15 2 1,7 2 8    
  C 11 15 8 10 14   2 9 5 4,14   6 16 1,7 12 3    
  D   3         11 1,4 12 8   9 14 15 10      
  E     3   8 4,5 14 2 9 15 10 7     11      
  F 8 11 9   6 12 1 16 4 5,13 14 2 7 10 3   2,5,8,13,15  
  G     7   4,5 9 10 13 3 16 11 8 6 14 14 1 2,4,5,12,14,15  
  H 14   10   3 11 7 15 6 5,13 12 1   8 8 9 2,4,5,8,13,16  
  I 16 1,4 6,11 1,4 12 10 13 6,11 15 3 5 14 8 9 7 2 1,4,6,8,11,14  
  J 9     3 7 1 4 5 8 2 6 10,12            
  K 10 7 15 8 2 14 9 3 16 11 4 13 1 5 6 12 1,6,10,12  
  L 5 13   5 15 8 16 6,11 7 1 9 10,12   3        
  M   10 5 7 9   15 8 1 12 3 4,11       6    
  N 15 2,6 2,6 11 10 3 12 14 13 7 8 16 9 4 1 5 2,5,6  
  O 3 9         5 8 10 6 2 4,11 15 12   7    
  P 4 8 1 12 11   6 7 14 9 15 5 3 2   10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
    -
-
-
13,14,16
-
1,4,5,8,10
6,10,11,12,13
-
1,7,13,16
2,4,5,13
2,10,11,12,14
2,3,8 - 4,11,16
2,4,5,13
-
-
-
     
                   
One of the missing numbers from Row N is a 3. There is no 3 in N2 or N3 (O1), and there is not a 3 in N16 (C16). So there has to be a 3 in N6 (B7). Therefore there is a 3 in H5 and an 11 in H6. There is a 3 in P13 (O1,N6,M11,C16,F15,L14). The 11 in Box M9-P12 is in Row M or O, and the same can be said for the 11 in Box M13-P16, so the 11 in Box M5-P8 is in P5 (H6). There is a 12 in P4 (F6,C15). There is a 12 in O14 (P4,M10,K16,C15), and another one in N7. There is a 13 in I7 and a 12 in I5. There is a 2 in C7 and a 5 in O7. There is a 5 in N16 and a 6 in M16, so there is a 2 or 6 in N2 and N3.  
                     
  1
2
5
6
  1
4
5
13
14
  2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
4
7
9
14
      12
14
16
         
  A 7 14 4 14 16 15 8 12 2 10 1,13 3 5,13 6 9 11 1,3,5,8,13,14  
  B 12     9 14   3 10 11 4,14   15 2 1,7 2 8    
  C 11 15 8 10 14   2 9 5 4,14   6 16 1,7 12 3    
  D   3         11 1,4 12 8   9 14 15 10      
  E     3   8 4,5 14 2 9 15 10 7     11      
  F 8 11 9   6 12 1 16 4 5,13 14 2 7 10 3   2,5,8,13,15  
  G     7   4,5 9 10 13 3 16 11 8 6 14 14 1 2,4,5,12,14,15  
  H 14   10   3 11 7 15 6 5,13 12 1   8   9 2,4,5,8,13,16  
  I 16 1,4 6,11 1,4 12 10 13 6,11 15 3 5 14 8 9 7 2 1,4,6,8,11,14  
  J 9     3 7 1 4 5 8 2 6 10,12   11        
  K 10 7 15 8 2 14 9 3 16 11 4 13 1 5 6 12 1,6,10,12  
  L 5 13   5 15 8 16 6,11 7 1 9 10,12   3        
  M 13 10 5 7 9 2 15 8 1 12 3 4 11 14,16 14,16 6 2,8,11,14,16  
  N 15 2,6 2,6 11 10 3 12 14 13 7 8 16 9 4 1 5 2,5,6  
  O 3 9 14,16 14,16     5 1,4 10 6 2 11 15 12 8 7 1,4,8,13  
  P 4 8 1 12 11   6 7 14 9 15 5 3 2 13 10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
    -
-
-
13,14,16
-
1,4,5,8,10
6,10,11,12,13
-
1,7,13,16
2,4,5,13
2,10,11,12,14
2,3,8 - 4,11,16
2,4,5,13
-
4,10,14 - 13,15,16
8,11,13,14,16
     
                                         
The numbers missing from Box M1-P4 are 13,14,16, so there is a 13 in M1 (H1,I1). The 11 in Box M13-P16 is either in M13 or M14 (E15), so there is a 4 in M12 and an 11 in O12. The numbers missing from Row M are 2,8,11,14,16, so there is an 11 in M13 (P14,I13,D13,C13). There is an 11 in J14 (M13,E15,A16). The numbers missing from Column 8 are 1,4,8, so there is an 8 in M8 (M9,M12). There is an 8 in O15, a 13 in P15, and an 8 in H14. There is a 14 and a 16 in M14 and M15, so there is a 2 in M6.  
                                         
  1
2
5
6
  1
4
5
13
14
  2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
4
7
9
14
  3
4
11
16
  12
14
16
         
  A 7 14 4 14 16 15 8 12 2 10 1,13 3 5 6 9 11 1,3,5,8,13,14  
  B 12     9     3 10 11 14   15 4 1,7 2 8    
  C 11 15 8 10 14   2 9 5 4   6 16 1,7 12 3    
  D   3         11 1,4 12 8   9 14 15 10 13    
  E     3   8 4,5 14 2 9 15 10 7   13 11      
  F 8 11 9   6 12 1 16 4 5,13 14 2 7 10 3   2,5,8,13,15  
  G     7   4,5 9 10 13 3 16 11 8 6 14   1 2,4,5,12,14,15  
  H 14   10   3 11 7 15 6 5,13 12 1   8   9 2,4,5,8,13,16  
  I 16 1,4 6,11 1,4 12 10 13 6,11 15 3 5 14 8 9 7 2 1,4,6,8,11,14  
  J 9     3 7 1 4 5 8 2 6 10 13 11        
  K 10 7 15 8 2 14 9 3 16 11 4 13 1 5 6 12 1,6,10,12  
  L 5 13   5 15 8 16 6,11 7 1 9 12 10 3 4 14    
  M 13 10 5 7 9 2 15 8 1 12 3 4 11 16 14 6 2,8,11,14,16  
  N 15 2,6 2,6 11 10 3 12 14 13 7 8 16 9 4 1 5 2,5,6  
  O 3 9 14,16 14,16     5 1,4 10 6 2 11 15 12 8 7 1,4,8,13  
  P 4 8 1 12 11 16 6 7 14 9 15 5 3 2 13 10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
    -
-
-
13,14,16
-
1,4,5,8,10
6,10,11,12,13
-
1,7,13,16
2,4,5,13
2,10,11,12,14
2,3,8 - 4,11,16
2,4,5,13
-
4,10,14 -
13,15,16
8,11,13,14,16
     
                                         
The numbers missing from Box I13-L16 are 4,10,13,14,15,16. The 13,15,16 are already in Row L, so they end up in Row J in Box I13-L16, and the 4,10,14 are in Row L. Therefore, the 13 is in J13 - which means that the 5 is in A13. There is a 13 in D16 (J13,P15) and another 13 in E14 (P15,J13,D16,G8). There is a 2 and a 4 in B13 and B15, so there is a 14 in B10 and a 4 in C10 - which means there is a 14 in C5. The numbers missing from Column 14 are 14 and 16, so there is a 14 in G14, a 16 in M14, and a 14 in M15. There is a 16 in P6 (only number missing). There is a 4 in L15 (D15,M15), a 14 in L16 (P16), and a 10 in L13. There is a 2 in B15 (L15), a 4 in B13, a 12 in L12, and a 10 in J12.  
                                         
  1
2
5
6
  1
4
5
13
14
  2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
4
7
9
14
  3
4
11
16
2
12
12
14
16
5
15
16
4
15
16
     
  A 7 1,14 4 1,14 16 15 8 12 2 10 13 3 5 6 9 11 1,3,5,8,13,14  
  B 12   13 9     3 10 11 14   15 4 1,7 2 8    
  C 11 15 8 10 14 13 2 9 5 4 1,7 6 16 1,7 12 3 1,7,13  
  D   3         11 4 12 8   9 14 15 10 13    
  E     3   8 5 14 2 9 15 10 7 12 13 11 4    
  F 8 11 9 13 6 12 1 16 4 5,13 14 2 7 10 3 15 2,5,8,13,15  
  G     7   4 9 10 13 3 16 11 8 6 14 5 1 2,4,5,12,14,15  
  H 14   10 13 3 11 7 15 6 5,13 12 1 2 8 16 9 2,4,5,8,13,16  
  I 16 1,4 6,11 1,4 12 10 13 6,11 15 3 5 14 8 9 7 2 1,4,6,8,11,14  
  J 9 12,14 12,14 3 7 1 4 5 8 2 6 10 13 11 15 16 12,14 - 15,16  
  K 10 7 15 8 2 14 9 3 16 11 4 13 1 5 6 12 1,6,10,12  
  L 5 13   5 15 8 16 6,11 7 1 9 12 10 3 4 14    
  M 13 10 5 7 9 2 15 8 1 12 3 4 11 16 14 6 2,8,11,14,16  
  N 15 2,6 2,6 11 10 3 12 14 13 7 8 16 9 4 1 5 2,5,6  
  O 3 9 14,16 14,16 13 4 5 1 10 6 2 11 15 12 8 7 1,4,8,13  
  P 4 8 1 12 11 16 6 7 14 9 15 5 3 2 13 10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
    -
-
-
13,14,16
1,5 - 6,7
1,4,5,8,10
6,10,11,12,13
-
1,7,13,16
2,4,5,13
2,10,11,12,14
2,3,8 - 4,11,16
2,4,5,13
-
4,10,14 - 13,15,16
8,11,13,14,16
     
                                         
There is a 13 in either F4 or H4 (M1,L2,E14,G8), so there is a 13 in B3 (D16). So there has to be a 13 in A11. There has to be a 13 in C6 (because the 1,7,13 are missing from Row C, and there is a 13 in D16 and A11). The numbers missing from Row O are 1,4,13, so the 13 is in O5 (G8,C6). So there is a 4 in O6, a 1 in O8, a 4 in D8. There is a 5 in E6 (O6) and a 4 in G5. The missing numbers from Column 16 are 4,15,16, so there is a 4 in E16 (F9,J7). The numbers missing from Column 13 are 2 and 12, so the 12 is in E13 and the 2 is in H13, a 15 in F16, the 16 is in J16, and the 15 is in J15. The numbers missing from Column 15 are the 5 and 16, so the 16 is in H15 and the 5 is in G15.  
                                         
  1
2
5
6
2
5
6
16
  1
4
5
13
14
  2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
4
7
9
14
  3
4
11
16
2
12
12
14
16
5
15
16
4
15
16
     
  A 7 1 4 14 16 15 8 12 2 10 13 3 5 6 9 11 1,3,5,8,13,14  
  B 12   13 9     3 10 11 14   15 4 1,7 2 8    
  C 11 15 8 10 14 13 2 9 5 4 1,7 6 16 1,7 12 3 1,7,13  
  D   3         11 4 12 8   9 14 15 10 13    
  E 1   3   8 5 14 2 9 15 10 7 12 13 11 4 1,6,16  
  F 8 11 9 5,13 6 12 1 16 4 5,13 14 2 7 10 3 15 2,5,8,13,15  
  G 2 12 7 15 4 9 10 13 3 16 11 8 6 14 5 1 2,4,5,12,14,15  
  H 14   10 13 3 11 7 15 6 5,13 12 1 2 8 16 9 2,4,5,8,13,16  
  I 16 4 6,11 1 12 10 13 6,11 15 3 5 14 8 9 7 2 1,4,6,8,11,14  
  J 9 14 12 3 7 1 4 5 8 2 6 10 13 11 15 16 12,14 - 15,16  
  K 10 7 15 8 2 14 9 3 16 11 4 13 1 5 6 12 1,6,10,12  
  L 5 13 11 5 15 8 16 6,11 7 1 9 12 10 3 4 14 2,5,6,11  
  M 13 10 5 7 9 2 15 8 1 12 3 4 11 16 14 6 2,8,11,14,16  
  N 15 2,6 2,6 11 10 3 12 14 13 7 8 16 9 4 1 5 2,5,6  
  O 3 9 14 16 13 4 5 1 10 6 2 11 15 12 8 7 1,4,8,13  
  P 4 8 1 12 11 16 6 7 14 9 15 5 3 2 13 10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
    2,5,6,16
-
-
13,14,16
1,5 - 6,7
1,4,5,8,10
6,10,11,12,13
-
1,7,13,16
2,4,5,13
2,10,11,12,14
2,3,8 - 4,11,16
2,4,5,13
-
4,10,14 - 13,15,16
8,11,13,14,16
     
                                         
One of the missing numbers from Column 1 is a 1. There can't be a 1 in L1 (L10), there can't be a 1 in D1 (A2/A4), and there can't be a 1 in G16, so the 1 has to be in E1. There has to be a 2 in G1 (G15,G13). The numbers missing from Row G are 12 and 15, so the 12 is in G2, and the 15 is in G4 - which means that the 14 is in J2, and the 12 is in J3. And this means that a 1 is in A2, and a 14 is in A4 - which means that a 16 is in O4, and a 14 is in O3. There is a 4 in I2 (A2), so there is a 1 in I4.  
                                         
    1
2
5
6
2
5
6
16
  2
5
1
4
5
13
14
  2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
4
7
9
14
  3
4
11
16
2
12
12
14
16
5
15
16
4
15
16
     
  A 7 1 4 14 16 15 8 12 2 10 13 3 5 6 9 11 1,3,5,8,13,14  
  B 12 6 13 9     3 10 11 14 16 15 4 1,7 2 8 1,5,6,7  
  C 11 15 8 10 14 13 2 9 5 4 1,7 6 16 1,7 12 3 1,7,13  
  D   3 16 2,5     11 4 12 8 1,7 9 14 15 10 13    
  E 1 16 3 6 8 5 14 2 9 15 10 7 12 13 11 4 1,6,16  
  F 8 11 9 13 6 12 1 16 4 5 14 2 7 10 3 15 2,5,8,13,15  
  G 2 12 7 15 4 9 10 13 3 16 11 8 6 14 5 1 2,4,5,12,14,15  
  H 14 5 10 4 3 11 7 15 6 13 12 1 2 8 16 9 2,4,5,8,13,16  
  I 16 4 11 1 12 10 13 6 15 3 5 14 8 9 7 2 1,4,6,8,11,14  
  J 9 14 12 3 7 1 4 5 8 2 6 10 13 11 15 16 12,14 - 15,16  
  K 10 7 15 8 2 14 9 3 16 11 4 13 1 5 6 12 1,6,10,12  
  L 5 13   2,5 15 8 16 11 7 1 9 12 10 3 4 14 2,5,6,11  
  M 13 10 5 7 9 2 15 8 1 12 3 4 11 16 14 6 2,8,11,14,16  
  N 15 2 6 11 10 3 12 14 13 7 8 16 9 4 1 5 2,5,6  
  O 3 9 14 16 13 4 5 1 10 6 2 11 15 12 8 7 1,4,8,13  
  P 4 8 1 12 11 16 6 7 14 9 15 5 3 2 13 10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
    2,5,6,16
-
2,5,6,11
13,14,16
1,5 - 6,7
1,4,5,8,10
6,10,11,12,13
-
1,7,13,16
2,4,5,13
2,10,11,12,14
2,3,8 - 4,11,16
2,4,5,13
-
4,10,14 - 13,15,16
8,11,13,14,16
     
                                         
There is a 16 in E2 (O4,I1,H15) and another 16 in D3 - and another in B11 (D3,A5,C13). The numbers missing from Column 2 are 2,5,6, so there is a 5 in H2, which means there is a 13 in H10 and a 5 in F10. Therefore there is a 13 in F4 and a 4 in H4. There is a 6 in E4. The numbers missing from Column 2 are the 2 and 5, so there is a 5 in B2 and a 2 in N2 - which means that there is a 6 in N3, an 11 in I3, a 6 in I8, and an 11 in L8.  
                                         
    1
2
5
6
2
5
6
16
  2
5
1
4
5
13
14
  2
5
12
13
1
3
4
6
8
11
1
4
6
9
11
12
4
7
9
14
  3
4
11
16
2
12
12
14
16
5
15
16
4
15
16
     
  A 7 1 4 14 16 15 8 12 2 10 13 3 5 6 9 11 1,3,5,8,13,14  
  B 12 6 13 9 5 7 3 10 11 14 16 15 4 1 2 8 1,5,6,7  
  C 11 15 8 10 14 13 2 9 5 4 1 6 16 7 12 3 1,7,13  
  D 5 3 16 2 1 6 11 4 12 8 7 9 14 15 10 13    
  E 1 16 3 6 8 5 14 2 9 15 10 7 12 13 11 4 1,6,16  
  F 8 11 9 13 6 12 1 16 4 5 14 2 7 10 3 15 2,5,8,13,15  
  G 2 12 7 15 4 9 10 13 3 16 11 8 6 14 5 1 2,4,5,12,14,15  
  H 14 5 10 4 3 11 7 15 6 13 12 1 2 8 16 9 2,4,5,8,13,16  
  I 16 4 11 1 12 10 13 6 15 3 5 14 8 9 7 2 1,4,6,8,11,14  
  J 9 14 12 3 7 1 4 5 8 2 6 10 13 11 15 16 12,14 - 15,16  
  K 10 7 15 8 2 14 9 3 16 11 4 13 1 5 6 12 1,6,10,12  
  L 6 13 2 5 15 8 16 11 7 1 9 12 10 3 4 14 2,5,6,11  
  M 13 10 5 7 9 2 15 8 1 12 3 4 11 16 14 6 2,8,11,14,16  
  N 15 2 6 11 10 3 12 14 13 7 8 16 9 4 1 5 2,5,6  
  O 3 9 14 16 13 4 5 1 10 6 2 11 15 12 8 7 1,4,8,13  
  P 4 8 1 12 11 16 6 7 14 9 15 5 3 2 13 10 3,9,11,12,13,16  
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
    2,5,6,16
-
2,5,6,11
13,14,16
1,5 - 6,7
1,4,5,8,10
6,10,11,12,13
-
1,7,13,16
2,4,5,13
2,10,11,12,14
2,3,8 - 4,11,16
2,4,5,13
-
4,10,14 - 13,15,16
8,11,13,14,16
     
                                         
The numbers missing from Row B are 1,5,7, so there is a 7 in B6 (E6,J6), a 1 in B14, a 7 in C14, a 5 in B5, a 6 in D6, a 1 in D5, a 1 in C11, and a 7 in D11. There is a 2 in D4 (G1), a 5 in D1, a 5 in L4, a 6 in L1, and a 2 in L3.  
                                         
                                       
  A 7 1 4 14 16 15 8 12 2 10 13 3 5 6 9 11    
  B 12 6 13 9 5 7 3 10 11 14 16 15 4 1 2 8      
  C 11 15 8 10 14 13 2 9 5 4 1 6 16 7 12 3    
  D 5 3 16 2 1 6 11 4 12 8 7 9 14 15 10 13    
  E 1 16 3 6 8 5 14 2 9 15 10 7 12 13 11 4    
  F 8 11 9 13 6 12 1 16 4 5 14 2 7 10 3 15    
  G 2 12 7 15 4 9 10 13 3 16 11 8 6 14 5 1    
  H 14 5 10 4 3 11 7 15 6 13 12 1 2 8 16 9    
  I 16 4 11 1 12 10 13 6 15 3 5 14 8 9 7 2    
  J 9 14 12 3 7 1 4 5 8 2 6 10 13 11 15 16    
  K 10 7 15 8 2 14 9 3 16 11 4 13 1 5 6 12      
  L 6 13 2 5 15 8 16 11 7 1 9 12 10 3 4 14      
  M 13 10 5 7 9 2 15 8 1 12 3 4 11 16 14 6    
  N 15 2 6 11 10 3 12 14 13 7 8 16 9 4 1 5      
  O 3 9 14 16 13 4 5 1 10 6 2 11 15 12 8 7      
  P 4 8 1 12 11 16 6 7 14 9 15 5 3 2 13 10      
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16      
                 
 
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