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Challenging Puzzle #51 - One Possible Solution Approach…
NB:  There is only one final solution to this Sudoku puzzle…
A B C D E F G H I
1                  
2 AA BB CC Reference to 3x3 Blocks AA, BB & CC
3                  
4                  
5 DD EE FF Reference to 3x3 Blocks DD, EE & FF
6                  
7                  
8 GG HH II Reference to 3x3 Blocks GG, HH & II
9                  
A B C D E F G H I
1           2       Challenging Puzzle #51 - November 20, 2005
2     6 9   5 3     Original puzzle as published © joe-ks.com
3   9 3 7     2 5  
4   5 4   2     9  
5     9   4   1 7  
6     8   7     3  
7   1 5       9 2  
8   6 2 8   1 7    
9       2          
A B C D E F G H I
1 5         2       Step 1: #5 is in Rows 2 & 3: #5 MUST go in Cell A1
2     6 9   5 3          (#5 in Column B @ B4 excludes use of Cell B1, &
3   9 3 7     2 5         #5 in Column C @ C7 excludes use of Cell C1)
4 7 5 4   2     9  
5     9   4   1 7   Step 2: #7 is in Rows 5 & 6: #7 MUST go in Cell A4...
6     8   7     3  
7   1 5       9 2  
8   6 2 8   1 7    
9       2          
A B C D E F G H I
1 5 478 17 1346 1368 2 468 1468 146789 Step 3: Determine all possible # combinations for vacant cells:
2 1248 2478 6 9 18 5 3 148 1478
3 148 9 3 7 168 468 2 5 1468 Obvious observations:  #2 in B6;  #4 in H8 ,& #7 in C9
4 7 5 4 136 2 368 68 9 68
5 236 23 9 356 4 368 1 7 2568 Step 4: re Block CC: #9 only shows up in Cell I1…
6 126 2 8 156 7 69 456 3 2456 Step 5: re Block DD: #1 only shows up in Cell A6…
7 348 1 5 346 36 3467 9 2 3468 Step 6: re Block EE: #9 only shows up in Cell F6...
8 349 6 2 8 359 1 7 4 345
9 3489 3478 7 2 3569 34679 4568 1468 134568
A B C D E F G H I
1 5         2     9 Step 7: #2 is in Columns B & C: #2 MUST go in Cell A2
2 2   6 9   5 3          (#2 in Row 3 @ G3 excludes use of Cell A3)
3   9 3 7     2 5  
4 7 5 4   2     9   Step 8: #7 is in Columns D & E: #7 MUST go in Cell F7
5     9   4   1 7 2      (#7 in Row 9 @ C9 excludes use of Cell F9)
6 1 2 8   7 9   3  
7   1 5     7 9 2   Step 9: #2 is in Column G & H: #2 MUST go in Cell I5
8   6 2 8   1 7 4        (#2 in Row 4 @ E4 excludes use of Cell I5, & 
9     7 2                  #2 in Row 6 @ B6 excluides use of Cell I6)
A B C D E F G H I
1 5   1     2     9 Step 10: Complete Column C: #1 MUST go in Cell C1...
2 2   6 9   5 3   7
3   9 3 7     2 5   Step 11: #7 is in Columns G & H: #7 MUST go in Cell I2
4 7 5 4   2     9        (#7 in Row 3 @ D3 excludes use of Cell I3)
5     9   4   1 7 2
6 1 2 8   7 9   3  
7   1 5     7 9 2  
8   6 2 8   1 7 4  
9     7 2          
A B C D E F G H I
1 5 7 1     2     9 Step 12: Complete Block DD: need #s 3 & 6…
2 2   6 9   5 3   7      #6 can't go in Cell B5 (cf #6 in Column B @ B8), so
3   9 3 7     2 5        #6 MUST go in Cell A5, & therefore #3 MUST go in Cell B5
4 7 5 4   2     9  
5 6 3 9   4   1 7 2 Step 13: #7 is in Rows 2 & 3: #7 MUST go in Cell B1...
6 1 2 8   7 9   3  
7   1 5     7 9 2  
8   6 2 8   1 7 4  
9     7 2          
A B C D E F G H I
1 5 7 1 346 368 2 468 68 9 Step 14: Determine all possible # combinations for vacant cells:
2 2 48 6 9 18 5 3 18 7
3 48 9 3 7 168 468 2 5 1468 Obvious observations:  #5 in D5; #8 in F5
4 7 5 4 136 2 368 68 9 68
5 6 3 9 5 4 8 1 7 2 Step 15: re Block EE: #1 only shows up in Cell D4…
6 1 2 8 56 7 9 456 3 456
7 348 1 5 346 36 7 9 2 368
8 39 6 2 8 359 1 7 4 35
9 3489 48 7 2 3569 346 568 168 13568
A B C D E F G H I
1 5 7 1 346 368 2 468 68 9 Step 16: Determine all possible # combinations for vacant cells:
2 2 48 6 9 18 5 3 18 7
3 48 9 3 7 168 46 2 5 1468 Obvious observations:  #6 in D6 (& therefore #3 in F4)
4 7 5 4 1 2 36 68 9 68
5 6 3 9 5 4 8 1 7 2 Step 17: re Row 2: #4 only shows up in Cell B2
6 1 2 8 6 7 9 456 3 456
7 348 1 5 346 36 7 9 2 368
8 39 6 2 8 359 1 7 4 35
9 3489 48 7 2 3569 346 568 168 13568
A B C D E F G H I
1 5 7 1     2     9 Step 18: Complete Block AA: #8 MUST go in Cell A3...
2 2 4 6 9   5 3   7
3 8 9 3 7     2 5   Step 19: #8 is now in Columns A & C: #8 MUST go in Cell B9...
4 7 5 4 1 2 3 8 9  
5 6 3 9 5 4 8 1 7 2 Step 20: #8 is now in Rows 8 & 9: #8 MUST go in Cell I7...
6 1 2 8 6 7 9   3  
7   1 5     7 9 2 8 Step 21: #8 is in Rows 5 & 6: #8 MUST go in Cell G4
8   6 2 8   1 7 4        (#8 from Step 20 @ I8 excludes use of Cell I4)
9   8 7 2          
A B C D E F G H I
1 5 7 1     2     9 Step 22: Complete Row 4: #6 MUST go in Cell I4...
2 2 4 6 9   5 3   7
3 8 9 3 7     2 5  
4 7 5 4 1 2</