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Medium Puzzle #42 - 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 4 5     8 6       Medium Puzzle #42 - November 11, 2005
2   1 6     7 4     Original puzzle as published © joe-ks.com
3     8 9     1 7  
4 8     3 1     4 9
5 1 2     6 8     7
6   6 4     9 2    
7     3 6     8 1  
8       8 9     6 3
9         5       4
A B C D E F G H I
1 4 5   1 8 6       Step 1: #1 is in Rows 2 & 3: #1 MUST go in Cell D1...
2   1 6     7 4    
3     8 9     1 7   Step 2: #2 is in Rows 5 & 6: #2 MUST go in Cell F4...
4 8     3 1 2   4 9
5 1 2     6 8     7 Step 3: #3 is in Rows 7 & 8: #3 MUST go in Cell F9
6   6 4     9 2          (cf #3 in Column D @ D4 excludes use of Cell D9)
7     3 6     8 1  
8       8 9     6 3
9         5 3     4
A B C D E F G H I
1 4 5   1 8 6       Step 4: #6 is in Columns B & C: #6 MUST go in Cell A9
2   1 6     7 4          (#6 in Row 7 @ D7 excludes use of Cell A7, &
3     8 9     1 7          #6 in Row 8 @ H8 excludes use of Cell A8)
4 8     3 1 2   4 9
5 1 2     6 8     7
6   6 4     9 2    
7     3 6     8 1  
8       8 9     6 3
9 6       5 3     4
A B C D E F G H I
1 4 5 7 1 8 6       Step 5: Block EE needs #4: #4 MUST go in Cell D5
2 9 1 6     7 4          (#4 in Row 6 @ C6 excludes use of Cells D6 & E6)
3     8 9     1 7  
4 8     3 1 2   4 9 Step 6: #7 is in Rows 2 & 3: #7 MUST go in Cell C1...
5 1 2   4 6 8     7
6   6 4     9 2     Step 7: Block AA needs #9: #9 MUST go in Cell A2
7     3 6     8 1        (#9 in Row 3 @ D3 excludes use of Cells A3 & B3)
8       8 9     6 3 Step 8: #8 is in Rows 7 & 8: #8 MUST go in Cell B9
9 6 8     5 3     4      (#8 in Column C @ C3 excludes use of Cell C9)
A B C D E F G H I
1 4 5 7 1 8 6       Step 8: Complete Block AA: need #s 2 & 3…
2 9 1 6     7 4          #2 can't go in Cell B3 (cf #2 in Column B @ B5), so
3 2 3 8 9     1 7        #2 MUST go in Cell A3, & therefore #3 MUST go in Cell B3
4 8 7   3 1 2   4 9
5 1 2   4 6 8     7 Step 9: Complete  Block EE: need #s 5 & 7…
6   6 4 5 7 9 2          #5 can't go in Cell E6 (cf #5 in Column E @ E9), so
7     3 6     8 1        #5 MUST go in Cell D6, & therefore #7 MUST go in Cell E6
8       8 9     6 3 Step 10: #7 is now in Rows 5 & 6: #7 MUST go in Cell B4
9 6 8     5 3     4      (#7 in Column C @ C1 excludes use of Cell C4)
A B C D E F G H I
1 4 5 7 1 8 6       Step 10: Block DD needs #3: #3 MUST go in Cell A6
2 9 1 6     7 4          (#3 in Column C @ C7 excludes use of Cell C4 & C5)
3 2 3 8 9     1 7  
4 8 7 5 3 1 2   4 9 Step 11: Complete Block DD: need #s 5 & 9…
5 1 2 9 4 6 8     7      #9 can't go in Cell C4 (cf #9 in Row 4 @ I4), so
6 3 6 4 5 7 9 2          #9 MUST go in Cell C5, & therefore #5 MUST go in Cell C4
7     3 6     8 1  
8       8 9     6 3
9 6 8     5 3     4
A B C D E F G H I
1 4 5 7 1 8 6       Step 12: Complete Column D: need #s 2 & 7…
2 9 1 6 2   7 4          #7 can't go in Cell D2 (cf #7 in Row 2 @ F2), so
3 2 3 8 9     1 7 6      #7 MUST go in Cell D9, & therefore #2 MUST go in Cell D2
4 8 7 5 3 1 2 6 4 9
5 1 2 9 4 6 8     7 Step 13: Complete Row 4: #6 MUST go in Cell G4...
6 3 6 4 5 7 9 2    
7     3 6     8 1   Step 14: #6 is now in Columns G & H: #6 MUST go in Cell I3
8       8 9     6 3      (#6 in Row 1 @ F1 excludes use of Cell I1, &
9 6 8   7 5 3     4        #6 in Row 2 @ C2 excludes use of Cell I2)
A B C D E F G H I
1 4 5 7 1 8 6       Step 15: Complete Row 6: need #s 1 & 8…
2 9 1 6 2   7 4          #1 can't go in Cell H6 (cf #1 in Column H @ H7), so
3 2 3 8 9 4 5 1 7 6      #1 MUST go in Cell I6, & therefore #8 MUST go in Cell H6
4 8 7 5 3 1 2 6 4 9
5 1 2 9 4 6 8     7 Step 16: Complete Row 3: need #s 4 & 5…
6 3 6 4 5 7 9 2 8 1      #5 can't go in Cell E3 (cf #5 in Column # @ E9), so
7     3 6     8 1        #5 MUST go in Cell F3, & therefore #4 MUST go in Cell E3
8       8 9     6 3
9 6 8   7 5 3     4
A B C D E F G H I
1 4 5 7 1 8 6       Step 17: Complete Block BB: #3 MUST go in Cell E2...
2 9 1 6 2 3 7 4    
3 2 3 8 9 4 5 1 7 6 Step 18: Complete Column E: #2 MUST go in Cell E7
4 8 7 5 3 1 2 6 4 9
5 1 2 9 4 6 8     7
6 3 6 4 5 7 9 2 8 1
7     3 6 2   8 1  
8       8 9     6 3
9 6 8   7 5 3     4
A B C D E F G H I
1 4 5 7 1 8 6       Step 19: Complete Block HH: need #s 1 & 4…
2 9 1 6 2 3 7 4 5 8      #1 can't go in Cell F7 (cf #1 in Row 7 @ H7), so
3 2 3 8 9 4 5 1 7 6      #1 MUST go in Cell F8, & therefore #4 MUST go in Cell F7
4 8 7 5 3 1 2 6 4 9
5 1 2 9 4 6 8     7 Step 20: Complete Row 2: need #s 5 & 8…
6 3 6 4 5 7 9 2 8 1      #8 can't go in Cell H2 (cf #8 in Column H @ H6), so
7     3 6 2 4 8 1        #8 MUST go in Cell I2, & therefore #5 MUST go in Cell H2
8       8 9 1   6 3
9 6 8   7 5 3     4
A B C D E F G H I
1 4 5 7 1 8 6       Step 21: Complete Block FF: need #s 3 & 5…
2 9 1 6 2 3 7 4 5 8      #5 can't go in Cell H5 (cf #5 in Column H @ H2), so
3 2 3 8 9 4 5 1 7 6