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Easy Puzzle #28 - One Possible Solution Approach…
NB:  There is only one final solution to this Sudoku puzzle…
Rules: Place a number from 1-9 in each empty cell so that each row, each column AND each 3x3 block contains all the numbers from 1-9.
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 8 4     7   9     Easy Puzzle #28 - October 28, 2005
2 9 7   4     5 1   Original puzzle as published © joe-ks.com
3         1     4 8
4   2 9 1          
5   6 4     8 1    
6 3         7 2 5  
7 2 3     4 9 8    
8     6     1   9 5
9     5   6     7 2
A B C D E F G H I
1 8 4     7   9     Step 1: #9 is in Rows 1 & 2: #9 MUST go in Cell D3
2 9 7   4     5 1        (#9 in Column F @ F7 excludes use of Cell F3)
3       9 1     4 8
4   2 9 1           Step 2: #5 is in Rows 8 & 9: #5 MUST go in Cell D7
5   6 4     8 1    
6 3         7 2 5  
7 2 3   5 4 9 8    
8     6     1   9 5
9     5   6     7 2
A B C D E F G H I
1 8 4     7   9     Step 3: #9 is in Columns A & C: #9 MUST go in Cell B9
2 9 7   4     5 1        (#9 in Row 8 @ H8 excludes use of Cell B8)
3       9 1     4 8
4   2 9 1          
5   6 4     8 1    
6 3         7 2 5  
7 2 3   5 4 9 8    
8     6     1   9 5
9   9 5   6     7 2
A B C D E F G H I
1 8 4     7   9     Step 4: #7 is in Rows 1 & 2: #7 MUST go in Cell G3
2 9 7   4     5 1  
3 6     9 1   7 4 8 Step 5: #6 is in Columns B & C: #6 MUST go in Cell A3
4   2 9 1          
5   6 4     8 1    
6 3         7 2 5  
7 2 3   5 4 9 8    
8     6     1   9 5
9   9 5   6     7 2
A B C D E F G H I
1 8 4     7   9     Step 6: Block AA needs #5: #5 MUST go in Cell B3
2 9 7   4     5 1       (#5 in Column C @ C9 excludes use of Cells C1, C2 & C3)
3 6 5   9 1   7 4 8
4   2 9 1           Step 7: #7 is in Columns E & F: #7 MUST go in Cell D8
5   6 4     8 1          (#7 in Row 9 excludes use of Cell D9)
6 3         7 2 5  
7 2 3   5 4 9 8    
8     6 7   1   9 5
9   9 5   6     7 2
A B C D E F G H I
1 8 4     7   9     Step 8: Block BB needs #8: #8 MUST go in Cell E2
2 9 7   4 8   5 1        (#8 in Row 1 @ A1 excludes use of Cells D1 & F1, &
3 6 5   9 1   7 4 8        #8 in Column F @ F5 excludes use of Cells F1, F2 & F3)
4   2 9 1          
5   6 4     8 1     Step 9: #7 is in Rows 8 & 9: #7 MUST go in Cell C7
6 3         7 2 5  
7 2 3 7 5 4 9 8    
8     6 7   1   9 5
9   9 5   6     7 2
A B C D E F G H I
1 8 4     7 5 9     Step 10: Block GG needs #1: #1 MUST go in Cell A9
2 9 7   4 8   5 1       (#1 in Row 8 @ F8 excludes use of Cells A8 & B8)
3 6 5   9 1   7 4 8
4   2 9 1           Step 11: #5 is in Rows 2 & 3: #5 MUST go in Cell F1
5   6 4     8 1          (#5 in Column D @ D7 excludes use of Cell D1)
6 3         7 2 5  
7 2 3 7 5 4 9 8    
8     6 7   1   9 5
9 1 9 5   6     7 2
A B C D E F G H I
1 8 4     7 5 9     Step 12: Complete Block GG: need #s 4 & 8…
2 9 7   4 8   5 1        #8 can't go in Cell A8 (cf #8 in Column A @ A1), so
3 6 5   9 1   7 4 8      #8 MUST go in Cell B8, & therefore #4 MUST go in Cell A8
4   2 9 1          
5   6 4     8 1     Step 13: #8 is now in Columns A& B: #8 MUST go in Cell C6
6 3   8     7 2 5  
7 2 3 7 5 4 9 8     Step 14: #4 is now in Rows 7 & 8: #4 MUST go in Cell G9
8 4 8 6 7   1   9 5
9 1 9 5   6   4 7 2
A B C D E F G H I
1 8 4     7 5 9     Step 15: #2 is in Rows 7 & 9: #2 MUST go in Cell E8
2 9 7   4 8   5 1  
3 6 5   9 1   7 4 8 Step 16: #1 is in Rows 4 & 5: #1 MUST go in Cell B6
4   2 9 1          
5   6 4     8 1    
6 3 1 8     7 2 5  
7 2 3 7 5 4 9 8    
8 4 8 6 7 2 1   9 5
9 1 9 5   6   4 7 2
A B C D E F G H I
1 8 4     7 5 9     Step 17: Complete Block HH: need #s 3 & 8…
2 9 7   4 8   5 1        #8 can't go in Cell F9 (cf #8 in Column F @ F5), so
3 6 5   9 1   7 4 8      #8 MUST go in Cell D9, & therefore #3 MUST go in Cell F9
4   2 9 1          
5   6 4     8 1     Step 18: #3 is now in Rows 7 & 9: #3 MUST go in Cell G8
6 3 1 8     7 2 5  
7 2 3 7 5 4 9 8    
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4     7 5 9     Step 19: Complete Row 3: need #s 2 & 3…
2 9 7   4 8   5 1        #3 can't go in Cell F3 (cf #3 in Column F @ F9), so
3 6 5 3 9 1 2 7 4 8      #3 MUST go in Cell C3, & therefore #2 MUST go in Cell F3
4   2 9 1          
5   6 4     8 1    
6 3 1 8     7 2 5  
7 2 3 7 5 4 9 8    
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4   3 7 5 9     Step 20: Complete Block BB: need #s 3 & 6…
2 9 7   4 8 6 5 1        #3 can't go in Cell F2 (cf #3 in Column F @ F9), so
3 6 5 3 9 1 2 7 4 8      #3 MUST go in Cell D1, & therefore #6 MUST go in Cell F2
4   2 9 1          
5   6 4     8 1    
6 3 1 8     7 2 5  
7 2 3 7 5 4 9 8    
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4   3 7 5 9     Step 21: Complete Column D: need #s 2 & 6…
2 9 7   4 8 6 5 1        #2 can't go in Cell D6 (cf #2 in Row 6 @ G6), so
3 6 5 3 9 1 2 7 4 8      #2 MUST go in Cell D5, & therefore #6 MUST go in Cell D6
4   2 9 1          
5   6 4 2   8 1    
6 3 1 8 6   7 2 5  
7 2 3 7 5 4 9 8    
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4   3 7 5 9     Step 22: Complete Row 6: need #s 4 & 9…
2 9 7   4 8 6 5 1        #4 can't go in Cell E6 (cf #4 in Column E @ E7), so
3 6 5 3 9 1 2 7 4 8      #4 MUST go in Cell I6, & therefore #9 MUST go in Cell E6
4   2 9 1          
5   6 4 2   8 1   9 Step 23: #9 in now in Rows 4 & 6: #9 MUST go in Cell I5
6 3 1 8 6 9 7 2 5 4      (#9 in Column H @ H8 excludes use of Cell H5)
7 2 3 7 5 4 9 8    
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4   3 7 5 9     Step 24: Block EE needs # 4: #4 MUST go in Cell F4
2 9 7   4 8 6 5 1        (#4 in Column E @ E7 excludes use of Cells E4 & E5)
3 6 5 3 9 1 2 7 4 8
4   2 9 1   4     7 Step 25: #7 is in Columns G & H: #7 MUST go in Cell I4
5   6 4 2   8 1   9
6 3 1 8 6 9 7 2 5 4
7 2 3 7 5 4 9 8    
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4   3 7 5 9     Step 26: #7 is in Rows 4 & 6: #7 MUST go in Cell A5
2 9 7   4 8 6 5 1  
3 6 5 3 9 1 2 7 4 8 Step 27: Complete Block DD: #5 MUST go in Cell A4...
4 5 2 9 1 3 4     7
5 7 6 4 2 5 8 1   9 Step 28: #5 is now in Rows 4 & 6: #5 MUST go in Cell E5...
6 3 1 8 6 9 7 2 5 4
7 2 3 7 5 4 9 8     Step 29: Complete Block EE: #3 MUST go in Cell E4...
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4   3 7 5 9     Step 30: #3 is in Rows 4 & 6: #3 MUST go in Cell H5...
2 9 7   4 8 6 5 1 3
3 6 5 3 9 1 2 7 4 8 Step 31: #3 is now in Columns G & H: #3 MUST go in Cell I2
4 5 2 9 1 3 4     7      (#3 in Row 1 @ D1 excludes use of Cell I1)
5 7 6 4 2 5 8 1 3 9
6 3 1 8 6 9 7 2 5 4
7 2 3 7 5 4 9 8    
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4 1 3 7 5 9     Step 32: #1 is in Rows 2 & 3: #1 MUST go in Cell C1...
2 9 7 2 4 8 6 5 1 3
3 6 5 3 9 1 2 7 4 8 Step 33: Complete Column C: #2 MUST go in Cell C2
4 5 2 9 1 3 4     7
5 7 6 4 2 5 8 1 3 9
6 3 1 8 6 9 7 2 5 4
7 2 3 7 5 4 9 8    
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4 1 3 7 5 9 2 6 Step 34: Complete Row 1: need #s 2 & 6…
2 9 7 2 4 8 6 5 1 3      #2 can't go in Cell I1 (cf #2 in Column I @ I9), so
3 6 5 3 9 1 2 7 4 8      #2 MUST go in Cell H1, & therefore #6 MUST go in Cell I1
4 5 2 9 1 3 4 6   7
5 7 6 4 2 5 8 1 3 9 Step 35: Complete Column G: #6 MUST go in Cell G4...
6 3 1 8 6 9 7 2 5 4
7 2 3 7 5 4 9 8    
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4 1 3 7 5 9 2 6 Step 36: Complete Block II: need #s 1 & 6…
2 9 7 2 4 8 6 5 1 3      #6 can't go in Cell I7 (cf #6 in Column I @ I1), so
3 6 5 3 9 1 2 7 4 8      #6 MUST go in Cell H7, & therefore #1 MUST go in Cell I7
4 5 2 9 1 3 4 6 8 7
5 7 6 4 2 5 8 1 3 9 Step 37: Complete Block FF (& Puzzle):
6 3 1 8 6 9 7 2 5 4      #8 MUST go in Cell H4.
7 2 3 7 5 4 9 8 6 1
8 4 8 6 7 2 1 3 9 5
9 1 9 5 8 6 3 4 7 2
A B C D E F G H I
1 8 4 1 3 7 5 9 2 6 45 Final Proof:
2 9 7 2 4 8 6 5 1 3 45      - All Rows add up to 45;
3 6 5 3 9 1 2 7 4 8 45
4 5 2 9 1 3 4 6 8 7 45
5 7 6 4 2 5 8 1 3 9 45
6 3 1 8 6 9 7 2 5 4 45
7 2 3 7 5 4 9 8 6 1 45
8 4 8 6 7 2 1 3 9 5 45
9 1 9 5 8 6 3 4 7 2 45
 
45 45 45 45 45 45 45 45 45        - All Columns add up to 45;
45 45 45      - All 3x3 Blocks add up to 45…
45 45 45
45 45 45

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