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Easy Puzzle #25 - 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   1 9   3   6 4   Easy Puzzle #25 - October 25, 2005  © joe-ks.com
2 3 4           7 1 One possible Solution Method follows below…
3       1 9 4      
4     6 3     4    
5 9   4   5   1   7
6     7   8 9 2    
7       5 7 3      
8 2 7   8       9 6
9   8     6     1  
A B C D E F G H I
1   1 9   3   6 4   Step 1: #9 is in Rows 1 & 2: #9 MUST go in Cell G2
2 3 4         9 7 1
3       1 9 4      
4     6 3     4     Step 2: #4 is in Rows 4 & 5: #4 MUST go in Cell D6
5 9   4   5   1   7
6     7 4 8 9 2    
7       5 7 3       Step 3: #7 is in Rows 7 & 8: #7 MUST go in Cell G9
8 2 7   8       9 6      (cf #7 in Column I @ I5 excludes use of Cell I9)
9   8     6   7 1  
A B C D E F G H I
1   1 9   3   6 4   Step 4: #9 is in Columns A & C: #9 MUST go in Cell B7
2 3 4         9 7 1
3       1 9 4      
4     6 3     4   9 Step 5: #4 is in Columns D & F: #4 MUST go in Cell E8
5 9   4   5   1   7
6     7 4 8 9 2    
7   9   5 7 3       Step 6: #9 is in Columns G & H: #9 MUST go in Cell I4
8 2 7   8 4     9 6      (cf #9 in Row 6 @ F6 excludes use of Cell I6)
9   8     6   7 1  
A B C D E F G H I
1   1 9   3   6 4   Step 7: Complete Column E: need #s 1 & 2…
2 3 4     2   9 7 1      #1 can't go in Cell E2 (cf #1 in Row 2 @ I2), so
3       1 9 4            #1 MUST go in Cell E4, & therefore #2 MUST go in Cell E2
4     6 3 1   4   9
5 9   4   5   1   7
6     7 4 8 9 2    
7   9   5 7 3      
8 2 7   8 4     9 6
9   8     6   7 1  
A B C D E F G H I
1   1 9   3   6 4   Step 8: #1 is in Columns D & E: #1 MUST go in Cell F8
2 3 4     2   9 7 1      (cf #1 in Row 9 @ H9 excludes use of Cell F9)
3       1 9 4      
4     6 3 1   4   9
5 9   4   5   1   7
6     7 4 8 9 2    
7   9   5 7 3      
8 2 7   8 4 1   9 6
9   8     6   7 1  
A B C D E F G H I
1   1 9   3   6 4   Step 9: Complete Block HH: need #s 2 & 9…
2 3 4     2   9 7 1      #9 can't go in Cell F9 (cf #9 in Column F @ F6), so
3       1 9 4            #9 MUST go in Cell D9, & therefore #2 MUST go in Cell F9
4     6 3 1   4   9
5 9   4 2 5   1   7 Step 10: Now #2 is in Columns E & F: #2 MUST go in Cell D5
6     7 4 8 9 2    
7   9   5 7 3      
8 2 7   8 4 1   9 6
9   8   9 6 2 7 1  
A B C D E F G H I
1   1 9 7 3   6 4   Step 11: Complete Block EE: need #s 6 & 7…
2 3 4     2   9 7 1      #6 can't go in Cell F4 (cf #6 in Row 4 @ C4), so
3       1 9 4            #6 MUST go in Cell F5, & therefore #7 MUST go in Cell F4
4     6 3 1 7 4   9
5 9   4 2 5 6 1   7 Step 12: Now #7 is in Columns E & F: #7 MUST go in Cell D1
6     7 4 8 9 2          (cf #7 in Row 2 @ H2 excludes use of Cell D2)
7   9   5 7 3      
8 2 7   8 4 1   9 6
9   8   9 6 2 7 1  
A B C D E F G H I
1   1 9 7 3   6 4   Step 13: Complete Column D: #6 MUST go in Cell D2
2 3 4   6 2   9 7 1
3       1 9 4      
4     6 3 1 7 4   9 Step 14: Complete Row 5: need #s 3 & 8…
5 9 3 4 2 5 6 1 8 7      #8 can't go in Cell B5 (cf #8 in Column B @ B9), so
6     7 4 8 9 2          #8 MUST go in Cell H5, & therefore #3 MUST go in Cell B5
7   9   5 7 3      
8 2 7   8 4 1   9 6
9   8   9 6 2 7 1  
A B C D E F G H I
1   1 9 7 3   6 4   Step 15: Row 4 needs #8: #8 MUST go in Cell A4
2 3 4   6 2   9 7 1      (cf #8 in Column B @ B9 excludes use of Cell B4, &
3 7     1 9 4              #8 in Column H @ H5 excludes use of Cell H4)
4 8   6 3 1 7 4   9
5 9 3 4 2 5 6 1 8 7 Step 16: #7 is in Rows 1 & 2: #7 MUST go in Cell A3
6     7 4 8 9 2          (#7 in Column B @ B8 excludes use of Cell B3, &
7   9   5 7 3              #7 in Column C @ C6 excludes use of Cell C3)
8 2 7   8 4 1   9 6
9   8   9 6 2 7 1  
A B C D E F G H I
1   1 9 7 3   6 4   Step 17: Block DD needs #1: #1 MUST go in Cell A6
2 3 4   6 2   9 7 1      (cf #1 in Column B @ B1 excludes use of Cells B4 & B6)
3 7     1 9 4      
4 8   6 3 1 7 4   9 Step 18: #1 is now in Columns A & B: #1 MUST go in Cell C7
5 9 3 4 2 5 6 1 8 7      (#1 in Row 8 @ F8 excludes Cell C8, &
6 1   7 4 8 9 2            #1 in Row 9 @ H9 excludes Cell C9)
7   9 1 5 7 3      
8 2 7   8 4 1   9 6
9   8   9 6 2 7 1  
A B C D E F G H I
1   1 9 7 3   6 4   Step 19: Complete Block DD: need #s 2 & 5…
2 3 4   6 2   9 7 1      #2 can't go in Cell B6 (cf #2 in Row 6 @ G6), so
3 7     1 9 4            #2 MUST go in Cell B4, & therefore #5 MUST go in Cell B6
4 8 2 6 3 1 7 4 5 9
5 9 3 4 2 5 6 1 8 7 Step 20: #5 is now in Rows 5 & 6: #5 MUST go in Cell H4
6 1 5 7 4 8 9 2    
7   9 1 5 7 3      
8 2 7   8 4 1   9 6
9   8   9 6 2 7 1  
A B C D E F G H I
1   1 9 7 3   6 4   Step 21: Complete Block FF: need #s 3 & 6…
2 3 4   6 2   9 7 1      #6 can't go in Cell I6 (cf #6 in Column I @ I8), so
3 7     1 9 4            #6 MUST go in Cell H6, & therefore #3 MUST go in Cell I6
4 8 2 6 3 1 7 4 5 9
5 9 3 4 2 5 6 1 8 7
6 1 5 7 4 8 9 2 6 3
7 6 9 1 5 7 3       Step 22: #6 is in Rows 8 & 9: #6 MUST go in Cell A7
8 2 7   8 4 1   9 6
9   8   9 6 2 7 1  
A B C D E F G H I
1 5 1 9 7 3   6 4   Step 23: Complete Column A: need #s 4 & 5…
2 3 4   6 2   9 7 1      #4 can't go in Cell A1 (cf #4 in Row 1 @ H1), so
3 7     1 9 4            #4 MUST go in Cell A9, & therefore #5 MUST go in Cell A1
4 8 2 6 3 1 7 4 5 9
5 9 3 4 2 5 6 1 8 7
6 1 5 7 4 8 9 2 6 3
7 6 9 1 5 7 3     4 Step 24: #4 is now in Rows 8 & 9: #4 MUST go in Cell I7
8 2 7   8 4 1   9 6      (#4 in Column G @ G4 excludes Cell G7, &
9 4 8   9 6 2 7 1          #4 in Column H @ H1 excludes Cell H7)
A B C D E F G H I
1 5 1 9 7 3 8 6 4   Step 25: Complete Column F: need #s 5 & 8…
2 3 4   6 2 5 9 7 1      #5 can't go in Cell F1 (cf #5 in Row 1 @ A1), so
3 7     1 9 4            #5 MUST go in Cell F2, & therefore #8 MUST go in Cell F1
4 8 2 6 3 1 7 4 5 9
5 9 3 4 2 5 6 1 8 7
6 1 5 7 4 8 9 2 6 3
7 6 9 1 5 7 3 8 2 4 Step 26: Complete Row 7: need #s 2 & 8…
8 2 7   8 4 1   9 6      #2 can't go in Cell G7 (cf #2 in Column G @ G6), so
9 4 8   9 6 2 7 1        #2 MUST go in Cell H7, & therefore #8 MUST go in Cell G7
A B C D E F G H I
1 5 1 9 7 3 8 6 4 2 Step 27: Complete Row 1: #2 MUST go in Cell I1
2 3 4 8 6 2 5 9 7 1
3 7     1 9 4       Step 28: Complete Row 2: #8 MUST go in Cell C2
4 8 2 6 3 1 7 4 5 9
5 9 3 4 2 5 6 1 8 7
6 1 5 7 4 8 9 2 6 3
7 6 9 1 5 7 3 8 2 4
8 2 7   8 4 1   9 6
9 4 8   9 6 2 7 1  
A B C D E F G H I
1 5 1 9 7 3 8 6 4 2 Step 29: Complete Column B: #6 MUST go in Cell B3
2 3 4 8 6 2 5 9 7 1
3 7 6   1 9 4   3 8 Step 30: Complete Column H: #3 MUST go in Cell H3
4 8 2 6 3 1 7 4 5 9
5 9 3 4 2 5 6 1 8 7 Step 31: Complete Column I: need #s 5 & 8…
6 1 5 7 4 8 9 2 6 3      #8 can't go in Cell I9 (cf #8 in Row 9 @ B9), so
7 6 9 1 5 7 3 8 2 4      #8 MUST go in Cell I3, & therefore #5 MUST go in Cell I9
8 2 7   8 4 1   9 6
9 4 8   9 6 2 7 1 5
A B C D E F G H I
1 5 1 9 7 3 8 6 4 2 Step 32: Complete Block GG: need #s 3 & 5…
2 3 4 8 6 2 5 9 7 1      #5 can't go in Cell C9 (cf #5 in Row 9 @ I9), so
3 7 6   1 9 4   3 8      #5 MUST go in Cell C8, & therefore #3 MUST go in Cell C9
4 8 2 6 3 1 7 4 5 9
5 9 3 4 2 5 6 1 8 7 Step 33: #3 is now in Rows 7 & 9: #3 MUST go in Cell G8
6 1 5 7 4 8 9 2 6 3
7 6 9 1 5 7 3 8 2 4
8 2 7 5 8 4 1   9 6
9 4 8 3 9 6 2 7 1 5
A B C D E F G H I
1 5 1 9 7 3 8 6 4 2 Step 34: Complete Column C: #2 MUST go in Cell C3
2 3 4 8 6 2 5 9 7 1
3 7 6 2 1 9 4 5 3 8
4 8 2 6 3 1 7 4 5 9
5 9 3 4 2 5 6 1 8 7 Step 35: Complete Column G (& Puzzle): need #s 3 & 5…
6 1 5 7 4 8 9 2 6 3      #3 can't go in Cell G3 (cf #3 in Row 3 @ H3), so
7 6 9 1 5 7 3 8 2 4      #3 MUST go in Cell G8, & therefore #5 MUST go in Cell G3
8 2 7 5 8 4 1 3 9 6
9 4 8 3 9 6 2 7 1 5
A B C D E F G H I
1 5 1 9 7 3 8 6 4 2 45 Final Proof:
2 3 4 8 6 2 5 9 7 1 45      - All Rows add up to 45;
3 7 6 2 1 9 4 5 3 8 45
4 8 2 6 3 1 7 4 5 9 45
5 9 3 4 2 5 6 1 8 7 45
6 1 5 7 4 8 9 2 6 3 45
7 6 9 1 5 7 3 8 2 4 45
8 2 7 5 8 4 1 3 9 6 45
9 4 8 3 9 6 2 7 1 5 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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