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Easy Puzzle #13 - 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       3 5     6   Easy Puzzle #13 - October 13, 2005
2   5 6 2   8 3   4 Original puzzle as published on joe-ks.com…
3 2 3           7  
4   8   5          
5   9   4 3   2 8 1
6 7       9     5  
7   7 4   8 1 9    
8   6         8 4  
9 3 2   9 4   6 1  
A B C D E F G H I
1       3 5     6 2 Step 1: #2 is in Rows 2 & 3: #2 MUST go in Cell I1
2   5 6 2   8 3   4      (cf #2 in Column G @ G5 excludes use of Cell G1)
3 2 3           7  
4   8   5           Step 2: #6 is in Rows 8 & 9: #6 MUST go in Cell D7
5   9   4 3   2 8 1
6 7       9     5  
7   7 4   8 1 9    
8   6         8 4  
9 3 2   9 4   6 1  
A B C D E F G H I
1     7 3 5     6 2 Step 3: #7 is in Columns A & B: #7 MUST go in Cell C1
2   5 6 2   8 3   4      (cf #7 in Row 3 @ Cell h3 excludes use of Cell C3)
3 2 3           7 8
4   8   5          
5   9   4 3   2 8 1 Step 4: #8 is in Columns G & H: #8 MUST go in Cell I3
6 7       9     5  
7   7 4   8 1 9    
8   6         8 4  
9 3 2   9 4   6 1  
A B C D E F G H I
1     7 3 5     6 2 Step 5: #5 is in Rows 1 & 2: #5 MUST go in Cell G3
2   5 6 2   8 3   4
3 2 3         5 7 8 Step 6: #5 is in Rows 4 & 6: #5 MUST go in Cell C6
4   8   5                (cf #5 in Column B @ B2 excludes use of Cell B6)
5   9 5 4 3   2 8 1
6 7       9     5   Step 7: #8 is in Rows 7 & 8: #8 MUST go in Cell C9
7   7 4   8 1 9    
8   6         8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8   7 3 5   1 6 2 Step 8: #8 is in Columns B & C: #8 MUST go in Cell A1
2   5 6 2   8 3   4      (cf #8 in Row 2 @ F2 excludes use of Cell A2)
3 2 3         5 7 8
4   8   5          
5   9 5 4 3   2 8 1 Step 9: #1 is in Columns H & I: #9 MUST go in Cell G1
6 7       9     5  
7   7 4   8 1 9    
8   6         8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5   1 6 2 Step 10: Complete Block CC: #9 MUST go in Cell H2
2   5 6 2   8 3 9 4
3 2 3         5 7 8 Step 11: #8 is in Columns E & F: #8 MUST go in Cell D6
4   8   5          
5   9 5 4 3   2 8 1 Step 12: Block AA needs #4: #4 MUST go in Cell B1
6 7     8 9     5        (#4 in Row 2 @ I2 excludes Cell A2, & #4 in Column C @
7   7 4   8 1 9            C7 excludes Cell C3)
8   6         8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 13: Complete Column B: #1 MUST go in Cell B6
2   5 6 2   8 3 9 4
3 2 3         5 7 8 Step 14: Complete Row 1: #9 MUST go in Cell F1
4   8   5          
5   9 5 4 3   2 8 1
6 7 1   8 9     5  
7   7 4   8 1 9    
8   6         8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 15: #7 is in Rows 1 & 3: #7 MUST go in Cell E2
2   5 6 2 7 8 3 9 4
3 2 3         5 7 8
4   8   5 1         Step 16: Block EE needs #1: #1 MUST go in Cell E4
5   9 5 4 3   2 8 1      (#1 in Column F @ F7 excludes use of F4, F5 & F6)
6 7 1   8 9     5  
7   7 4   8 1 9 2   Step 17: Block II needs #2: #2 MUST go in Cell H7
8   6         8 4        (#2 in Column I @ I1 excludes use of I7, I8 & I9)
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 18: Complete Row 2: #1 MUST go in Cell A2
2 1 5 6 2 7 8 3 9 4
3 2 3         5 7 8 Step 19: #9 is in Rows 5 & 6: #9 MUST go in Cell I4
4   8   5 1       9      (#9 in Column G @ G7 excludes G4, & #9 in Column H @
5   9 5 4 3   2 8 1        H2 excludes H4)
6 7 1   8 9     5  
7   7 4   8 1 9 2  
8   6         8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 20: Complete Block AA: #9 MUST go in Cell C3
2 1 5 6 2 7 8 3 9 4
3 2 3 9       5 7 8 Step 21: Complete Column H: #3 MUST go in Cell H4
4   8   5 1     3 9
5   9 5 4 3   2 8 1 Step 22: #1 is in Column A & B: #1 MUST go in Cell C8
6 7 1   8 9     5  
7   7 4   8 1 9 2  
8   6 1       8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 23: Complete Column C: need #s 2 & 3…
2 1 5 6 2 7 8 3 9 4      #3 can't go in Cell C4 (cf #3 in Row 4 @ H3), so
3 2 3 9       5 7 8      #3 MUST go in Cell C6, & therefore #2 MUST go in Cell C4
4   8 2 5 1     3 9
5   9 5 4 3   2 8 1
6 7 1 3 8 9     5  
7   7 4   8 1 9 2  
8   6 1       8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 24: Complete Column E: Need #s 2 & 6…
2 1 5 6 2 7 8 3 9 4      #2 can't go in Cell E3 (cf #2 in Row 2 @ A3), so
3 2 3 9   6   5 7 8      #2 MUST go in Cell E8, & therefore #6 MUST go in Cell E3
4   8 2 5 1     3 9
5   9 5 4 3   2 8 1 Step 25: #6 is in Columns G & H: #6 MUST go in Cell I6
6 7 1 3 8 9     5 6
7   7 4   8 1 9 2  
8   6 1   2   8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 26: Complete Row 5: need #s 6 & 7…
2 1 5 6 2 7 8 3 9 4      #7 can't go in Cell A5 (cf #7 in Column A @ A6), so
3 2 3 9 1 6 4 5 7 8      #7 MUST go in Cell F5, & therefore #6 MUST go in Cell A5
4   8 2 5 1     3 9
5 6 9 5 4 3 7 2 8 1 Step 27: Complete Row 3: need #s 1 & 4…
6 7 1 3 8 9     5 6      #4 can't go in Cell D3 (cf #4 in Column D @ D5), so
7   7 4   8 1 9 2        #4 MUST go in Cell F4, & therefore #1 MUST go in Cell D3
8   6 1   2   8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 28: Complete Block DD: #4 MUST go in Cell A4
2 1 5 6 2 7 8 3 9 4
3 2 3 9 1 6 4 5 7 8 Step 29: Complete Block FF: need #s 4 & 7…
4 4 8 2 5 1   7 3 9      #4 can't go in Cell G4 (see Step 28), so
5 6 9 5 4 3 7 2 8 1      #4 MUST go in Cell G6, & therefore #7 MUST go in Cell G4
6 7 1 3 8 9   4 5 6
7   7 4   8 1 9 2  
8   6 1   2   8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 30: Complete Row 4: #6 MUST go in Cell F4
2 1 5 6 2 7 8 3 9 4
3 2 3 9 1 6 4 5 7 8 Step 31: Complete Row 6: #2 MUST go in Cell F6
4 4 8 2 5 1 6 7 3 9
5 6 9 5 4 3 7 2 8 1 Step 32: Complete Block GG: need #s 5 & 9…
6 7 1 3 8 9 2 4 5 6      #9 can't go in Cell A7 (cf #9 in Row 7 @ G7), so
7 5 7 4   8 1 9 2        #9 MUST go in Cell A8, & therefore #5 MUST go in Cell A7
8 9 6 1   2   8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 33: Complete Column D: need #s 6 & 7…
2 1 5 6 2 7 8 3 9 4      #7 can't go in Cell D7 (cf #7 in Row 7 @ B7), so
3 2 3 9 1 6 4 5 7 8      #7 MUST go in Cell D8, & therefore #6 MUST go in Cell D7
4 4 8 2 5 1 6 7 3 9
5 6 9 5 4 3 7 2 8 1
6 7 1 3 8 9 2 4 5 6
7 5 7 4 6 8 1 9 2  
8 9 6 1 7 2   8 4  
9 3 2 8 9 4   6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 34: Complete Row 7: #3 MUST go in Cell I7
2 1 5 6 2 7 8 3 9 4
3 2 3 9 1 6 4 5 7 8 Step 35: Complete Column F: need #s 3 & 5…
4 4 8 2 5 1 6 7 3 9      #3 can't go in Cell F9 (cf #3 in Row 9 @ A9), so
5 6 9 5 4 3 7 2 8 1      #3 MUST go in Cell F8, & therefore #5 MUST go in Cell F9
6 7 1 3 8 9 2 4 5 6
7 5 7 4 6 8 1 9 2 3
8 9 6 1 7 2 3 8 4  
9 3 2 8 9 4 5 6 1  
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 Step 36: Complete Row 8: #5 MUST go in Cell I8
2 1 5 6 2 7 8 3 9 4
3 2 3 9 1 6 4 5 7 8 Step 37: Complete Row 9, Column I & Block II:
4 4 8 2 5 1 6 7 3 9      #7 MUST go in Cell I9.
5 6 9 5 4 3 7 2 8 1
6 7 1 3 8 9 2 4 5 6
7 5 7 4 6 8 1 9 2 3
8 9 6 1 7 2 3 8 4 5
9 3 2 8 9 4 5 6 1 7
A B C D E F G H I
1 8 4 7 3 5 9 1 6 2 45 Final Proof:
2 1 5 6 2 7 8 3 9 4 45      - All Rows add up to 45;
3 2 3 9 1 6 4 5 7 8 45
4 4 8 2 5 1 6 7 3 9 45
5 6 9 5 4 3 7 2 8 1 45
6 7 1 3 8 9 2 4 5 6 45
7 5 7 4 6 8 1 9 2 3 45
8 9 6 1 7 2 3 8 4 5 45
9 3 2 8 9 4 5 6 1 7 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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