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Easy Puzzle #24 - 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       2 6   Easy Puzzle #24 - October 24, 2005
2 2   4 9 8         One possible Solution Method follows below…
3 5 1   6       3 8
4 7   6   1     9  
5   2   3   4   1  
6   9     6   3   2
7 6 8       1     3
8         5 9 8   6
9   5 2       7    
A B C D E F G H I
1     8       2 6   Step 1: #6 is in Columns A & C: #6 MUST go in Cell B2
2 2 6 4 9 8              (cf #6 in Row 1 @ I1 excludes use of Cell B1)
3 5 1   6       3 8
4 7   6   1     9   Step 2: #8 is in Columns G & I: #8 MUST go in Cell H6
5   2   3   4   1  
6   9     6   3 8 2
7 6 8       1     3
8         5 9 8   6
9   5 2       7    
A B C D E F G H I
1     8       2 6   Step 3: #8 is in Column B & C: #8 MUST go in Cell A5
2 2 6 4 9 8              (cf #8 in row 6 @ H6 excludes use of Cell A6)
3 5 1   6       3 8
4 7   6   1     9   Step 4: #9 is in Columns D & F: #9 MUST go in Cell E5
5 8 2   3 9 4   1  
6   9     6   3 8 2
7 6 8       1     3
8         5 9 8   6
9   5 2       7    
A B C D E F G H I
1     8       2 6   Step 5: #6 is in Columns H & I: #6 MUST go in Cell G5
2 2 6 4 9 8              (cf #6 in row 4 @ C4 excludes use of Cell G4)
3 5 1   6       3 8
4 7   6   1     9  
5 8 2   3 9 4 6 1  
6   9     6   3 8 2
7 6 8       1     3
8         5 9 8   6
9   5 2       7    
A B C D E F G H I
1     8       2 6   Step 6: Block II needs #1: #1 MUST go in Cell I9
2 2 6 4 9 8   1          (NB: #1 in Column H @ H5 excludes use of H7,H8,H9
3 5 1   6       3 8        & #1 in Row 7 @ F7 excludes use of G7)
4 7   6   1     9  
5 8 2   3 9 4 6 1   Step 7: Block CC needs #1: #1 MUST go in Cell G2
6   9     6   3 8 2      (cf #1 in Columns H & I exclude Cells H2, I1 & I2,
7 6 8       1     3        & #1 in Row 3 @ B3 excludes Cell G3)
8         5 9 8   6
9   5 2       7   1
A B C D E F G H I
1     8 1     2 6   Step 8: #1 is in Rows 2 & 3: #1 MUST go in Cell D1
2 2 6 4 9 8   1          (#1 in Column E @ E4 excludes use of Cell E1, &
3 5 1   6       3 8        #1 in Column F @ F7 excludes use of Cell F1)
4 7 3 6   1     9  
5 8 2   3 9 4 6 1   Step 9: #3 is in Rows 5 & 6: #3 MUST go in Cell B4
6   9     6   3 8 2
7 6 8       1     3
8         5 9 8   6
9   5 2       7   1
A B C D E F G H I
1     8 1     2 6   Step 10:  Block DD needs #4: #4 MUST go in Cell A6
2 2 6 4 9 8   1          (NB: #4 in Column C @ C2 excludes use of C5 & C6
3 5 1   6       3 8
4 7 3 6   1     9  
5 8 2   3 9 4 6 1  
6 4 9     6   3 8 2
7 6 8       1     3
8         5 9 8   6
9   5 2       7   1
A B C D E F G H I
1     8 1     2 6   Step 11: Complete Block DD: need #s 1 & 5…
2 2 6 4 9 8   1          #1 can't go in Cell C5 (cf #1 in Row 5 @ H5), so
3 5 1   6       3 8      #1 MUST go in Cell C6, & therefore #5 MUST go in Cell C5
4 7 3 6   1     9  
5 8 2 5 3 9 4 6 1   Step 12: #1 is in Rows 7 & 9: #1 MUST go in Cell A8
6 4 9 1   6   3 8 2      (cf #1 in Column B @ B3 excludes use of Cell B8, &
7 6 8       1     3        #1 in Column C @ C6 excludes use of Cell C8)
8 1       5 9 8   6
9   5 2       7   1
A B C D E F G H I
1 3   8 1     2 6   Step 13: Complete Row 5: #7 MUST go in Cell I5
2 2 6 4 9 8   1    
3 5 1   6       3 8 Step 14: Block AA needs #3: #3 MUST go in Cell A1
4 7 3 6   1     9        (#3 in Column B excludes Cell B1, & #3 in Row 3 @ H3
5 8 2 5 3 9 4 6 1 7        excludes use of Cell C3)
6 4 9 1   6   3 8 2
7 6 8       1     3 Step 15: Now #3 is in Columns A & B: #3 MUST go in Cell C8
8 1   3   5 9 8   6      (#3 in Row 7 @ I7 excludes use of Cell C7)
9   5 2       7   1
A B C D E F G H I
1 3 7 8 1     2 6   Step 16: Complete Block AA: need #s 7 & 9…
2 2 6 4 9 8   1          #9 can't go in Cell B1 (cf #9 in Column B @ B6), so
3 5 1 9 6       3 8      #9 MUST go in Cell C3, & therefore #7 MUST go in Cell B1
4 7 3 6   1     9  
5 8 2 5 3 9 4 6 1 7
6 4 9 1   6   3 8 2
7 6 8       1     3
8 1   3   5 9 8   6
9   5 2       7   1
A B C D E F G H I
1 3 7 8 1     2 6   Step 17: Complete Column A: #9 MUST go in Cell A9
2 2 6 4 9 8   1    
3 5 1 9 6       3 8 Step 18: Complete Column B: #4 MUST go in Cell B8...
4 7 3 6   1     9  
5 8 2 5 3 9 4 6 1 7 Step 19: Complete Column C (& Block GG):
6 4 9 1   6   3 8 2      #7 MUST go in Cell C7
7 6 8 7     1     3
8 1 4 3   5 9 8   6
9 9 5 2       7   1
A B C D E F G H I
1 3 7 8 1     2 6 9 Step 20: Block II needs #9: #9 MUST go in Cell G7
2 2 6 4 9 8   1          (cf #9 in Column H excludes use of Cells, H7, H8 & H9)
3 5 1 9 6       3 8
4 7 3 6   1     9   Step 21: Now #9 is in Columns G & H: #9 MUST go in Cell I1
5 8 2 5 3 9 4 6 1 7      (cf #9 in Row 2 @ D2 excludes use of Cell I2)
6 4 9 1   6   3 8 2
7 6 8 7     1 9   3
8 1 4 3   5 9 8   6
9 9 5 2       7   1
A B C D E F G H I
1 3 7 8 1 4 5 2 6 9 Step 22: Complete Row 1: need #s 4 & 5…
2 2 6 4 9 8   1          #4 can't go in Cell F1 (cf #4 in Column 4 @ F5), so
3 5 1 9 6       3 8      #4 MUST go in Cell E1, & therefore #5 MUST go in Cell F1
4 7 3 6   1     9  
5 8 2 5 3 9 4 6 1 7 Step 23: Complete Row 6: need #s 5 & 7…
6 4 9 1 5 6 7 3 8 2      #5 can't go in Cell F6 (see #5 added in Step 22 @ F1), so
7 6 8 7     1 9   3      #5 MUST go in Cell D6, & therefore #7 MUST go in Cell F6
8 1 4 3   5 9 8   6
9 9 5 2       7   1
A B C D E F G H I
1 3 7 8 1 4 5 2 6 9 Step 24: Block CC needs #4: #4 MUST go in Cell G3
2 2 6 4 9 8   1          (cf #4 in Row 2 @ C2 excludes use of Cells H2 & I2)
3 5 1 9 6     4 3 8
4 7 3 6   1     9 4 Step 25: Block FF needs #4: #4 MUST go in Cell I4
5 8 2 5 3 9 4 6 1 7      (cf #4 added in Step 24 excludes use of Cell G4)
6 4 9 1 5 6 7 3 8 2
7 6 8 7     1 9   3
8 1 4 3   5 9 8   6
9 9 5 2       7   1
A B C D E F G H I
1 3 7 8 1 4 5 2 6 9 Step 26: Complete Row 3: need #s 2 & 7…
2 2 6 4 9 8   1          #7 can't go in Cell F3 (cf #7 in Column F @ F6), so
3 5 1 9 6 7 2 4 3 8      #7 MUST go in Cell E3, & therefore #2 MUST go in Cell F3
4 7 3 6   1   5 9 4
5 8 2 5 3 9 4 6 1 7 Step 27: Complete Block FF: #5 MUST go in Cell G4...
6 4 9 1 5 6 7 3 8 2
7 6 8 7     1 9   3
8 1 4 3   5 9 8   6
9 9 5 2       7   1
A B C D E F G H I
1 3 7 8 1 4 5 2 6 9 Step 28: Complete Row 4: need #s 2 & 8…
2 2 6 4 9 8   1          #2 can't go in Cell F4 (cf #2 in Column F @ F3), so
3 5 1 9 6 7 2 4 3 8      #2 MUST go in Cell D4, & therefore #8 MUST go in Cell F4
4 7 3 6 2 1 8 5 9 4
5 8 2 5 3 9 4 6 1 7 Step 29: Complete Row 8: need #s 2 & 7…
6 4 9 1 5 6 7 3 8 2      #2 can't go in Cell D8 (cf #2 added in Step 28 @ D4), so
7 6 8 7     1 9   3      #2 MUST go in Cell H8, & therefore #7 MUST go in Cell D8
8 1 4 3 7 5 9 8 2 6
9 9 5 2       7   1
A B C D E F G H I
1 3 7 8 1 4 5 2 6 9 Step 30: Complete Column D: need #s 4 & 8…
2 2 6 4 9 8   1          #8 can't go in Cell D7 (cf #8 in Row 7 @ B7), so
3 5 1 9 6 7 2 4 3 8      #8 MUST go in Cell D9, & therefore #4 MUST go in Cell D7
4 7 3 6 2 1 8 5 9 4
5 8 2 5 3 9 4 6 1 7 Step 31: Complete Block II: need #s 4 & 5…
6 4 9 1 5 6 7 3 8 2      #4 can't go in Cell H7 (cf #4 added in Step 30 @ D7), so
7 6 8 7 4   1 9 5 3      #4 MUST go in Cell H9, & therefore #5 MUST go in Cell H7
8 1 4 3 7 5 9 8 2 6
9 9 5 2 8     7 4 1
A B C D E F G H I
1 3 7 8 1 4 5 2 6 9 Step 32: Complete Block BB: #3 MUST go in Cell F2...
2 2 6 4 9 8 3 1 7 5
3 5 1 9 6 7 2 4 3 8 Step 33: Complete Block CC: need #s 5 & 7…
4 7 3 6 2 1 8 5 9 4      #7 can't go in Cell I2 (cf #7 in Column I @ I5), so
5 8 2 5 3 9 4 6 1 7      #7 MUST go in Cell H2, & therefore #5 MUST go in Cell I2
6 4 9 1 5 6 7 3 8 2
7 6 8 7 4   1 9 5 3
8 1 4 3 7 5 9 8 2 6
9 9 5 2 8     7 4 1
A B C D E F G H I
1 3 7 8 1 4 5 2 6 9 Step 34: Complete Column E: need #s 2 & 3…
2 2 6 4 9 8 3 1 7 5      #2 can't go in Cell E9 (cf #2 in Row 9 @ C9), so
3 5 1 9 6 7 2 4 3 8      #2 MUST go in Cell E7, & therefore #3 MUST go in Cell E9
4 7 3 6 2 1 8 5 9 4
5 8 2 5 3 9 4 6 1 7 Step 35: Complete Column F (& Block HH & the Puzzle):
6 4 9 1 5 6 7 3 8 2      #6 MUST go in Cell F9.
7 6 8 7 4 2 1 9 5 3
8 1 4 3 7 5 9 8 2 6
9 9 5 2 8 3 6 7 4 1
A B C D E F G H I
1 3 7 8 1 4 5 2 6 9 45 Final Proof:
2 2 6 4 9 8 3 1 7 5 45      - All Rows add up to 45;
3 5 1 9 6 7 2 4 3 8 45
4 7 3 6 2 1 8 5 9 4 45
5 8 2 5 3 9 4 6 1 7 45
6 4 9 1 5 6 7 3 8 2 45
7 6 8 7 4 2 1 9 5 3 45
8 1 4 3 7 5 9 8 2 6 45
9 9 5 2 8 3 6 7 4 1 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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