| Junior Puzzle #9 - 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 | 7 | 5 | 8 | 1 | 3 | Junior Puzzle #9 - November 15, 2005 | |||||
| 2 | 1 | 3 | 9 | 7 | 6 | 8 | Original puzzle as published © joe-ks.com | ||||
| 3 | 8 | 9 | 2 | 5 | 4 | 1 | 7 | ||||
| 4 | 5 | 7 | 8 | 2 | 3 | 4 | 6 | ||||
| 5 | 4 | 1 | 6 | 3 | 5 | 2 | 9 | 7 | |||
| 6 | 3 | 9 | 2 | 6 | 5 | 1 | 8 | ||||
| 7 | 4 | 7 | 5 | 3 | 8 | 9 | 6 | ||||
| 8 | 5 | 6 | 4 | 1 | 7 | 2 | |||||
| 9 | 7 | 9 | 2 | 3 | 5 | ||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 7 | 5 | 4 | 8 | 1 | 3 | Step 1: #4 is in Columns A & B: #4 MUST go in Cell C1... | ||||
| 2 | 1 | 3 | 9 | 7 | 6 | 8 | |||||
| 3 | 8 | 9 | 2 | 5 | 4 | 1 | 7 | Step 2: #8 is in Columns D & F: #8 MUST go in Cell E5... | |||
| 4 | 5 | 7 | 8 | 2 | 3 | 4 | 6 | ||||
| 5 | 4 | 1 | 6 | 3 | 8 | 5 | 2 | 9 | 7 | Step 3: #8 is in Columns G & I: #8 MUST go in Cell H8... | |
| 6 | 3 | 9 | 2 | 6 | 5 | 1 | 8 | ||||
| 7 | 4 | 7 | 5 | 3 | 8 | 9 | 6 | ||||
| 8 | 5 | 6 | 4 | 1 | 7 | 8 | 2 | ||||
| 9 | 7 | 9 | 2 | 3 | 5 | ||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 7 | 5 | 4 | 8 | 1 | 3 | Step 4: Complete Column C: #1 MUST go in Cell C9... | ||||
| 2 | 1 | 3 | 9 | 7 | 6 | 8 | |||||
| 3 | 8 | 9 | 2 | 5 | 4 | 1 | 7 | Step 5: Complete Block II: need #s 1 & 4… | |||
| 4 | 5 | 7 | 8 | 2 | 3 | 4 | 6 | #1 can't go in Cell G9 (cf #1 added in Step 4 in Row 9), so | |||
| 5 | 4 | 1 | 6 | 3 | 8 | 5 | 2 | 9 | 7 | #1 MUST go in Cell I7, & therefore #4 MUST go in Cell G9 | |
| 6 | 3 | 9 | 2 | 6 | 5 | 1 | 8 | ||||
| 7 | 4 | 7 | 5 | 3 | 8 | 9 | 6 | 1 | |||
| 8 | 5 | 6 | 4 | 1 | 7 | 8 | 2 | ||||
| 9 | 1 | 7 | 9 | 2 | 4 | 3 | 5 | ||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 7 | 5 | 4 | 8 | 1 | 3 | Step 6: Complete Row 4: need #s 1 & 9… | ||||
| 2 | 1 | 3 | 9 | 7 | 6 | 8 | #1 can't go in Cell F4 (cf #1 in Column F @ F8), so | ||||
| 3 | 8 | 9 | 2 | 5 | 4 | 1 | 7 | #1 MUST go in Cell D4, & therefore #9 MUST go in Cell F4 | |||
| 4 | 5 | 7 | 8 | 1 | 2 | 9 | 3 | 4 | 6 | ||
| 5 | 4 | 1 | 6 | 3 | 8 | 5 | 2 | 9 | 7 | Step 7: Complete Column F: #7 MUST go in Cell F6... | |
| 6 | 3 | 9 | 2 | 6 | 7 | 5 | 1 | 8 | |||
| 7 | 4 | 7 | 5 | 3 | 8 | 9 | 6 | 1 | |||
| 8 | 5 | 6 | 4 | 1 | 7 | 8 | 2 | ||||
| 9 | 1 | 7 | 9 | 2 | 4 | 3 | 5 | ||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 7 | 5 | 4 | 8 | 1 | 3 | 6 | Step 8: Complete Block FF: #4 MUST go in Cell D6... | |||
| 2 | 1 | 3 | 9 | 7 | 6 | 8 | |||||
| 3 | 6 | 8 | 9 | 2 | 5 | 4 | 1 | 7 | Step 9: Complete Column G: #6 MUST go in Cell G1... | ||
| 4 | 5 | 7 | 8 | 1 | 2 | 9 | 3 | 4 | 6 | ||
| 5 | 4 | 1 | 6 | 3 | 8 | 5 | 2 | 9 | 7 | Step 10: #6 is now in Rows 1 & 2: #6 MUST go in Cell A3… | |
| 6 | 3 | 9 | 2 | 4 | 6 | 7 | 5 | 1 | 8 | ||
| 7 | 4 | 7 | 5 | 3 | 8 | 9 | 6 | 1 | Step 11: #6 is now in Columns A & C: #6 MUST go in Cell B9 | ||
| 8 | 5 | 6 | 4 | 1 | 7 | 8 | 2 | (#6 in Row 8 @ D8 excludes use of Cell B8) | |||
| 9 | 6 | 1 | 7 | 9 | 2 | 4 | 3 | 5 | |||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 7 | 5 | 4 | 8 | 1 | 3 | 6 | 2 | Step 12: Complete Row 7: #2 MUST go in Cell A7... | ||
| 2 | 1 | 2 | 3 | 9 | 7 | 6 | 8 | ||||
| 3 | 6 | 8 | 9 | 2 | 5 | 4 | 1 | 7 | Step 13: Complete Block AA: #2 MUST go in Cell B2... | ||
| 4 | 5 | 7 | 8 | 1 | 2 | 9 | 3 | 4 | 6 | ||
| 5 | 4 | 1 | 6 | 3 | 8 | 5 | 2 | 9 | 7 | Step 14: #2 is now in Rows 2 & 3: #2 MUST go in Cell H1 | |
| 6 | 3 | 9 | 2 | 4 | 6 | 7 | 5 | 1 | 8 | (#2 in Column I @ I8 excludes use of Cell I1) | |
| 7 | 2 | 4 | 7 | 5 | 3 | 8 | 9 | 6 | 1 | ||
| 8 | 5 | 6 | 4 | 1 | 7 | 8 | 2 | ||||
| 9 | 6 | 1 | 7 | 9 | 2 | 4 | 3 | 5 | |||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 7 | 5 | 4 | 8 | 1 | 3 | 6 | 2 | Step 15: Complete Column H: #5 MUST go in Cell H2... | ||
| 2 | 1 | 2 | 3 | 9 | 7 | 6 | 8 | 5 | |||
| 3 | 6 | 8 | 9 | 2 | 5 | 4 | 1 | 7 | Step 16: Complete Column B: #3 MUST go in Cell B8... | ||
| 4 | 5 | 7 | 8 | 1 | 2 | 9 | 3 | 4 | 6 | ||
| 5 | 4 | 1 | 6 | 3 | 8 | 5 | 2 | 9 | 7 | ||
| 6 | 3 | 9 | 2 | 4 | 6 | 7 | 5 | 1 | 8 | ||
| 7 | 2 | 4 | 7 | 5 | 3 | 8 | 9 | 6 | 1 | ||
| 8 | 3 | 5 | 6 | 4 | 1 | 7 | 8 | 2 | |||
| 9 | 6 | 1 | 7 | 9 | 2 | 4 | 3 | 5 | |||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 7 | 5 | 4 | 8 | 1 | 3 | 6 | 2 | 9 | Step 17: Complete Row 1: #9 MUST go in Cell I1... | |
| 2 | 1 | 2 | 3 | 9 | 7 | 6 | 8 | 5 | 4 | ||
| 3 | 6 | 8 | 9 | 2 | 5 | 4 | 1 | 7 | 3 | Step 18: Complete Row 2: #4 MUST go in Cell I2... | |
| 4 | 5 | 7 | 8 | 1 | 2 | 9 | 3 | 4 | 6 | ||
| 5 | 4 | 1 | 6 | 3 | 8 | 5 | 2 | 9 | 7 | Step 19: Complete Row 3: #3 MUST go in Cell I3... | |
| 6 | 3 | 9 | 2 | 4 | 6 | 7 | 5 | 1 | 8 | ||
| 7 | 2 | 4 | 7 | 5 | 3 | 8 | 9 | 6 | 1 | Step 20: Complete Row 8: #9 MUST go in Cell A8... | |
| 8 | 9 | 3 | 5 | 6 | 4 | 1 | 7 | 8 | 2 | ||
| 9 | 8 | 6 | 1 | 7 | 9 | 2 | 4 | 3 | 5 | Step 21: Complete Row 9: #8 MUST go in Cell A9… | |
| A | B | C | D | E | F | G | H | I | |||
| 1 | 7 | 5 | 4 | 8 | 1 | 3 | 6 | 2 | 9 | 45 | Final Proof: |
| 2 | 1 | 2 | 3 | 9 | 7 | 6 | 8 | 5 | 4 | 45 | - All Rows add up to 45; |
| 3 | 6 | 8 | 9 | 2 | 5 | 4 | 1 | 7 | 3 | 45 | |
| 4 | 5 | 7 | 8 | 1 | 2 | 9 | 3 | 4 | 6 | 45 | |
| 5 | 4 | 1 | 6 | 3 | 8 | 5 | 2 | 9 | 7 | 45 | |
| 6 | 3 | 9 | 2 | 4 | 6 | 7 | 5 | 1 | 8 | 45 | |
| 7 | 2 | 4 | 7 | 5 | 3 | 8 | 9 | 6 | 1 | 45 | |
| 8 | 9 | 3 | 5 | 6 | 4 | 1 | 7 | 8 | 2 | 45 | |
| 9 | 8 | 6 | 1 | 7 | 9 | 2 | 4 | 3 | 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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