| Easy Puzzle #16 - 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 | 5 | Easy Puzzle #16 - October 16, 2005 | |||||||
| 2 | 3 | 6 | 5 | 8 | 2 | 4 | Original puzzle as published on joe-ks.com… | |||||
| 3 | 9 | 8 | 6 | 1 | ||||||||
| 4 | 2 | 3 | 6 | 8 | ||||||||
| 5 | 5 | 8 | 6 | 4 | ||||||||
| 6 | 8 | 7 | 1 | 2 | ||||||||
| 7 | 4 | 1 | 9 | 7 | 8 | 5 | ||||||
| 8 | 9 | 2 | 1 | 7 | 6 | |||||||
| 9 | 4 | 3 | ||||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 3 | 5 | Step 1: #9 is in Rows 1 & 3: #9 MUST go in Cell I2… | |||||||
| 2 | 3 | 6 | 5 | 8 | 2 | 4 | 9 | |||||
| 3 | 9 | 8 | 6 | 1 | ||||||||
| 4 | 2 | 3 | 6 | 8 | Step 2: #2 is in Rows 4 & 6: #2 MUST go in Cell F5… | |||||||
| 5 | 5 | 8 | 6 | 2 | 4 | (#2 in Column D @ D2 excludes use of Cell D5) | ||||||
| 6 | 8 | 7 | 1 | 2 | ||||||||
| 7 | 4 | 1 | 9 | 7 | 8 | 5 | Step 3: #4 is in Rows 7 & 9: #4 MUST go in Cell G8… | |||||
| 8 | 9 | 2 | 1 | 4 | 7 | 6 | ||||||
| 9 | 4 | 3 | ||||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 3 | 5 | Step 4: #1 is in Rows 1 & 3: #1 MUST go in Cell F2… | |||||||
| 2 | 3 | 6 | 5 | 8 | 1 | 2 | 4 | 9 | ||||
| 3 | 9 | 8 | 6 | 1 | ||||||||
| 4 | 2 | 3 | 6 | 8 | Step 5: #9 is in Rows 7 & 8: #9 MUST go in Cell G9… | |||||||
| 5 | 5 | 8 | 6 | 2 | 4 | (#9 in Column I @ I2 excludes use of Cell I9) | ||||||
| 6 | 8 | 7 | 1 | 2 | ||||||||
| 7 | 4 | 1 | 9 | 7 | 8 | 5 | ||||||
| 8 | 9 | 2 | 1 | 4 | 7 | 6 | ||||||
| 9 | 4 | 9 | 3 | |||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 3 | 5 | Step 6: Complete Row 2: #7 MUST go in Cell C2… | |||||||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | |||
| 3 | 9 | 8 | 6 | 1 | ||||||||
| 4 | 2 | 3 | 4 | 6 | 8 | Step 7: Block EE needs #4: #4 MUST go in Cell E4 | ||||||
| 5 | 5 | 8 | 6 | 2 | 4 | (#4 in Column F @ F9 excludes use of Cells F4 & F6, & | ||||||
| 6 | 8 | 7 | 1 | 2 | #4 in Row 5 @ I5 excludes use of Cell D5) | |||||||
| 7 | 4 | 1 | 9 | 7 | 8 | 5 | ||||||
| 8 | 9 | 2 | 1 | 4 | 7 | 6 | ||||||
| 9 | 4 | 9 | 3 | |||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 3 | 5 | 6 | Step 8: Complete Column H: need #s 6 & 9… | ||||||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | #9 can't go in Cell H1 (cf #9 in Row 1 @ E1), so | ||
| 3 | 9 | 8 | 6 | 1 | #9 MUST go in Cell H5, & therefore #6 MUST go in Cell H1 | |||||||
| 4 | 2 | 3 | 4 | 6 | 8 | |||||||
| 5 | 5 | 8 | 6 | 2 | 9 | 4 | Step 9: Complete Column B: need #s 3 & 7… | |||||
| 6 | 3 | 8 | 7 | 1 | 2 | #7 can't go in Cell B6 (cf #7 in Row 7 @ F7), so | ||||||
| 7 | 4 | 1 | 9 | 7 | 8 | 5 | #7 MUST go in Cell B9, & therefore #3 MUST go in Cell B6 | |||||
| 8 | 9 | 2 | 1 | 4 | 7 | 6 | ||||||
| 9 | 7 | 4 | 9 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 3 | 5 | 6 | Step 10: #5 is in Rows 1 & 2: #5 MUST go in Cell C3… | ||||||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | |||
| 3 | 9 | 8 | 5 | 6 | 1 | |||||||
| 4 | 2 | 3 | 4 | 6 | 8 | Step 11: #1 is in Rows 7 & 8: #1 MUST go in Cell I9… | ||||||
| 5 | 5 | 8 | 6 | 2 | 9 | 4 | ||||||
| 6 | 3 | 8 | 7 | 1 | 2 | |||||||
| 7 | 4 | 1 | 9 | 7 | 8 | 5 | ||||||
| 8 | 9 | 2 | 1 | 4 | 7 | 6 | ||||||
| 9 | 7 | 4 | 9 | 3 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 3 | 5 | 6 | Step 12: Complete Block II: #2 MUST go in Cell I7… | ||||||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | |||
| 3 | 9 | 8 | 5 | 6 | 1 | |||||||
| 4 | 2 | 3 | 4 | 6 | 8 | Step 13: Block EE needs #1: #1 MUST go in Cell D5 | ||||||
| 5 | 5 | 8 | 1 | 6 | 2 | 9 | 4 | (#1 in Column F @ F2 excludes use of Cells F4 & F6) | ||||
| 6 | 3 | 8 | 7 | 1 | 2 | |||||||
| 7 | 4 | 1 | 9 | 7 | 8 | 5 | 2 | |||||
| 8 | 9 | 2 | 1 | 4 | 7 | 6 | ||||||
| 9 | 7 | 4 | 9 | 3 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 3 | 5 | 6 | Step 14: Complete Row 5: need #s 3 & 7… | ||||||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | #3 can't go in Cell A5 (cf #3 in Column A @ A2), so | ||
| 3 | 9 | 8 | 5 | 6 | 1 | #3 MUST go in Cell G5, & therefore #7 MUST go in Cell A5 | ||||||
| 4 | 2 | 3 | 4 | 6 | 8 | |||||||
| 5 | 7 | 5 | 8 | 1 | 6 | 2 | 3 | 9 | 4 | Step 15: Complete Row 7: need #s 3 & 6… | ||
| 6 | 3 | 8 | 7 | 1 | 2 | #6 can't go in Cell E7 (cf #6 in Column E @ E5), so | ||||||
| 7 | 6 | 4 | 1 | 9 | 3 | 7 | 8 | 5 | 2 | #6 MUST go in Cell A7, & therefore #3 MUST go in Cell E7 | ||
| 8 | 9 | 2 | 1 | 4 | 7 | 6 | ||||||
| 9 | 7 | 4 | 9 | 3 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 3 | 5 | 6 | Step 16: Complete Column G: #7 MUST go in Cell G3… | ||||||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | |||
| 3 | 9 | 8 | 5 | 2 | 6 | 7 | 1 | |||||
| 4 | 2 | 3 | 4 | 6 | 8 | Step 17: Complete Column E: need #s 2 & 5… | ||||||
| 5 | 7 | 5 | 8 | 1 | 6 | 2 | 3 | 9 | 4 | #5 can't go in Cell E3 (cf #5 in Row 3 @ C3), so | ||
| 6 | 3 | 8 | 7 | 1 | 2 | #5 MUST go in Cell E9, & therefore #2 MUST go in Cell E3 | ||||||
| 7 | 6 | 4 | 1 | 9 | 3 | 7 | 8 | 5 | 2 | |||
| 8 | 9 | 2 | 1 | 4 | 7 | 6 | ||||||
| 9 | 7 | 5 | 4 | 9 | 3 | 1 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 7 | 9 | 3 | 5 | 6 | Step 18: #7 is in Rows 2 & 3: #7 MUST go in Cell D1… | |||||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | |||
| 3 | 9 | 8 | 5 | 2 | 6 | 7 | 1 | |||||
| 4 | 2 | 3 | 4 | 6 | 8 | Step 19: Complete Block HH: need #s 6 & 8… | ||||||
| 5 | 7 | 5 | 8 | 1 | 6 | 2 | 3 | 9 | 4 | #8 can't go in Cell D9 (cf #8 in Column D @ D6), so | ||
| 6 | 3 | 8 | 7 | 1 | 2 | #8 MUST go in Cell F8, & therefore #6 MUST go in Cell D9 | ||||||
| 7 | 6 | 4 | 1 | 9 | 3 | 7 | 8 | 5 | 2 | |||
| 8 | 9 | 2 | 1 | 8 | 4 | 7 | 6 | |||||
| 9 | 7 | 6 | 5 | 4 | 9 | 3 | 1 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 7 | 9 | 3 | 5 | 6 | Step 20: Complete Block BB: #4 MUST go in Cell D3… | |||||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | |||
| 3 | 9 | 8 | 5 | 4 | 2 | 6 | 7 | 1 | Step 21: Complete Block FF: need #s 5 & 7… | |||
| 4 | 2 | 3 | 4 | 6 | 8 | 7 | #7 can't go in Cell I6 (cf #7 in Row 6 @ E6), so | |||||
| 5 | 7 | 5 | 8 | 1 | 6 | 2 | 3 | 9 | 4 | #7 MUST go in Cell I4, & therefore #5 MUST go in Cell I6 | ||
| 6 | 3 | 8 | 7 | 1 | 2 | 5 | ||||||
| 7 | 6 | 4 | 1 | 9 | 3 | 7 | 8 | 5 | 2 | |||
| 8 | 9 | 2 | 1 | 8 | 4 | 7 | 6 | |||||
| 9 | 7 | 6 | 5 | 4 | 9 | 3 | 1 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 7 | 9 | 3 | 5 | 6 | 8 | Step 22: Complete Block CC: need #s 3 & 8… | ||||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | #3 can't go in Cell I1 (cf #3 in Row 1 @ F1), so | ||
| 3 | 9 | 8 | 5 | 4 | 2 | 6 | 7 | 1 | 3 | #3 MUST go in Cell I3, & therefore #8 MUST go in Cell I1 | ||
| 4 | 2 | 3 | 4 | 5 | 6 | 8 | 7 | |||||
| 5 | 7 | 5 | 8 | 1 | 6 | 2 | 3 | 9 | 4 | Step 23: Complete Block EE: need #5 & 9… | ||
| 6 | 3 | 8 | 7 | 9 | 1 | 2 | 5 | #5 can't go in Cell F6 (cf #5 in Row 6 @ I6), so | ||||
| 7 | 6 | 4 | 1 | 9 | 3 | 7 | 8 | 5 | 2 | #5 MUST go in Cell F4, & therefore #9 MUST go in Cell F6 | ||
| 8 | 9 | 2 | 1 | 8 | 4 | 7 | 6 | |||||
| 9 | 7 | 6 | 5 | 4 | 9 | 3 | 1 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 7 | 9 | 3 | 5 | 6 | 8 | Step 24: Complete Row 4: need #s 1 & 9… | ||||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | #1 can't go in Cell C4 (cf #1 in Column C @ C7), so | ||
| 3 | 9 | 8 | 5 | 4 | 2 | 6 | 7 | 1 | 3 | #1 MUST go in Cell A4, & therefore #9 MUST go in Cell C4 | ||
| 4 | 1 | 2 | 9 | 3 | 4 | 5 | 6 | 8 | 7 | |||
| 5 | 7 | 5 | 8 | 1 | 6 | 2 | 3 | 9 | 4 | |||
| 6 | 3 | 8 | 7 | 9 | 1 | 2 | 5 | |||||
| 7 | 6 | 4 | 1 | 9 | 3 | 7 | 8 | 5 | 2 | |||
| 8 | 9 | 2 | 1 | 8 | 4 | 7 | 6 | |||||
| 9 | 7 | 6 | 5 | 4 | 9 | 3 | 1 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 2 | 1 | 4 | 7 | 9 | 3 | 5 | 6 | 8 | Step 25: Complete Row 6 (& Block DD): need #s 4 & 6… | ||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | #6 can't go in Cell A6 (cf #6 in Column A @ A6), so | ||
| 3 | 9 | 8 | 5 | 4 | 2 | 6 | 7 | 1 | 3 | #6 MUST go in Cell C6, & therefore #4 MUST go in Cell A6 | ||
| 4 | 1 | 2 | 9 | 3 | 4 | 5 | 6 | 8 | 7 | |||
| 5 | 7 | 5 | 8 | 1 | 6 | 2 | 3 | 9 | 4 | Step 26: Complete Row 1 (& Block AA): need #s 2 & 4… | ||
| 6 | 4 | 3 | 6 | 8 | 7 | 9 | 1 | 2 | 5 | #4 can't go in Cell A1 (cf Step #4 added in Step 25), so | ||
| 7 | 6 | 4 | 1 | 9 | 3 | 7 | 8 | 5 | 2 | #4 MUST go in Cell C1, & therefore #2 MUST go in Cell A1 | ||
| 8 | 9 | 2 | 1 | 8 | 4 | 7 | 6 | |||||
| 9 | 7 | 6 | 5 | 4 | 9 | 3 | 1 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 2 | 1 | 4 | 7 | 9 | 3 | 5 | 6 | 8 | Step 27: Complete Column A: need #s 5 & 8… | ||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | #5 can’t go in Cell A9 (cf #5 in Row 9 @ E9), so | ||
| 3 | 9 | 8 | 5 | 4 | 2 | 6 | 7 | 1 | 3 | #5 MUST go in Cell A8, & therefore #8 MUST go in Cell A9 | ||
| 4 | 1 | 2 | 9 | 3 | 4 | 5 | 6 | 8 | 7 | |||
| 5 | 7 | 5 | 8 | 1 | 6 | 2 | 3 | 9 | 4 | |||
| 6 | 4 | 3 | 6 | 8 | 7 | 9 | 1 | 2 | 5 | |||
| 7 | 6 | 4 | 1 | 9 | 3 | 7 | 8 | 5 | 2 | |||
| 8 | 5 | 9 | 2 | 1 | 8 | 4 | 7 | 6 | ||||
| 9 | 8 | 7 | 6 | 5 | 4 | 9 | 3 | 1 | ||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 2 | 1 | 4 | 7 | 9 | 3 | 5 | 6 | 8 | Step 28: Complete Column C (& Block GG): need #s 2 & 3… | ||
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | #2 can’t go in Cell C8 (cf #2 in Row 8 @ D8), so | ||
| 3 | 9 | 8 | 5 | 4 | 2 | 6 | 7 | 1 | 3 | #2 MUST go in Cell C9, & therefore #3 MUST go in Cell C8. | ||
| 4 | 1 | 2 | 9 | 3 | 4 | 5 | 6 | 8 | 7 | |||
| 5 | 7 | 5 | 8 | 1 | 6 | 2 | 3 | 9 | 4 | |||
| 6 | 4 | 3 | 6 | 8 | 7 | 9 | 1 | 2 | 5 | |||
| 7 | 6 | 4 | 1 | 9 | 3 | 7 | 8 | 5 | 2 | |||
| 8 | 5 | 9 | 3 | 2 | 1 | 8 | 4 | 7 | 6 | |||
| 9 | 8 | 7 | 2 | 6 | 5 | 4 | 9 | 3 | 1 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 2 | 1 | 4 | 7 | 9 | 3 | 5 | 6 | 8 | 45 | Final Proof: | |
| 2 | 3 | 6 | 7 | 5 | 8 | 1 | 2 | 4 | 9 | 45 | - All Rows add up to 45; | |
| 3 | 9 | 8 | 5 | 4 | 2 | 6 | 7 | 1 | 3 | 45 | ||
| 4 | 1 | 2 | 9 | 3 | 4 | 5 | 6 | 8 | 7 | 45 | ||
| 5 | 7 | 5 | 8 | 1 | 6 | 2 | 3 | 9 | 4 | 45 | ||
| 6 | 4 | 3 | 6 | 8 | 7 | 9 | 1 | 2 | 5 | 45 | ||
| 7 | 6 | 4 | 1 | 9 | 3 | 7 | 8 | 5 | 2 | 45 | ||
| 8 | 5 | 9 | 3 | 2 | 1 | 8 | 4 | 7 | 6 | 45 | ||
| 9 | 8 | 7 | 2 | 6 | 5 | 4 | 9 | 3 | 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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