| Easy Puzzle #15 - 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 | 4 | 8 | 1 | 6 | 3 | Easy Puzzle #15 - October 15, 2005 | |||||
| 2 | 2 | 9 | 7 | 4 | Original puzzle as published on joe-ks.com… | ||||||
| 3 | 8 | 9 | 5 | 7 | 2 | ||||||
| 4 | 1 | 3 | 2 | 6 | 8 | 9 | |||||
| 5 | 3 | 2 | |||||||||
| 6 | 9 | 4 | 5 | 7 | |||||||
| 7 | 6 | ||||||||||
| 8 | 8 | 7 | 2 | 5 | 9 | ||||||
| 9 | 6 | 7 | 5 | 8 | 3 | 1 | |||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 8 | 1 | 2 | 6 | 3 | Step 1: #2 is in Rows 2 & 3: #2 MUST go in Cell F1… | ||||
| 2 | 2 | 9 | 7 | 4 | |||||||
| 3 | 8 | 9 | 5 | 7 | 2 | ||||||
| 4 | 1 | 3 | 2 | 6 | 8 | 9 | Step 2: #9 is in Rows 4 & 6: #9 MUST go in Cell F5… | ||||
| 5 | 3 | 9 | 2 | (cf #9 in Column D @ D2 excludes use of Cell D5) | |||||||
| 6 | 9 | 4 | 5 | 7 | |||||||
| 7 | 6 | Step 3: #6 is in Rows 7 & 9: #6 MUST go in Cell F8… | |||||||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | |||||
| 9 | 6 | 7 | 5 | 8 | 3 | 1 | |||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 8 | 1 | 2 | 9 | 6 | 3 | Step 4: Row #9 needs #9: #9 MUST go in Cell A9… | |||
| 2 | 2 | 9 | 7 | 4 | (#9 in Column F @ F5 excludes use of Cell F9, & | ||||||
| 3 | 8 | 9 | 5 | 7 | 2 | #9 in Column # @ I4 excludes use of Cell I9) | |||||
| 4 | 1 | 3 | 2 | 6 | 8 | 9 | |||||
| 5 | 3 | 9 | 2 | Step 5: #9 is in Rows 2 & 3: #9 MUST go in Cell G1… | |||||||
| 6 | 9 | 4 | 5 | 7 | |||||||
| 7 | 6 | ||||||||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | |||||
| 9 | 9 | 6 | 7 | 5 | 8 | 3 | 1 | ||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 8 | 1 | 2 | 9 | 6 | 3 | Step 6: Complete Row 9: need #s 2 & 4… | |||
| 2 | 2 | 9 | 7 | 4 | #2 can't go in Cell F9 (cf #2 in Column F @ F1), so | ||||||
| 3 | 8 | 9 | 5 | 7 | 2 | #2 MUST go in Cell I9, & therefore #4 MUST go in Cell F9 | |||||
| 4 | 1 | 3 | 2 | 6 | 8 | 9 | |||||
| 5 | 3 | 9 | 2 | ||||||||
| 6 | 9 | 4 | 5 | 7 | Step 7: #7 is in Columns G & I: #7 MUST go in Cell H7… | ||||||
| 7 | 6 | 7 | |||||||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | |||||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 8: Complete Row 1: need #s 5 & 7… | |
| 2 | 2 | 9 | 7 | 4 | #7 can't go in Cell C1 (cf #7 in Column C @ C9), so | ||||||
| 3 | 8 | 9 | 5 | 7 | 2 | #7 MUST go in Cell B1, & therefore #5 MUST go in Cell C1 | |||||
| 4 | 1 | 3 | 2 | 6 | 8 | 9 | |||||
| 5 | 3 | 9 | 2 | ||||||||
| 6 | 9 | 4 | 5 | 7 | |||||||
| 7 | 6 | 7 | |||||||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | |||||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 9: #6 is in Columns E & F: #6 MUST go in Cell D3… | |
| 2 | 2 | 9 | 7 | 4 | |||||||
| 3 | 8 | 9 | 6 | 5 | 7 | 2 | |||||
| 4 | 1 | 3 | 2 | 6 | 8 | 9 | Step 10: #6 is in Columns G & H: #6 MUST go in Cell I5… | ||||
| 5 | 3 | 9 | 2 | 6 | |||||||
| 6 | 9 | 4 | 5 | 7 | |||||||
| 7 | 6 | 7 | |||||||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | |||||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 11: #4 is in Rows 1 & 2: #4 MUST go in Cell E3… | |
| 2 | 2 | 9 | 7 | 4 | |||||||
| 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | ||||
| 4 | 1 | 3 | 2 | 6 | 8 | 9 | Step 12: #3 is in Rows 4 & 5: #3 MUST go in Cell H6… | ||||
| 5 | 3 | 9 | 2 | 6 | (#3 in Column G @ G9 excludes use of Cell G6) | ||||||
| 6 | 9 | 4 | 5 | 3 | 7 | ||||||
| 7 | 6 | 7 | |||||||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | |||||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 13: Complete Block BB: #3 MUST go in Cell F2… | |
| 2 | 2 | 9 | 7 | 3 | 4 | ||||||
| 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | ||||
| 4 | 1 | 3 | 2 | 6 | 8 | 9 | Step 14: Complete Block II: need #s 4 & 8… | ||||
| 5 | 3 | 9 | 2 | 6 | #8 can't go in Cell I8 (cf #8 in Row 8 @ A8), so | ||||||
| 6 | 9 | 4 | 5 | 3 | 7 | #8 MUST go in Cell I7, & therefore #4 MUST go in Cell I8 | |||||
| 7 | 6 | 7 | 8 | ||||||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | 4 | ||||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 15: Complete Row 3: need #s 1 & 3… | |
| 2 | 2 | 9 | 7 | 3 | 4 | #3 can't go in Cell I3 (cf #3 in Column I @ I1), so | |||||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | #3 MUST go in Cell A3, & therefore #1 MUST go in Cell I3 | |
| 4 | 1 | 3 | 2 | 6 | 8 | 9 | |||||
| 5 | 3 | 9 | 2 | 6 | Step 16: Block FF needs #1: #1 MUST go in Cell G6… | ||||||
| 6 | 9 | 4 | 5 | 1 | 3 | 7 | (cf #1 in Row 4 @ B4 excludes G4, & #1 in Column H | ||||
| 7 | 6 | 7 | 8 | @ H9 excludes H5) | |||||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | 4 | ||||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 17: Complete Column E: #9 MUST go in Cell E7… | |
| 2 | 2 | 9 | 7 | 3 | 4 | ||||||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | Step 18: Complete Column H: #5 MUST go in Cell H5… | |
| 4 | 1 | 3 | 2 | 6 | 8 | 9 | |||||
| 5 | 3 | 9 | 2 | 5 | 6 | ||||||
| 6 | 9 | 4 | 5 | 1 | 3 | 7 | |||||
| 7 | 9 | 6 | 7 | 8 | |||||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | 4 | ||||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 19: Complete Block FF: #4 MUST go in Cell G4… | |
| 2 | 2 | 9 | 7 | 3 | 4 | ||||||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | ||
| 4 | 1 | 3 | 2 | 6 | 4 | 8 | 9 | Step 20: Complete Block HH: need #s 1 & 3… | |||
| 5 | 3 | 9 | 2 | 5 | 6 | #3 can't go in Cell F7 (cf #3 in Column F @ F2), so | |||||
| 6 | 9 | 4 | 5 | 1 | 3 | 7 | #3 MUST go in Cell D7, & therefore #1 MUST go in Cell F7 | ||||
| 7 | 3 | 9 | 1 | 6 | 7 | 8 | |||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | 4 | ||||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 21: Complete Column D: #1 MUST go in Cell D5… | |
| 2 | 2 | 9 | 7 | 3 | 8 | 4 | 5 | ||||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | ||
| 4 | 1 | 3 | 2 | 6 | 4 | 8 | 9 | Step 22: Complete Grid CC: need #s 5 & 8… | |||
| 5 | 1 | 3 | 9 | 2 | 5 | 6 | #5 can't go in Cell G2 (cf #5 in Column G @ G8), so | ||||
| 6 | 9 | 4 | 5 | 1 | 3 | 7 | #5 MUST go in I2, & therefore #8 MUST go in Cell G2 | ||||
| 7 | 3 | 9 | 1 | 6 | 7 | 8 | |||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | 4 | ||||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 23: Complete Grid EE: need #s 7 & 8… | |
| 2 | 2 | 9 | 7 | 3 | 8 | 4 | 5 | #7 can't go in Cell F6 (cf #7 in Row 6 @ Cell I6), so | |||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | #7 MUST go in Cell F4, & therefore #8 MUST go in Cell F6 | |
| 4 | 1 | 3 | 2 | 6 | 7 | 4 | 8 | 9 | |||
| 5 | 1 | 3 | 9 | 2 | 5 | 6 | |||||
| 6 | 9 | 4 | 5 | 8 | 1 | 3 | 7 | ||||
| 7 | 3 | 9 | 1 | 6 | 7 | 8 | |||||
| 8 | 8 | 7 | 2 | 6 | 5 | 9 | 4 | ||||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 24: Complete Row 4: #5 MUST go in Cell A4… | |
| 2 | 2 | 9 | 7 | 3 | 8 | 4 | 5 | ||||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | ||
| 4 | 5 | 1 | 3 | 2 | 6 | 7 | 4 | 8 | 9 | Step 25: Complete Row 8: need #s 1 & 3… | |
| 5 | 1 | 3 | 9 | 2 | 5 | 6 | Irony: #1 & #3 along Row 4 (@ B4 & C4) give it away! | ||||
| 6 | 9 | 4 | 5 | 8 | 1 | 3 | 7 | #1 can't go in Cell B8, so #1 MUST go in Cell C8, & | |||
| 7 | 3 | 9 | 1 | 6 | 7 | 8 | therefore #3 MUST go in Cell B8… | ||||
| 8 | 8 | 3 | 1 | 7 | 2 | 6 | 5 | 9 | 4 | ||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 26: Complete Column B: need #s 4 & 5… | |
| 2 | 2 | 9 | 7 | 3 | 8 | 4 | 5 | #5 can't go in Cell B5 (cf #5 in Row 5 @ H5), so | |||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | #5 MUST go in Cell B7, & therefore #4 MUST go in Cell B5 | |
| 4 | 5 | 1 | 3 | 2 | 6 | 7 | 4 | 8 | 9 | ||
| 5 | 4 | 1 | 3 | 9 | 2 | 5 | 6 | ||||
| 6 | 9 | 4 | 5 | 8 | 1 | 3 | 7 | ||||
| 7 | 5 | 3 | 9 | 1 | 6 | 7 | 8 | ||||
| 8 | 8 | 3 | 1 | 7 | 2 | 6 | 5 | 9 | 4 | ||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 27: Complete Block GG: need #s 2 & 4… | |
| 2 | 2 | 9 | 7 | 3 | 8 | 4 | 5 | #4 can't go in Cell A7 (cf #4 in Column A @ A4), so | |||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | #4 MUST go in Cell C7, & therefore #2 MUST go in Cell A7 | |
| 4 | 5 | 1 | 3 | 2 | 6 | 7 | 4 | 8 | 9 | ||
| 5 | 4 | 1 | 3 | 9 | 2 | 5 | 6 | ||||
| 6 | 9 | 4 | 5 | 8 | 1 | 3 | 7 | ||||
| 7 | 2 | 5 | 4 | 3 | 9 | 1 | 6 | 7 | 8 | ||
| 8 | 8 | 3 | 1 | 7 | 2 | 6 | 5 | 9 | 4 | ||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 28: Complete Row 6: need #s 2 & 6… | |
| 2 | 2 | 9 | 7 | 3 | 8 | 4 | 5 | #2 can't go in Cell A6 (cf #2 in Column A @ A7), so | |||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | #2 MUST go in Cell C6, & therefore #6 MUST go in Cell A6 | |
| 4 | 5 | 1 | 3 | 2 | 6 | 7 | 4 | 8 | 9 | ||
| 5 | 4 | 1 | 3 | 9 | 2 | 5 | 6 | ||||
| 6 | 6 | 9 | 2 | 4 | 5 | 8 | 1 | 3 | 7 | ||
| 7 | 2 | 5 | 4 | 3 | 9 | 1 | 6 | 7 | 8 | ||
| 8 | 8 | 3 | 1 | 7 | 2 | 6 | 5 | 9 | 4 | ||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 29: Complete Row 5 (& Block DD): need #s 7 & 8… | |
| 2 | 2 | 9 | 7 | 3 | 8 | 4 | 5 | #7 can't go in Cell C5 (cf #7 in Column C @ C9), so | |||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | #7 MUST go in Cell A5, & therefore #8 MUST go in Cell C5 | |
| 4 | 5 | 1 | 3 | 2 | 6 | 7 | 4 | 8 | 9 | ||
| 5 | 7 | 4 | 8 | 1 | 3 | 9 | 2 | 5 | 6 | ||
| 6 | 6 | 9 | 2 | 4 | 5 | 8 | 1 | 3 | 7 | ||
| 7 | 2 | 5 | 4 | 3 | 9 | 1 | 6 | 7 | 8 | ||
| 8 | 8 | 3 | 1 | 7 | 2 | 6 | 5 | 9 | 4 | ||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | Step 30: Complete Column A: #1 MUST go in Cell A2… | |
| 2 | 1 | 2 | 6 | 9 | 7 | 3 | 8 | 4 | 5 | ||
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | Step 31: Complete Column C (& Row 2 & Block AA): | |
| 4 | 5 | 1 | 3 | 2 | 6 | 7 | 4 | 8 | 9 | #6 MUST go in Cell C3. | |
| 5 | 7 | 4 | 8 | 1 | 3 | 9 | 2 | 5 | 6 | ||
| 6 | 6 | 9 | 2 | 4 | 5 | 8 | 1 | 3 | 7 | ||
| 7 | 2 | 5 | 4 | 3 | 9 | 1 | 6 | 7 | 8 | ||
| 8 | 8 | 3 | 1 | 7 | 2 | 6 | 5 | 9 | 4 | ||
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 4 | 7 | 5 | 8 | 1 | 2 | 9 | 6 | 3 | 45 | Final Proof: |
| 2 | 1 | 2 | 6 | 9 | 7 | 3 | 8 | 4 | 5 | 45 | - All Rows add up to 45; |
| 3 | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 2 | 1 | 45 | |
| 4 | 5 | 1 | 3 | 2 | 6 | 7 | 4 | 8 | 9 | 45 | |
| 5 | 7 | 4 | 8 | 1 | 3 | 9 | 2 | 5 | 6 | 45 | |
| 6 | 6 | 9 | 2 | 4 | 5 | 8 | 1 | 3 | 7 | 45 | |
| 7 | 2 | 5 | 4 | 3 | 9 | 1 | 6 | 7 | 8 | 45 | |
| 8 | 8 | 3 | 1 | 7 | 2 | 6 | 5 | 9 | 4 | 45 | |
| 9 | 9 | 6 | 7 | 5 | 8 | 4 | 3 | 1 | 2 | 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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