| Easy Puzzle #26 - 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 | 4 | 6 | 8 | Easy Puzzle #26 - October 26, 2005 | |||||||
| 2 | 6 | 9 | One possible Solution Method © joe-ks.com | |||||||||
| 3 | 1 | 4 | 5 | 9 | 7 | 2 | ||||||
| 4 | 5 | 3 | 2 | 8 | 7 | |||||||
| 5 | 9 | 6 | ||||||||||
| 6 | 4 | 7 | 2 | 1 | 9 | |||||||
| 7 | 7 | 3 | 8 | 4 | 9 | |||||||
| 8 | 5 | 6 | 1 | |||||||||
| 9 | 2 | 9 | 5 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 8 | Step 1: #6 is in Rows 1 & 2: #6 MUST go in Cell I3… | |||||||
| 2 | 6 | 9 | ||||||||||
| 3 | 1 | 4 | 5 | 9 | 7 | 2 | 6 | |||||
| 4 | 5 | 3 | 2 | 8 | 7 | Step 2: #9 is in Rows 7 & 9: #9 MUST go in Cell A8 | ||||||
| 5 | 9 | 6 | (cf #9 in Column B @ B5 excludes use of Cell B8 | |||||||||
| 6 | 4 | 7 | 2 | 1 | 9 | |||||||
| 7 | 7 | 3 | 8 | 4 | 9 | |||||||
| 8 | 9 | 5 | 6 | 1 | ||||||||
| 9 | 2 | 9 | 5 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 8 | Step 3: #2 is in Columns G & H: #2 MUST go in Cell I7… | |||||||
| 2 | 6 | 9 | ||||||||||
| 3 | 1 | 4 | 5 | 9 | 7 | 2 | 6 | Step 4: #9 is in Columns D & F: #9 MUST go in Cell E4 | ||||
| 4 | 5 | 3 | 2 | 9 | 8 | 7 | (#9 in Row 5 @ B5 excludes use of Cell E5, & | |||||
| 5 | 9 | 6 | #9 in Row 6 @ I6 excludes use of Cell E6) | |||||||||
| 6 | 4 | 7 | 2 | 1 | 9 | |||||||
| 7 | 7 | 3 | 8 | 4 | 9 | 2 | ||||||
| 8 | 9 | 5 | 6 | 1 | ||||||||
| 9 | 2 | 9 | 5 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 8 | Step 5: Complete Row 3: need #s 3 & 8… | |||||||
| 2 | 6 | 9 | #3 can't go in Cell A3 (cf #3 in Column A @ A1), so | |||||||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #3 MUST go in Cell E3, & therefore #8 MUST go in Cell A3 | ||
| 4 | 5 | 3 | 2 | 9 | 8 | 7 | ||||||
| 5 | 9 | 6 | ||||||||||
| 6 | 4 | 7 | 2 | 1 | 9 | |||||||
| 7 | 7 | 3 | 8 | 4 | 9 | 2 | ||||||
| 8 | 9 | 5 | 6 | 1 | ||||||||
| 9 | 2 | 9 | 5 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 8 | Step 6: Column A needs #6: #6 MUST go in Cell A7 | |||||||
| 2 | 6 | 9 | (#6 in Row 2 @ C2 excludes use of Cell A2, & | |||||||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | (#6 in Row 5 @ H5 excludes use of Cell A5) | ||
| 4 | 5 | 3 | 2 | 9 | 8 | 7 | ||||||
| 5 | 9 | 6 | ||||||||||
| 6 | 4 | 7 | 2 | 1 | 9 | |||||||
| 7 | 6 | 7 | 3 | 8 | 4 | 9 | 2 | |||||
| 8 | 9 | 5 | 6 | 1 | ||||||||
| 9 | 2 | 9 | 5 | 3 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 8 | Step 7: Block GG needs #1: #1 MUST go in Cell C9 | |||||||
| 2 | 6 | 9 | (#1 in Column B @ B3 excludes use of Cells B8 & B9) | |||||||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | |||
| 4 | 5 | 3 | 2 | 9 | 8 | 7 | Step 8: #1 is now in Columns B & C: #1 MUST go in Cell A5 | |||||
| 5 | 1 | 9 | 6 | |||||||||
| 6 | 4 | 7 | 2 | 1 | 9 | |||||||
| 7 | 6 | 7 | 3 | 8 | 4 | 9 | 2 | |||||
| 8 | 9 | 5 | 6 | 1 | ||||||||
| 9 | 2 | 1 | 9 | 5 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 1 | 8 | Step 9: Complete Column A: #7 MUST go in Cell A2… | ||||||
| 2 | 7 | 6 | 9 | |||||||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | |||
| 4 | 5 | 3 | 2 | 9 | 8 | 7 | Step 10: #4 is in Columns D & F: #4 MUST go in Cell E5 | |||||
| 5 | 1 | 9 | 4 | 6 | (#4 in Row 6 @ A6 excludes use of Cell E6) | |||||||
| 6 | 4 | 7 | 2 | 1 | 9 | |||||||
| 7 | 6 | 7 | 3 | 8 | 4 | 9 | 2 | Step 11: #1 is in Columns H & I: #1 MUST go in Cell G1… | ||||
| 8 | 9 | 5 | 6 | 1 | ||||||||
| 9 | 2 | 1 | 9 | 5 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 1 | 8 | Step 12: Complete Row 7: need #s 1 & 5… | ||||||
| 2 | 7 | 6 | 9 | #1 can't go in Cell G7 (cf #1 in Column G @ G1), so | ||||||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #1 MUST go in Cell E7, & therefore # 5 MUST go in Cell G7 | ||
| 4 | 5 | 3 | 2 | 9 | 8 | 7 | ||||||
| 5 | 1 | 9 | 4 | 6 | ||||||||
| 6 | 4 | 7 | 2 | 1 | 9 | |||||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 5 | 6 | 1 | ||||||||
| 9 | 2 | 1 | 9 | 5 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 1 | 8 | Step 13: Complete Column G: need #s 3 & 4… | ||||||
| 2 | 7 | 6 | 9 | #3 can't go in Cell G9 (cf #3 in Row 9 @ I9), so | ||||||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #3 MUST go in Cell G5, & therefore #4 MUST go in Cell G9 | ||
| 4 | 5 | 3 | 2 | 9 | 8 | 7 | ||||||
| 5 | 1 | 9 | 4 | 3 | 6 | Step 14: #4 is now in Rows 7 & 9: #4 MUST go in Cell B8… | ||||||
| 6 | 4 | 7 | 2 | 1 | 9 | |||||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 6 | 1 | |||||||
| 9 | 2 | 1 | 9 | 5 | 4 | 3 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 1 | 8 | Step 15: Complete Block GG: #8 MUST go in Cell B9… | ||||||
| 2 | 7 | 6 | 9 | |||||||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | Step 16: Complete Block II: need #s 7 & 8… | ||
| 4 | 5 | 3 | 2 | 9 | 8 | 7 | #8 can't go in Cell H9 (cf #8 added in Step 15 @ B9), so | |||||
| 5 | 1 | 9 | 4 | 3 | 6 | #8 MUST go in Cell H8, & therefore #7 MUST go in Cell H9 | ||||||
| 6 | 4 | 7 | 2 | 1 | 9 | |||||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 6 | 8 | 1 | ||||||
| 9 | 2 | 8 | 1 | 9 | 5 | 4 | 7 | 3 | ||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 1 | 8 | Step 17: Complete Column I: need #s 4 & 5… | ||||||
| 2 | 7 | 6 | 9 | 4 | #4 can't go in Cell I5 (cf #4 in Row 5 @ E5), so | |||||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #4 MUST go in Cell I2, & therefore #5 MUST go in Cell I5 | ||
| 4 | 5 | 3 | 2 | 9 | 8 | 7 | ||||||
| 5 | 1 | 9 | 4 | 3 | 6 | 5 | Step 18: #6 is in Columns A & C: #6 MUST go in Cell B6… | |||||
| 6 | 4 | 6 | 7 | 2 | 1 | 9 | ||||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 6 | 8 | 1 | ||||||
| 9 | 2 | 8 | 1 | 9 | 5 | 4 | 7 | 3 | ||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 6 | 1 | 5 | 8 | Step 19: Complete Block CC: need #s 3 & 5… | |||||
| 2 | 7 | 6 | 9 | 3 | 4 | #3 can't go in Cell H1 (cf #3 in Row 1 @ A1), so | ||||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #3 MUST go in Cell H2, & therefore #5 MUST go in Cell H1 | ||
| 4 | 5 | 3 | 2 | 9 | 8 | 4 | 7 | |||||
| 5 | 1 | 9 | 4 | 3 | 6 | 5 | Step 20: Complete Block FF: #4 MUST go in Cell H4… | |||||
| 6 | 4 | 6 | 7 | 2 | 1 | 9 | ||||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | Step 21: Complete Row 9: #6 MUST go in Cell E9… | ||
| 8 | 9 | 4 | 5 | 6 | 8 | 1 | ||||||
| 9 | 2 | 8 | 1 | 9 | 6 | 5 | 4 | 7 | 3 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 4 | 7 | 6 | 1 | 5 | 8 | Step 22: #7 is in Rows 2 & 3: #7 MUST go in Cell E1… | ||||
| 2 | 7 | 6 | 9 | 3 | 4 | |||||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | |||
| 4 | 5 | 3 | 2 | 6 | 9 | 1 | 8 | 4 | 7 | Step 23: #6 is in Rows 5 & 6: #6 MUST go in Cell D4 | ||
| 5 | 1 | 9 | 4 | 3 | 6 | 5 | (cf #6 in Column F @ F1 excludes use of Cell F4) | |||||
| 6 | 4 | 6 | 7 | 2 | 1 | 9 | ||||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | Step 24: Complete Row 4: #1 MUST go in Cell F4… | ||
| 8 | 9 | 4 | 5 | 6 | 8 | 1 | ||||||
| 9 | 2 | 8 | 1 | 9 | 6 | 5 | 4 | 7 | 3 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 4 | 7 | 6 | 1 | 5 | 8 | Step 25: Complete Column B: need #s 2 & 5… | |||
| 2 | 7 | 5 | 6 | 9 | 3 | 4 | #5 can't go in Cell B1 (cf #5 in Row 1 @ H1), so | |||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #5 MUST go in Cell B2, & therefore #2 MUST go in Cell B1 | ||
| 4 | 5 | 3 | 2 | 6 | 9 | 1 | 8 | 4 | 7 | |||
| 5 | 1 | 9 | 4 | 3 | 6 | 5 | Step 26: #5 is in Columns D & F: #5 MUST go in Cell E6… | |||||
| 6 | 4 | 6 | 7 | 5 | 2 | 1 | 9 | |||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 6 | 8 | 1 | ||||||
| 9 | 2 | 8 | 1 | 9 | 6 | 5 | 4 | 7 | 3 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 9 | 4 | 7 | 6 | 1 | 5 | 8 | Step 27: Complete Block AA: #9 MUST go in Cell C1… | ||
| 2 | 7 | 5 | 6 | 1 | 9 | 3 | 4 | |||||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | |||
| 4 | 5 | 3 | 2 | 6 | 9 | 1 | 8 | 4 | 7 | Step 28: #1 is in Collumns E & F: #1 MUST go in Cell D2… | ||
| 5 | 1 | 9 | 4 | 3 | 6 | 5 | ||||||
| 6 | 4 | 6 | 7 | 5 | 2 | 1 | 9 | |||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 6 | 8 | 1 | ||||||
| 9 | 2 | 8 | 1 | 9 | 6 | 5 | 4 | 7 | 3 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 9 | 4 | 7 | 6 | 1 | 5 | 8 | Step 29: Complete Column E: need #s 2 & 8… | ||
| 2 | 7 | 5 | 6 | 1 | 8 | 9 | 3 | 4 | #8 can't go in Cell E8 (cf #8 in Row 8 @ H8), so | |||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #8 MUST go in Cell E2, & therefore #2 MUST go in Cell E8 | ||
| 4 | 5 | 3 | 2 | 6 | 9 | 1 | 8 | 4 | 7 | |||
| 5 | 1 | 9 | 4 | 3 | 6 | 5 | ||||||
| 6 | 4 | 6 | 7 | 5 | 2 | 1 | 9 | |||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 2 | 6 | 8 | 1 | |||||
| 9 | 2 | 8 | 1 | 9 | 6 | 5 | 4 | 7 | 3 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 9 | 4 | 7 | 6 | 1 | 5 | 8 | Step 30: Complete Row 2: #2 MUST go in Cell F2… | ||
| 2 | 7 | 5 | 6 | 1 | 8 | 2 | 9 | 3 | 4 | |||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | |||
| 4 | 5 | 3 | 2 | 6 | 9 | 1 | 8 | 4 | 7 | Step 31: Row 5 needs #2: #2 MUST go in Cell D5 | ||
| 5 | 1 | 9 | 2 | 4 | 3 | 6 | 5 | (#2 from Step 30 @ F2 excludes use of Cell F5, & | ||||
| 6 | 4 | 6 | 7 | 5 | 2 | 1 | 9 | #2 in Column C @ C4 excludes use of Cell C5) | ||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 2 | 6 | 8 | 1 | |||||
| 9 | 2 | 8 | 1 | 9 | 6 | 5 | 4 | 7 | 3 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 9 | 4 | 7 | 6 | 1 | 5 | 8 | Step 32: Block EE needs #3: #3 MUST go in Cell D6 | ||
| 2 | 7 | 5 | 6 | 1 | 8 | 2 | 9 | 3 | 4 | NB: Because #s 7 & 8 are the only other numbers required | ||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | to complete Blocks DD & EE, both numbers MUST fill | ||
| 4 | 5 | 3 | 2 | 6 | 9 | 1 | 8 | 4 | 7 | Cells C5 & C6 AND F5 & F6 - so neither #7 or #8 can | ||
| 5 | 1 | 9 | 2 | 4 | 3 | 6 | 5 | go in Cell D6! | ||||
| 6 | 4 | 6 | 7 | 3 | 5 | 2 | 1 | 9 | ||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 2 | 6 | 8 | 1 | |||||
| 9 | 2 | 8 | 1 | 9 | 6 | 5 | 4 | 7 | 3 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 9 | 4 | 7 | 6 | 1 | 5 | 8 | Step 33: Complete Column D: #7 MUST go in Cell D8… | ||
| 2 | 7 | 5 | 6 | 1 | 8 | 2 | 9 | 3 | 4 | |||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | |||
| 4 | 5 | 3 | 2 | 6 | 9 | 1 | 8 | 4 | 7 | Step 34: Complete Row 8: #3 MUST go in Cell F8… | ||
| 5 | 1 | 9 | 2 | 4 | 3 | 6 | 5 | |||||
| 6 | 4 | 6 | 7 | 3 | 5 | 2 | 1 | 9 | ||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 7 | 2 | 3 | 6 | 8 | 1 | |||
| 9 | 2 | 8 | 1 | 9 | 6 | 5 | 4 | 7 | 3 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 9 | 4 | 7 | 6 | 1 | 5 | 8 | Step 35: Complete Row 5: need #s 7 & 8… | ||
| 2 | 7 | 5 | 6 | 1 | 8 | 2 | 9 | 3 | 4 | #7 can't go in Cell C5 (cf #7 in Column C @ C6), so | ||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #7 MUST go in Cell F5, & therefore #8 MUST go in Cell C5 | ||
| 4 | 5 | 3 | 2 | 6 | 9 | 1 | 8 | 4 | 7 | |||
| 5 | 1 | 9 | 8 | 2 | 4 | 7 | 3 | 6 | 5 | Step 36: Complete Block EE (& Puzzle): | ||
| 6 | 4 | 6 | 7 | 3 | 5 | 8 | 2 | 1 | 9 | #8 MUST go in Cell F6. | ||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 7 | 2 | 3 | 6 | 8 | 1 | |||
| 9 | 2 | 8 | 1 | 9 | 6 | 5 | 4 | 7 | 3 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 9 | 4 | 7 | 6 | 1 | 5 | 8 | 45 | Final Proof: | |
| 2 | 7 | 5 | 6 | 1 | 8 | 2 | 9 | 3 | 4 | 45 | - All Rows add up to 45; | |
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | 45 | ||
| 4 | 5 | 3 | 2 | 6 | 9 | 1 | 8 | 4 | 7 | 45 | ||
| 5 | 1 | 9 | 8 | 2 | 4 | 7 | 3 | 6 | 5 | 45 | ||
| 6 | 4 | 6 | 7 | 3 | 5 | 8 | 2 | 1 | 9 | 45 | ||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | 45 | ||
| 8 | 9 | 4 | 5 | 7 | 2 | 3 | 6 | 8 | 1 | 45 | ||
| 9 | 2 | 8 | 1 | 9 | 6 | 5 | 4 | 7 | 3 | 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 | ||||||||||
Send your Comments to joe-ks.com