
| Easy Puzzle #25 - 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 | 6 | 4 | Easy Puzzle #25 - October 25, 2005 © joe-ks.com | |||||
| 2 | 3 | 4 | 7 | 1 | One possible Solution Method follows below… | ||||||
| 3 | 1 | 9 | 4 | ||||||||
| 4 | 6 | 3 | 4 | ||||||||
| 5 | 9 | 4 | 5 | 1 | 7 | ||||||
| 6 | 7 | 8 | 9 | 2 | |||||||
| 7 | 5 | 7 | 3 | ||||||||
| 8 | 2 | 7 | 8 | 9 | 6 | ||||||
| 9 | 8 | 6 | 1 | ||||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 3 | 6 | 4 | Step 1: #9 is in Rows 1 & 2: #9 MUST go in Cell G2… | |||||
| 2 | 3 | 4 | 9 | 7 | 1 | ||||||
| 3 | 1 | 9 | 4 | ||||||||
| 4 | 6 | 3 | 4 | Step 2: #4 is in Rows 4 & 5: #4 MUST go in Cell D6… | |||||||
| 5 | 9 | 4 | 5 | 1 | 7 | ||||||
| 6 | 7 | 4 | 8 | 9 | 2 | ||||||
| 7 | 5 | 7 | 3 | Step 3: #7 is in Rows 7 & 8: #7 MUST go in Cell G9 | |||||||
| 8 | 2 | 7 | 8 | 9 | 6 | (cf #7 in Column I @ I5 excludes use of Cell I9) | |||||
| 9 | 8 | 6 | 7 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 3 | 6 | 4 | Step 4: #9 is in Columns A & C: #9 MUST go in Cell B7… | |||||
| 2 | 3 | 4 | 9 | 7 | 1 | ||||||
| 3 | 1 | 9 | 4 | ||||||||
| 4 | 6 | 3 | 4 | 9 | Step 5: #4 is in Columns D & F: #4 MUST go in Cell E8… | ||||||
| 5 | 9 | 4 | 5 | 1 | 7 | ||||||
| 6 | 7 | 4 | 8 | 9 | 2 | ||||||
| 7 | 9 | 5 | 7 | 3 | Step 6: #9 is in Columns G & H: #9 MUST go in Cell I4 | ||||||
| 8 | 2 | 7 | 8 | 4 | 9 | 6 | (cf #9 in Row 6 @ F6 excludes use of Cell I6) | ||||
| 9 | 8 | 6 | 7 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 3 | 6 | 4 | Step 7: Complete Column E: need #s 1 & 2… | |||||
| 2 | 3 | 4 | 2 | 9 | 7 | 1 | #1 can't go in Cell E2 (cf #1 in Row 2 @ I2), so | ||||
| 3 | 1 | 9 | 4 | #1 MUST go in Cell E4, & therefore #2 MUST go in Cell E2 | |||||||
| 4 | 6 | 3 | 1 | 4 | 9 | ||||||
| 5 | 9 | 4 | 5 | 1 | 7 | ||||||
| 6 | 7 | 4 | 8 | 9 | 2 | ||||||
| 7 | 9 | 5 | 7 | 3 | |||||||
| 8 | 2 | 7 | 8 | 4 | 9 | 6 | |||||
| 9 | 8 | 6 | 7 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 3 | 6 | 4 | Step 8: #1 is in Columns D & E: #1 MUST go in Cell F8 | |||||
| 2 | 3 | 4 | 2 | 9 | 7 | 1 | (cf #1 in Row 9 @ H9 excludes use of Cell F9) | ||||
| 3 | 1 | 9 | 4 | ||||||||
| 4 | 6 | 3 | 1 | 4 | 9 | ||||||
| 5 | 9 | 4 | 5 | 1 | 7 | ||||||
| 6 | 7 | 4 | 8 | 9 | 2 | ||||||
| 7 | 9 | 5 | 7 | 3 | |||||||
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | ||||
| 9 | 8 | 6 | 7 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 3 | 6 | 4 | Step 9: Complete Block HH: need #s 2 & 9… | |||||
| 2 | 3 | 4 | 2 | 9 | 7 | 1 | #9 can't go in Cell F9 (cf #9 in Column F @ F6), so | ||||
| 3 | 1 | 9 | 4 | #9 MUST go in Cell D9, & therefore #2 MUST go in Cell F9 | |||||||
| 4 | 6 | 3 | 1 | 4 | 9 | ||||||
| 5 | 9 | 4 | 2 | 5 | 1 | 7 | Step 10: Now #2 is in Columns E & F: #2 MUST go in Cell D5 | ||||
| 6 | 7 | 4 | 8 | 9 | 2 | ||||||
| 7 | 9 | 5 | 7 | 3 | |||||||
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | ||||
| 9 | 8 | 9 | 6 | 2 | 7 | 1 | |||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 7 | 3 | 6 | 4 | Step 11: Complete Block EE: need #s 6 & 7… | ||||
| 2 | 3 | 4 | 2 | 9 | 7 | 1 | #6 can't go in Cell F4 (cf #6 in Row 4 @ C4), so | ||||
| 3 | 1 | 9 | 4 | #6 MUST go in Cell F5, & therefore #7 MUST go in Cell F4 | |||||||
| 4 | 6 | 3 | 1 | 7 | 4 | 9 | |||||
| 5 | 9 | 4 | 2 | 5 | 6 | 1 | 7 | Step 12: Now #7 is in Columns E & F: #7 MUST go in Cell D1 | |||
| 6 | 7 | 4 | 8 | 9 | 2 | (cf #7 in Row 2 @ H2 excludes use of Cell D2) | |||||
| 7 | 9 | 5 | 7 | 3 | |||||||
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | ||||
| 9 | 8 | 9 | 6 | 2 | 7 | 1 | |||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 7 | 3 | 6 | 4 | Step 13: Complete Column D: #6 MUST go in Cell D2… | ||||
| 2 | 3 | 4 | 6 | 2 | 9 | 7 | 1 | ||||
| 3 | 1 | 9 | 4 | ||||||||
| 4 | 6 | 3 | 1 | 7 | 4 | 9 | Step 14: Complete Row 5: need #s 3 & 8… | ||||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | #8 can't go in Cell B5 (cf #8 in Column B @ B9), so | |
| 6 | 7 | 4 | 8 | 9 | 2 | #8 MUST go in Cell H5, & therefore #3 MUST go in Cell B5 | |||||
| 7 | 9 | 5 | 7 | 3 | |||||||
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | ||||
| 9 | 8 | 9 | 6 | 2 | 7 | 1 | |||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 7 | 3 | 6 | 4 | Step 15: Row 4 needs #8: #8 MUST go in Cell A4 | ||||
| 2 | 3 | 4 | 6 | 2 | 9 | 7 | 1 | (cf #8 in Column B @ B9 excludes use of Cell B4, & | |||
| 3 | 7 | 1 | 9 | 4 | #8 in Column H @ H5 excludes use of Cell H4) | ||||||
| 4 | 8 | 6 | 3 | 1 | 7 | 4 | 9 | ||||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | Step 16: #7 is in Rows 1 & 2: #7 MUST go in Cell A3 | |
| 6 | 7 | 4 | 8 | 9 | 2 | (#7 in Column B @ B8 excludes use of Cell B3, & | |||||
| 7 | 9 | 5 | 7 | 3 | #7 in Column C @ C6 excludes use of Cell C3) | ||||||
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | ||||
| 9 | 8 | 9 | 6 | 2 | 7 | 1 | |||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 7 | 3 | 6 | 4 | Step 17: Block DD needs #1: #1 MUST go in Cell A6 | ||||
| 2 | 3 | 4 | 6 | 2 | 9 | 7 | 1 | (cf #1 in Column B @ B1 excludes use of Cells B4 & B6) | |||
| 3 | 7 | 1 | 9 | 4 | |||||||
| 4 | 8 | 6 | 3 | 1 | 7 | 4 | 9 | Step 18: #1 is now in Columns A & B: #1 MUST go in Cell C7 | |||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | (#1 in Row 8 @ F8 excludes Cell C8, & | |
| 6 | 1 | 7 | 4 | 8 | 9 | 2 | #1 in Row 9 @ H9 excludes Cell C9) | ||||
| 7 | 9 | 1 | 5 | 7 | 3 | ||||||
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | ||||
| 9 | 8 | 9 | 6 | 2 | 7 | 1 | |||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 7 | 3 | 6 | 4 | Step 19: Complete Block DD: need #s 2 & 5… | ||||
| 2 | 3 | 4 | 6 | 2 | 9 | 7 | 1 | #2 can't go in Cell B6 (cf #2 in Row 6 @ G6), so | |||
| 3 | 7 | 1 | 9 | 4 | #2 MUST go in Cell B4, & therefore #5 MUST go in Cell B6 | ||||||
| 4 | 8 | 2 | 6 | 3 | 1 | 7 | 4 | 5 | 9 | ||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | Step 20: #5 is now in Rows 5 & 6: #5 MUST go in Cell H4… | |
| 6 | 1 | 5 | 7 | 4 | 8 | 9 | 2 | ||||
| 7 | 9 | 1 | 5 | 7 | 3 | ||||||
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | ||||
| 9 | 8 | 9 | 6 | 2 | 7 | 1 | |||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 1 | 9 | 7 | 3 | 6 | 4 | Step 21: Complete Block FF: need #s 3 & 6… | ||||
| 2 | 3 | 4 | 6 | 2 | 9 | 7 | 1 | #6 can't go in Cell I6 (cf #6 in Column I @ I8), so | |||
| 3 | 7 | 1 | 9 | 4 | #6 MUST go in Cell H6, & therefore #3 MUST go in Cell I6 | ||||||
| 4 | 8 | 2 | 6 | 3 | 1 | 7 | 4 | 5 | 9 | ||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | ||
| 6 | 1 | 5 | 7 | 4 | 8 | 9 | 2 | 6 | 3 | ||
| 7 | 6 | 9 | 1 | 5 | 7 | 3 | Step 22: #6 is in Rows 8 & 9: #6 MUST go in Cell A7… | ||||
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | ||||
| 9 | 8 | 9 | 6 | 2 | 7 | 1 | |||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 5 | 1 | 9 | 7 | 3 | 6 | 4 | Step 23: Complete Column A: need #s 4 & 5… | |||
| 2 | 3 | 4 | 6 | 2 | 9 | 7 | 1 | #4 can't go in Cell A1 (cf #4 in Row 1 @ H1), so | |||
| 3 | 7 | 1 | 9 | 4 | #4 MUST go in Cell A9, & therefore #5 MUST go in Cell A1 | ||||||
| 4 | 8 | 2 | 6 | 3 | 1 | 7 | 4 | 5 | 9 | ||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | ||
| 6 | 1 | 5 | 7 | 4 | 8 | 9 | 2 | 6 | 3 | ||
| 7 | 6 | 9 | 1 | 5 | 7 | 3 | 4 | Step 24: #4 is now in Rows 8 & 9: #4 MUST go in Cell I7 | |||
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | (#4 in Column G @ G4 excludes Cell G7, & | |||
| 9 | 4 | 8 | 9 | 6 | 2 | 7 | 1 | #4 in Column H @ H1 excludes Cell H7) | |||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 5 | 1 | 9 | 7 | 3 | 8 | 6 | 4 | Step 25: Complete Column F: need #s 5 & 8… | ||
| 2 | 3 | 4 | 6 | 2 | 5 | 9 | 7 | 1 | #5 can't go in Cell F1 (cf #5 in Row 1 @ A1), so | ||
| 3 | 7 | 1 | 9 | 4 | #5 MUST go in Cell F2, & therefore #8 MUST go in Cell F1 | ||||||
| 4 | 8 | 2 | 6 | 3 | 1 | 7 | 4 | 5 | 9 | ||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | ||
| 6 | 1 | 5 | 7 | 4 | 8 | 9 | 2 | 6 | 3 | ||
| 7 | 6 | 9 | 1 | 5 | 7 | 3 | 8 | 2 | 4 | Step 26: Complete Row 7: need #s 2 & 8… | |
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | #2 can't go in Cell G7 (cf #2 in Column G @ G6), so | |||
| 9 | 4 | 8 | 9 | 6 | 2 | 7 | 1 | #2 MUST go in Cell H7, & therefore #8 MUST go in Cell G7 | |||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 5 | 1 | 9 | 7 | 3 | 8 | 6 | 4 | 2 | Step 27: Complete Row 1: #2 MUST go in Cell I1… | |
| 2 | 3 | 4 | 8 | 6 | 2 | 5 | 9 | 7 | 1 | ||
| 3 | 7 | 1 | 9 | 4 | Step 28: Complete Row 2: #8 MUST go in Cell C2… | ||||||
| 4 | 8 | 2 | 6 | 3 | 1 | 7 | 4 | 5 | 9 | ||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | ||
| 6 | 1 | 5 | 7 | 4 | 8 | 9 | 2 | 6 | 3 | ||
| 7 | 6 | 9 | 1 | 5 | 7 | 3 | 8 | 2 | 4 | ||
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | ||||
| 9 | 4 | 8 | 9 | 6 | 2 | 7 | 1 | ||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 5 | 1 | 9 | 7 | 3 | 8 | 6 | 4 | 2 | Step 29: Complete Column B: #6 MUST go in Cell B3… | |
| 2 | 3 | 4 | 8 | 6 | 2 | 5 | 9 | 7 | 1 | ||
| 3 | 7 | 6 | 1 | 9 | 4 | 3 | 8 | Step 30: Complete Column H: #3 MUST go in Cell H3… | |||
| 4 | 8 | 2 | 6 | 3 | 1 | 7 | 4 | 5 | 9 | ||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | Step 31: Complete Column I: need #s 5 & 8… | |
| 6 | 1 | 5 | 7 | 4 | 8 | 9 | 2 | 6 | 3 | #8 can't go in Cell I9 (cf #8 in Row 9 @ B9), so | |
| 7 | 6 | 9 | 1 | 5 | 7 | 3 | 8 | 2 | 4 | #8 MUST go in Cell I3, & therefore #5 MUST go in Cell I9 | |
| 8 | 2 | 7 | 8 | 4 | 1 | 9 | 6 | ||||
| 9 | 4 | 8 | 9 | 6 | 2 | 7 | 1 | 5 | |||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 5 | 1 | 9 | 7 | 3 | 8 | 6 | 4 | 2 | Step 32: Complete Block GG: need #s 3 & 5… | |
| 2 | 3 | 4 | 8 | 6 | 2 | 5 | 9 | 7 | 1 | #5 can't go in Cell C9 (cf #5 in Row 9 @ I9), so | |
| 3 | 7 | 6 | 1 | 9 | 4 | 3 | 8 | #5 MUST go in Cell C8, & therefore #3 MUST go in Cell C9 | |||
| 4 | 8 | 2 | 6 | 3 | 1 | 7 | 4 | 5 | 9 | ||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | Step 33: #3 is now in Rows 7 & 9: #3 MUST go in Cell G8… | |
| 6 | 1 | 5 | 7 | 4 | 8 | 9 | 2 | 6 | 3 | ||
| 7 | 6 | 9 | 1 | 5 | 7 | 3 | 8 | 2 | 4 | ||
| 8 | 2 | 7 | 5 | 8 | 4 | 1 | 9 | 6 | |||
| 9 | 4 | 8 | 3 | 9 | 6 | 2 | 7 | 1 | 5 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 5 | 1 | 9 | 7 | 3 | 8 | 6 | 4 | 2 | Step 34: Complete Column C: #2 MUST go in Cell C3… | |
| 2 | 3 | 4 | 8 | 6 | 2 | 5 | 9 | 7 | 1 | ||
| 3 | 7 | 6 | 2 | 1 | 9 | 4 | 5 | 3 | 8 | ||
| 4 | 8 | 2 | 6 | 3 | 1 | 7 | 4 | 5 | 9 | ||
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | Step 35: Complete Column G (& Puzzle): need #s 3 & 5… | |
| 6 | 1 | 5 | 7 | 4 | 8 | 9 | 2 | 6 | 3 | #3 can't go in Cell G3 (cf #3 in Row 3 @ H3), so | |
| 7 | 6 | 9 | 1 | 5 | 7 | 3 | 8 | 2 | 4 | #3 MUST go in Cell G8, & therefore #5 MUST go in Cell G3 | |
| 8 | 2 | 7 | 5 | 8 | 4 | 1 | 3 | 9 | 6 | ||
| 9 | 4 | 8 | 3 | 9 | 6 | 2 | 7 | 1 | 5 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 5 | 1 | 9 | 7 | 3 | 8 | 6 | 4 | 2 | 45 | Final Proof: |
| 2 | 3 | 4 | 8 | 6 | 2 | 5 | 9 | 7 | 1 | 45 | - All Rows add up to 45; |
| 3 | 7 | 6 | 2 | 1 | 9 | 4 | 5 | 3 | 8 | 45 | |
| 4 | 8 | 2 | 6 | 3 | 1 | 7 | 4 | 5 | 9 | 45 | |
| 5 | 9 | 3 | 4 | 2 | 5 | 6 | 1 | 8 | 7 | 45 | |
| 6 | 1 | 5 | 7 | 4 | 8 | 9 | 2 | 6 | 3 | 45 | |
| 7 | 6 | 9 | 1 | 5 | 7 | 3 | 8 | 2 | 4 | 45 | |
| 8 | 2 | 7 | 5 | 8 | 4 | 1 | 3 | 9 | 6 | 45 | |
| 9 | 4 | 8 | 3 | 9 | 6 | 2 | 7 | 1 | 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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