| Easy Puzzle #9 - 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 | 6 | 7 | 1 | 9 | Easy Puzzle #9 - October 9, 2005 | |||||||
| 2 | 5 | 2 | 6 | 3 | 4 | One possible Solution Method follows below… | ||||||
| 3 | 8 | 3 | 7 | 6 | ||||||||
| 4 | 8 | 4 | 7 | |||||||||
| 5 | 8 | 7 | 2 | 3 | ||||||||
| 6 | 4 | 3 | 7 | 9 | ||||||||
| 7 | 6 | 3 | 2 | |||||||||
| 8 | 9 | 4 | 3 | 7 | 8 | |||||||
| 9 | 1 | 9 | 6 | 4 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 6 | 7 | 1 | 9 | Step 1: #7 is in Rows 1 & 3: #7 MUST go in Cell A2 | |||||||
| 2 | 7 | 5 | 2 | 6 | 3 | 4 | ||||||
| 3 | 8 | 3 | 7 | 6 | ||||||||
| 4 | 8 | 4 | 7 | Step 2: #3 is in Rows 7 & 8: #3 MUST go in Cell I9 | ||||||||
| 5 | 8 | 7 | 2 | 3 | (cf #3 in Column H @ H2 excludes use of Cell H9) | |||||||
| 6 | 4 | 3 | 7 | 9 | ||||||||
| 7 | 6 | 3 | 2 | |||||||||
| 8 | 9 | 4 | 3 | 7 | 8 | |||||||
| 9 | 1 | 9 | 6 | 4 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 6 | 7 | 1 | 9 | Step 3: #2 is in Columns D & F: #2 MUST go in Cell E8 | |||||||
| 2 | 7 | 5 | 2 | 6 | 3 | 4 | (#2 in Row 7 @ I7 excludes use of Cell E7) | |||||
| 3 | 8 | 3 | 7 | 6 | ||||||||
| 4 | 8 | 4 | 7 | |||||||||
| 5 | 8 | 7 | 2 | 3 | ||||||||
| 6 | 4 | 3 | 7 | 9 | ||||||||
| 7 | 6 | 3 | 2 | |||||||||
| 8 | 9 | 4 | 3 | 2 | 7 | 8 | ||||||
| 9 | 1 | 9 | 6 | 4 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 6 | 7 | 1 | 9 | Step 4: #3 is in Rows 2 & 3: #3 MUST go in Cell A1 | ||||||
| 2 | 7 | 5 | 2 | 6 | 3 | 4 | (#3 in Column B @ B6 excludes use of Cell B1) | |||||
| 3 | 8 | 3 | 7 | 6 | ||||||||
| 4 | 8 | 4 | 7 | Step 5: #6 is in Rows 7 & 9: #6 MUST go in Cell G8 | ||||||||
| 5 | 8 | 7 | 2 | 3 | (#6 in Column I @ I3 excludes use of Cell I8) | |||||||
| 6 | 4 | 3 | 7 | 9 | ||||||||
| 7 | 6 | 3 | 2 | |||||||||
| 8 | 9 | 4 | 3 | 2 | 7 | 6 | 8 | |||||
| 9 | 1 | 9 | 6 | 4 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 6 | 4 | 7 | 1 | 9 | Step 6: Block AA needs #4: #4 MUST go in Cell C3 | |||||
| 2 | 7 | 5 | 2 | 6 | 3 | 4 | (#4 in Column B @ B8 excludes Cells B1 & B3, & | |||||
| 3 | 8 | 4 | 3 | 7 | 6 | #4 in Row 2 @ I2 excludes Cell C2) | ||||||
| 4 | 8 | 4 | 7 | |||||||||
| 5 | 8 | 7 | 2 | 3 | Step 7: Now #4 is in Rows 2 & 3: #4 MUST go in Cell D1 | |||||||
| 6 | 4 | 3 | 7 | 9 | ||||||||
| 7 | 6 | 3 | 2 | |||||||||
| 8 | 9 | 4 | 3 | 2 | 7 | 6 | 8 | |||||
| 9 | 1 | 9 | 6 | 4 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 6 | 4 | 7 | 1 | 9 | Step 8: Block AA needs #1: #1 MUST go in Cell B3 | |||||
| 2 | 7 | 5 | 2 | 6 | 1 | 3 | 4 | (#1 in Column C @ C9 excludes Cell C2, & | ||||
| 3 | 8 | 1 | 4 | 3 | 7 | 6 | #1 in Row 1 @ F1 excludes Cell B1) | |||||
| 4 | 8 | 4 | 7 | |||||||||
| 5 | 8 | 7 | 2 | 3 | Step 9: Now #1 is in Rows 1 & 3: #1 MUST go in Cell G2… | |||||||
| 6 | 4 | 3 | 7 | 9 | ||||||||
| 7 | 6 | 3 | 2 | |||||||||
| 8 | 9 | 4 | 3 | 2 | 7 | 6 | 8 | |||||
| 9 | 1 | 9 | 6 | 4 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 6 | 4 | 7 | 1 | 9 | Step 10: Complete Block AA: need #s 2 & 9… | ||||
| 2 | 7 | 5 | 9 | 2 | 6 | 1 | 3 | 4 | #2 can't go in Cell C2 (cf #2 in Row 2 @ D2), so | |||
| 3 | 8 | 1 | 4 | 3 | 7 | 6 | #2 MUST go in Cell B1, & therefore #9 MUST go in Cell C2 | |||||
| 4 | 8 | 4 | 7 | |||||||||
| 5 | 8 | 7 | 2 | 3 | ||||||||
| 6 | 4 | 3 | 7 | 2 | 9 | Step 11: Complete Column G: need #s 2 & 5… | ||||||
| 7 | 6 | 3 | 5 | 2 | #2 can't go in Cell G7 (cf #2 in Row 7 @ I7), so | |||||||
| 8 | 9 | 4 | 3 | 2 | 7 | 6 | 8 | #2 MUST go in Cell G6, & therefore #5 MUST go in Cell G7 | ||||
| 9 | 1 | 9 | 6 | 4 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 6 | 4 | 7 | 1 | 9 | Step 12: Complete Row 2: #8 MUST go in Cell E2… | ||||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | |||
| 3 | 8 | 1 | 4 | 3 | 7 | 6 | ||||||
| 4 | 8 | 4 | 7 | Step 13: Complete Row 8: need #s 1 & 5… | ||||||||
| 5 | 8 | 7 | 2 | 3 | #1 can't go in Cell C8 (cf #1 in Column C @ C9), so | |||||||
| 6 | 4 | 3 | 7 | 2 | 9 | #1 MUST go in Cell I8, & therefore #5 MUST go in Cell C8 | ||||||
| 7 | 6 | 3 | 5 | 2 | ||||||||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 6 | 8 | 1 | |||
| 9 | 1 | 9 | 6 | 4 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | Step 14: Complete Row 1: need #s 5 & 8… | ||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | #8 can't go in Cell H1 (cf #8 in Column H @ H8), so | ||
| 3 | 8 | 1 | 4 | 3 | 7 | 6 | #8 MUST go in Cell I1, & therefore #5 MUST go in Cell H1 | |||||
| 4 | 2 | 8 | 4 | 7 | ||||||||
| 5 | 8 | 7 | 2 | 3 | Step 15: Complete Column C: #2 MUST go in Cell C4… | |||||||
| 6 | 4 | 3 | 7 | 2 | 9 | |||||||
| 7 | 6 | 3 | 5 | 2 | ||||||||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 6 | 8 | 1 | |||
| 9 | 1 | 9 | 6 | 4 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | Step 16: Complete Block BB: need #s 5 & 9… | ||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | #9 can't go in Cell D3 (cf #9 in Column D @ D9), so | ||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #9 MUST go in Cell F3, & therefore #5 MUST go in Cell D3 | ||
| 4 | 2 | 8 | 4 | 7 | ||||||||
| 5 | 8 | 7 | 2 | 3 | Step 17: Complete Block CC: #2 MUST go in Cell H3… | |||||||
| 6 | 4 | 3 | 7 | 2 | 9 | |||||||
| 7 | 6 | 3 | 5 | 2 | ||||||||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 6 | 8 | 1 | |||
| 9 | 1 | 9 | 6 | 4 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | Step 18: Complete Column I: #5 MUST go in Cell I5… | ||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | |||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | Step 19: Block DD needs #5: #5 MUST go in Cell A4 | ||
| 4 | 5 | 2 | 8 | 4 | 7 | (#5 from Step 18 @ I5 excludes use of Cells A5 & B5, & | ||||||
| 5 | 8 | 7 | 2 | 3 | 5 | #5 in Column B @ B2 excludes use of Cell B4) | ||||||
| 6 | 4 | 3 | 7 | 2 | 9 | |||||||
| 7 | 6 | 3 | 5 | 9 | 2 | Step 20: #9 is in Rows 8 & 9: #9 MUST go in Cell H7… | ||||||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 6 | 8 | 1 | |||
| 9 | 1 | 9 | 6 | 4 | 3 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | Step 21: Complete Column A: need #s 1 & 2… | ||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | #1 can't go in Cell A9 (cf #1 in Row 9 @ C9), so | ||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #1 MUST go in Cell A5, & therefore #2 MUST go in Cell A9 | ||
| 4 | 5 | 2 | 8 | 4 | 7 | |||||||
| 5 | 1 | 8 | 7 | 2 | 3 | 6 | 5 | Step 22: Complete Block FF: need #s 1 & 6… | ||||
| 6 | 4 | 3 | 7 | 2 | 1 | 9 | #1 can't go in Cell H5 (cf #1 from Step 21 in A5), so | |||||
| 7 | 6 | 3 | 5 | 9 | 2 | #1 MUST go in Cell H6, & therefore #6 MUST go in Cell H5 | ||||||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 6 | 8 | 1 | |||
| 9 | 2 | 1 | 9 | 6 | 4 | 7 | 3 | Step 23: Complete Block II: #7 MUST go in Cell H9… | ||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 2 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | Step 24: Complete Row 9: need #s 5 & 8… | ||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | #5 can't go in Cell B9 (cf #5 in Column B @ B2), so | ||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #5 MUST go in Cell F9, & therefore #8 MUST go in Cell B9 | ||
| 4 | 5 | 2 | 8 | 4 | 7 | |||||||
| 5 | 1 | 8 | 7 | 2 | 3 | 6 | 5 | |||||
| 6 | 4 | 3 | 7 | 2 | 1 | 9 | ||||||
| 7 | 6 | 3 | 5 | 9 | 2 | |||||||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 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 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | Step 25: Complete Block DD: need #s 6 & 9… | ||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | #6 can't go in Cell B5 (cf #6 in Row 5 @ H5), so | ||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #6 MUST go in Cell B4, & therefore #9 MUST go in Cell B5 | ||
| 4 | 5 | 6 | 2 | 8 | 4 | 7 | ||||||
| 5 | 1 | 9 | 8 | 7 | 2 | 3 | 6 | 5 | Step 26: Complete Block GG: #7 MUST go in Cell B7… | |||
| 6 | 4 | 3 | 7 | 2 | 1 | 9 | ||||||
| 7 | 6 | 7 | 3 | 5 | 9 | 2 | ||||||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 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 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | Step 27: Complete Row 5: #4 MUST go in Cell E5… | ||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | |||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | Step 28: Now #4 is in Columns D & E: #4 MUST go in Cell F7 | ||
| 4 | 5 | 6 | 2 | 8 | 4 | 7 | ||||||
| 5 | 1 | 9 | 8 | 7 | 4 | 2 | 3 | 6 | 5 | |||
| 6 | 4 | 3 | 7 | 2 | 1 | 9 | ||||||
| 7 | 6 | 7 | 3 | 4 | 5 | 9 | 2 | |||||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 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 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | Step 29: Complete Column F: need #s 3 & 8… | ||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | #8 can't go in Cell F4 (cf #8 in Row 4 @ G4), so | ||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #8 MUST go in Cell F6, & therefore #3 MUST go in Cell F4 | ||
| 4 | 5 | 6 | 2 | 3 | 8 | 4 | 7 | |||||
| 5 | 1 | 9 | 8 | 7 | 4 | 2 | 3 | 6 | 5 | |||
| 6 | 4 | 3 | 7 | 8 | 2 | 1 | 9 | |||||
| 7 | 6 | 7 | 3 | 4 | 5 | 9 | 2 | |||||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 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 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | Step 30: Complete Row 4: need #s 1 & 9… | ||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | #9 can't go in Cell D4 (cf #9 in Column D @ D9), so | ||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #9 MUST go in Cell E4, & therefore #1 MUST go in Cell D4 | ||
| 4 | 5 | 6 | 2 | 1 | 9 | 3 | 8 | 4 | 7 | |||
| 5 | 1 | 9 | 8 | 7 | 4 | 2 | 3 | 6 | 5 | Step 31: Complete Row 7: need #s 1 & 8… | ||
| 6 | 4 | 3 | 7 | 8 | 2 | 1 | 9 | #1 can't go in Cell D7 (cf #1 from Step 30 @ D4), so | ||||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | #1 MUST go in Cell E7, & therefore #8 MUST go in Cell D7 | ||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 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 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | Step 32: Complete Block EE: need #s 5 & 6… | ||
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | #6 can't go in Cell E6 (cf #6 in Column E @ E9), so | ||
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | #6 MUST go in Cell D6, & therefore #5 MUST go in Cell D6. | ||
| 4 | 5 | 6 | 2 | 1 | 9 | 3 | 8 | 4 | 7 | |||
| 5 | 1 | 9 | 8 | 7 | 4 | 2 | 3 | 6 | 5 | |||
| 6 | 4 | 3 | 7 | 6 | 5 | 8 | 2 | 1 | 9 | |||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | |||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 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 | 6 | 4 | 7 | 1 | 9 | 5 | 8 | 45 | Final Proof: | |
| 2 | 7 | 5 | 9 | 2 | 8 | 6 | 1 | 3 | 4 | 45 | - All Rows add up to 45; | |
| 3 | 8 | 1 | 4 | 5 | 3 | 9 | 7 | 2 | 6 | 45 | ||
| 4 | 5 | 6 | 2 | 1 | 9 | 3 | 8 | 4 | 7 | 45 | ||
| 5 | 1 | 9 | 8 | 7 | 4 | 2 | 3 | 6 | 5 | 45 | ||
| 6 | 4 | 3 | 7 | 6 | 5 | 8 | 2 | 1 | 9 | 45 | ||
| 7 | 6 | 7 | 3 | 8 | 1 | 4 | 5 | 9 | 2 | 45 | ||
| 8 | 9 | 4 | 5 | 3 | 2 | 7 | 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 | ||||||||||
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