
| Easy Puzzle #24 - 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 | 8 | 2 | 6 | Easy Puzzle #24 - October 24, 2005 | |||||||
| 2 | 2 | 4 | 9 | 8 | One possible Solution Method follows below… | ||||||
| 3 | 5 | 1 | 6 | 3 | 8 | ||||||
| 4 | 7 | 6 | 1 | 9 | |||||||
| 5 | 2 | 3 | 4 | 1 | |||||||
| 6 | 9 | 6 | 3 | 2 | |||||||
| 7 | 6 | 8 | 1 | 3 | |||||||
| 8 | 5 | 9 | 8 | 6 | |||||||
| 9 | 5 | 2 | 7 | ||||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 8 | 2 | 6 | Step 1: #6 is in Columns A & C: #6 MUST go in Cell B2 | |||||||
| 2 | 2 | 6 | 4 | 9 | 8 | (cf #6 in Row 1 @ I1 excludes use of Cell B1) | |||||
| 3 | 5 | 1 | 6 | 3 | 8 | ||||||
| 4 | 7 | 6 | 1 | 9 | Step 2: #8 is in Columns G & I: #8 MUST go in Cell H6 | ||||||
| 5 | 2 | 3 | 4 | 1 | |||||||
| 6 | 9 | 6 | 3 | 8 | 2 | ||||||
| 7 | 6 | 8 | 1 | 3 | |||||||
| 8 | 5 | 9 | 8 | 6 | |||||||
| 9 | 5 | 2 | 7 | ||||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 8 | 2 | 6 | Step 3: #8 is in Column B & C: #8 MUST go in Cell A5 | |||||||
| 2 | 2 | 6 | 4 | 9 | 8 | (cf #8 in row 6 @ H6 excludes use of Cell A6) | |||||
| 3 | 5 | 1 | 6 | 3 | 8 | ||||||
| 4 | 7 | 6 | 1 | 9 | Step 4: #9 is in Columns D & F: #9 MUST go in Cell E5… | ||||||
| 5 | 8 | 2 | 3 | 9 | 4 | 1 | |||||
| 6 | 9 | 6 | 3 | 8 | 2 | ||||||
| 7 | 6 | 8 | 1 | 3 | |||||||
| 8 | 5 | 9 | 8 | 6 | |||||||
| 9 | 5 | 2 | 7 | ||||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 8 | 2 | 6 | Step 5: #6 is in Columns H & I: #6 MUST go in Cell G5 | |||||||
| 2 | 2 | 6 | 4 | 9 | 8 | (cf #6 in row 4 @ C4 excludes use of Cell G4) | |||||
| 3 | 5 | 1 | 6 | 3 | 8 | ||||||
| 4 | 7 | 6 | 1 | 9 | |||||||
| 5 | 8 | 2 | 3 | 9 | 4 | 6 | 1 | ||||
| 6 | 9 | 6 | 3 | 8 | 2 | ||||||
| 7 | 6 | 8 | 1 | 3 | |||||||
| 8 | 5 | 9 | 8 | 6 | |||||||
| 9 | 5 | 2 | 7 | ||||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 8 | 2 | 6 | Step 6: Block II needs #1: #1 MUST go in Cell I9 | |||||||
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | (NB: #1 in Column H @ H5 excludes use of H7,H8,H9 | ||||
| 3 | 5 | 1 | 6 | 3 | 8 | & #1 in Row 7 @ F7 excludes use of G7) | |||||
| 4 | 7 | 6 | 1 | 9 | |||||||
| 5 | 8 | 2 | 3 | 9 | 4 | 6 | 1 | Step 7: Block CC needs #1: #1 MUST go in Cell G2 | |||
| 6 | 9 | 6 | 3 | 8 | 2 | (cf #1 in Columns H & I exclude Cells H2, I1 & I2, | |||||
| 7 | 6 | 8 | 1 | 3 | & #1 in Row 3 @ B3 excludes Cell G3) | ||||||
| 8 | 5 | 9 | 8 | 6 | |||||||
| 9 | 5 | 2 | 7 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 8 | 1 | 2 | 6 | Step 8: #1 is in Rows 2 & 3: #1 MUST go in Cell D1 | ||||||
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | (#1 in Column E @ E4 excludes use of Cell E1, & | ||||
| 3 | 5 | 1 | 6 | 3 | 8 | #1 in Column F @ F7 excludes use of Cell F1) | |||||
| 4 | 7 | 3 | 6 | 1 | 9 | ||||||
| 5 | 8 | 2 | 3 | 9 | 4 | 6 | 1 | Step 9: #3 is in Rows 5 & 6: #3 MUST go in Cell B4… | |||
| 6 | 9 | 6 | 3 | 8 | 2 | ||||||
| 7 | 6 | 8 | 1 | 3 | |||||||
| 8 | 5 | 9 | 8 | 6 | |||||||
| 9 | 5 | 2 | 7 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 8 | 1 | 2 | 6 | Step 10: Block DD needs #4: #4 MUST go in Cell A6 | ||||||
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | (NB: #4 in Column C @ C2 excludes use of C5 & C6 | ||||
| 3 | 5 | 1 | 6 | 3 | 8 | ||||||
| 4 | 7 | 3 | 6 | 1 | 9 | ||||||
| 5 | 8 | 2 | 3 | 9 | 4 | 6 | 1 | ||||
| 6 | 4 | 9 | 6 | 3 | 8 | 2 | |||||
| 7 | 6 | 8 | 1 | 3 | |||||||
| 8 | 5 | 9 | 8 | 6 | |||||||
| 9 | 5 | 2 | 7 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 8 | 1 | 2 | 6 | Step 11: Complete Block DD: need #s 1 & 5… | ||||||
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | #1 can't go in Cell C5 (cf #1 in Row 5 @ H5), so | ||||
| 3 | 5 | 1 | 6 | 3 | 8 | #1 MUST go in Cell C6, & therefore #5 MUST go in Cell C5 | |||||
| 4 | 7 | 3 | 6 | 1 | 9 | ||||||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | Step 12: #1 is in Rows 7 & 9: #1 MUST go in Cell A8 | ||
| 6 | 4 | 9 | 1 | 6 | 3 | 8 | 2 | (cf #1 in Column B @ B3 excludes use of Cell B8, & | |||
| 7 | 6 | 8 | 1 | 3 | #1 in Column C @ C6 excludes use of Cell C8) | ||||||
| 8 | 1 | 5 | 9 | 8 | 6 | ||||||
| 9 | 5 | 2 | 7 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 8 | 1 | 2 | 6 | Step 13: Complete Row 5: #7 MUST go in Cell I5… | |||||
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | |||||
| 3 | 5 | 1 | 6 | 3 | 8 | Step 14: Block AA needs #3: #3 MUST go in Cell A1 | |||||
| 4 | 7 | 3 | 6 | 1 | 9 | (#3 in Column B excludes Cell B1, & #3 in Row 3 @ H3 | |||||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | excludes use of Cell C3) | |
| 6 | 4 | 9 | 1 | 6 | 3 | 8 | 2 | ||||
| 7 | 6 | 8 | 1 | 3 | Step 15: Now #3 is in Columns A & B: #3 MUST go in Cell C8 | ||||||
| 8 | 1 | 3 | 5 | 9 | 8 | 6 | (#3 in Row 7 @ I7 excludes use of Cell C7) | ||||
| 9 | 5 | 2 | 7 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 2 | 6 | Step 16: Complete Block AA: need #s 7 & 9… | ||||
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | #9 can't go in Cell B1 (cf #9 in Column B @ B6), so | ||||
| 3 | 5 | 1 | 9 | 6 | 3 | 8 | #9 MUST go in Cell C3, & therefore #7 MUST go in Cell B1 | ||||
| 4 | 7 | 3 | 6 | 1 | 9 | ||||||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | ||
| 6 | 4 | 9 | 1 | 6 | 3 | 8 | 2 | ||||
| 7 | 6 | 8 | 1 | 3 | |||||||
| 8 | 1 | 3 | 5 | 9 | 8 | 6 | |||||
| 9 | 5 | 2 | 7 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 2 | 6 | Step 17: Complete Column A: #9 MUST go in Cell A9… | ||||
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | |||||
| 3 | 5 | 1 | 9 | 6 | 3 | 8 | Step 18: Complete Column B: #4 MUST go in Cell B8... | ||||
| 4 | 7 | 3 | 6 | 1 | 9 | ||||||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | Step 19: Complete Column C (& Block GG): | |
| 6 | 4 | 9 | 1 | 6 | 3 | 8 | 2 | #7 MUST go in Cell C7… | |||
| 7 | 6 | 8 | 7 | 1 | 3 | ||||||
| 8 | 1 | 4 | 3 | 5 | 9 | 8 | 6 | ||||
| 9 | 9 | 5 | 2 | 7 | 1 | ||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 2 | 6 | 9 | Step 20: Block II needs #9: #9 MUST go in Cell G7 | |||
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | (cf #9 in Column H excludes use of Cells, H7, H8 & H9) | ||||
| 3 | 5 | 1 | 9 | 6 | 3 | 8 | |||||
| 4 | 7 | 3 | 6 | 1 | 9 | Step 21: Now #9 is in Columns G & H: #9 MUST go in Cell I1 | |||||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | (cf #9 in Row 2 @ D2 excludes use of Cell I2) | |
| 6 | 4 | 9 | 1 | 6 | 3 | 8 | 2 | ||||
| 7 | 6 | 8 | 7 | 1 | 9 | 3 | |||||
| 8 | 1 | 4 | 3 | 5 | 9 | 8 | 6 | ||||
| 9 | 9 | 5 | 2 | 7 | 1 | ||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 4 | 5 | 2 | 6 | 9 | Step 22: Complete Row 1: need #s 4 & 5… | |
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | #4 can't go in Cell F1 (cf #4 in Column 4 @ F5), so | ||||
| 3 | 5 | 1 | 9 | 6 | 3 | 8 | #4 MUST go in Cell E1, & therefore #5 MUST go in Cell F1 | ||||
| 4 | 7 | 3 | 6 | 1 | 9 | ||||||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | Step 23: Complete Row 6: need #s 5 & 7… | |
| 6 | 4 | 9 | 1 | 5 | 6 | 7 | 3 | 8 | 2 | #5 can't go in Cell F6 (see #5 added in Step 22 @ F1), so | |
| 7 | 6 | 8 | 7 | 1 | 9 | 3 | #5 MUST go in Cell D6, & therefore #7 MUST go in Cell F6 | ||||
| 8 | 1 | 4 | 3 | 5 | 9 | 8 | 6 | ||||
| 9 | 9 | 5 | 2 | 7 | 1 | ||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 4 | 5 | 2 | 6 | 9 | Step 24: Block CC needs #4: #4 MUST go in Cell G3 | |
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | (cf #4 in Row 2 @ C2 excludes use of Cells H2 & I2) | ||||
| 3 | 5 | 1 | 9 | 6 | 4 | 3 | 8 | ||||
| 4 | 7 | 3 | 6 | 1 | 9 | 4 | Step 25: Block FF needs #4: #4 MUST go in Cell I4 | ||||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | (cf #4 added in Step 24 excludes use of Cell G4) | |
| 6 | 4 | 9 | 1 | 5 | 6 | 7 | 3 | 8 | 2 | ||
| 7 | 6 | 8 | 7 | 1 | 9 | 3 | |||||
| 8 | 1 | 4 | 3 | 5 | 9 | 8 | 6 | ||||
| 9 | 9 | 5 | 2 | 7 | 1 | ||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 4 | 5 | 2 | 6 | 9 | Step 26: Complete Row 3: need #s 2 & 7… | |
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | #7 can't go in Cell F3 (cf #7 in Column F @ F6), so | ||||
| 3 | 5 | 1 | 9 | 6 | 7 | 2 | 4 | 3 | 8 | #7 MUST go in Cell E3, & therefore #2 MUST go in Cell F3 | |
| 4 | 7 | 3 | 6 | 1 | 5 | 9 | 4 | ||||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | Step 27: Complete Block FF: #5 MUST go in Cell G4... | |
| 6 | 4 | 9 | 1 | 5 | 6 | 7 | 3 | 8 | 2 | ||
| 7 | 6 | 8 | 7 | 1 | 9 | 3 | |||||
| 8 | 1 | 4 | 3 | 5 | 9 | 8 | 6 | ||||
| 9 | 9 | 5 | 2 | 7 | 1 | ||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 4 | 5 | 2 | 6 | 9 | Step 28: Complete Row 4: need #s 2 & 8… | |
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | #2 can't go in Cell F4 (cf #2 in Column F @ F3), so | ||||
| 3 | 5 | 1 | 9 | 6 | 7 | 2 | 4 | 3 | 8 | #2 MUST go in Cell D4, & therefore #8 MUST go in Cell F4 | |
| 4 | 7 | 3 | 6 | 2 | 1 | 8 | 5 | 9 | 4 | ||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | Step 29: Complete Row 8: need #s 2 & 7… | |
| 6 | 4 | 9 | 1 | 5 | 6 | 7 | 3 | 8 | 2 | #2 can't go in Cell D8 (cf #2 added in Step 28 @ D4), so | |
| 7 | 6 | 8 | 7 | 1 | 9 | 3 | #2 MUST go in Cell H8, & therefore #7 MUST go in Cell D8 | ||||
| 8 | 1 | 4 | 3 | 7 | 5 | 9 | 8 | 2 | 6 | ||
| 9 | 9 | 5 | 2 | 7 | 1 | ||||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 4 | 5 | 2 | 6 | 9 | Step 30: Complete Column D: need #s 4 & 8… | |
| 2 | 2 | 6 | 4 | 9 | 8 | 1 | #8 can't go in Cell D7 (cf #8 in Row 7 @ B7), so | ||||
| 3 | 5 | 1 | 9 | 6 | 7 | 2 | 4 | 3 | 8 | #8 MUST go in Cell D9, & therefore #4 MUST go in Cell D7 | |
| 4 | 7 | 3 | 6 | 2 | 1 | 8 | 5 | 9 | 4 | ||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | Step 31: Complete Block II: need #s 4 & 5… | |
| 6 | 4 | 9 | 1 | 5 | 6 | 7 | 3 | 8 | 2 | #4 can't go in Cell H7 (cf #4 added in Step 30 @ D7), so | |
| 7 | 6 | 8 | 7 | 4 | 1 | 9 | 5 | 3 | #4 MUST go in Cell H9, & therefore #5 MUST go in Cell H7 | ||
| 8 | 1 | 4 | 3 | 7 | 5 | 9 | 8 | 2 | 6 | ||
| 9 | 9 | 5 | 2 | 8 | 7 | 4 | 1 | ||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 4 | 5 | 2 | 6 | 9 | Step 32: Complete Block BB: #3 MUST go in Cell F2... | |
| 2 | 2 | 6 | 4 | 9 | 8 | 3 | 1 | 7 | 5 | ||
| 3 | 5 | 1 | 9 | 6 | 7 | 2 | 4 | 3 | 8 | Step 33: Complete Block CC: need #s 5 & 7… | |
| 4 | 7 | 3 | 6 | 2 | 1 | 8 | 5 | 9 | 4 | #7 can't go in Cell I2 (cf #7 in Column I @ I5), so | |
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | #7 MUST go in Cell H2, & therefore #5 MUST go in Cell I2 | |
| 6 | 4 | 9 | 1 | 5 | 6 | 7 | 3 | 8 | 2 | ||
| 7 | 6 | 8 | 7 | 4 | 1 | 9 | 5 | 3 | |||
| 8 | 1 | 4 | 3 | 7 | 5 | 9 | 8 | 2 | 6 | ||
| 9 | 9 | 5 | 2 | 8 | 7 | 4 | 1 | ||||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 4 | 5 | 2 | 6 | 9 | Step 34: Complete Column E: need #s 2 & 3… | |
| 2 | 2 | 6 | 4 | 9 | 8 | 3 | 1 | 7 | 5 | #2 can't go in Cell E9 (cf #2 in Row 9 @ C9), so | |
| 3 | 5 | 1 | 9 | 6 | 7 | 2 | 4 | 3 | 8 | #2 MUST go in Cell E7, & therefore #3 MUST go in Cell E9 | |
| 4 | 7 | 3 | 6 | 2 | 1 | 8 | 5 | 9 | 4 | ||
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | Step 35: Complete Column F (& Block HH & the Puzzle): | |
| 6 | 4 | 9 | 1 | 5 | 6 | 7 | 3 | 8 | 2 | #6 MUST go in Cell F9. | |
| 7 | 6 | 8 | 7 | 4 | 2 | 1 | 9 | 5 | 3 | ||
| 8 | 1 | 4 | 3 | 7 | 5 | 9 | 8 | 2 | 6 | ||
| 9 | 9 | 5 | 2 | 8 | 3 | 6 | 7 | 4 | 1 | ||
| A | B | C | D | E | F | G | H | I | |||
| 1 | 3 | 7 | 8 | 1 | 4 | 5 | 2 | 6 | 9 | 45 | Final Proof: |
| 2 | 2 | 6 | 4 | 9 | 8 | 3 | 1 | 7 | 5 | 45 | - All Rows add up to 45; |
| 3 | 5 | 1 | 9 | 6 | 7 | 2 | 4 | 3 | 8 | 45 | |
| 4 | 7 | 3 | 6 | 2 | 1 | 8 | 5 | 9 | 4 | 45 | |
| 5 | 8 | 2 | 5 | 3 | 9 | 4 | 6 | 1 | 7 | 45 | |
| 6 | 4 | 9 | 1 | 5 | 6 | 7 | 3 | 8 | 2 | 45 | |
| 7 | 6 | 8 | 7 | 4 | 2 | 1 | 9 | 5 | 3 | 45 | |
| 8 | 1 | 4 | 3 | 7 | 5 | 9 | 8 | 2 | 6 | 45 | |
| 9 | 9 | 5 | 2 | 8 | 3 | 6 | 7 | 4 | 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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