| Medium Puzzle #41 - One Possible Solution Approach | ||||||||||||
| NB: There is only one final solution to this Sudoku puzzle | ||||||||||||
| 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 | 8 | 4 | Medium Puzzle #41 - November 10, 2005 | ||||||||
| 2 | 4 | 1 | 9 | Original puzzle as published © joe-ks.com | ||||||||
| 3 | 2 | 7 | 5 | |||||||||
| 4 | 6 | 7 | 9 | 5 | 8 | 3 | ||||||
| 5 | 1 | 3 | 6 | 5 | 2 | |||||||
| 6 | 2 | 3 | 5 | 1 | 4 | 6 | ||||||
| 7 | 4 | 8 | 7 | |||||||||
| 8 | 5 | 4 | 3 | |||||||||
| 9 | 3 | 6 | 9 | |||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 8 | 4 | Step 1: #4 is in Columns B& C: #4 MUST go in Cell A5... | ||||||||
| 2 | 4 | 1 | 9 | |||||||||
| 3 | 2 | 7 | 5 | Step 2: #8 is in Columns D & F: #8 MUST go in Cell E6 | ||||||||
| 4 | 6 | 7 | 9 | 5 | 8 | 3 | (#8 in Row 4 @ Cell H4 excludes use of Cell E4) | |||||
| 5 | 4 | 1 | 3 | 6 | 5 | 2 | 9 | |||||
| 6 | 2 | 3 | 5 | 8 | 1 | 4 | 6 | Step 3: #9 is in Columns G & H: #9 MUST go in Cell I5... | ||||
| 7 | 4 | 8 | 7 | |||||||||
| 8 | 5 | 4 | 3 | |||||||||
| 9 | 3 | 6 | 9 | |||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 8 | 4 | Step 4: #4 is in Rows 1 & 2: #4 MUST go in Cell D3 | ||||||||
| 2 | 4 | 1 | 9 | (#4 in Column # @ E8 excludes use of Cell E3) | ||||||||
| 3 | 2 | 4 | 7 | 5 | ||||||||
| 4 | 6 | 7 | 9 | 5 | 8 | 3 | Step 5: #3 is in Rows 8 & 9: #3 MUST go in Cell E7 | |||||
| 5 | 4 | 1 | 3 | 6 | 5 | 2 | 9 | (#3 in Column D @ D5 excludes use of Cell D7) | ||||
| 6 | 2 | 3 | 5 | 8 | 1 | 4 | 6 | |||||
| 7 | 4 | 3 | 8 | 7 | ||||||||
| 8 | 5 | 4 | 3 | |||||||||
| 9 | 3 | 6 | 9 | |||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 8 | 4 | Step 6: Complete Block DD: #8 MUST go in Cell B5... | ||||||||
| 2 | 4 | 1 | 9 | |||||||||
| 3 | 2 | 4 | 7 | 5 | Step 7: Complete Block FF: #7 MUST go in Cell H5... | |||||||
| 4 | 6 | 7 | 9 | 5 | 8 | 3 | ||||||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | Step 8: #7 is now in Rows 4 & 5: #7 MUST go in Cell D6 | ||
| 6 | 2 | 3 | 5 | 7 | 8 | 1 | 4 | 6 | (#7 in Column F @ F3 excludes use of Cell F6) | |||
| 7 | 4 | 3 | 8 | 7 | ||||||||
| 8 | 5 | 4 | 3 | Step 9: #7 is now in Columns D & F: #7 MUST go in Cell E9 | ||||||||
| 9 | 3 | 6 | 7 | 9 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 8 | 4 | Step 10: Block EE needs #9: #9 MUST go in Cell F6 | ||||||||
| 2 | 4 | 1 | 9 | (#9 in Row 4 @ C4 excludes use of Cells D4, E4 & F4) | ||||||||
| 3 | 2 | 4 | 7 | 1 | 5 | |||||||
| 4 | 6 | 7 | 9 | 5 | 8 | 3 | Step 11: #1 is in Rows 1 & 2: #1 MUST go in Cell H3 | |||||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | (#1 in Column G @ G6 excludes use of Cell G3) | ||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | |||
| 7 | 4 | 3 | 8 | 7 | Step 12: #4 is in Rows 7 & 8: #4 MUST go in Cell I9 | |||||||
| 8 | 5 | 4 | 3 | (#4 in Column H @ H6 excludes use of Cell H9) | ||||||||
| 9 | 3 | 6 | 7 | 9 | 4 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 8 | 5 | 4 | Step 13: #5 is in Columns B & C: #5 MUST go in Cell A2 | |||||||
| 2 | 5 | 4 | 1 | 9 | (#5 in Row 3 @ I3 excludes use of Cell A3) | |||||||
| 3 | 2 | 4 | 7 | 1 | 5 | |||||||
| 4 | 6 | 7 | 9 | 5 | 8 | 3 | Step 14: #5 is now in Rows 2 & 3: #5 MUST go in Cell E1 | |||||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | (#5 in Column F @ F5 excludes use of clel F1) | ||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | Step 15: #5 is now in Columns E & F: #5 MUST go in Cell D7 | ||
| 7 | 4 | 5 | 3 | 8 | 7 | (#5 in Row 8 @ B8 excludes use of Cell D8) | ||||||
| 8 | 5 | 4 | 3 | |||||||||
| 9 | 3 | 6 | 7 | 9 | 5 | 4 | Step 16: #5 is now in Rows 7 & 8: #5 MUST go in Cell H9 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 8 | 5 | 4 | Step 17: Complete Column E: need #s 2 & 9 | ||||||
| 2 | 5 | 4 | 1 | 9 | #2 can't go in Cell E3 (cf #2 in Row 3 @ C3), so | |||||||
| 3 | 2 | 4 | 9 | 7 | 1 | 5 | #2 MUST go in Column E @ E4, & therefore | |||||
| 4 | 6 | 7 | 9 | 2 | 5 | 8 | 3 | #9 MUST go in Column E @ Cell E3 | ||||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | |||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | Step 18: #9 is now in Rows 2 & 3: #9 MUST go in Cell B1 | ||
| 7 | 4 | 5 | 3 | 8 | 7 | (#9 in Column C @ C4 excludes use of Cell C1) | ||||||
| 8 | 5 | 4 | 3 | |||||||||
| 9 | 3 | 6 | 7 | 9 | 5 | 4 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 8 | 5 | 4 | Step 19: Complete Row 4: need #s 1 & 4 | ||||||
| 2 | 5 | 4 | 1 | 9 | #4 can't go in Cell D4 (cf #4 in Column D @ D3), so | |||||||
| 3 | 2 | 4 | 9 | 7 | 1 | 5 | #4 MUST go in Cell F4, & #1 MUST go in Cell D4 | |||||
| 4 | 6 | 7 | 9 | 1 | 2 | 4 | 5 | 8 | 3 | |||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | Step 20: #9 is in Columns E & F: #9 MUST go in Cell D8... | ||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | |||
| 7 | 9 | 4 | 5 | 3 | 8 | 7 | Step 21: #9 is now in Rows 8 & 9: #9 MUST go in Cell A7 | |||||
| 8 | 5 | 9 | 4 | 3 | (#9 in Column B @ B1 excludes use of Cell B7) | |||||||
| 9 | 3 | 6 | 7 | 9 | 5 | 4 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 7 | 8 | 5 | 4 | Step 22: Complete Column A: need #s 7 & 8 | |||||
| 2 | 5 | 4 | 1 | 7 | 9 | #7 can't go in Column A @ Cell A3 (cf #7 in Row 3 @ F3), so | ||||||
| 3 | 8 | 2 | 4 | 9 | 7 | 1 | 5 | #7 MUST go in Column A @ Cell A8, & therefore | ||||
| 4 | 6 | 7 | 9 | 1 | 2 | 4 | 5 | 8 | 3 | #8 MUST go in Column A @ Cell A3 | ||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | |||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | Step 23: #7 is in Columns H & I: #7 MUST go in Cell G2 | ||
| 7 | 9 | 4 | 5 | 3 | 8 | 7 | (#7 in Row 3 @ F3 excludes use of Cell G3) | |||||
| 8 | 7 | 5 | 9 | 4 | 3 | |||||||
| 9 | 3 | 6 | 7 | 9 | 5 | 4 | Step 24: #7 is now in Rows 2 & 3: #7 MUST go in Cell C1... | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 7 | 8 | 5 | 3 | 4 | Step 25: Complete Row 3: need #s 3 & 6 | ||||
| 2 | 5 | 4 | 3 | 2 | 1 | 7 | 9 | #3 can't go in Row 3 @ Cell B3 (cf #3 in Column B @ B6), so | ||||
| 3 | 8 | 6 | 2 | 4 | 9 | 7 | 3 | 1 | 5 | #3 MUST go in Row 3 @ G3, & therefore #6 MUST go in B3 | ||
| 4 | 6 | 7 | 9 | 1 | 2 | 4 | 5 | 8 | 3 | |||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | Step 26: Complete Block AA: #3 MUST go in Cell C2 | ||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | |||
| 7 | 9 | 4 | 5 | 3 | 8 | 7 | Step 27: #3 is now in Rows 2 & 3: #3 MUST go in Cell F1 | |||||
| 8 | 7 | 5 | 9 | 4 | 3 | |||||||
| 9 | 3 | 6 | 7 | 9 | 5 | 4 | Step 28: Complete Column D: #2 MUST go in Cell D2... | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 7 | 8 | 5 | 3 | 4 | 6 | 2 | Step 29: Complete Block BB: #6 MUST go in Cell F2 | ||
| 2 | 5 | 4 | 3 | 2 | 1 | 6 | 7 | 9 | ||||
| 3 | 8 | 6 | 2 | 4 | 9 | 7 | 3 | 1 | 5 | Step 30: #6 is now in Rows 2 & 3: #6 MUSt go in Cell H1 | ||
| 4 | 6 | 7 | 9 | 1 | 2 | 4 | 5 | 8 | 3 | (#6 in Column I @ I6 excludes use of Cell I1) | ||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | |||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | Step 31: Complete Column H: #2 MUST go in Cell H7 | ||
| 7 | 9 | 4 | 5 | 3 | 8 | 2 | 7 | |||||
| 8 | 7 | 5 | 9 | 4 | 3 | Step 32: #2 is now in Columns G & H: #2 MUST go in Cell I1 | ||||||
| 9 | 3 | 6 | 7 | 9 | 5 | 4 | (#2 in Row 2 @ D2 excludes use of Cell I2) | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 7 | 8 | 5 | 3 | 4 | 6 | 2 | Step 33: Complete Column I: need #s 1 & 8 | ||
| 2 | 5 | 4 | 3 | 2 | 1 | 6 | 7 | 9 | 8 | #1 can't go in Column I @ I2 (cf #1 in Row 2 @ E2), so | ||
| 3 | 8 | 6 | 2 | 4 | 9 | 7 | 3 | 1 | 5 | #1 MUST go in Column I @ I8, & therefore #8 MUST go in I2 | ||
| 4 | 6 | 7 | 9 | 1 | 2 | 4 | 5 | 8 | 3 | |||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | Step 34: Complete Column G: need #s 6 & 8 | ||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | #8 can't go in Column G @ G7 (cf #8 in Row 7 @ F7), so | ||
| 7 | 9 | 4 | 5 | 3 | 8 | 6 | 2 | 7 | #8 MUST go in Cell G8, & therefore #6 MUST go in Cell G7 | |||
| 8 | 7 | 5 | 9 | 4 | 8 | 3 | 1 | |||||
| 9 | 3 | 6 | 7 | 9 | 5 | 4 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 7 | 8 | 5 | 3 | 4 | 6 | 2 | Step 35: Complete Row 7: #1 MUST go in Cell B7... | ||
| 2 | 5 | 4 | 3 | 2 | 1 | 6 | 7 | 9 | 8 | |||
| 3 | 8 | 6 | 2 | 4 | 9 | 7 | 3 | 1 | 5 | Step 36: #1 is now in Rows 7 & 8: #1 MUST go in Cell F9 | ||
| 4 | 6 | 7 | 9 | 1 | 2 | 4 | 5 | 8 | 3 | |||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | Step 37: Complete Block HH: #2 MUST go in Cell F8 | ||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | |||
| 7 | 9 | 1 | 4 | 5 | 3 | 8 | 6 | 2 | 7 | |||
| 8 | 7 | 5 | 9 | 4 | 2 | 8 | 3 | 1 | ||||
| 9 | 3 | 6 | 7 | 1 | 9 | 5 | 4 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 7 | 8 | 5 | 3 | 4 | 6 | 2 | Step 38: Complete Row 8: #6 MUST go in Cell C8 | ||
| 2 | 5 | 4 | 3 | 2 | 1 | 6 | 7 | 9 | 8 | |||
| 3 | 8 | 6 | 2 | 4 | 9 | 7 | 3 | 1 | 5 | |||
| 4 | 6 | 7 | 9 | 1 | 2 | 4 | 5 | 8 | 3 | |||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | |||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | |||
| 7 | 9 | 1 | 4 | 5 | 3 | 8 | 6 | 2 | 7 | |||
| 8 | 7 | 5 | 6 | 9 | 4 | 2 | 8 | 3 | 1 | |||
| 9 | 3 | 6 | 7 | 1 | 9 | 5 | 4 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 7 | 8 | 5 | 3 | 4 | 6 | 2 | Step 39: Complete Block GG (& Puzzle): need #s 2 & 8 | ||
| 2 | 5 | 4 | 3 | 2 | 1 | 6 | 7 | 9 | 8 | #8 can't go in Cell B9 (cf #8 in Column B @ B5), so | ||
| 3 | 8 | 6 | 2 | 4 | 9 | 7 | 3 | 1 | 5 | #8 MUST go in Cell C9, & therefore #2 MUST go in Cell B9 | ||
| 4 | 6 | 7 | 9 | 1 | 2 | 4 | 5 | 8 | 3 | |||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | |||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | |||
| 7 | 9 | 1 | 4 | 5 | 3 | 8 | 6 | 2 | 7 | |||
| 8 | 7 | 5 | 6 | 9 | 4 | 2 | 8 | 3 | 1 | |||
| 9 | 3 | 2 | 8 | 6 | 7 | 1 | 9 | 5 | 4 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 9 | 7 | 8 | 5 | 3 | 4 | 6 | 2 | 45 | Final Proof: | |
| 2 | 5 | 4 | 3 | 2 | 1 | 6 | 7 | 9 | 8 | 45 | - All Rows add up to 45; | |
| 3 | 8 | 6 | 2 | 4 | 9 | 7 | 3 | 1 | 5 | 45 | ||
| 4 | 6 | 7 | 9 | 1 | 2 | 4 | 5 | 8 | 3 | 45 | ||
| 5 | 4 | 8 | 1 | 3 | 6 | 5 | 2 | 7 | 9 | 45 | ||
| 6 | 2 | 3 | 5 | 7 | 8 | 9 | 1 | 4 | 6 | 45 | ||
| 7 | 9 | 1 | 4 | 5 | 3 | 8 | 6 | 2 | 7 | 45 | ||
| 8 | 7 | 5 | 6 | 9 | 4 | 2 | 8 | 3 | 1 | 45 | ||
| 9 | 3 | 2 | 8 | 6 | 7 | 1 | 9 | 5 | 4 | 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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