| Diabolical Puzzle #50 - 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 | 3 | 6 | Diabolical Puzzle #50 - November 19, 2005 | |||||||||
| 2 | 7 | 5 | 2 | 1 | Original puzzle as published © joe-ks.com | |||||||
| 3 | ||||||||||||
| 4 | 7 | 2 | 5 | |||||||||
| 5 | 4 | 1 | 2 | 6 | ||||||||
| 6 | 2 | 9 | 4 | 3 | ||||||||
| 7 | 8 | 5 | 9 | 7 | ||||||||
| 8 | 2 | 6 | 7 | 1 | 3 | 8 | ||||||
| 9 | 8 | 5 | ||||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 3 | 6 | Step 1: #7 is in Columns A & C: #7 MUST go in Cell B9... | |||||||||
| 2 | 7 | 5 | 2 | 1 | ||||||||
| 3 | 3 | Step 2: #3 is in Columns G & I: #3 MUST go in Cell H3 | ||||||||||
| 4 | 7 | 2 | 5 | (#3 in Row 1 @ C1 excludes use of Cell H1) | ||||||||
| 5 | 4 | 1 | 2 | 6 | ||||||||
| 6 | 2 | 9 | 4 | 3 | ||||||||
| 7 | 8 | 5 | 9 | 7 | ||||||||
| 8 | 2 | 6 | 7 | 1 | 3 | 8 | ||||||
| 9 | 7 | 8 | 5 | |||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 6 | Step 3: #s possible for blank cells… | ||||||||
| 2 | 7 | 5 | 2 | 1 | ||||||||
| 3 | 3 | |||||||||||
| 4 | 7 | 2 | 5 | |||||||||
| 5 | 4 | 1 | 2 | 6 | ||||||||
| 6 | 2 | 9 | 8 | 4 | 3 | |||||||
| 7 | 8 | 5 | 9 | 7 | ||||||||
| 8 | 2 | 6 | 7 | 1 | 3 | 8 | ||||||
| 9 | 7 | 8 | 5 | 1 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 6 | Step 4: #1 is in Rows 8 & 9: #1 MUST go in Cell A7... | ||||||||
| 2 | 7 | 5 | 2 | 1 | ||||||||
| 3 | 3 | |||||||||||
| 4 | 7 | 2 | 5 | |||||||||
| 5 | 4 | 1 | 2 | 6 | ||||||||
| 6 | 2 | 9 | 8 | 4 | 3 | |||||||
| 7 | 1 | 8 | 5 | 9 | 7 | |||||||
| 8 | 2 | 6 | 7 | 1 | 3 | 8 | ||||||
| 9 | 7 | 8 | 5 | 1 | ||||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 6 | Step 5: #s possible for blank cells… | ||||||||
| 2 | 7 | 5 | 2 | 1 | Unique #s in Blue… | |||||||
| 3 | 6 | 3 | i.e. For Cell B3, look at #s in: Block AA (1,3,7,5), | |||||||||
| 4 | 7 | 2 | 5 | 9 | Row 3 (3), & Column B (1,5,4,9,8,2,7) | |||||||
| 5 | 4 | 1 | 2 | 6 | Therefore, only #6 can go in Cell B3… | |||||||
| 6 | 2 | 9 | 8 | 4 | 3 | |||||||
| 7 | 1 | 8 | 5 | 9 | 7 | … similarly for unique #s: | ||||||
| 8 | 2 | 6 | 7 | 1 | 3 | 8 | #9 in Cell H4; and #4 in Cell G9 | |||||
| 9 | 7 | 8 | 5 | 4 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 6 | 5 | Step 6: #5 is in Rows 7 & 9: #5 MUST go in Cell I8... | |||||||
| 2 | 7 | 5 | 2 | 1 | ||||||||
| 3 | 6 | 3 | Step 7: #5 is now in Columns G & I: #5 MUST go in Cell H1... | |||||||||
| 4 | 7 | 2 | 5 | 9 | ||||||||
| 5 | 4 | 1 | 2 | 6 | ||||||||
| 6 | 2 | 9 | 8 | 4 | 3 | |||||||
| 7 | 1 | 8 | 5 | 9 | 7 | |||||||
| 8 | 2 | 6 | 7 | 1 | 3 | 8 | 5 | |||||
| 9 | 7 | 8 | 5 | 4 | 1 | |||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 6 | 5 | Step 7: #s possible for blank cells… | |||||||
| 2 | 7 | 5 | 8 | 2 | 1 | Unique #s in Blue… | ||||||
| 3 | 6 | 3 | #8 in G2; #3 in B4; #8 in I4; #9 in C9 | |||||||||
| 4 | 3 | 7 | 2 | 5 | 9 | 8 | ||||||
| 5 | 4 | 1 | 2 | 6 | ||||||||
| 6 | 2 | 9 | 8 | 4 | 3 | |||||||
| 7 | 1 | 8 | 5 | 9 | 7 | |||||||
| 8 | 2 | 6 | 7 | 1 | 3 | 8 | 5 | |||||
| 9 | 7 | 9 | 8 | 5 | 4 | 1 | ||||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 6 | 5 | Step 8: #s possible for blank cells… | |||||||
| 2 | 7 | 5 | 4 | 8 | 2 | 1 | Unique #s in Blue… | |||||
| 3 | 6 | 7 | 3 | #4 in C2; #7 in G3; #6 in A4; #5 in A5; #7 in I5; #4 in A8; and | ||||||||
| 4 | 6 | 3 | 7 | 2 | 5 | 9 | 8 | #3 in A9 | ||||
| 5 | 5 | 4 | 1 | 2 | 6 | 7 | ||||||
| 6 | 2 | 9 | 8 | 4 | 3 | |||||||
| 7 | 1 | 8 | 5 | 9 | 7 | |||||||
| 8 | 4 | 2 | 6 | 7 | 1 | 3 | 8 | 5 | ||||
| 9 | 3 | 7 | 9 | 8 | 5 | 4 | 1 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 6 | 5 | Step 9: #2 is in Columns A & B: #2 MUST go in Cell C3… | |||||||
| 2 | 7 | 5 | 4 | 8 | 2 | 1 | ||||||
| 3 | 6 | 2 | 7 | 3 | Step 10: Complete Column G: #1 MUST go in Cell G6... | |||||||
| 4 | 6 | 3 | 7 | 2 | 5 | 9 | 8 | |||||
| 5 | 5 | 4 | 1 | 2 | 6 | 7 | Step 11: #9 is in Rows 7 & 9: #9 MUST go in Cell E8… | |||||
| 6 | 2 | 9 | 8 | 1 | 4 | 3 | ||||||
| 7 | 1 | 8 | 5 | 9 | 7 | |||||||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | |||
| 9 | 3 | 7 | 9 | 8 | 5 | 4 | 1 | |||||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 6 | 5 | Step 12: #s possible for blank cells… | |||||||
| 2 | 7 | 5 | 4 | 8 | 2 | 1 | Unique #s in Blue… | |||||
| 3 | 6 | 2 | 7 | 3 | #4 in F4; #6 in E9 | |||||||
| 4 | 6 | 3 | 7 | 1 | 2 | 4 | 5 | 9 | 8 | |||
| 5 | 5 | 4 | 1 | 2 | 6 | 7 | Step 13: Complete Row 9: #2 MUST go in Cell I9... | |||||
| 6 | 2 | 9 | 8 | 1 | 4 | 3 | ||||||
| 7 | 1 | 8 | 5 | 9 | 7 | Step 14: #1 is in Rows 5 & 6: #1 MUST go in Cell D4... | ||||||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | |||
| 9 | 3 | 7 | 9 | 8 | 6 | 5 | 4 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 6 | 5 | Step 14: #s possible for blank cells… | |||||||
| 2 | 7 | 5 | 4 | 3 | 8 | 2 | 1 | Unique #s in Blue… | ||||
| 3 | 6 | 2 | 7 | 3 | #3 in E2; #8 in E5; #$ in E7; #6 in I7 | |||||||
| 4 | 6 | 3 | 7 | 1 | 2 | 4 | 5 | 9 | 8 | |||
| 5 | 5 | 4 | 1 | 8 | 2 | 6 | 7 | |||||
| 6 | 2 | 9 | 8 | 1 | 4 | 3 | ||||||
| 7 | 1 | 8 | 5 | 4 | 9 | 7 | 6 | |||||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | |||
| 9 | 3 | 7 | 9 | 8 | 6 | 5 | 4 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 7 | 6 | 5 | Step 15: #s possible for blank cells… | ||||||
| 2 | 7 | 5 | 4 | 3 | 8 | 2 | 1 | Unique #s in Blue… | ||||
| 3 | 6 | 2 | 7 | 3 | #7 in E1; | |||||||
| 4 | 6 | 3 | 7 | 1 | 2 | 4 | 5 | 9 | 8 | |||
| 5 | 5 | 4 | 1 | 8 | 2 | 6 | 7 | Step 16: #7 is now in Columns D & E: #7 MUST go in Cell F6 | ||||
| 6 | 2 | 9 | 8 | 7 | 1 | 4 | 3 | (#7 in Row 5 @ I5 excludes use of Cell F5) | ||||
| 7 | 1 | 8 | 5 | 4 | 9 | 7 | 6 | |||||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | |||
| 9 | 3 | 7 | 9 | 8 | 6 | 5 | 4 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 7 | 6 | 5 | Step 17: #s possible for blank cells… | ||||||
| 2 | 7 | 5 | 4 | 3 | 8 | 2 | 1 | Unique #s in Blue… | ||||
| 3 | 6 | 2 | 1 | 7 | 3 | #5 in E6 | ||||||
| 4 | 6 | 3 | 7 | 1 | 2 | 4 | 5 | 9 | 8 | |||
| 5 | 5 | 4 | 1 | 8 | 2 | 6 | 7 | Step 18: Complete Column E: #1 MUST go in Cell E3… | ||||
| 6 | 2 | 9 | 8 | 6 | 5 | 7 | 1 | 4 | 3 | |||
| 7 | 1 | 8 | 5 | 4 | 9 | 7 | 6 | Step 19: #6 is in Rows 4 & 5: #6 MUST go in Cell D6... | ||||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | |||
| 9 | 3 | 7 | 9 | 8 | 6 | 5 | 4 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 7 | 6 | 5 | Step 20: #s possible for blank cells… | ||||||
| 2 | 7 | 5 | 4 | 9 | 3 | 6 | 8 | 2 | 1 | Unique #s in Blue… | ||
| 3 | 6 | 2 | 1 | 7 | 3 | #9 in D2 | ||||||
| 4 | 6 | 3 | 7 | 1 | 2 | 4 | 5 | 9 | 8 | |||
| 5 | 5 | 4 | 1 | 3 | 8 | 9 | 2 | 6 | 7 | Step 21: #9 is now in Columns D & E: #9 MUST go in Cell F5... | ||
| 6 | 2 | 9 | 8 | 6 | 5 | 7 | 1 | 4 | 3 | |||
| 7 | 1 | 8 | 5 | 4 | 9 | 7 | 6 | Step 22: #6 is in Rows 1 & 3: #6 MUST go in Cell F2... | ||||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | |||
| 9 | 3 | 7 | 9 | 8 | 6 | 5 | 4 | 1 | 2 | Step 23: Complete Block EE: #3 MUST go in Cell D5... | ||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 7 | 6 | 5 | Step 24: Complete Row 7: need #s 2 & 3… | ||||||
| 2 | 7 | 5 | 4 | 9 | 3 | 6 | 8 | 2 | 1 | #3 can't go in Cell D7 (cf #3 in Column D @ D5), so | ||
| 3 | 6 | 2 | 1 | 7 | 3 | #3 MUST go in Cell F7, & therefore #2 MUST go in Cell D7 | ||||||
| 4 | 6 | 3 | 7 | 1 | 2 | 4 | 5 | 9 | 8 | |||
| 5 | 5 | 4 | 1 | 3 | 8 | 9 | 2 | 6 | 7 | |||
| 6 | 2 | 9 | 8 | 6 | 5 | 7 | 1 | 4 | 3 | |||
| 7 | 1 | 8 | 5 | 2 | 4 | 3 | 9 | 7 | 6 | |||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | |||
| 9 | 3 | 7 | 9 | 8 | 6 | 5 | 4 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 1 | 3 | 4 | 7 | 2 | 6 | 5 | Step 25: #s possible for blank cells… | ||||
| 2 | 7 | 5 | 4 | 9 | 3 | 6 | 8 | 2 | 1 | Unique #s in Blue… | ||
| 3 | 6 | 2 | 5 | 1 | 8 | 7 | 3 | #4 in D1; #8 in F3 | ||||
| 4 | 6 | 3 | 7 | 1 | 2 | 4 | 5 | 9 | 8 | |||
| 5 | 5 | 4 | 1 | 3 | 8 | 9 | 2 | 6 | 7 | Step 26: #2 is in Rows 2 & 3: #2 MUST go in Cell F1... | ||
| 6 | 2 | 9 | 8 | 6 | 5 | 7 | 1 | 4 | 3 | |||
| 7 | 1 | 8 | 5 | 2 | 4 | 3 | 9 | 7 | 6 | Step 27: #5 is in Columns E & F: #5 MUST go in Cell D3... | ||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | |||
| 9 | 3 | 7 | 9 | 8 | 6 | 5 | 4 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 8 | 1 | 3 | 4 | 7 | 2 | 6 | 5 | Step 28: Complete Block AA: need #s 8 & 9… | |||
| 2 | 7 | 5 | 4 | 9 | 3 | 6 | 8 | 2 | 1 | #8 can't go in Cell A3 (cf #8 in Row 3 @ F3), so | ||
| 3 | 9 | 6 | 2 | 5 | 1 | 8 | 7 | 3 | #8 MUST go in Cell A1, & therefore #9 MUST go in Cell A3 | |||
| 4 | 6 | 3 | 7 | 1 | 2 | 4 | 5 | 9 | 8 | |||
| 5 | 5 | 4 | 1 | 3 | 8 | 9 | 2 | 6 | 7 | |||
| 6 | 2 | 9 | 8 | 6 | 5 | 7 | 1 | 4 | 3 | |||
| 7 | 1 | 8 | 5 | 2 | 4 | 3 | 9 | 7 | 6 | |||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | |||
| 9 | 3 | 7 | 9 | 8 | 6 | 5 | 4 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 8 | 1 | 3 | 4 | 7 | 2 | 6 | 5 | 9 | Step 29: Complete Block CC (& Puzzle): need #s 4 & 9… | ||
| 2 | 7 | 5 | 4 | 9 | 3 | 6 | 8 | 2 | 1 | #4 can't go in Cell I1 (cf #4 in Row 1 @ D1), so | ||
| 3 | 9 | 6 | 2 | 5 | 1 | 8 | 7 | 3 | 4 | #4 MUST go in Cell I3, & therefore #9 MUST go in Cell I1. | ||
| 4 | 6 | 3 | 7 | 1 | 2 | 4 | 5 | 9 | 8 | |||
| 5 | 5 | 4 | 1 | 3 | 8 | 9 | 2 | 6 | 7 | |||
| 6 | 2 | 9 | 8 | 6 | 5 | 7 | 1 | 4 | 3 | |||
| 7 | 1 | 8 | 5 | 2 | 4 | 3 | 9 | 7 | 6 | |||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | |||
| 9 | 3 | 7 | 9 | 8 | 6 | 5 | 4 | 1 | 2 | |||
| A | B | C | D | E | F | G | H | I | ||||
| 1 | 8 | 1 | 3 | 4 | 7 | 2 | 6 | 5 | 9 | 45 | Final Proof: | |
| 2 | 7 | 5 | 4 | 9 | 3 | 6 | 8 | 2 | 1 | 45 | - All Rows add up to 45; | |
| 3 | 9 | 6 | 2 | 5 | 1 | 8 | 7 | 3 | 4 | 45 | ||
| 4 | 6 | 3 | 7 | 1 | 2 | 4 | 5 | 9 | 8 | 45 | ||
| 5 | 5 | 4 | 1 | 3 | 8 | 9 | 2 | 6 | 7 | 45 | ||
| 6 | 2 | 9 | 8 | 6 | 5 | 7 | 1 | 4 | 3 | 45 | ||
| 7 | 1 | 8 | 5 | 2 | 4 | 3 | 9 | 7 | 6 | 45 | ||
| 8 | 4 | 2 | 6 | 7 | 9 | 1 | 3 | 8 | 5 | 45 | ||
| 9 | 3 | 7 | 9 | 8 | 6 | 5 | 4 | 1 | 2 | 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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