Analysis of zz-www.sudokuoftheday.co.uk-20060830-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: ...9...2...9.....5..47.3..8.95.6.4..6...975..3.......685......3....25.8.9.....7.. initial
Autosolve
position: ...9...2...9.....5..47.39.8.95.6.4..6...975..3..5..89685..792.34...25.899...3.75. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 1,7 => CTR => A1: 5 * DIS # H7: 4 => CTR => H7: 1,6 * DIS # B5: 1,2 => CTR => B5: 4,8 * DIS # C5: 1,2 => CTR => C5: 8 * DIS # D4: 1,2 => CTR => D4: 3,8 * DIS # F4: 1,2 => CTR => F4: 8 * DIS # A3: 5 => CTR => A3: 1,2 * DIS # H4: 1,3 => CTR => H4: 7 * DIS # I4: 7 => CTR => I4: 1,2 * DIS # B5: 1,2 => CTR => B5: 4,8 * DIS # C5: 1,2 => CTR => C5: 8 * DIS # D7: 1,6 => CTR => D7: 4 * DIS # D7: 1,6 => CTR => D7: 4 * DIS # D9: 1,6 => CTR => D9: 4,8 * DIS # H7: 4 => CTR => H7: 1,6 * DIS # H7: 6 => CTR => H7: 1,4 * DIS # D9: 1,4 => CTR => D9: 6,8 * CNT 17 HDP CHAINS / 65 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 1,7 => CTR => A1: 5 * DIS A1: 5 # B3: 2 => CTR => B3: 1,6 * PRF A1: 5 + B3: 1,6 # E1: 8 => SOL * STA A1: 5 + B3: 1,6 + E1: 8 * CNT 3 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...9...2...9.....5..47.3..8.95.6.4..6...975..3.......685......3....25.8.9.....7.. | initial |
| ...9...2...9.....5..47.39.8.95.6.4..6...975..3..5..89685..792.34...25.899...3.75. | autosolve |
| 563984127789612345214753968195368472648297531372541896856479213437125689921836754 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A2: 1,7 E3: 1,5 I1: 4,7 H2: 4,7 H3: 1,6 A4: 1,2 E6: 1,4 H5: 1,3 I5: 1,2 C7: 1,6 B8: 3,7 C8: 3,7 D8: 1,6 G8: 1,6 I9: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D8,G8: 1.. / D8 = 1 => 17 pairs (_) / G8 = 1 => 0 pairs (X) A3,B3: 2.. / A3 = 2 => 15 pairs (_) / B3 = 2 => 23 pairs (_) D2,F2: 2.. / D2 = 2 => 15 pairs (_) / F2 = 2 => 15 pairs (_) I4,I5: 2.. / I4 = 2 => 15 pairs (_) / I5 = 2 => 16 pairs (_) B9,C9: 2.. / B9 = 2 => 13 pairs (_) / C9 = 2 => 18 pairs (_) A3,A4: 2.. / A3 = 2 => 15 pairs (_) / A4 = 2 => 23 pairs (_) G1,G2: 3.. / G1 = 3 => 14 pairs (_) / G2 = 3 => 16 pairs (_) D4,D5: 3.. / D4 = 3 => 15 pairs (_) / D5 = 3 => 0 pairs (X) H4,H5: 3.. / H4 = 3 => 0 pairs (X) / H5 = 3 => 15 pairs (_) B8,C8: 3.. / B8 = 3 => 16 pairs (_) / C8 = 3 => 13 pairs (_) B2,G2: 3.. / B2 = 3 => 14 pairs (_) / G2 = 3 => 16 pairs (_) D4,H4: 3.. / D4 = 3 => 15 pairs (_) / H4 = 3 => 0 pairs (X) D5,H5: 3.. / D5 = 3 => 0 pairs (X) / H5 = 3 => 15 pairs (_) C1,C8: 3.. / C1 = 3 => 16 pairs (_) / C8 = 3 => 13 pairs (_) I1,H2: 4.. / I1 = 4 => 0 pairs (X) / H2 = 4 => 16 pairs (_) B5,B6: 4.. / B5 = 4 => 15 pairs (_) / B6 = 4 => 0 pairs (X) H7,I9: 4.. / H7 = 4 => 0 pairs (X) / I9 = 4 => 16 pairs (_) B5,D5: 4.. / B5 = 4 => 15 pairs (_) / D5 = 4 => 0 pairs (X) D7,H7: 4.. / D7 = 4 => 16 pairs (_) / H7 = 4 => 0 pairs (X) H2,H7: 4.. / H2 = 4 => 16 pairs (_) / H7 = 4 => 0 pairs (X) I1,I9: 4.. / I1 = 4 => 0 pairs (X) / I9 = 4 => 16 pairs (_) A1,A3: 5.. / A1 = 5 => 15 pairs (_) / A3 = 5 => 0 pairs (X) E1,E3: 5.. / E1 = 5 => 0 pairs (X) / E3 = 5 => 15 pairs (_) A1,E1: 5.. / A1 = 5 => 15 pairs (_) / E1 = 5 => 0 pairs (X) A3,E3: 5.. / A3 = 5 => 0 pairs (X) / E3 = 5 => 15 pairs (_) H7,G8: 6.. / H7 = 6 => 0 pairs (X) / G8 = 6 => 17 pairs (_) B3,H3: 6.. / B3 = 6 => 0 pairs (X) / H3 = 6 => 17 pairs (_) D8,G8: 6.. / D8 = 6 => 0 pairs (X) / G8 = 6 => 17 pairs (_) H3,H7: 6.. / H3 = 6 => 17 pairs (_) / H7 = 6 => 0 pairs (X) A1,A2: 7.. / A1 = 7 => 0 pairs (X) / A2 = 7 => 16 pairs (_) I1,H2: 7.. / I1 = 7 => 16 pairs (_) / H2 = 7 => 0 pairs (X) B6,C6: 7.. / B6 = 7 => 16 pairs (_) / C6 = 7 => 13 pairs (_) H4,I4: 7.. / H4 = 7 => 16 pairs (_) / I4 = 7 => 0 pairs (X) B8,C8: 7.. / B8 = 7 => 13 pairs (_) / C8 = 7 => 16 pairs (_) A1,I1: 7.. / A1 = 7 => 0 pairs (X) / I1 = 7 => 16 pairs (_) A2,H2: 7.. / A2 = 7 => 16 pairs (_) / H2 = 7 => 0 pairs (X) B6,B8: 7.. / B6 = 7 => 16 pairs (_) / B8 = 7 => 13 pairs (_) C6,C8: 7.. / C6 = 7 => 13 pairs (_) / C8 = 7 => 16 pairs (_) H2,H4: 7.. / H2 = 7 => 0 pairs (X) / H4 = 7 => 16 pairs (_) I1,I4: 7.. / I1 = 7 => 16 pairs (_) / I4 = 7 => 0 pairs (X) E1,E2: 8.. / E1 = 8 => 17 pairs (_) / E2 = 8 => 15 pairs (_) B5,C5: 8.. / B5 = 8 => 0 pairs (X) / C5 = 8 => 15 pairs (_) D4,F4: 8.. / D4 = 8 => 0 pairs (X) / F4 = 8 => 15 pairs (_) D9,F9: 8.. / D9 = 8 => 15 pairs (_) / F9 = 8 => 0 pairs (X) B2,E2: 8.. / B2 = 8 => 17 pairs (_) / E2 = 8 => 15 pairs (_) C1,C5: 8.. / C1 = 8 => 0 pairs (X) / C5 = 8 => 15 pairs (_) D4,D9: 8.. / D4 = 8 => 0 pairs (X) / D9 = 8 => 15 pairs (_) F4,F9: 8.. / F4 = 8 => 15 pairs (_) / F9 = 8 => 0 pairs (X) * DURATION: 0:01:05.282339 START: 02:12:36.969579 END: 02:13:42.251918 2019-05-01 * CP COUNT: (48) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B8,C7,C8,D8,E3,E6,G8,H2,H3,H5,I1,I5,I9) * ...9...2...9.....5..47.39.8.95.6.4..6...975..3..5..89685..792.34...25.899...3.75. * PAIR A2: 1,7 BLK 1 A1: 1,7,5 # reduction candidate for 1,7 A1: 1,7 => CTR * .8.95..2...928...5524713968295.614.76483975123..5428968516792434..12568996243875. A1: 5 # 15 pairs * PAIR E3: 1,5 BLK 2 E1: 1,5,4,8 # reduction candidate for 1,5 E1: 1,5 # 17 pairs E1: 4,8 # 16 pairs * PAIR E3: 1,5 ROW 3 A3: 1,5,2 # reduction candidate for 1,5 A3: 1,5 # 23 pairs A3: 2 # 15 pairs * PAIR H3: 1,6 BLK 3 G1: 1,6,3 # reduction candidate for 1,6 G1: 1,6 # 16 pairs G2: 1,6,3 # reduction candidate for 1,6 G2: 1,6 # 14 pairs * PAIR H3: 1,6 ROW 3 B3: 1,6,2 # reduction candidate for 1,6 B3: 2 # 23 pairs B3: 1,6 # 15 pairs * PAIR H3: 1,6 COL H H7: 1,6,4 # reduction candidate for 1,6 H7: 4 => CTR * 7..95..241.9.8.375524713968295.6.4.76.8.975.23.754289685167924347312568996..3.751 H7: 1,6 # 16 pairs * PAIR A4: 1,2 BLK 4 B5: 1,2,4,8 # reduction candidate for 1,2 B5: 1,2 => CTR * ...9...24..924..75..4753968.95368417618497532347512896851679243473125689962834751 B5: 4,8 # 16 pairs C5: 1,2,8 # reduction candidate for 1,2 C5: 1,2 => CTR * ..89...2...9.8...5..47.39.8.95.6.4..68.49753.34751289685..79243473.256899...34751 C5: 8 # 15 pairs B6: 1,2,4,7 # reduction candidate for 1,2 B6: 1,2 # 18 pairs C6: 1,2,7 # reduction candidate for 1,2 C6: 1,2 # 16 pairs * PAIR A4: 1,2 ROW 4 D4: 1,2,3,8 # reduction candidate for 1,2 D4: 1,2 => CTR * 7..95..241.9.8..755247139682951684376..3975123..5..89685..792.34...25.899..83.751 D4: 3,8 # 16 pairs F4: 1,2,8 # reduction candidate for 1,2 F4: 1,2 => CTR * 7..95..241.9284.75524713968295861437648397512317542896851679243473125689962438751 F4: 8 # 15 pairs I4: 1,2,7 # reduction candidate for 1,2 I4: 1,2 # 16 pairs * PAIR A4: 1,2 COL A A3: 1,2,5 # reduction candidate for 1,2 A3: 5 => CTR * .8.95..2...928...5524713968295.614.76483975123..5428968516792434..12568996243875. A3: 1,2 # 15 pairs * PAIR E6: 1,4 BLK 5 D5: 1,4,2,3 # reduction candidate for 1,4 D5: 1,4 # 21 pairs F6: 1,4,2 # reduction candidate for 1,4 F6: 1,4 # 15 pairs * PAIR E6: 1,4 ROW 6 B6: 1,4,2,7 # reduction candidate for 1,4 B6: 2,7 # 16 pairs B6: 1,4 # 15 pairs * PAIR E6: 1,4 COL E E1: 1,4,5,8 # reduction candidate for 1,4 E1: 1,4 # 15 pairs E2: 1,4,8 # reduction candidate for 1,4 E2: 1,4 # 17 pairs * PAIR H5: 1,3 BLK 6 H4: 1,3,7 # reduction candidate for 1,3 H4: 1,3 => CTR * 7..95..241.9.8.375524713968295.6.4.76...975.23..5428968516792434..12568996..3.751 H4: 7 # 16 pairs * PAIR H5: 1,3 ROW 5 D5: 1,3,2,4 # reduction candidate for 1,3 D5: 2,4 # 17 pairs D5: 1,3 # 16 pairs * PAIR I5: 1,2 BLK 6 I4: 1,2,7 # reduction candidate for 1,2 I4: 7 => CTR * 7..95..241.9.8..75524713968295.6.4.76...975.23..5428968516792434..125689962.3.751 I4: 1,2 # 16 pairs * PAIR I5: 1,2 ROW 5 B5: 1,2,4,8 # reduction candidate for 1,2 B5: 1,2 => CTR * ...9...24..924..75..4753968.95368417618497532347512896851679243473125689962834751 B5: 4,8 # 16 pairs C5: 1,2,8 # reduction candidate for 1,2 C5: 1,2 => CTR * ..89...2...9.8...5..47.39.8.95.6.4..68.49753.34751289685..79243473.256899...34751 C5: 8 # 15 pairs D5: 1,2,3,4 # reduction candidate for 1,2 D5: 1,2 # 16 pairs * PAIR C7: 1,6 BLK 7 B9: 1,6,2 # reduction candidate for 1,6 B9: 1,6 # 18 pairs C9: 1,6,2 # reduction candidate for 1,6 C9: 1,6 # 13 pairs * PAIR C7: 1,6 ROW 7 D7: 1,6,4 # reduction candidate for 1,6 D7: 1,6 => CTR * 7..95..241.9.8.375524713968295.6.4.76.8.975.23.754289685167924347312568996..3.751 D7: 4 # 16 pairs H7: 1,6,4 # reduction candidate for 1,6 H7: 1,6 # 16 pairs * PAIR C7: 1,6 COL C C1: 1,6,3,8 # reduction candidate for 1,6 C1: 3,8 # 17 pairs C1: 1,6 # 17 pairs * PAIR D8: 1,6 BLK 8 D7: 1,6,4 # reduction candidate for 1,6 D7: 1,6 => CTR * 7..95..241.9.8.375524713968295.6.4.76.8.975.23.754289685167924347312568996..3.751 D7: 4 # 16 pairs D9: 1,6,4,8 # reduction candidate for 1,6 D9: 1,6 => CTR * ...9...2...9.....5..47.39.8.9586.4376..3975123..5..89685..792.34...25.899...3875. D9: 4,8 # 16 pairs F9: 1,6,4,8 # reduction candidate for 1,6 F9: 1,6 # 16 pairs * PAIR D8: 1,6 COL D D2: 1,6,2,4 # reduction candidate for 1,6 D2: 2,4 # 16 pairs D2: 1,6 # 15 pairs * PAIR G8: 1,6 BLK 9 H7: 1,6,4 # reduction candidate for 1,6 H7: 4 => CTR * 7..95..241.9.8.375524713968295.6.4.76.8.975.23.754289685167924347312568996..3.751 H7: 1,6 # 16 pairs * PAIR G8: 1,6 COL G G1: 1,6,3 # reduction candidate for 1,6 G1: 1,6 # 16 pairs G2: 1,6,3 # reduction candidate for 1,6 G2: 1,6 # 14 pairs * PAIR I9: 1,4 BLK 9 H7: 1,4,6 # reduction candidate for 1,4 H7: 6 => CTR * ..39..6277.9..63452647539181953684726482975313725148968514792634..625189926831754 H7: 1,4 # 17 pairs * PAIR I9: 1,4 ROW 9 D9: 1,4,6,8 # reduction candidate for 1,4 D9: 1,4 => CTR * 7..95..241.9284.75524713968295861437648397512317542896851679243473125689962438751 D9: 6,8 # 16 pairs F9: 1,4,6,8 # reduction candidate for 1,4 F9: 1,4 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060830-absurd-base-pr-000.dot * REASONING * DIS # A1: 1,7 => CTR => A1: 5 * DIS # H7: 4 => CTR => H7: 1,6 * DIS # B5: 1,2 => CTR => B5: 4,8 * DIS # C5: 1,2 => CTR => C5: 8 * DIS # D4: 1,2 => CTR => D4: 3,8 * DIS # F4: 1,2 => CTR => F4: 8 * DIS # A3: 5 => CTR => A3: 1,2 * DIS # H4: 1,3 => CTR => H4: 7 * DIS # I4: 7 => CTR => I4: 1,2 * DIS # B5: 1,2 => CTR => B5: 4,8 * DIS # C5: 1,2 => CTR => C5: 8 * DIS # D7: 1,6 => CTR => D7: 4 * DIS # D7: 1,6 => CTR => D7: 4 * DIS # D9: 1,6 => CTR => D9: 4,8 * DIS # H7: 4 => CTR => H7: 1,6 * DIS # H7: 6 => CTR => H7: 1,4 * DIS # D9: 1,4 => CTR => D9: 6,8 * CNT 17 HDP CHAINS / 65 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B8,C7,C8,D8,E3,E6,G8,H2,H3,H5,I1,I5,I9) * ...9...2...9.....5..47.39.8.95.6.4..6...975..3..5..89685..792.34...25.899...3.75. * PAIR A2: 1,7 BLK 1 A1: 1,7,5 # reduction candidate for 1,7 A1: 1,7 => CTR * .8.95..2...928...5524713968295.614.76483975123..5428968516792434..12568996243875. * PAIR H3: 1,6 BLK 3 G1: 1,6,3 # reduction candidate for 1,6 G1: 1,6 # 16 pairs G2: 1,6,3 # reduction candidate for 1,6 G2: 1,6 # 17 pairs * PAIR H3: 1,6 ROW 3 B3: 1,6,2 # reduction candidate for 1,6 B3: 2 => CTR * 5..9...277.9....45.247539682953684716481975323..5428968564792134...25.899..83.754 * PAIR RESTART * PAIR H3: 1,6 BLK 3 G1: 1,6,3 # reduction candidate for 1,6 G1: 1,6 # 16 pairs G2: 1,6,3 # reduction candidate for 1,6 G2: 1,6 # 14 pairs * PAIR E6: 1,4 COL E E1: 1,4,8 # reduction candidate for 1,4 E1: 8 => SOLVED * 563984127789612345214753968195368472648297531372541896856479213437125689921836754 * DURATION: 0:00:09.106737 START: 02:14:27.315668 END: 02:14:36.422405 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060830-absurd-base-pr-001.dot * REASONING * DIS # A1: 1,7 => CTR => A1: 5 * DIS A1: 5 # B3: 2 => CTR => B3: 1,6 * PRF A1: 5 + B3: 1,6 # E1: 8 => SOL * STA A1: 5 + B3: 1,6 + E1: 8 * CNT 3 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060830, absurd
Solution
position: 563984127789612345214753968195368472648297531372541896856479213437125689921836754 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* DIS # A1: 1,7 => CTR => A1: 5 * INC # A1: 5 => UNS * INC # E1: 1,5 => UNS * INC # E1: 4,8 => UNS * INC # A3: 1,5 => UNS * INC # A3: 2 => UNS * INC # G1: 1,6 => UNS * INC # G2: 1,6 => UNS * INC # B3: 1,6 => UNS * INC # B3: 2 => UNS * INC # H7: 1,6 => UNS * DIS # H7: 4 => CTR => H7: 1,6 * DIS # B5: 1,2 => CTR => B5: 4,8 * INC # B5: 4,8 => UNS * DIS # C5: 1,2 => CTR => C5: 8 * INC # C5: 8 => UNS * INC # B6: 1,2 => UNS * INC # C6: 1,2 => UNS * DIS # D4: 1,2 => CTR => D4: 3,8 * INC # D4: 3,8 => UNS * DIS # F4: 1,2 => CTR => F4: 8 * INC # F4: 8 => UNS * INC # I4: 1,2 => UNS * INC # A3: 1,2 => UNS * DIS # A3: 5 => CTR => A3: 1,2 * INC # D5: 1,4 => UNS * INC # F6: 1,4 => UNS * INC # B6: 1,4 => UNS * INC # B6: 2,7 => UNS * INC # E1: 1,4 => UNS * INC # E2: 1,4 => UNS * DIS # H4: 1,3 => CTR => H4: 7 * INC # H4: 7 => UNS * INC # D5: 1,3 => UNS * INC # D5: 2,4 => UNS * INC # I4: 1,2 => UNS * DIS # I4: 7 => CTR => I4: 1,2 * DIS # B5: 1,2 => CTR => B5: 4,8 * INC # B5: 4,8 => UNS * DIS # C5: 1,2 => CTR => C5: 8 * INC # C5: 8 => UNS * INC # D5: 1,2 => UNS * INC # B9: 1,6 => UNS * INC # C9: 1,6 => UNS * DIS # D7: 1,6 => CTR => D7: 4 * INC # D7: 4 => UNS * INC # H7: 1,6 => UNS * INC # C1: 1,6 => UNS * INC # C1: 3,8 => UNS * DIS # D7: 1,6 => CTR => D7: 4 * INC # D7: 4 => UNS * DIS # D9: 1,6 => CTR => D9: 4,8 * INC # D9: 4,8 => UNS * INC # F9: 1,6 => UNS * INC # D2: 1,6 => UNS * INC # D2: 2,4 => UNS * INC # H7: 1,6 => UNS * DIS # H7: 4 => CTR => H7: 1,6 * INC # G1: 1,6 => UNS * INC # G2: 1,6 => UNS * INC # H7: 1,4 => UNS * DIS # H7: 6 => CTR => H7: 1,4 * DIS # D9: 1,4 => CTR => D9: 6,8 * INC # D9: 6,8 => UNS * INC # F9: 1,4 => UNS * CNT 65 HDP CHAINS / 65 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 1,7 => CTR => A1: 5 * INC A1: 5 # G1: 1,6 => UNS * INC A1: 5 # G2: 1,6 => UNS * INC A1: 5 # B3: 1,6 => UNS * DIS A1: 5 # B3: 2 => CTR => B3: 1,6 * INC A1: 5 + B3: 1,6 # G1: 1,6 => UNS * INC A1: 5 + B3: 1,6 # G2: 1,6 => UNS * INC A1: 5 + B3: 1,6 # E1: 1,4 => UNS * PRF A1: 5 + B3: 1,6 # E1: 8 => SOL * STA A1: 5 + B3: 1,6 + E1: 8 * CNT 9 HDP CHAINS / 9 HYP OPENED