Analysis of zz-www.sudokuoftheday.co.uk-20190121-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: 9.......5....2....843...9..6..9..2.7...81..4..9.......5..1...8......74..42..8.... initial
Autosolve
position: 9.2..8..5....298.4843..19..6..9..2.7...81..49.9......85..1...8......74..42..8.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 1,7 => CTR => B2: 5,6 * DIS # H3: 7 => CTR => H3: 2,6 * DIS # I8: 2,6 => CTR => I8: 1,3 * DIS # C2: 5,7 => CTR => C2: 1,6 * DIS # B8: 1,3 => CTR => B8: 6,8 * DIS # I8: 2,6 => CTR => I8: 1,3 * PRF # A6: 2 => SOL * DIS # H9: 6,7 => CTR => H9: 5,9 * DIS # G1: 6,7 => CTR => G1: 1,3 * CNT 9 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 1,7 => CTR => B2: 5,6 * DIS B2: 5,6 # H3: 7 => CTR => H3: 2,6 * DIS B2: 5,6 + H3: 2,6 # I8: 2,6 => CTR => I8: 1,3 * DIS B2: 5,6 + H3: 2,6 + I8: 1,3 # I7: 3 => CTR => I7: 2,6 * DIS B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 # B5: 3 => CTR => B5: 5,7 * PRF B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 + B5: 5,7 # A6: 2 => SOL * STA B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 + B5: 5,7 + A6: 2 * CNT 6 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9.......5....2....843...9..6..9..2.7...81..4..9.......5..1...8......74..42..8.... | initial |
| 9.2..8..5....298.4843..19..6..9..2.7...81..49.9......85..1...8......74..42..8.... | autosolve |
| 962438175751629834843571926618943257375812649294765318536194782189257463427386591 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A2: 1,7 I3: 2,6 C5: 5,7 A8: 1,3 G7: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I8,I9: 1.. / I8 = 1 => 0 pairs (X) / I9 = 1 => 5 pairs (_) C9,I9: 1.. / C9 = 1 => 0 pairs (X) / I9 = 1 => 5 pairs (_) G1,G6: 1.. / G1 = 1 => 7 pairs (_) / G6 = 1 => 19 pairs (_) H3,I3: 2.. / H3 = 2 => 9 pairs (_) / I3 = 2 => 0 pairs (X) A5,A6: 2.. / A5 = 2 => 7 pairs (_) / A6 = 2 => 0 pairs (*) F7,D8: 2.. / F7 = 2 => 0 pairs (X) / D8 = 2 => 10 pairs (_) A5,F5: 2.. / A5 = 2 => 7 pairs (_) / F5 = 2 => 0 pairs (*) F7,I7: 2.. / F7 = 2 => 0 pairs (X) / I7 = 2 => 10 pairs (_) D6,D8: 2.. / D6 = 2 => 0 pairs (X) / D8 = 2 => 10 pairs (_) H3,H8: 2.. / H3 = 2 => 9 pairs (_) / H8 = 2 => 0 pairs (X) D2,H2: 3.. / D2 = 3 => 6 pairs (_) / H2 = 3 => 10 pairs (_) D1,E1: 4.. / D1 = 4 => 5 pairs (_) / E1 = 4 => 0 pairs (X) C4,C6: 4.. / C4 = 4 => 11 pairs (_) / C6 = 4 => 5 pairs (_) E7,F7: 4.. / E7 = 4 => 6 pairs (_) / F7 = 4 => 11 pairs (_) D1,D6: 4.. / D1 = 4 => 5 pairs (_) / D6 = 4 => 0 pairs (X) B2,C2: 5.. / B2 = 5 => 6 pairs (_) / C2 = 5 => 0 pairs (X) D3,E3: 5.. / D3 = 5 => 7 pairs (_) / E3 = 5 => 7 pairs (_) F5,G5: 6.. / F5 = 6 => 9 pairs (_) / G5 = 6 => 19 pairs (_) D6,E6: 7.. / D6 = 7 => 10 pairs (_) / E6 = 7 => 6 pairs (_) A2,A5: 7.. / A2 = 7 => 7 pairs (_) / A5 = 7 => 0 pairs (X) B4,C4: 8.. / B4 = 8 => 5 pairs (_) / C4 = 8 => 5 pairs (_) B8,C8: 8.. / B8 = 8 => 5 pairs (_) / C8 = 8 => 5 pairs (_) B4,B8: 8.. / B4 = 8 => 5 pairs (_) / B8 = 8 => 5 pairs (_) C4,C8: 8.. / C4 = 8 => 5 pairs (_) / C8 = 8 => 5 pairs (_) E7,E8: 9.. / E7 = 9 => 16 pairs (_) / E8 = 9 => 5 pairs (_) H8,H9: 9.. / H8 = 9 => 0 pairs (X) / H9 = 9 => 5 pairs (_) C7,E7: 9.. / C7 = 9 => 5 pairs (_) / E7 = 9 => 16 pairs (_) C9,H9: 9.. / C9 = 9 => 0 pairs (X) / H9 = 9 => 5 pairs (_) * DURATION: 0:00:28.479152 START: 03:06:25.895829 END: 03:06:54.374981 2019-05-01 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,C5,G7,I3) * 9.2..8..5....298.4843..19..6..9..2.7...81..49.9......85..1...8......74..42..8.... * PAIR A2: 1,7 BLK 1 B1: 1,7,6 # reduction candidate for 1,7 B1: 1,7 # 9 pairs B2: 1,7,5,6 # reduction candidate for 1,7 B2: 1,7 => CTR * 962..8..5715.298.4843..19.66..9..2.7..7816.49.9.....685791..68......74..42..8.... B2: 5,6 # 6 pairs C2: 1,7,5,6 # reduction candidate for 1,7 C2: 1,7 # 12 pairs * PAIR A2: 1,7 ROW 2 H2: 1,7,3,6 # reduction candidate for 1,7 H2: 1,7 # 10 pairs H2: 3,6 # 7 pairs * PAIR I3: 2,6 BLK 3 H3: 2,6,7 # reduction candidate for 2,6 H3: 7 => CTR * 9.24.8..57...298.4843..19726..9..2.72..81..49.9.27...85.914278....59742.427.8.591 H3: 2,6 # 9 pairs * PAIR I3: 2,6 COL I I7: 2,6,3 # reduction candidate for 2,6 I7: 2,6 # 9 pairs I8: 2,6,1,3 # reduction candidate for 2,6 I8: 2,6 => CTR * 9124683757..3298148437519..6.193.2.72..81..49.9.27..385.9142.833...974..42..83.91 I8: 1,3 # 7 pairs * PAIR C5: 5,7 BLK 4 B5: 5,7,3 # reduction candidate for 5,7 B5: 3 # 12 pairs B5: 5,7 # 10 pairs * PAIR C5: 5,7 COL C C2: 5,7,1,6 # reduction candidate for 5,7 C2: 5,7 => CTR * 912468375765329814843..19266.19..237237816.49.9.....685791..68.....9745.42..8.79. C2: 1,6 # 7 pairs * PAIR A8: 1,3 BLK 7 B8: 1,3,6,8 # reduction candidate for 1,3 B8: 1,3 => CTR * 9.2468.757..3298.48437519..68.93.2.72..81..49.9.27..385.9142.83318.974..42..83.91 B8: 6,8 # 6 pairs * PAIR A8: 1,3 ROW 8 I8: 1,3,2,6 # reduction candidate for 1,3 I8: 2,6 => CTR * 9124683757..3298148437519..6.193.2.72..81..49.9.27..385.9142.833...974..42..83.91 I8: 1,3 # 7 pairs * PAIR A8: 1,3 COL A A6: 1,3,2 # reduction candidate for 1,3 A6: 2 => SOLVED * 962438175751629834843571926618943257375812649294765318536194782189257463427386591 A6: 1,3 # 7 pairs * PAIR G7: 6,7 BLK 9 G9: 6,7,5 # reduction candidate for 6,7 G9: 6,7 # 18 pairs H9: 6,7,5,9 # reduction candidate for 6,7 H9: 6,7 => CTR * 9.2.687.5....298.48435719266..9..257...81634939....1685..194682...257493429.8.571 H9: 5,9 # 6 pairs * PAIR G7: 6,7 ROW 7 B7: 6,7,3 # reduction candidate for 6,7 B7: 6,7 # 8 pairs C7: 6,7,9 # reduction candidate for 6,7 C7: 6,7 # 16 pairs * PAIR G7: 6,7 COL G G1: 6,7,1,3 # reduction candidate for 6,7 G1: 6,7 => CTR * 9.24.8..57..3298148437.19..6..9.42572..8163493942751685..142.8.1...9742.42.683591 G1: 1,3 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190121-absurd-base-pr-000.dot * REASONING * DIS # B2: 1,7 => CTR => B2: 5,6 * DIS # H3: 7 => CTR => H3: 2,6 * DIS # I8: 2,6 => CTR => I8: 1,3 * DIS # C2: 5,7 => CTR => C2: 1,6 * DIS # B8: 1,3 => CTR => B8: 6,8 * DIS # I8: 2,6 => CTR => I8: 1,3 * PRF # A6: 2 => SOL * DIS # H9: 6,7 => CTR => H9: 5,9 * DIS # G1: 6,7 => CTR => G1: 1,3 * CNT 9 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,C5,G7,I3) * 9.2..8..5....298.4843..19..6..9..2.7...81..49.9......85..1...8......74..42..8.... * PAIR A2: 1,7 BLK 1 B1: 1,7,6 # reduction candidate for 1,7 B1: 1,7 # 9 pairs B2: 1,7,5,6 # reduction candidate for 1,7 B2: 1,7 => CTR * 962..8..5715.298.4843..19.66..9..2.7..7816.49.9.....685791..68......74..42..8.... C2: 1,7,5,6 # reduction candidate for 1,7 C2: 1,7 # 12 pairs * PAIR A2: 1,7 ROW 2 H2: 1,7,3,6 # reduction candidate for 1,7 H2: 3,6 # 10 pairs H2: 1,7 # 10 pairs * PAIR RESTART * PAIR A2: 1,7 BLK 1 B1: 1,7,6 # reduction candidate for 1,7 B1: 1,7 # 9 pairs C2: 1,7,5,6 # reduction candidate for 1,7 C2: 1,7 # 12 pairs * PAIR A2: 1,7 ROW 2 H2: 1,7,3,6 # reduction candidate for 1,7 H2: 3,6 # 10 pairs H2: 1,7 # 10 pairs * PAIR I3: 2,6 BLK 3 H3: 2,6,7 # reduction candidate for 2,6 H3: 7 => CTR * 9.24.8..57...298.4843..19726..9..2.72..81..49.9.27...85.914278....59742.427.8.591 * PAIR I3: 2,6 COL I I7: 2,6,3 # reduction candidate for 2,6 I7: 2,6 # 14 pairs I8: 2,6,1,3 # reduction candidate for 2,6 I8: 2,6 => CTR * 912468.757.63298148437519..6819342572..81.349.9.27.1.85.9142.831385974..42.683591 * RESTART * PAIR I3: 2,6 COL I I7: 2,6,3 # reduction candidate for 2,6 I7: 3 => CTR * 9.2..8..5....298.4843..19.26..9..2.7...81..49.9......85..1.2.833....7421421.8..96 * PAIR RESTART * PAIR C5: 5,7 BLK 4 B5: 5,7,3 # reduction candidate for 5,7 B5: 3 => CTR * 9.2.68.75...329814843..192661.9..2.7.3.816549.9...2.685791..6823..297451421685793 * PAIR A8: 1,3 COL A A6: 1,3,2 # reduction candidate for 1,3 A6: 2 => SOLVED * 962438175751629834843571926618943257375812649294765318536194782189257463427386591 * DURATION: 0:00:12.137858 START: 03:07:09.898349 END: 03:07:22.036207 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190121-absurd-base-pr-001.dot * REASONING * DIS # B2: 1,7 => CTR => B2: 5,6 * DIS B2: 5,6 # H3: 7 => CTR => H3: 2,6 * DIS B2: 5,6 + H3: 2,6 # I8: 2,6 => CTR => I8: 1,3 * DIS B2: 5,6 + H3: 2,6 + I8: 1,3 # I7: 3 => CTR => I7: 2,6 * DIS B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 # B5: 3 => CTR => B5: 5,7 * PRF B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 + B5: 5,7 # A6: 2 => SOL * STA B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 + B5: 5,7 + A6: 2 * CNT 6 HDP CHAINS / 19 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190121, absurd
Solution
position: 962438175751629834843571926618943257375812649294765318536194782189257463427386591 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:
* INC # B1: 1,7 => UNS * DIS # B2: 1,7 => CTR => B2: 5,6 * INC # B2: 5,6 => UNS * INC # C2: 1,7 => UNS * INC # H2: 1,7 => UNS * INC # H2: 3,6 => UNS * INC # H3: 2,6 => UNS * DIS # H3: 7 => CTR => H3: 2,6 * INC # I7: 2,6 => UNS * DIS # I8: 2,6 => CTR => I8: 1,3 * INC # I8: 1,3 => UNS * INC # B5: 5,7 => UNS * INC # B5: 3 => UNS * DIS # C2: 5,7 => CTR => C2: 1,6 * INC # C2: 1,6 => UNS * DIS # B8: 1,3 => CTR => B8: 6,8 * INC # B8: 6,8 => UNS * INC # I8: 1,3 => UNS * DIS # I8: 2,6 => CTR => I8: 1,3 * INC # A6: 1,3 => UNS * PRF # A6: 2 => SOL * INC # G9: 6,7 => UNS * DIS # H9: 6,7 => CTR => H9: 5,9 * INC # H9: 5,9 => UNS * INC # B7: 6,7 => UNS * INC # C7: 6,7 => UNS * DIS # G1: 6,7 => CTR => G1: 1,3 * INC # G1: 1,3 => UNS * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 1,7 => UNS * DIS # B2: 1,7 => CTR => B2: 5,6 * INC B2: 5,6 # C2: 1,7 => UNS * INC B2: 5,6 # H2: 1,7 => UNS * INC B2: 5,6 # H2: 3,6 => UNS * INC B2: 5,6 # B1: 1,7 => UNS * INC B2: 5,6 # C2: 1,7 => UNS * INC B2: 5,6 # H2: 1,7 => UNS * INC B2: 5,6 # H2: 3,6 => UNS * INC B2: 5,6 # H3: 2,6 => UNS * DIS B2: 5,6 # H3: 7 => CTR => H3: 2,6 * INC B2: 5,6 + H3: 2,6 # I7: 2,6 => UNS * DIS B2: 5,6 + H3: 2,6 # I8: 2,6 => CTR => I8: 1,3 * INC B2: 5,6 + H3: 2,6 + I8: 1,3 # I7: 2,6 => UNS * DIS B2: 5,6 + H3: 2,6 + I8: 1,3 # I7: 3 => CTR => I7: 2,6 * INC B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 # B5: 5,7 => UNS * DIS B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 # B5: 3 => CTR => B5: 5,7 * INC B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 + B5: 5,7 # A6: 1,3 => UNS * PRF B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 + B5: 5,7 # A6: 2 => SOL * STA B2: 5,6 + H3: 2,6 + I8: 1,3 + I7: 2,6 + B5: 5,7 + A6: 2 * CNT 19 HDP CHAINS / 19 HYP OPENED