Analysis of zz-www.sudokuoftheday.co.uk-20060630-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: .....247...5.....22.6.4.........91...623.8...87....3..6..........8.64..7..7.8.5.. initial
Autosolve
position: 18.6.24757458.16.22.6.4......4..91..9623187548714563296......4...8.64..74.7.835.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H3: 3,9 => CTR => H3: 1,8 * PRF # B7: 3,9 => SOL * DIS # H3: 3,9 => CTR => H3: 1,8 * DIS # H8: 1 => CTR => H8: 3,9 * DIS # H3: 8,9 => CTR => H3: 1,3 * PRF # G7: 2 => SOL * PRF # B7: 3,5 => SOL * DIS # B8: 3,5 => CTR => B8: 1,2,9 * PRF # B7: 3,9 => SOL * PRF # B7: 3,5 => SOL * DIS # B8: 3,5 => CTR => B8: 1,2,9 * PRF # G7: 2,9 => SOL * DIS # G7: 8 => CTR => G7: 2,9 * DIS # H9: 9 => CTR => H9: 1,6 * CNT 14 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H3: 3,9 => CTR => H3: 1,8 * PRF H3: 1,8 # B7: 3,9 => SOL * STA H3: 1,8 + B7: 3,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....247...5.....22.6.4.........91...623.8...87....3..6..........8.64..7..7.8.5.. | initial |
| 18.6.24757458.16.22.6.4......4..91..9623187548714563296......4...8.64..74.7.835.. | autosolve |
| 183692475745831692296547813354729186962318754871456329639175248518264937427983561 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C1: 3,9 B3: 3,9 E1: 3,9 E2: 3,9 D3: 5,7 F3: 5,7 H2: 3,9 G3: 8,9 A4: 3,5 B4: 3,5 D4: 2,7 E4: 2,7 H4: 6,8 I4: 6,8 C7: 3,9 A8: 3,5 E7: 2,7 F7: 5,7 G8: 2,9 I9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H3,I3: 1.. / H3 = 1 => 22 pairs (_) / I3 = 1 => 0 pairs (X) D4,E4: 2.. / D4 = 2 => 18 pairs (_) / E4 = 2 => 14 pairs (_) G7,G8: 2.. / G7 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) B9,D9: 2.. / B9 = 2 => 21 pairs (_) / D9 = 2 => 17 pairs (_) E4,E7: 2.. / E4 = 2 => 14 pairs (_) / E7 = 2 => 18 pairs (_) C1,B3: 3.. / C1 = 3 => 0 pairs (*) / B3 = 3 => 0 pairs (X) E1,E2: 3.. / E1 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) A4,B4: 3.. / A4 = 3 => 17 pairs (_) / B4 = 3 => 0 pairs (X) I7,H8: 3.. / I7 = 3 => 0 pairs (X) / H8 = 3 => 0 pairs (_) C1,E1: 3.. / C1 = 3 => 0 pairs (*) / E1 = 3 => 0 pairs (X) E2,H2: 3.. / E2 = 3 => 0 pairs (*) / H2 = 3 => 0 pairs (X) A4,A8: 3.. / A4 = 3 => 17 pairs (_) / A8 = 3 => 0 pairs (X) C1,C7: 3.. / C1 = 3 => 0 pairs (*) / C7 = 3 => 0 pairs (X) I3,I7: 3.. / I3 = 3 => 0 pairs (*) / I7 = 3 => 0 pairs (X) D3,F3: 5.. / D3 = 5 => 17 pairs (_) / F3 = 5 => 15 pairs (_) A4,B4: 5.. / A4 = 5 => 0 pairs (X) / B4 = 5 => 17 pairs (_) A4,A8: 5.. / A4 = 5 => 0 pairs (X) / A8 = 5 => 17 pairs (_) F3,F7: 5.. / F3 = 5 => 15 pairs (_) / F7 = 5 => 17 pairs (_) H4,I4: 6.. / H4 = 6 => 0 pairs (X) / I4 = 6 => 22 pairs (_) H9,I9: 6.. / H9 = 6 => 22 pairs (_) / I9 = 6 => 0 pairs (X) H4,H9: 6.. / H4 = 6 => 0 pairs (X) / H9 = 6 => 22 pairs (_) I4,I9: 6.. / I4 = 6 => 22 pairs (_) / I9 = 6 => 0 pairs (X) D3,F3: 7.. / D3 = 7 => 15 pairs (_) / F3 = 7 => 17 pairs (_) D4,E4: 7.. / D4 = 7 => 14 pairs (_) / E4 = 7 => 18 pairs (_) E4,E7: 7.. / E4 = 7 => 18 pairs (_) / E7 = 7 => 14 pairs (_) F3,F7: 7.. / F3 = 7 => 17 pairs (_) / F7 = 7 => 15 pairs (_) H4,I4: 8.. / H4 = 8 => 22 pairs (_) / I4 = 8 => 0 pairs (X) G7,I7: 8.. / G7 = 8 => 0 pairs (X) / I7 = 8 => 0 pairs (_) G3,G7: 8.. / G3 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) H3,H4: 8.. / H3 = 8 => 0 pairs (X) / H4 = 8 => 22 pairs (_) C1,B3: 9.. / C1 = 9 => 0 pairs (X) / B3 = 9 => 0 pairs (_) E1,E2: 9.. / E1 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) C1,E1: 9.. / C1 = 9 => 0 pairs (X) / E1 = 9 => 0 pairs (_) E2,H2: 9.. / E2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) C1,C7: 9.. / C1 = 9 => 0 pairs (X) / C7 = 9 => 0 pairs (_) * DURATION: 0:00:56.733108 START: 00:12:40.902002 END: 00:13:37.635110 2019-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B3,B4,C1,C7,D3,D4,E1,E2,E4,E7,F3,F7,G3,G8,H2,H4,I4,I9) * 18.6.24757458.16.22.6.4......4..91..9623187548714563296......4...8.64..74.7.835.. * PAIR B3: 3,9 ROW 3 H3: 3,9,1,8 # reduction candidate for 3,9 H3: 3,9 => CTR * 18.6.24757458.16.22.6.4...1..4..91869623187548714563296......4...8.64..74.7.835.. H3: 1,8 # 21 pairs * PAIR B3: 3,9 COL B B7: 3,9,1,2,5 # reduction candidate for 3,9 B7: 3,9 => SOLVED * 183692475745831692296547813354729186962318754871456329639175248518264937427983561 B7: 1,2,5 # 20 pairs B8: 3,9,1,2,5 # reduction candidate for 3,9 B8: 3,9 # 20 pairs * PAIR D3: 5,7 COL D D7: 5,7,1,2,9 # reduction candidate for 5,7 D7: 5,7 # 20 pairs D7: 1,2,9 # 20 pairs * PAIR H2: 3,9 BLK 3 H3: 3,9,1,8 # reduction candidate for 3,9 H3: 3,9 => CTR * 18.6.24757458.16.22.6.4...1..4..91869623187548714563296......4...8.64..74.7.835.. H3: 1,8 # 21 pairs * PAIR H2: 3,9 COL H H8: 3,9,1 # reduction candidate for 3,9 H8: 1 => CTR * 1836924757458316922.6.4......4..91..9623187548714563296......43..8.64.174.7.835.6 H8: 3,9 # 26 pairs * PAIR G3: 8,9 BLK 3 H3: 8,9,1,3 # reduction candidate for 8,9 H3: 8,9 => CTR * 1836924757458316.22.6.4...1..4..91..9623187548714563296......43..8.64..74.7.835.6 H3: 1,3 # 22 pairs * PAIR G3: 8,9 COL G G7: 8,9,2 # reduction candidate for 8,9 G7: 2 => SOLVED * 183692475745831692296547813354729186962318754871456329639175248518264937427983561 G7: 8,9 # 20 pairs * PAIR B4: 3,5 COL B B7: 3,5,1,2,9 # reduction candidate for 3,5 B7: 3,5 => SOLVED * 183692475745831692296547813354729186962318754871456329639175248518264937427983561 B7: 1,2,9 # 20 pairs B8: 3,5,1,2,9 # reduction candidate for 3,5 B8: 3,5 => CTR * 183692475745831692296.4.831..4..91..9623187548714563296......4...8.64..74.7.835.. B8: 1,2,9 # 20 pairs * PAIR D4: 2,7 COL D D7: 2,7,1,5,9 # reduction candidate for 2,7 D7: 2,7 # 20 pairs D7: 1,5,9 # 20 pairs * PAIR C7: 3,9 BLK 7 B7: 3,9,1,2,5 # reduction candidate for 3,9 B7: 3,9 => SOLVED * 183692475745831692296547813354729186962318754871456329639175248518264937427983561 B7: 1,2,5 # 20 pairs B8: 3,9,1,2,5 # reduction candidate for 3,9 B8: 3,9 # 20 pairs * PAIR A8: 3,5 BLK 7 B7: 3,5,1,2,9 # reduction candidate for 3,5 B7: 3,5 => SOLVED * 183692475745831692296547813354729186962318754871456329639175248518264937427983561 B7: 1,2,9 # 20 pairs B8: 3,5,1,2,9 # reduction candidate for 3,5 B8: 3,5 => CTR * 183692475745831692296.4.831..4..91..9623187548714563296......4...8.64..74.7.835.. B8: 1,2,9 # 20 pairs * PAIR E7: 2,7 BLK 8 D7: 2,7,1,5,9 # reduction candidate for 2,7 D7: 2,7 # 20 pairs D7: 1,5,9 # 20 pairs * PAIR F7: 5,7 BLK 8 D7: 5,7,1,2,9 # reduction candidate for 5,7 D7: 5,7 # 20 pairs D7: 1,2,9 # 20 pairs * PAIR G8: 2,9 BLK 9 G7: 2,9,8 # reduction candidate for 2,9 G7: 2,9 => SOLVED * 183692475745831692296547813354729186962318754871456329639175248518264937427983561 G7: 8 => CTR * 189632475745891632236.4.9..354..91..9623187548714563296.3...8415.8.642974.7.8356. * PAIR G8: 2,9 ROW 8 B8: 2,9,1,3,5 # reduction candidate for 2,9 B8: 2,9 # 23 pairs D8: 2,9,1,5 # reduction candidate for 2,9 D8: 2,9 # 22 pairs * PAIR I9: 1,6 BLK 9 H9: 1,6,9 # reduction candidate for 1,6 H9: 9 => CTR * 18.6.2475745891632236.4.981354..91689623187548714563296.3...84...8.642.74.7.83596 H9: 1,6 # 26 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060630-absurd-base-pr-000.dot * REASONING * DIS # H3: 3,9 => CTR => H3: 1,8 * PRF # B7: 3,9 => SOL * DIS # H3: 3,9 => CTR => H3: 1,8 * DIS # H8: 1 => CTR => H8: 3,9 * DIS # H3: 8,9 => CTR => H3: 1,3 * PRF # G7: 2 => SOL * PRF # B7: 3,5 => SOL * DIS # B8: 3,5 => CTR => B8: 1,2,9 * PRF # B7: 3,9 => SOL * PRF # B7: 3,5 => SOL * DIS # B8: 3,5 => CTR => B8: 1,2,9 * PRF # G7: 2,9 => SOL * DIS # G7: 8 => CTR => G7: 2,9 * DIS # H9: 9 => CTR => H9: 1,6 * CNT 14 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B3,B4,C1,C7,D3,D4,E1,E2,E4,E7,F3,F7,G3,G8,H2,H4,I4,I9) * 18.6.24757458.16.22.6.4......4..91..9623187548714563296......4...8.64..74.7.835.. * PAIR B3: 3,9 ROW 3 H3: 3,9,1,8 # reduction candidate for 3,9 H3: 3,9 => CTR * 18.6.24757458.16.22.6.4...1..4..91869623187548714563296......4...8.64..74.7.835.. * PAIR B3: 3,9 COL B B7: 3,9,1,2,5 # reduction candidate for 3,9 B7: 3,9 => SOLVED * 183692475745831692296547813354729186962318754871456329639175248518264937427983561 * DURATION: 0:00:03.640084 START: 00:14:13.207657 END: 00:14:16.847741 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060630-absurd-base-pr-001.dot * REASONING * DIS # H3: 3,9 => CTR => H3: 1,8 * PRF H3: 1,8 # B7: 3,9 => SOL * STA H3: 1,8 + B7: 3,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060630, absurd
Solution
position: 183692475745831692296547813354729186962318754871456329639175248518264937427983561 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 # H3: 3,9 => CTR => H3: 1,8 * INC # H3: 1,8 => UNS * PRF # B7: 3,9 => SOL * INC # B7: 1,2,5 => UNS * INC # B8: 3,9 => UNS * INC # D7: 5,7 => UNS * INC # D7: 1,2,9 => UNS * DIS # H3: 3,9 => CTR => H3: 1,8 * INC # H3: 1,8 => UNS * INC # H8: 3,9 => UNS * DIS # H8: 1 => CTR => H8: 3,9 * DIS # H3: 8,9 => CTR => H3: 1,3 * INC # H3: 1,3 => UNS * INC # G7: 8,9 => UNS * PRF # G7: 2 => SOL * PRF # B7: 3,5 => SOL * INC # B7: 1,2,9 => UNS * DIS # B8: 3,5 => CTR => B8: 1,2,9 * INC # B8: 1,2,9 => UNS * INC # D7: 2,7 => UNS * INC # D7: 1,5,9 => UNS * PRF # B7: 3,9 => SOL * INC # B7: 1,2,5 => UNS * INC # B8: 3,9 => UNS * PRF # B7: 3,5 => SOL * INC # B7: 1,2,9 => UNS * DIS # B8: 3,5 => CTR => B8: 1,2,9 * INC # B8: 1,2,9 => UNS * INC # D7: 2,7 => UNS * INC # D7: 1,5,9 => UNS * INC # D7: 5,7 => UNS * INC # D7: 1,2,9 => UNS * PRF # G7: 2,9 => SOL * DIS # G7: 8 => CTR => G7: 2,9 * INC # B8: 2,9 => UNS * INC # D8: 2,9 => UNS * INC # H9: 1,6 => UNS * DIS # H9: 9 => CTR => H9: 1,6 * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # H3: 3,9 => CTR => H3: 1,8 * PRF H3: 1,8 # B7: 3,9 => SOL * STA H3: 1,8 + B7: 3,9 * CNT 2 HDP CHAINS / 2 HYP OPENED