Analysis of zz-www.sudokuoftheday.co.uk-20060415-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: 2.38.9...............5...1.89..3.1....76....9.......82.4.1..8.65...869.1...3..7.. initial
Autosolve
position: 2.38.9..........9.9..5...1.89..3.1...276.8..9...9...82.491..8.65.2.869.1...39.7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 7 => CTR => D2: 2,4 * DIS # H9: 4,5 => CTR => H9: 2 * PRF # D2: 2 => SOL * DIS # H9: 4,5 => CTR => H9: 2 * DIS # F9: 2 => CTR => F9: 4,5 * CNT 5 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 7 => CTR => D2: 2,4 * PRF D2: 2,4 # A6: 1,6 => SOL * STA D2: 2,4 + A6: 1,6 * CNT 2 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2.38.9...............5...1.89..3.1....76....9.......82.4.1..8.65...869.1...3..7.. | initial |
| 2.38.9..........9.9..5...1.89..3.1...276.8..9...9...82.491..8.65.2.869.1...39.7.. | autosolve |
| 213869574458271693976543218895432167327618459164957382749125836532786941681394725 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) H1: 6,7 I2: 3,8 I3: 3,8 D4: 2,4 H4: 6,7 H5: 4,5 A7: 3,7 B8: 3,7 A9: 1,6 D8: 4,7 H8: 3,4 I9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,E1: 1.. / B1 = 1 => 14 pairs (_) / E1 = 1 => 19 pairs (_) A5,E5: 1.. / A5 = 1 => 18 pairs (_) / E5 = 1 => 18 pairs (_) F2,F6: 1.. / F2 = 1 => 16 pairs (_) / F6 = 1 => 17 pairs (_) G2,G3: 2.. / G2 = 2 => 15 pairs (_) / G3 = 2 => 12 pairs (_) D4,F4: 2.. / D4 = 2 => 13 pairs (_) / F4 = 2 => 0 pairs (*) H7,H9: 2.. / H7 = 2 => 0 pairs (X) / H9 = 2 => 14 pairs (_) F9,H9: 2.. / F9 = 2 => 0 pairs (X) / H9 = 2 => 14 pairs (_) D2,D4: 2.. / D2 = 2 => 0 pairs (*) / D4 = 2 => 0 pairs (X) F2,F3: 3.. / F2 = 3 => 15 pairs (_) / F3 = 3 => 12 pairs (_) I2,I3: 3.. / I2 = 3 => 12 pairs (_) / I3 = 3 => 15 pairs (_) G5,G6: 3.. / G5 = 3 => 13 pairs (_) / G6 = 3 => 17 pairs (_) A7,B8: 3.. / A7 = 3 => 0 pairs (X) / B8 = 3 => 16 pairs (_) H7,H8: 3.. / H7 = 3 => 16 pairs (_) / H8 = 3 => 0 pairs (X) F2,I2: 3.. / F2 = 3 => 15 pairs (_) / I2 = 3 => 12 pairs (_) F3,I3: 3.. / F3 = 3 => 12 pairs (_) / I3 = 3 => 15 pairs (_) A5,G5: 3.. / A5 = 3 => 17 pairs (_) / G5 = 3 => 13 pairs (_) A7,H7: 3.. / A7 = 3 => 0 pairs (X) / H7 = 3 => 16 pairs (_) B8,H8: 3.. / B8 = 3 => 16 pairs (_) / H8 = 3 => 0 pairs (X) B6,B8: 3.. / B6 = 3 => 0 pairs (X) / B8 = 3 => 16 pairs (_) D8,F9: 4.. / D8 = 4 => 0 pairs (X) / F9 = 4 => 16 pairs (_) D8,H8: 4.. / D8 = 4 => 0 pairs (X) / H8 = 4 => 16 pairs (_) H4,G6: 6.. / H4 = 6 => 12 pairs (_) / G6 = 6 => 18 pairs (_) C4,H4: 6.. / C4 = 6 => 18 pairs (_) / H4 = 6 => 12 pairs (_) H1,H4: 6.. / H1 = 6 => 18 pairs (_) / H4 = 6 => 12 pairs (_) H1,I1: 7.. / H1 = 7 => 12 pairs (_) / I1 = 7 => 18 pairs (_) E6,F6: 7.. / E6 = 7 => 13 pairs (_) / F6 = 7 => 17 pairs (_) H4,I4: 7.. / H4 = 7 => 18 pairs (_) / I4 = 7 => 12 pairs (_) A7,B8: 7.. / A7 = 7 => 16 pairs (_) / B8 = 7 => 0 pairs (X) B8,D8: 7.. / B8 = 7 => 0 pairs (X) / D8 = 7 => 16 pairs (_) A2,A7: 7.. / A2 = 7 => 0 pairs (X) / A7 = 7 => 16 pairs (_) D2,D8: 7.. / D2 = 7 => 0 pairs (X) / D8 = 7 => 16 pairs (_) H1,H4: 7.. / H1 = 7 => 12 pairs (_) / H4 = 7 => 18 pairs (_) I1,I4: 7.. / I1 = 7 => 18 pairs (_) / I4 = 7 => 12 pairs (_) I2,I3: 8.. / I2 = 8 => 15 pairs (_) / I3 = 8 => 12 pairs (_) B9,C9: 8.. / B9 = 8 => 14 pairs (_) / C9 = 8 => 14 pairs (_) * DURATION: 0:00:37.506807 START: 22:24:25.759909 END: 22:25:03.266716 2019-04-30 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B8,D4,D8,H1,H4,H5,H8,I2,I3,I9) * 2.38.9..........9.9..5...1.89..3.1...276.8..9...9...82.491..8.65.2.869.1...39.7.. * PAIR D4: 2,4 BLK 5 F4: 2,4,5 # reduction candidate for 2,4 F4: 5 # 18 pairs F4: 2,4 # 17 pairs * PAIR D4: 2,4 COL D D2: 2,4,7 # reduction candidate for 2,4 D2: 7 => CTR * 2.38.9......7...9.97.5...1.89.23.1...276.8..9...9...827491..8365324869.1...39.7.. D2: 2,4 # 16 pairs * PAIR H5: 4,5 BLK 6 I4: 4,5,7 # reduction candidate for 4,5 I4: 4,5 # 18 pairs G5: 4,5,3 # reduction candidate for 4,5 G5: 4,5 # 17 pairs G6: 4,5,3,6 # reduction candidate for 4,5 G6: 4,5 # 14 pairs * PAIR H5: 4,5 ROW 5 E5: 4,5,1 # reduction candidate for 4,5 E5: 4,5 # 18 pairs E5: 1 # 18 pairs * PAIR H5: 4,5 COL H H9: 4,5,2 # reduction candidate for 4,5 H9: 4,5 => CTR * 2.38.9...7......9.9..5...1.89.23.1...276.8..9.3.9...823491..826572486931...3927.. H9: 2 # 14 pairs * PAIR A9: 1,6 BLK 7 B9: 1,6,8 # reduction candidate for 1,6 B9: 1,6 # 14 pairs C9: 1,6,8 # reduction candidate for 1,6 C9: 1,6 # 14 pairs * PAIR A9: 1,6 COL A A2: 1,6,4,7 # reduction candidate for 1,6 A2: 1,6 # 23 pairs A6: 1,6,3,4 # reduction candidate for 1,6 A6: 1,6 # 21 pairs * PAIR D8: 4,7 COL D D2: 4,7,2 # reduction candidate for 4,7 D2: 2 => SOLVED * 213869574458271693976543218895432167327618459164957382749125836532786941681394725 D2: 4,7 # 13 pairs * PAIR I9: 4,5 BLK 9 H9: 4,5,2 # reduction candidate for 4,5 H9: 4,5 => CTR * 2.38.9...7......9.9..5...1.89.23.1...276.8..9.3.9...823491..826572486931...3927.. H9: 2 # 14 pairs * PAIR I9: 4,5 ROW 9 F9: 4,5,2 # reduction candidate for 4,5 F9: 2 => CTR * 2.38.9......7...9.97.5...1.89..3.1...276.8..9...9...82.491..8.65.2486931...3927.. F9: 4,5 # 14 pairs * PAIR I9: 4,5 COL I I1: 4,5,7 # reduction candidate for 4,5 I1: 4,5 # 12 pairs I4: 4,5,7 # reduction candidate for 4,5 I4: 4,5 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060415-absurd-base-pr-000.dot * REASONING * DIS # D2: 7 => CTR => D2: 2,4 * DIS # H9: 4,5 => CTR => H9: 2 * PRF # D2: 2 => SOL * DIS # H9: 4,5 => CTR => H9: 2 * DIS # F9: 2 => CTR => F9: 4,5 * CNT 5 HDP CHAINS / 23 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B8,D4,D8,H1,H4,H5,H8,I2,I3,I9) * 2.38.9..........9.9..5...1.89..3.1...276.8..9...9...82.491..8.65.2.869.1...39.7.. * PAIR D4: 2,4 BLK 5 F4: 2,4,5 # reduction candidate for 2,4 F4: 5 # 18 pairs F4: 2,4 # 17 pairs * PAIR D4: 2,4 COL D D2: 2,4,7 # reduction candidate for 2,4 D2: 7 => CTR * 2.38.9......7...9.97.5...1.89.23.1...276.8..9...9...827491..8365324869.1...39.7.. * PAIR RESTART * PAIR A9: 1,6 BLK 7 B9: 1,6,8 # reduction candidate for 1,6 B9: 1,6 # 20 pairs C9: 1,6,8 # reduction candidate for 1,6 C9: 1,6 # 18 pairs * PAIR A9: 1,6 COL A A2: 1,6,4 # reduction candidate for 1,6 A2: 1,6 # 23 pairs A6: 1,6,3,4 # reduction candidate for 1,6 A6: 1,6 => SOLVED * 213869574458271693976543218895432167327618459164957382749125836532786941681394725 * DURATION: 0:00:06.401678 START: 22:25:17.554981 END: 22:25:23.956659 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060415-absurd-base-pr-001.dot * REASONING * DIS # D2: 7 => CTR => D2: 2,4 * PRF D2: 2,4 # A6: 1,6 => SOL * STA D2: 2,4 + A6: 1,6 * CNT 2 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060415, absurd
Solution
position: 213869574458271693976543218895432167327618459164957382749125836532786941681394725 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 # F4: 2,4 => UNS * INC # F4: 5 => UNS * INC # D2: 2,4 => UNS * DIS # D2: 7 => CTR => D2: 2,4 * INC # I4: 4,5 => UNS * INC # G5: 4,5 => UNS * INC # G6: 4,5 => UNS * INC # E5: 4,5 => UNS * INC # E5: 1 => UNS * DIS # H9: 4,5 => CTR => H9: 2 * INC # H9: 2 => UNS * INC # B9: 1,6 => UNS * INC # C9: 1,6 => UNS * INC # A2: 1,6 => UNS * INC # A6: 1,6 => UNS * INC # D2: 4,7 => UNS * PRF # D2: 2 => SOL * DIS # H9: 4,5 => CTR => H9: 2 * INC # H9: 2 => UNS * INC # F9: 4,5 => UNS * DIS # F9: 2 => CTR => F9: 4,5 * INC # I1: 4,5 => UNS * INC # I4: 4,5 => UNS * CNT 23 HDP CHAINS / 23 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F4: 2,4 => UNS * INC # F4: 5 => UNS * INC # D2: 2,4 => UNS * DIS # D2: 7 => CTR => D2: 2,4 * INC D2: 2,4 # B9: 1,6 => UNS * INC D2: 2,4 # C9: 1,6 => UNS * INC D2: 2,4 # A2: 1,6 => UNS * PRF D2: 2,4 # A6: 1,6 => SOL * STA D2: 2,4 + A6: 1,6 * CNT 8 HDP CHAINS / 8 HYP OPENED