Analysis of zz-www.sudokuoftheday.co.uk-20060507-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: ..6....9..1...4..5...6..4..5.9741.2....3.6....3.92...77.1.......8..6..5.....1.8.. initial
Autosolve
position: ..61...9..1...4..5...6..4..569741328...3.6....3.92...77.1.....6.8..6..5.6...1.8.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D7: 2,8 => CTR => D7: 4,5 * DIS # G2: 2,7 => CTR => G2: 6 * DIS # B1: 2,7 => CTR => B1: 4,5 * DIS # G8: 2,7 => CTR => G8: 1,9 * DIS # I3: 2,3 => CTR => I3: 1 * DIS # A1: 2,3 => CTR => A1: 4,8 * DIS # A6: 4,8 => CTR => A6: 1 * DIS # E3: 5,8 => CTR => E3: 3,7,9 * DIS # F3: 5,8 => CTR => F3: 2,3,9 * DIS # H6: 1,4 => CTR => H6: 6 * DIS # A5: 1,4 => CTR => A5: 2,8 * PRF # D9: 2,4 => SOL * DIS # G8: 2,9 => CTR => G8: 1,7 * PRF # B7: 2,9 => SOL * DIS # H9: 3,4 => CTR => H9: 7 * CNT 15 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D7: 2,8 => CTR => D7: 4,5 * DIS D7: 4,5 # G2: 2,7 => CTR => G2: 6 * PRF D7: 4,5 + G2: 6 => SOL * STA D7: 4,5 + G2: 6 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6....9..1...4..5...6..4..5.9741.2....3.6....3.92...77.1.......8..6..5.....1.8.. | initial |
| ..61...9..1...4..5...6..4..569741328...3.6....3.92...77.1.....6.8..6..5.6...1.8.. | autosolve |
| 846135792912874635357692481569741328278356914134928567791583246483267159625419873 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) D2: 2,8 G1: 2,7 I1: 2,3 C6: 4,8 E5: 5,8 F6: 5,8 H5: 1,4 D8: 2,4 G7: 2,9 H7: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H3,I3: 1.. / H3 = 1 => 0 pairs (X) / I3 = 1 => 14 pairs (_) A5,A6: 1.. / A5 = 1 => 0 pairs (X) / A6 = 1 => 12 pairs (_) G8,I8: 1.. / G8 = 1 => 12 pairs (_) / I8 = 1 => 0 pairs (X) A1,B1: 4.. / A1 = 4 => 0 pairs (X) / B1 = 4 => 11 pairs (_) E5,F6: 5.. / E5 = 5 => 11 pairs (_) / F6 = 5 => 0 pairs (X) G5,G6: 5.. / G5 = 5 => 0 pairs (X) / G6 = 5 => 11 pairs (_) D7,D9: 5.. / D7 = 5 => 0 pairs (*) / D9 = 5 => 0 pairs (X) E5,G5: 5.. / E5 = 5 => 11 pairs (_) / G5 = 5 => 0 pairs (X) F6,G6: 5.. / F6 = 5 => 0 pairs (X) / G6 = 5 => 11 pairs (_) B7,D7: 5.. / B7 = 5 => 10 pairs (_) / D7 = 5 => 0 pairs (*) C3,C9: 5.. / C3 = 5 => 10 pairs (_) / C9 = 5 => 0 pairs (*) G2,H2: 6.. / G2 = 6 => 12 pairs (_) / H2 = 6 => 0 pairs (X) G6,H6: 6.. / G6 = 6 => 0 pairs (X) / H6 = 6 => 12 pairs (_) G2,G6: 6.. / G2 = 6 => 12 pairs (_) / G6 = 6 => 0 pairs (X) H2,H6: 6.. / H2 = 6 => 0 pairs (X) / H6 = 6 => 12 pairs (_) B5,C5: 7.. / B5 = 7 => 10 pairs (_) / C5 = 7 => 11 pairs (_) F8,F9: 7.. / F8 = 7 => 10 pairs (_) / F9 = 7 => 0 pairs (X) G8,H9: 7.. / G8 = 7 => 0 pairs (X) / H9 = 7 => 10 pairs (_) F8,G8: 7.. / F8 = 7 => 10 pairs (_) / G8 = 7 => 0 pairs (X) F9,H9: 7.. / F9 = 7 => 0 pairs (X) / H9 = 7 => 10 pairs (_) H2,H3: 8.. / H2 = 8 => 0 pairs (X) / H3 = 8 => 14 pairs (_) E5,F6: 8.. / E5 = 8 => 0 pairs (X) / F6 = 8 => 11 pairs (_) D2,D7: 8.. / D2 = 8 => 16 pairs (_) / D7 = 8 => 0 pairs (X) G5,I5: 9.. / G5 = 9 => 12 pairs (_) / I5 = 9 => 0 pairs (X) A2,E2: 9.. / A2 = 9 => 12 pairs (_) / E2 = 9 => 11 pairs (_) * DURATION: 0:00:24.090385 START: 22:58:42.391895 END: 22:59:06.482280 2019-04-30 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,D2,D8,E5,F6,G1,G7,H5,H7,I1) * ..61...9..1...4..5...6..4..569741328...3.6....3.92...77.1.....6.8..6..5.6...1.8.. * PAIR D2: 2,8 BLK 2 F1: 2,8,3,5 # reduction candidate for 2,8 F1: 2,8 # 11 pairs F3: 2,8,3,5,9 # reduction candidate for 2,8 F3: 2,8 # 17 pairs * PAIR D2: 2,8 ROW 2 A2: 2,8,3,9 # reduction candidate for 2,8 A2: 2,8 # 19 pairs C2: 2,8,3,7 # reduction candidate for 2,8 C2: 2,8 # 17 pairs * PAIR D2: 2,8 COL D D7: 2,8,4,5 # reduction candidate for 2,8 D7: 2,8 => CTR * 4.6185.93.1.2.4685..56..4..569741328...3.6.14134928567751....46.8.46.15.64.51.87. D7: 4,5 # 17 pairs * PAIR G1: 2,7 BLK 3 G2: 2,7,6 # reduction candidate for 2,7 G2: 2,7 => CTR * ..61...93.1...4.65...6..481569741328...3.65.9.3.9256.77.1...936.8..6715.6...1.87. G2: 6 # 12 pairs * PAIR G1: 2,7 ROW 1 B1: 2,7,4,5 # reduction candidate for 2,7 B1: 2,7 => CTR * 4.6185.93.1.2.4685..56..4..569741328...3.6.141349285677518...46.8.46.15.64.51.87. B1: 4,5 # 11 pairs * PAIR G1: 2,7 COL G G8: 2,7,1,9 # reduction candidate for 2,7 G8: 2,7 => CTR * ..61...9..1...4685...6..41.569741328...3.6.49.3.92..677.18..936.8..6..516...1.874 G8: 1,9 # 11 pairs * PAIR I1: 2,3 BLK 3 I3: 2,3,1 # reduction candidate for 2,3 I3: 2,3 => CTR * ..61...9..1...4685...6..41.569741328...3.6.4..3.92..677.189..36.8..6..5.6...1.87. I3: 1 # 14 pairs * PAIR I1: 2,3 ROW 1 A1: 2,3,4,8 # reduction candidate for 2,3 A1: 2,3 => CTR * .461...9..1.2.4..5..56..4..569741328...3.6.14.3.92...77.18...46.8.46..5.6.451.8.. A1: 4,8 # 11 pairs F1: 2,3,5,8 # reduction candidate for 2,3 F1: 2,3 # 15 pairs * PAIR I1: 2,3 COL I I8: 2,3,1,4,9 # reduction candidate for 2,3 I8: 2,3 # 17 pairs I9: 2,3,4,9 # reduction candidate for 2,3 I9: 2,3 # 16 pairs * PAIR C6: 4,8 BLK 4 A5: 4,8,1,2 # reduction candidate for 4,8 A5: 4,8 # 15 pairs C5: 4,8,2,7 # reduction candidate for 4,8 C5: 4,8 # 14 pairs A6: 4,8,1 # reduction candidate for 4,8 A6: 4,8 => CTR * ..61..79.91...4685...6.941.5697413281..386549.3.9251677.189.236.8..6795169..13874 A6: 1 # 12 pairs * PAIR E5: 5,8 COL E E1: 5,8,3,7 # reduction candidate for 5,8 E1: 5,8 # 12 pairs E3: 5,8,3,7,9 # reduction candidate for 5,8 E3: 5,8 => CTR * 8461.5.9..1.2.4685..568.4..569741328..8356.14.3.9285677518...46.8.46..5.6..51.8.. E3: 3,7,9 # 10 pairs * PAIR F6: 5,8 COL F F1: 5,8,2,3 # reduction candidate for 5,8 F1: 5,8 # 11 pairs F3: 5,8,2,3,9 # reduction candidate for 5,8 F3: 5,8 => CTR * ..61.3792.1.2.46.5..56.84..569741328...38651..3.92..677.183..46.8.467.5.6..51.87. F3: 2,3,9 # 10 pairs * PAIR H5: 1,4 BLK 6 I5: 1,4,9 # reduction candidate for 1,4 I5: 1,4 # 12 pairs H6: 1,4,6 # reduction candidate for 1,4 H6: 1,4 => CTR * ..61...93.1...4.65...6..481569741328...3.65.9.3.9256.77.1...936.8..6715.6...1.87. H6: 6 # 12 pairs * PAIR H5: 1,4 ROW 5 A5: 1,4,2,8 # reduction candidate for 1,4 A5: 1,4 => CTR * ..61..79.91...4685...6.941.5697413281..386549.3.9251677.189.236.8..6795169..13874 A5: 2,8 # 13 pairs * PAIR D8: 2,4 BLK 8 D7: 2,4,5,8 # reduction candidate for 2,4 D7: 2,4 # 18 pairs D9: 2,4,5 # reduction candidate for 2,4 D9: 2,4 => SOLVED * 846135792912874635357692481569741328278356914134928567791583246483267159625419873 D9: 5 # 10 pairs * PAIR D8: 2,4 ROW 8 A8: 2,4,3,9 # reduction candidate for 2,4 A8: 2,4 # 13 pairs C8: 2,4,3 # reduction candidate for 2,4 C8: 2,4 # 12 pairs I8: 2,4,1,3,9 # reduction candidate for 2,4 I8: 2,4 # 16 pairs * PAIR G7: 2,9 BLK 9 G8: 2,9,1,7 # reduction candidate for 2,9 G8: 2,9 => CTR * ..61...9..1...4685...6..41.569741328...3.6.49.3.92..677.189..36.8..67.516...13874 G8: 1,7 # 11 pairs I8: 2,9,1,3,4 # reduction candidate for 2,9 I8: 2,9 # 14 pairs I9: 2,9,3,4 # reduction candidate for 2,9 I9: 2,9 # 12 pairs * PAIR G7: 2,9 ROW 7 B7: 2,9,4,5 # reduction candidate for 2,9 B7: 2,9 => SOLVED * 846135792912874635357692481569741328278356914134928567791583246483267159625419873 B7: 4,5 # 11 pairs F7: 2,9,3,8 # reduction candidate for 2,9 F7: 2,9 # 13 pairs * PAIR H7: 3,4 BLK 9 I8: 3,4,1,2,9 # reduction candidate for 3,4 I8: 3,4 # 15 pairs H9: 3,4,7 # reduction candidate for 3,4 H9: 3,4 => CTR * ..61..293.1...4..5...6..4..569741328...3.6....3.92...77.1.....6.8..6.7516...178.. H9: 7 # 10 pairs I9: 3,4,2,9 # reduction candidate for 3,4 I9: 3,4 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060507-absurd-base-pr-000.dot * REASONING * DIS # D7: 2,8 => CTR => D7: 4,5 * DIS # G2: 2,7 => CTR => G2: 6 * DIS # B1: 2,7 => CTR => B1: 4,5 * DIS # G8: 2,7 => CTR => G8: 1,9 * DIS # I3: 2,3 => CTR => I3: 1 * DIS # A1: 2,3 => CTR => A1: 4,8 * DIS # A6: 4,8 => CTR => A6: 1 * DIS # E3: 5,8 => CTR => E3: 3,7,9 * DIS # F3: 5,8 => CTR => F3: 2,3,9 * DIS # H6: 1,4 => CTR => H6: 6 * DIS # A5: 1,4 => CTR => A5: 2,8 * PRF # D9: 2,4 => SOL * DIS # G8: 2,9 => CTR => G8: 1,7 * PRF # B7: 2,9 => SOL * DIS # H9: 3,4 => CTR => H9: 7 * CNT 15 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,D2,D8,E5,F6,G1,G7,H5,H7,I1) * ..61...9..1...4..5...6..4..569741328...3.6....3.92...77.1.....6.8..6..5.6...1.8.. * PAIR D2: 2,8 BLK 2 F1: 2,8,3,5 # reduction candidate for 2,8 F1: 2,8 # 11 pairs F3: 2,8,3,5,9 # reduction candidate for 2,8 F3: 2,8 # 17 pairs * PAIR D2: 2,8 ROW 2 A2: 2,8,3,9 # reduction candidate for 2,8 A2: 2,8 # 19 pairs C2: 2,8,3,7 # reduction candidate for 2,8 C2: 2,8 # 17 pairs * PAIR D2: 2,8 COL D D7: 2,8,4,5 # reduction candidate for 2,8 D7: 2,8 => CTR * 4.6185.93.1.2.4685..56..4..569741328...3.6.14134928567751....46.8.46.15.64.51.87. * PAIR RESTART * PAIR G1: 2,7 BLK 3 G2: 2,7,6 # reduction candidate for 2,7 G2: 2,7 => CTR * 8461...93.1.8.4.65...6..481569741328...3.65.9.3.9256.77.14.8936.8..6715.6...1387. G2: 6 => SOLVED * 846135792912874635357692481569741328278356914134928567791583246483267159625419873 * DURATION: 0:00:05.499700 START: 22:59:33.013290 END: 22:59:38.512990 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060507-absurd-base-pr-001.dot * REASONING * DIS # D7: 2,8 => CTR => D7: 4,5 * DIS D7: 4,5 # G2: 2,7 => CTR => G2: 6 * PRF D7: 4,5 + G2: 6 => SOL * STA D7: 4,5 + G2: 6 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060507, absurd
Solution
position: 846135792912874635357692481569741328278356914134928567791583246483267159625419873 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 # F1: 2,8 => UNS * INC # F3: 2,8 => UNS * INC # A2: 2,8 => UNS * INC # C2: 2,8 => UNS * DIS # D7: 2,8 => CTR => D7: 4,5 * INC # D7: 4,5 => UNS * DIS # G2: 2,7 => CTR => G2: 6 * INC # G2: 6 => UNS * DIS # B1: 2,7 => CTR => B1: 4,5 * INC # B1: 4,5 => UNS * DIS # G8: 2,7 => CTR => G8: 1,9 * INC # G8: 1,9 => UNS * DIS # I3: 2,3 => CTR => I3: 1 * INC # I3: 1 => UNS * DIS # A1: 2,3 => CTR => A1: 4,8 * INC # A1: 4,8 => UNS * INC # F1: 2,3 => UNS * INC # I8: 2,3 => UNS * INC # I9: 2,3 => UNS * INC # A5: 4,8 => UNS * INC # C5: 4,8 => UNS * DIS # A6: 4,8 => CTR => A6: 1 * INC # A6: 1 => UNS * INC # E1: 5,8 => UNS * DIS # E3: 5,8 => CTR => E3: 3,7,9 * INC # E3: 3,7,9 => UNS * INC # F1: 5,8 => UNS * DIS # F3: 5,8 => CTR => F3: 2,3,9 * INC # F3: 2,3,9 => UNS * INC # I5: 1,4 => UNS * DIS # H6: 1,4 => CTR => H6: 6 * INC # H6: 6 => UNS * DIS # A5: 1,4 => CTR => A5: 2,8 * INC # A5: 2,8 => UNS * INC # D7: 2,4 => UNS * PRF # D9: 2,4 => SOL * INC # D9: 5 => UNS * INC # A8: 2,4 => UNS * INC # C8: 2,4 => UNS * INC # I8: 2,4 => UNS * DIS # G8: 2,9 => CTR => G8: 1,7 * INC # G8: 1,7 => UNS * INC # I8: 2,9 => UNS * INC # I9: 2,9 => UNS * PRF # B7: 2,9 => SOL * INC # B7: 4,5 => UNS * INC # F7: 2,9 => UNS * INC # I8: 3,4 => UNS * DIS # H9: 3,4 => CTR => H9: 7 * INC # H9: 7 => UNS * INC # I9: 3,4 => UNS * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 2,8 => UNS * INC # F3: 2,8 => UNS * INC # A2: 2,8 => UNS * INC # C2: 2,8 => UNS * DIS # D7: 2,8 => CTR => D7: 4,5 * DIS D7: 4,5 # G2: 2,7 => CTR => G2: 6 * PRF D7: 4,5 + G2: 6 => SOL * STA D7: 4,5 + G2: 6 * CNT 7 HDP CHAINS / 6 HYP OPENED