Analysis of zz-www.sudokuoftheday.co.uk-20190327-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: 1...5..7..4..6..9..79...5.4........63..64....9....31...2...9......4......56.372.. initial
Autosolve
position: 13.95467..4.76..9.6793..5.4....9...63..64.9..96..731...2.5.9.6..9.426....56.372.9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 5 => CTR => C2: 2,8 * DIS # C2: 8 => CTR => C2: 2,5 * DIS # F3: 1,8 => CTR => F3: 2 * DIS # H3: 2 => CTR => H3: 1,8 * DIS # I2: 2,8 => CTR => I2: 1,3 * DIS # I5: 2,8 => CTR => I5: 5,7 * DIS # I2: 3,8 => CTR => I2: 1,2 * DIS # G7: 3,8 => CTR => G7: 4,7 * DIS # F4: 1,8 => CTR => F4: 5 * DIS # G4: 3 => CTR => G4: 4,7 * DIS # F5: 5 => CTR => F5: 1,8 * DIS # D4: 1 => CTR => D4: 2,8 * DIS # H6: 2,8 => CTR => H6: 4,5 * DIS # I8: 7,8 => CTR => I8: 1,3,5 * DIS # A7: 7 => CTR => A7: 4,8 * DIS # H9: 1 => CTR => H9: 4,8 * DIS # D4: 2 => CTR => D4: 1,8 * CNT 17 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 5 => CTR => C2: 2,8 * DIS C2: 2,8 # F3: 1,8 => CTR => F3: 2 * DIS C2: 2,8 + F3: 2 # I2: 2,8 => CTR => I2: 1,3 * DIS C2: 2,8 + F3: 2 + I2: 1,3 # G7: 3,8 => CTR => G7: 4,7 * DIS C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 # G8: 7 => CTR => G8: 3,8 * PRF C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 + G8: 3,8 # I7: 1,3 => SOL * STA C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 + G8: 3,8 + I7: 1,3 * CNT 6 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1...5..7..4..6..9..79...5.4........63..64....9....31...2...9......4......56.372.. | initial |
| 13.95467..4.76..9.6793..5.4....9...63..64.9..96..731...2.5.9.6..9.426....56.372.9 | autosolve |
| 138954672542768391679312584217895436385641927964273158421589763793426815856137249 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 2,8 A2: 2,5 E3: 1,8 I1: 2,8 G2: 3,8 A4: 2,5 B4: 1,8 C4: 4,7 B5: 1,8 D6: 2,8 H4: 3,4 C7: 1,3 A8: 7,8 C8: 1,3 A9: 4,8 E7: 1,8 D9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,H3: 1.. / I2 = 1 => 23 pairs (_) / H3 = 1 => 0 pairs (X) B4,B5: 1.. / B4 = 1 => 0 pairs (*) / B5 = 1 => 0 pairs (X) C7,C8: 1.. / C7 = 1 => 16 pairs (_) / C8 = 1 => 15 pairs (_) E7,D9: 1.. / E7 = 1 => 0 pairs (X) / D9 = 1 => 16 pairs (_) F2,I2: 1.. / F2 = 1 => 0 pairs (X) / I2 = 1 => 23 pairs (_) B5,F5: 1.. / B5 = 1 => 18 pairs (_) / F5 = 1 => 0 pairs (*) D9,H9: 1.. / D9 = 1 => 16 pairs (_) / H9 = 1 => 0 pairs (X) D4,D9: 1.. / D4 = 1 => 0 pairs (X) / D9 = 1 => 16 pairs (_) E3,E7: 1.. / E3 = 1 => 16 pairs (_) / E7 = 1 => 0 pairs (X) F2,F3: 2.. / F2 = 2 => 0 pairs (X) / F3 = 2 => 20 pairs (_) D4,D6: 2.. / D4 = 2 => 0 pairs (X) / D6 = 2 => 21 pairs (_) C1,I1: 2.. / C1 = 2 => 0 pairs (X) / I1 = 2 => 19 pairs (_) F3,H3: 2.. / F3 = 2 => 20 pairs (_) / H3 = 2 => 0 pairs (X) A4,D4: 2.. / A4 = 2 => 21 pairs (_) / D4 = 2 => 0 pairs (X) A2,A4: 2.. / A2 = 2 => 0 pairs (X) / A4 = 2 => 21 pairs (_) G2,I2: 3.. / G2 = 3 => 19 pairs (_) / I2 = 3 => 0 pairs (X) G4,H4: 3.. / G4 = 3 => 0 pairs (X) / H4 = 3 => 17 pairs (_) C7,C8: 3.. / C7 = 3 => 15 pairs (_) / C8 = 3 => 16 pairs (_) H4,H8: 3.. / H4 = 3 => 17 pairs (_) / H8 = 3 => 0 pairs (X) C4,C6: 4.. / C4 = 4 => 21 pairs (_) / C6 = 4 => 21 pairs (_) A7,A9: 4.. / A7 = 4 => 16 pairs (_) / A9 = 4 => 19 pairs (_) G7,H9: 4.. / G7 = 4 => 19 pairs (_) / H9 = 4 => 16 pairs (_) C6,H6: 4.. / C6 = 4 => 21 pairs (_) / H6 = 4 => 21 pairs (_) A7,G7: 4.. / A7 = 4 => 16 pairs (_) / G7 = 4 => 19 pairs (_) A9,H9: 4.. / A9 = 4 => 19 pairs (_) / H9 = 4 => 16 pairs (_) G4,G7: 4.. / G4 = 4 => 16 pairs (_) / G7 = 4 => 19 pairs (_) A2,C2: 5.. / A2 = 5 => 21 pairs (_) / C2 = 5 => 0 pairs (X) F4,F5: 5.. / F4 = 5 => 21 pairs (_) / F5 = 5 => 0 pairs (X) H8,I8: 5.. / H8 = 5 => 18 pairs (_) / I8 = 5 => 16 pairs (_) A4,F4: 5.. / A4 = 5 => 0 pairs (X) / F4 = 5 => 21 pairs (_) A2,A4: 5.. / A2 = 5 => 21 pairs (_) / A4 = 5 => 0 pairs (X) C4,C5: 7.. / C4 = 7 => 21 pairs (_) / C5 = 7 => 21 pairs (_) G4,I5: 7.. / G4 = 7 => 21 pairs (_) / I5 = 7 => 21 pairs (_) A7,A8: 7.. / A7 = 7 => 0 pairs (X) / A8 = 7 => 20 pairs (_) C4,G4: 7.. / C4 = 7 => 21 pairs (_) / G4 = 7 => 21 pairs (_) C5,I5: 7.. / C5 = 7 => 21 pairs (_) / I5 = 7 => 21 pairs (_) C1,C2: 8.. / C1 = 8 => 19 pairs (_) / C2 = 8 => 0 pairs (X) B4,B5: 8.. / B4 = 8 => 18 pairs (_) / B5 = 8 => 0 pairs (*) E7,D9: 8.. / E7 = 8 => 16 pairs (_) / D9 = 8 => 0 pairs (X) C1,I1: 8.. / C1 = 8 => 19 pairs (_) / I1 = 8 => 0 pairs (X) E3,E7: 8.. / E3 = 8 => 0 pairs (X) / E7 = 8 => 16 pairs (_) * DURATION: 0:00:58.323762 START: 04:50:19.623207 END: 04:51:17.946969 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A8,A9,B4,B5,C1,C4,C7,C8,D6,D9,E3,E7,G2,H4,I1) * 13.95467..4.76..9.6793..5.4....9...63..64.9..96..731...2.5.9.6..9.426....56.372.9 * PAIR C1: 2,8 BLK 1 C2: 2,8,5 # reduction candidate for 2,8 C2: 5 => CTR * 13895467224576..9.6793.25.45..29...63..6459..96.8731.5.2.589.6..9.426.5..561372.9 C2: 2,8 # 21 pairs * PAIR A2: 2,5 BLK 1 C2: 2,5,8 # reduction candidate for 2,5 C2: 8 => CTR * 13295467854876.39.6793..5142...954363.564.92796427318542.519.6..9.426.5..56.37249 C2: 2,5 # 19 pairs * PAIR E3: 1,8 BLK 2 F2: 1,8,2 # reduction candidate for 1,8 F2: 1,8 # 20 pairs F3: 1,8,2 # reduction candidate for 1,8 F3: 1,8 => CTR * 1329546785487623916793..5242...957363.764.95296.2731...2.5.9.6..9.426....56.372.9 F3: 2 # 20 pairs * PAIR E3: 1,8 ROW 3 H3: 1,8,2 # reduction candidate for 1,8 H3: 2 => CTR * 1329546785487623916793..5242...95.363..64.9.296.273185.2.5.9.6..9.426....56.372.9 H3: 1,8 # 20 pairs * PAIR I1: 2,8 BLK 3 I2: 2,8,1,3 # reduction candidate for 2,8 I2: 2,8 => CTR * 13.95467..4.76139.679382514...19...63..64.9..96..731...2.5.9.6..9.426....56.372.9 I2: 1,3 # 18 pairs H3: 2,8,1 # reduction candidate for 2,8 H3: 2,8 # 23 pairs * PAIR I1: 2,8 COL I I5: 2,8,5,7 # reduction candidate for 2,8 I5: 2,8 => CTR * 13.95467..4576.893679318524..4.9.7363.764.9..96.873145.2.58946.89.426357456137289 I5: 5,7 # 18 pairs I6: 2,8,5 # reduction candidate for 2,8 I6: 2,8 # 23 pairs * PAIR G2: 3,8 BLK 3 I2: 3,8,1,2 # reduction candidate for 3,8 I2: 3,8 => CTR * 13.95467..4.761.9.679382514...19...63..64.9..96..731...2.5.9.6..9.426....56.372.9 I2: 1,2 # 20 pairs * PAIR G2: 3,8 COL G G7: 3,8,4,7 # reduction candidate for 3,8 G7: 3,8 => CTR * 13.95467..4.76..9.6793..5.4....9.4363..64.9.7964.731...2.5.9.6..9.426....56.372.9 G7: 4,7 # 18 pairs G8: 3,8,7 # reduction candidate for 3,8 G8: 3,8 # 19 pairs * PAIR A4: 2,5 BLK 4 C5: 2,5,7 # reduction candidate for 2,5 C5: 2,5 # 21 pairs C6: 2,5,4 # reduction candidate for 2,5 C6: 2,5 # 21 pairs * PAIR B4: 1,8 ROW 4 D4: 1,8,2 # reduction candidate for 1,8 D4: 1,8 # 21 pairs F4: 1,8,5 # reduction candidate for 1,8 F4: 1,8 => CTR * 13.95467.24576..9.67931258458.291..631.64592896287314..2.589.6..9.426....561372.9 F4: 5 # 21 pairs * PAIR C4: 4,7 ROW 4 G4: 4,7,3 # reduction candidate for 4,7 G4: 3 => CTR * 13.95467..4.76.8936793..514..7.9.3463..64.9.7964.7315.723519468.9.426735456.372.9 G4: 4,7 # 17 pairs * PAIR B5: 1,8 ROW 5 F5: 1,8,5 # reduction candidate for 1,8 F5: 5 => CTR * 13.95467.24576839167931258458.291.3631.64592896287314..2.589.6..9.426....561372.9 F5: 1,8 # 21 pairs * PAIR D6: 2,8 BLK 5 D4: 2,8,1 # reduction candidate for 2,8 D4: 1 => CTR * 13.95467.54.76..9167938152428.195..631.648952965273148.2.519.6..91426....56837219 D4: 2,8 # 16 pairs * PAIR D6: 2,8 ROW 6 H6: 2,8,4,5 # reduction candidate for 2,8 H6: 2,8 => CTR * 13.95467..4.76..9.6793..514..7.9.4363..64.9.7964.731.542.519768.9.426.5..56.37249 H6: 4,5 # 18 pairs I6: 2,8,5 # reduction candidate for 2,8 I6: 2,8 # 23 pairs * PAIR H4: 3,4 BLK 6 G4: 3,4,7 # reduction candidate for 3,4 G4: 7 # 21 pairs G4: 3,4 # 21 pairs * PAIR C7: 1,3 ROW 7 I7: 1,3,7,8 # reduction candidate for 1,3 I7: 7,8 # 24 pairs I7: 1,3 # 16 pairs * PAIR A8: 7,8 BLK 7 A7: 7,8,4 # reduction candidate for 7,8 A7: 7,8 # 19 pairs A7: 4 # 16 pairs * PAIR A8: 7,8 ROW 8 G8: 7,8,3 # reduction candidate for 7,8 G8: 7,8 # 18 pairs I8: 7,8,1,3,5 # reduction candidate for 7,8 I8: 7,8 => CTR * 13.95467..4.76.8936793..514....9..363..64.9..96..731...23519.6..9142635..56837249 I8: 1,3,5 # 17 pairs * PAIR C8: 1,3 ROW 8 H8: 1,3,5,8 # reduction candidate for 1,3 H8: 1,3 # 16 pairs I8: 1,3,5,7,8 # reduction candidate for 1,3 I8: 1,3 # 20 pairs * PAIR A9: 4,8 BLK 7 A7: 4,8,7 # reduction candidate for 4,8 A7: 7 => CTR * 13.95467..4.76.8936793..514....9...63..64.9..96..731..72351946889.426...456.372.9 A7: 4,8 # 20 pairs * PAIR A9: 4,8 ROW 9 H9: 4,8,1 # reduction candidate for 4,8 H9: 1 => CTR * 13295467854876239167938152428.19573631764895.96.2731...2.51946..91426...456837219 H9: 4,8 # 16 pairs * PAIR E7: 1,8 ROW 7 I7: 1,8,3,7 # reduction candidate for 1,8 I7: 3,7 # 18 pairs I7: 1,8 # 18 pairs * PAIR D9: 1,8 ROW 9 H9: 1,8,4 # reduction candidate for 1,8 H9: 1,8 # 19 pairs H9: 4 # 16 pairs * PAIR D9: 1,8 COL D D4: 1,8,2 # reduction candidate for 1,8 D4: 2 => CTR * 13.95467.24576..9.67931258458.291..631.64592896287314..2.589.6..9.426....561372.9 D4: 1,8 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190327-absurd-base-pr-000.dot * REASONING * DIS # C2: 5 => CTR => C2: 2,8 * DIS # C2: 8 => CTR => C2: 2,5 * DIS # F3: 1,8 => CTR => F3: 2 * DIS # H3: 2 => CTR => H3: 1,8 * DIS # I2: 2,8 => CTR => I2: 1,3 * DIS # I5: 2,8 => CTR => I5: 5,7 * DIS # I2: 3,8 => CTR => I2: 1,2 * DIS # G7: 3,8 => CTR => G7: 4,7 * DIS # F4: 1,8 => CTR => F4: 5 * DIS # G4: 3 => CTR => G4: 4,7 * DIS # F5: 5 => CTR => F5: 1,8 * DIS # D4: 1 => CTR => D4: 2,8 * DIS # H6: 2,8 => CTR => H6: 4,5 * DIS # I8: 7,8 => CTR => I8: 1,3,5 * DIS # A7: 7 => CTR => A7: 4,8 * DIS # H9: 1 => CTR => H9: 4,8 * DIS # D4: 2 => CTR => D4: 1,8 * CNT 17 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A8,A9,B4,B5,C1,C4,C7,C8,D6,D9,E3,E7,G2,H4,I1) * 13.95467..4.76..9.6793..5.4....9...63..64.9..96..731...2.5.9.6..9.426....56.372.9 * PAIR C1: 2,8 BLK 1 C2: 2,8,5 # reduction candidate for 2,8 C2: 5 => CTR * 13895467224576..9.6793.25.45..29...63..6459..96.8731.5.2.589.6..9.426.5..561372.9 * PAIR E3: 1,8 BLK 2 F2: 1,8,2 # reduction candidate for 1,8 F2: 1,8 # 23 pairs F3: 1,8,2 # reduction candidate for 1,8 F3: 1,8 => CTR * 13.95467.54.762.916793..5242...95..63..64.952965273148.2.5.9.6..9.426....56.372.9 * RESTART * PAIR I1: 2,8 BLK 3 I2: 2,8,1,3 # reduction candidate for 2,8 I2: 2,8 => CTR * 13.95467.54.76139.6793825142..195..63..64.92.96.2731...2.5.9.6..9.426....56.372.9 * PAIR G2: 3,8 COL G G7: 3,8,4,7 # reduction candidate for 3,8 G7: 3,8 => CTR * 13895467254276..9.6793.25.42...954363..64.9279642731...2.5.9.6..9.426....56.372.9 G8: 3,8,7 # reduction candidate for 3,8 G8: 3,8 # 23 pairs * RESTART * PAIR G2: 3,8 COL G G8: 3,8,7 # reduction candidate for 3,8 G8: 7 => CTR * 13895467254276.8936793825142...953463..6489279642731...23519.6..9.426....56.372.9 * PAIR RESTART * PAIR C7: 1,3 ROW 7 I7: 1,3,7,8 # reduction candidate for 1,3 I7: 1,3 => SOLVED * 138954672542768391679312584217895436385641927964273158421589763793426815856137249 * DURATION: 0:00:10.130844 START: 04:51:58.084565 END: 04:52:08.215409 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190327-absurd-base-pr-001.dot * REASONING * DIS # C2: 5 => CTR => C2: 2,8 * DIS C2: 2,8 # F3: 1,8 => CTR => F3: 2 * DIS C2: 2,8 + F3: 2 # I2: 2,8 => CTR => I2: 1,3 * DIS C2: 2,8 + F3: 2 + I2: 1,3 # G7: 3,8 => CTR => G7: 4,7 * DIS C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 # G8: 7 => CTR => G8: 3,8 * PRF C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 + G8: 3,8 # I7: 1,3 => SOL * STA C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 + G8: 3,8 + I7: 1,3 * CNT 6 HDP CHAINS / 10 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190327, absurd
Solution
position: 138954672542768391679312584217895436385641927964273158421589763793426815856137249 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 # C2: 2,8 => UNS * DIS # C2: 5 => CTR => C2: 2,8 * INC # C2: 2,5 => UNS * DIS # C2: 8 => CTR => C2: 2,5 * INC # F2: 1,8 => UNS * DIS # F3: 1,8 => CTR => F3: 2 * INC # F3: 2 => UNS * INC # H3: 1,8 => UNS * DIS # H3: 2 => CTR => H3: 1,8 * DIS # I2: 2,8 => CTR => I2: 1,3 * INC # I2: 1,3 => UNS * INC # H3: 2,8 => UNS * DIS # I5: 2,8 => CTR => I5: 5,7 * INC # I5: 5,7 => UNS * INC # I6: 2,8 => UNS * DIS # I2: 3,8 => CTR => I2: 1,2 * INC # I2: 1,2 => UNS * DIS # G7: 3,8 => CTR => G7: 4,7 * INC # G7: 4,7 => UNS * INC # G8: 3,8 => UNS * INC # C5: 2,5 => UNS * INC # C6: 2,5 => UNS * INC # D4: 1,8 => UNS * DIS # F4: 1,8 => CTR => F4: 5 * INC # F4: 5 => UNS * INC # G4: 4,7 => UNS * DIS # G4: 3 => CTR => G4: 4,7 * INC # F5: 1,8 => UNS * DIS # F5: 5 => CTR => F5: 1,8 * INC # D4: 2,8 => UNS * DIS # D4: 1 => CTR => D4: 2,8 * DIS # H6: 2,8 => CTR => H6: 4,5 * INC # H6: 4,5 => UNS * INC # I6: 2,8 => UNS * INC # G4: 3,4 => UNS * INC # G4: 7 => UNS * INC # I7: 1,3 => UNS * INC # I7: 7,8 => UNS * INC # A7: 7,8 => UNS * INC # A7: 4 => UNS * INC # G8: 7,8 => UNS * DIS # I8: 7,8 => CTR => I8: 1,3,5 * INC # I8: 1,3,5 => UNS * INC # H8: 1,3 => UNS * INC # I8: 1,3 => UNS * INC # A7: 4,8 => UNS * DIS # A7: 7 => CTR => A7: 4,8 * INC # H9: 4,8 => UNS * DIS # H9: 1 => CTR => H9: 4,8 * INC # I7: 1,8 => UNS * INC # I7: 3,7 => UNS * INC # H9: 1,8 => UNS * INC # H9: 4 => UNS * INC # D4: 1,8 => UNS * DIS # D4: 2 => CTR => D4: 1,8 * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 2,8 => UNS * DIS # C2: 5 => CTR => C2: 2,8 * INC C2: 2,8 # F2: 1,8 => UNS * DIS C2: 2,8 # F3: 1,8 => CTR => F3: 2 * DIS C2: 2,8 + F3: 2 # I2: 2,8 => CTR => I2: 1,3 * DIS C2: 2,8 + F3: 2 + I2: 1,3 # G7: 3,8 => CTR => G7: 4,7 * INC C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 # G8: 3,8 => UNS * INC C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 # G8: 3,8 => UNS * DIS C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 # G8: 7 => CTR => G8: 3,8 * PRF C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 + G8: 3,8 # I7: 1,3 => SOL * STA C2: 2,8 + F3: 2 + I2: 1,3 + G7: 4,7 + G8: 3,8 + I7: 1,3 * CNT 10 HDP CHAINS / 10 HYP OPENED