Analysis of zz-www.sudokuoftheday.co.uk-20190418-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: ...6....33.6..89..7.9.3..2....1...5.5.7.62.39....9....6......1..537..2..2....6... initial
Autosolve
position: .256.9..33.62.89..78943.62.96.143.5.5.7862.39.3.597.6.6...2..1..537..2962....6... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E2: 1,7 => SOL * DIS # G1: 1,7 => CTR => G1: 4,8 * DIS # E2: 7 => CTR => E2: 1,5 * DIS # I2: 4,7 => CTR => I2: 1,5 * DIS # I2: 4,7 => CTR => I2: 1,5 * DIS # I4: 7 => CTR => I4: 2,8 * DIS # C9: 4,8 => CTR => C9: 1 * PRF # I7: 7 => SOL * PRF # E9: 5 => SOL * PRF # A8: 4 => SOL * CNT 10 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E2: 1,7 => SOL * STA E2: 1,7 * CNT 1 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6....33.6..89..7.9.3..2....1...5.5.7.62.39....9....6......1..537..2..2....6... | initial |
| .256.9..33.62.89..78943.62.96.143.5.5.7862.39.3.597.6.6...2..1..537..2962....6... | autosolve |
| 125679843346218975789435621962143758517862439834597162698324517453781296271956384 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) A1: 1,4 B2: 1,4 E1: 1,7 F3: 1,5 H2: 4,7 I3: 1,5 C4: 2,8 B5: 1,4 G4: 7,8 G5: 1,4 B7: 7,9 C7: 4,8 B9: 7,9 D7: 3,9 F7: 4,5 E8: 1,8 F8: 1,4 D9: 3,9 G7: 3,5 G9: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B2: 1.. / A1 = 1 => 0 pairs (*) / B2 = 1 => 0 pairs (X) A8,C9: 1.. / A8 = 1 => 0 pairs (X) / C9 = 1 => 23 pairs (_) F3,I3: 1.. / F3 = 1 => 13 pairs (_) / I3 = 1 => 0 pairs (*) B5,G5: 1.. / B5 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) C9,E9: 1.. / C9 = 1 => 23 pairs (_) / E9 = 1 => 0 pairs (X) B2,B5: 1.. / B2 = 1 => 0 pairs (X) / B5 = 1 => 0 pairs (_) C6,C9: 1.. / C6 = 1 => 0 pairs (X) / C9 = 1 => 23 pairs (_) F3,F8: 1.. / F3 = 1 => 13 pairs (_) / F8 = 1 => 0 pairs (*) C4,C6: 2.. / C4 = 2 => 24 pairs (_) / C6 = 2 => 10 pairs (_) I4,I6: 2.. / I4 = 2 => 10 pairs (_) / I6 = 2 => 24 pairs (_) C4,I4: 2.. / C4 = 2 => 24 pairs (_) / I4 = 2 => 10 pairs (_) C6,I6: 2.. / C6 = 2 => 10 pairs (_) / I6 = 2 => 24 pairs (_) D7,D9: 3.. / D7 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) G7,G9: 3.. / G7 = 3 => 13 pairs (_) / G9 = 3 => 0 pairs (*) D7,G7: 3.. / D7 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) D9,G9: 3.. / D9 = 3 => 13 pairs (_) / G9 = 3 => 0 pairs (*) A1,B2: 4.. / A1 = 4 => 0 pairs (X) / B2 = 4 => 0 pairs (_) F7,F8: 4.. / F7 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) B5,G5: 4.. / B5 = 4 => 0 pairs (X) / G5 = 4 => 0 pairs (_) A8,F8: 4.. / A8 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) B2,B5: 4.. / B2 = 4 => 0 pairs (*) / B5 = 4 => 0 pairs (X) E2,F3: 5.. / E2 = 5 => 13 pairs (_) / F3 = 5 => 0 pairs (*) I2,I3: 5.. / I2 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) F7,E9: 5.. / F7 = 5 => 13 pairs (_) / E9 = 5 => 0 pairs (*) G7,G9: 5.. / G7 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) E2,I2: 5.. / E2 = 5 => 13 pairs (_) / I2 = 5 => 0 pairs (*) F3,I3: 5.. / F3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) F7,G7: 5.. / F7 = 5 => 13 pairs (_) / G7 = 5 => 0 pairs (*) E9,G9: 5.. / E9 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) E2,E9: 5.. / E2 = 5 => 13 pairs (_) / E9 = 5 => 0 pairs (*) F3,F7: 5.. / F3 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) E1,E2: 7.. / E1 = 7 => 21 pairs (_) / E2 = 7 => 0 pairs (X) G4,I4: 7.. / G4 = 7 => 20 pairs (_) / I4 = 7 => 0 pairs (X) B7,B9: 7.. / B7 = 7 => 13 pairs (_) / B9 = 7 => 0 pairs (*) B7,I7: 7.. / B7 = 7 => 13 pairs (_) / I7 = 7 => 0 pairs (*) G1,G4: 7.. / G1 = 7 => 0 pairs (X) / G4 = 7 => 20 pairs (_) G1,H1: 8.. / G1 = 8 => 25 pairs (_) / H1 = 8 => 22 pairs (_) E8,E9: 8.. / E8 = 8 => 26 pairs (_) / E9 = 8 => 10 pairs (_) C7,I7: 8.. / C7 = 8 => 27 pairs (_) / I7 = 8 => 10 pairs (_) A8,E8: 8.. / A8 = 8 => 10 pairs (_) / E8 = 8 => 26 pairs (_) A6,A8: 8.. / A6 = 8 => 26 pairs (_) / A8 = 8 => 10 pairs (_) H1,H9: 8.. / H1 = 8 => 22 pairs (_) / H9 = 8 => 25 pairs (_) B7,B9: 9.. / B7 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) D7,D9: 9.. / D7 = 9 => 13 pairs (_) / D9 = 9 => 0 pairs (*) B7,D7: 9.. / B7 = 9 => 0 pairs (*) / D7 = 9 => 0 pairs (X) B9,D9: 9.. / B9 = 9 => 13 pairs (_) / D9 = 9 => 0 pairs (*) * DURATION: 0:01:11.024725 START: 05:23:35.201358 END: 05:24:46.226083 2019-05-01 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,B5,B7,B9,C4,C7,D7,D9,E1,E8,F3,F7,F8,G4,G5,G7,G9,H2,I3) * .256.9..33.62.89..78943.62.96.143.5.5.7862.39.3.597.6.6...2..1..537..2962....6... * PAIR A1: 1,4 ROW 1 G1: 1,4,7,8 # reduction candidate for 1,4 G1: 7,8 # 25 pairs G1: 1,4 # 10 pairs * PAIR A1: 1,4 COL A A6: 1,4,8 # reduction candidate for 1,4 A6: 1,4 # 10 pairs A8: 1,4,8 # reduction candidate for 1,4 A8: 1,4 # 26 pairs * PAIR B2: 1,4 ROW 2 I2: 1,4,5,7 # reduction candidate for 1,4 I2: 5,7 # 21 pairs I2: 1,4 # 14 pairs * PAIR E1: 1,7 BLK 2 E2: 1,7,5 # reduction candidate for 1,7 E2: 1,7 => SOLVED * 125679843346218975789435621962143758517862439834597162698324517453781296271956384 E2: 5 # 13 pairs * PAIR E1: 1,7 ROW 1 G1: 1,7,4,8 # reduction candidate for 1,7 G1: 1,7 => CTR * 42561978331627894578943562.96.143.5.547862139.3.59746.6...2..1..537.42962....6... G1: 4,8 # 23 pairs * PAIR F3: 1,5 BLK 2 E2: 1,5,7 # reduction candidate for 1,5 E2: 7 => CTR * .256.9..33.627894578943562196.143.5.547862139.3.59746.6...2451.4537812962.1.563.4 E2: 1,5 # 21 pairs * PAIR H2: 4,7 BLK 3 G1: 4,7,1,8 # reduction candidate for 4,7 G1: 4,7 # 25 pairs H1: 4,7,8 # reduction candidate for 4,7 H1: 4,7 # 25 pairs I2: 4,7,1,5 # reduction candidate for 4,7 I2: 4,7 => CTR * 125679.8334625897.78943162596.143.5.5.7862.39.3.597.616...2531..537.42962.13865.. I2: 1,5 # 21 pairs * PAIR H2: 4,7 COL H H9: 4,7,8 # reduction candidate for 4,7 H9: 8 # 25 pairs H9: 4,7 # 22 pairs * PAIR I3: 1,5 BLK 3 I2: 1,5,4,7 # reduction candidate for 1,5 I2: 4,7 => CTR * 125679.8334625897.78943162596.143.5.5.7862.39.3.597.616...2531..537.42962.13865.. I2: 1,5 # 21 pairs * PAIR C4: 2,8 BLK 4 C6: 2,8,1,4 # reduction candidate for 2,8 C6: 1,4 # 26 pairs C6: 2,8 # 10 pairs * PAIR C4: 2,8 ROW 4 I4: 2,8,7 # reduction candidate for 2,8 I4: 7 => CTR * .256.9..33.62.89..78943.62.9621438575.7862.39.3.597.6267.92.31..537..29629.3.657. I4: 2,8 # 20 pairs * PAIR B5: 1,4 BLK 4 A6: 1,4,8 # reduction candidate for 1,4 A6: 1,4 # 10 pairs C6: 1,4,2,8 # reduction candidate for 1,4 C6: 1,4 # 26 pairs * PAIR G4: 7,8 BLK 6 I4: 7,8,2 # reduction candidate for 7,8 I4: 7,8 # 24 pairs I4: 2 # 10 pairs * PAIR G4: 7,8 COL G G1: 7,8,1,4 # reduction candidate for 7,8 G1: 7,8 # 25 pairs G1: 1,4 # 10 pairs * PAIR G5: 1,4 BLK 6 G6: 1,4,8 # reduction candidate for 1,4 G6: 1,4 # 25 pairs I6: 1,4,2,8 # reduction candidate for 1,4 I6: 1,4 # 10 pairs * PAIR G5: 1,4 COL G G1: 1,4,7,8 # reduction candidate for 1,4 G1: 7,8 # 25 pairs G1: 1,4 # 10 pairs * PAIR C7: 4,8 BLK 7 A8: 4,8,1 # reduction candidate for 4,8 A8: 4,8 # 23 pairs C9: 4,8,1 # reduction candidate for 4,8 C9: 4,8 => CTR * 4256791833162589..7894316259621437585.7862.39.31597.626...2..1.1537842962...165.. C9: 1 # 23 pairs * PAIR C7: 4,8 ROW 7 I7: 4,8,7 # reduction candidate for 4,8 I7: 7 => SOLVED * 125679843346218975789435621962143758517862439834597162698324517453781296271956384 I7: 4,8 # 13 pairs * PAIR C7: 4,8 COL C C6: 4,8,1,2 # reduction candidate for 4,8 C6: 4,8 # 28 pairs C6: 1,2 # 14 pairs * PAIR E8: 1,8 BLK 8 E9: 1,8,5 # reduction candidate for 1,8 E9: 5 => SOLVED * 125679843346218975789435621962143758517862439834597162698324517453781296271956384 E9: 1,8 # 13 pairs * PAIR E8: 1,8 ROW 8 A8: 1,8,4 # reduction candidate for 1,8 A8: 4 => SOLVED * 125679843346218975789435621962143758517862439834597162698324517453781296271956384 A8: 1,8 # 13 pairs * PAIR F8: 1,4 ROW 8 A8: 1,4,8 # reduction candidate for 1,4 A8: 1,4 # 26 pairs A8: 8 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190418-absurd-base-pr-000.dot * REASONING * PRF # E2: 1,7 => SOL * DIS # G1: 1,7 => CTR => G1: 4,8 * DIS # E2: 7 => CTR => E2: 1,5 * DIS # I2: 4,7 => CTR => I2: 1,5 * DIS # I2: 4,7 => CTR => I2: 1,5 * DIS # I4: 7 => CTR => I4: 2,8 * DIS # C9: 4,8 => CTR => C9: 1 * PRF # I7: 7 => SOL * PRF # E9: 5 => SOL * PRF # A8: 4 => SOL * CNT 10 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,B5,B7,B9,C4,C7,D7,D9,E1,E8,F3,F7,F8,G4,G5,G7,G9,H2,I3) * .256.9..33.62.89..78943.62.96.143.5.5.7862.39.3.597.6.6...2..1..537..2962....6... * PAIR A1: 1,4 ROW 1 G1: 1,4,7,8 # reduction candidate for 1,4 G1: 7,8 # 25 pairs G1: 1,4 # 10 pairs * PAIR A1: 1,4 COL A A6: 1,4,8 # reduction candidate for 1,4 A6: 1,4 # 10 pairs A8: 1,4,8 # reduction candidate for 1,4 A8: 1,4 # 26 pairs * PAIR B2: 1,4 ROW 2 I2: 1,4,5,7 # reduction candidate for 1,4 I2: 5,7 # 21 pairs I2: 1,4 # 14 pairs * PAIR E1: 1,7 BLK 2 E2: 1,7,5 # reduction candidate for 1,7 E2: 1,7 => SOLVED * 125679843346218975789435621962143758517862439834597162698324517453781296271956384 * DURATION: 0:00:06.836691 START: 05:25:27.543263 END: 05:25:34.379954 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190418-absurd-base-pr-001.dot * REASONING * PRF # E2: 1,7 => SOL * STA E2: 1,7 * CNT 1 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190418, absurd
Solution
position: 125679843346218975789435621962143758517862439834597162698324517453781296271956384 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 # G1: 1,4 => UNS * INC # G1: 7,8 => UNS * INC # A6: 1,4 => UNS * INC # A8: 1,4 => UNS * INC # I2: 1,4 => UNS * INC # I2: 5,7 => UNS * PRF # E2: 1,7 => SOL * INC # E2: 5 => UNS * DIS # G1: 1,7 => CTR => G1: 4,8 * INC # G1: 4,8 => UNS * INC # E2: 1,5 => UNS * DIS # E2: 7 => CTR => E2: 1,5 * INC # G1: 4,7 => UNS * INC # H1: 4,7 => UNS * DIS # I2: 4,7 => CTR => I2: 1,5 * INC # I2: 1,5 => UNS * INC # H9: 4,7 => UNS * INC # H9: 8 => UNS * INC # I2: 1,5 => UNS * DIS # I2: 4,7 => CTR => I2: 1,5 * INC # C6: 2,8 => UNS * INC # C6: 1,4 => UNS * INC # I4: 2,8 => UNS * DIS # I4: 7 => CTR => I4: 2,8 * INC # A6: 1,4 => UNS * INC # C6: 1,4 => UNS * INC # I4: 7,8 => UNS * INC # I4: 2 => UNS * INC # G1: 7,8 => UNS * INC # G1: 1,4 => UNS * INC # G6: 1,4 => UNS * INC # I6: 1,4 => UNS * INC # G1: 1,4 => UNS * INC # G1: 7,8 => UNS * INC # A8: 4,8 => UNS * DIS # C9: 4,8 => CTR => C9: 1 * INC # C9: 1 => UNS * INC # I7: 4,8 => UNS * PRF # I7: 7 => SOL * INC # C6: 4,8 => UNS * INC # C6: 1,2 => UNS * INC # E9: 1,8 => UNS * PRF # E9: 5 => SOL * INC # A8: 1,8 => UNS * PRF # A8: 4 => SOL * INC # A8: 1,4 => UNS * INC # A8: 8 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 1,4 => UNS * INC # G1: 7,8 => UNS * INC # A6: 1,4 => UNS * INC # A8: 1,4 => UNS * INC # I2: 1,4 => UNS * INC # I2: 5,7 => UNS * PRF # E2: 1,7 => SOL * STA E2: 1,7 * CNT 7 HDP CHAINS / 7 HYP OPENED