Analysis of zz-www.sudokuoftheday.co.uk-20060529-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: .8.1......2..8.46..6....7.....9.....1..42..35....3.84..145.....6.....9..97...2... initial
Autosolve
position: .8.1......2..8.46..6.2..7...4.9.....19.42.635.5..31849.145.....63....9..97...2... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 3,7 => CTR => F1: 4,5,6,9 * DIS # F2: 3,7 => CTR => F2: 5,9 * DIS # G1: 2,3 => CTR => G1: 5 * DIS # I7: 2,3 => CTR => I7: 6,7,8 * PRF # I3: 1,3 => SOL * DIS # C2: 1,3 => CTR => C2: 7,9 * DIS # I9: 1,3 => CTR => I9: 4,6,8 * DIS # C4: 3,8 => CTR => C4: 6 * DIS # C6: 6 => CTR => C6: 2,7 * DIS # F4: 5,6 => CTR => F4: 8 * DIS # E1: 5,6 => CTR => E1: 4,7,9 * DIS # C6: 2 => CTR => C6: 6,7 * DIS # I4: 1,2 => CTR => I4: 7 * DIS # C8: 5 => CTR => C8: 2,8 * DIS # H7: 2,8 => CTR => H7: 7 * DIS # I7: 2,8 => CTR => I7: 3,6,7 * DIS # C8: 5,8 => CTR => C8: 2 * DIS # H8: 7,8 => CTR => H8: 1,2,5 * DIS # E8: 4,7 => CTR => E8: 1 * DIS # F1: 4,7 => CTR => F1: 3,5,6,9 * DIS # I7: 2,3 => CTR => I7: 6,7,8 * DIS # G1: 2,3 => CTR => G1: 5 * CNT 22 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 3,7 => CTR => F1: 4,5,6,9 * DIS F1: 4,5,6,9 # F2: 3,7 => CTR => F2: 5,9 * DIS F1: 4,5,6,9 + F2: 5,9 # G1: 2,3 => CTR => G1: 5 * PRF F1: 4,5,6,9 + F2: 5,9 + G1: 5 # I3: 1,3 => SOL * STA F1: 4,5,6,9 + F2: 5,9 + G1: 5 + I3: 1,3 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.1......2..8.46..6....7.....9.....1..42..35....3.84..145.....6.....9..97...2... | initial |
| .8.1......2..8.46..6.2..7...4.9.....19.42.635.5..31849.145.....63....9..97...2... | autosolve |
| 483176592729385461561249783346958127198427635257631849814593276632714958975862314 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) D2: 3,7 I1: 2,3 I2: 1,3 A4: 3,8 C5: 7,8 A6: 2,7 E4: 5,6 F5: 7,8 D6: 6,7 G4: 1,2 A7: 2,8 C9: 5,8 D8: 7,8 F8: 4,7 G7: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 0 pairs (X) / C3 = 1 => 16 pairs (_) E8,E9: 1.. / E8 = 1 => 16 pairs (_) / E9 = 1 => 0 pairs (X) C2,I2: 1.. / C2 = 1 => 0 pairs (X) / I2 = 1 => 16 pairs (_) G4,G9: 1.. / G4 = 1 => 17 pairs (_) / G9 = 1 => 0 pairs (X) A6,C6: 2.. / A6 = 2 => 21 pairs (_) / C6 = 2 => 0 pairs (X) A7,C8: 2.. / A7 = 2 => 0 pairs (X) / C8 = 2 => 21 pairs (_) A6,A7: 2.. / A6 = 2 => 21 pairs (_) / A7 = 2 => 0 pairs (X) C6,C8: 2.. / C6 = 2 => 0 pairs (X) / C8 = 2 => 21 pairs (_) A4,C4: 3.. / A4 = 3 => 21 pairs (_) / C4 = 3 => 0 pairs (X) F7,D9: 3.. / F7 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) D2,D9: 3.. / D2 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) A1,A3: 4.. / A1 = 4 => 16 pairs (_) / A3 = 4 => 23 pairs (_) I8,I9: 4.. / I8 = 4 => 0 pairs (X) / I9 = 4 => 18 pairs (_) E9,I9: 4.. / E9 = 4 => 0 pairs (X) / I9 = 4 => 18 pairs (_) E4,F4: 5.. / E4 = 5 => 16 pairs (_) / F4 = 5 => 0 pairs (X) C8,C9: 5.. / C8 = 5 => 0 pairs (X) / C9 = 5 => 18 pairs (_) A2,F2: 5.. / A2 = 5 => 16 pairs (_) / F2 = 5 => 21 pairs (_) C8,H8: 5.. / C8 = 5 => 0 pairs (X) / H8 = 5 => 18 pairs (_) G1,G9: 5.. / G1 = 5 => 17 pairs (_) / G9 = 5 => 0 pairs (X) E1,F1: 6.. / E1 = 6 => 0 pairs (X) / F1 = 6 => 16 pairs (_) C4,C6: 6.. / C4 = 6 => 20 pairs (_) / C6 = 6 => 0 pairs (X) I7,I9: 6.. / I7 = 6 => 16 pairs (_) / I9 = 6 => 0 pairs (X) C6,D6: 6.. / C6 = 6 => 0 pairs (X) / D6 = 6 => 20 pairs (_) D6,D9: 6.. / D6 = 6 => 20 pairs (_) / D9 = 6 => 0 pairs (X) F5,D6: 7.. / F5 = 7 => 20 pairs (_) / D6 = 7 => 0 pairs (X) H4,I4: 7.. / H4 = 7 => 0 pairs (X) / I4 = 7 => 16 pairs (_) C5,F5: 7.. / C5 = 7 => 0 pairs (X) / F5 = 7 => 20 pairs (_) H3,I3: 8.. / H3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) F4,F5: 8.. / F4 = 8 => 20 pairs (_) / F5 = 8 => 0 pairs (X) D8,D9: 8.. / D8 = 8 => 16 pairs (_) / D9 = 8 => 0 pairs (*) C5,F5: 8.. / C5 = 8 => 20 pairs (_) / F5 = 8 => 0 pairs (X) A4,A7: 8.. / A4 = 8 => 0 pairs (X) / A7 = 8 => 21 pairs (_) H1,H3: 9.. / H1 = 9 => 18 pairs (_) / H3 = 9 => 19 pairs (_) E7,F7: 9.. / E7 = 9 => 16 pairs (_) / F7 = 9 => 0 pairs (X) C2,F2: 9.. / C2 = 9 => 17 pairs (_) / F2 = 9 => 19 pairs (_) * DURATION: 0:00:38.189470 START: 23:28:51.089583 END: 23:29:29.279053 2019-04-30 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,C5,C9,D2,D6,D8,E4,F5,F8,G4,G7,I1,I2) * .8.1......2..8.46..6.2..7...4.9.....19.42.635.5..31849.145.....63....9..97...2... * PAIR D2: 3,7 BLK 2 F1: 3,7,4,5,6,9 # reduction candidate for 3,7 F1: 3,7 => CTR * 48.16.5...2.38.461.6124.7.8.4.9561.719.428635.56731849.145932.663.8749..97.6123.4 F1: 4,5,6,9 # 15 pairs F2: 3,7,5,9 # reduction candidate for 3,7 F2: 3,7 => CTR * .8.1....3529.8.46136124.7.88439.....19742.635.5..31849.145....663.8.49..97...2..4 F2: 5,9 # 16 pairs * PAIR D2: 3,7 ROW 2 A2: 3,7,5 # reduction candidate for 3,7 A2: 3,7 # 21 pairs C2: 3,7,1,9 # reduction candidate for 3,7 C2: 3,7 # 20 pairs * PAIR I1: 2,3 BLK 3 G1: 2,3,5 # reduction candidate for 2,3 G1: 2,3 => CTR * .8.1......2..8.46..6.2..7..8439..1..19742.635.5..31849.145.....635...9..978..251. G1: 5 # 17 pairs * PAIR I1: 2,3 COL I I7: 2,3,6,7,8 # reduction candidate for 2,3 I7: 2,3 => CTR * .8.1......2..8.46..6.2..7.8.46958..7198427635.5.631849.145.....63....9.497..42..6 I7: 6,7,8 # 15 pairs * PAIR I2: 1,3 BLK 3 I3: 1,3,8 # reduction candidate for 1,3 I3: 1,3 => SOLVED * 483176592729385461561249783346958127198427635257631849814593276632714958975862314 I3: 8 # 15 pairs * PAIR I2: 1,3 ROW 2 C2: 1,3,7,9 # reduction candidate for 1,3 C2: 1,3 => CTR * .8.1.....52.78946..6.2..7...4.9.....19.427635.5.631849.1459....63.8749..97.3125.. C2: 7,9 # 17 pairs * PAIR I2: 1,3 COL I I9: 1,3,4,6,8 # reduction candidate for 1,3 I9: 1,3 => CTR * .8.176..2.2.38.461.612.47.8.4.965..719742863525..31849.145....663..179.497.642... I9: 4,6,8 # 15 pairs * PAIR A4: 3,8 BLK 4 C4: 3,8,6 # reduction candidate for 3,8 C4: 3,8 => CTR * .8.1765..729385461.612..7...4.9.....1974286352567318498145.3276632817954975642318 C4: 6 # 20 pairs * PAIR A6: 2,7 BLK 4 C6: 2,7,6 # reduction candidate for 2,7 C6: 6 => CTR * .83176592729385461.612..7..3489.....1974286352567318498145.3276632817954975642318 C6: 2,7 # 20 pairs * PAIR E4: 5,6 BLK 5 F4: 5,6,8 # reduction candidate for 5,6 F4: 5,6 => CTR * .8.1..5...2938.461.612..7..3489..127197428635256731849814593276632817954975642318 F4: 8 # 20 pairs * PAIR E4: 5,6 COL E E1: 5,6,4,7,9 # reduction candidate for 5,6 E1: 5,6 => CTR * 48.1..5.2.2138.46..6.24.7.8.4.9..1.719.42.635.5..31849.14593276632874951975612384 E1: 4,7,9 # 16 pairs * PAIR D6: 6,7 ROW 6 C6: 6,7,2 # reduction candidate for 6,7 C6: 2 => CTR * .8.1......2..8.46..6.2..7...46958...198427635752631849.145.....63....9..97...2... C6: 6,7 # 21 pairs * PAIR G4: 1,2 BLK 6 H4: 1,2,7 # reduction candidate for 1,2 H4: 1,2 # 16 pairs I4: 1,2,7 # reduction candidate for 1,2 I4: 1,2 => CTR * .8.1.6....2978.461.612..7.8.46958172198427635.5.63184981457932663.8149.797.362..4 I4: 7 # 16 pairs * PAIR A7: 2,8 BLK 7 C8: 2,8,5 # reduction candidate for 2,8 C8: 5 => CTR * .8.1......2..8.46..6.2..7...4.9.....19.42.635.526318492145..3..635...9..9783.2... C8: 2,8 # 18 pairs * PAIR A7: 2,8 ROW 7 H7: 2,8,7 # reduction candidate for 2,8 H7: 2,8 => CTR * .8.1.6592.2.78.463.6.2.3718346958271198427635257631849814579326632814957975362184 H7: 7 # 17 pairs I7: 2,8,3,6,7 # reduction candidate for 2,8 I7: 2,8 => CTR * .8.1......2..8.46..6.2..7...46958..7198427635.5.631849.145.....63....9.497..42..6 I7: 3,6,7 # 15 pairs * PAIR C9: 5,8 BLK 7 C8: 5,8,2 # reduction candidate for 5,8 C8: 5,8 => CTR * .8.1......2.78.46..6.2..7..84.9.....19.42.635.526318492145..3..63....9..97.3.2... C8: 2 # 21 pairs * PAIR C9: 5,8 ROW 9 H9: 5,8,1 # reduction candidate for 5,8 H9: 5,8 # 19 pairs H9: 1 # 18 pairs * PAIR D8: 7,8 ROW 8 H8: 7,8,1,2,5 # reduction candidate for 7,8 H8: 7,8 => CTR * .8.1....3.2..8.461.612..7.88439....719742.635.5..31849.145.....635...9.2978..2..4 H8: 1,2,5 # 15 pairs I8: 7,8,1,2,4 # reduction candidate for 7,8 I8: 7,8 # 20 pairs * PAIR F8: 4,7 BLK 8 E8: 4,7,1 # reduction candidate for 4,7 E8: 4,7 => CTR * .8.1..5...2.38.461.612..7...4.9..1..19.42.635.56731849.145.32.66328..9..97.6123.4 E8: 1 # 16 pairs * PAIR F8: 4,7 ROW 8 I8: 4,7,1,2,8 # reduction candidate for 4,7 I8: 4,7 # 19 pairs I8: 1,2,8 # 19 pairs * PAIR F8: 4,7 COL F F1: 4,7,3,5,6,9 # reduction candidate for 4,7 F1: 4,7 => CTR * 48.167....2.38.461.6124.7...4.95.1..19742863525673184981459327.63.8.49..97..12..4 F1: 3,5,6,9 # 15 pairs * PAIR G7: 2,3 BLK 9 I7: 2,3,6,7,8 # reduction candidate for 2,3 I7: 2,3 => CTR * .8.1......2..8.46..6.2..7.8.46958..7198427635.5.631849.145.....63....9.497..42..6 I7: 6,7,8 # 15 pairs * PAIR G7: 2,3 COL G G1: 2,3,5 # reduction candidate for 2,3 G1: 2,3 => CTR * .8.1......2..8.46..6.2..7..8439..1..19742.635.5..31849.145.....635...9..978..251. G1: 5 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060529-absurd-base-pr-000.dot * REASONING * DIS # F1: 3,7 => CTR => F1: 4,5,6,9 * DIS # F2: 3,7 => CTR => F2: 5,9 * DIS # G1: 2,3 => CTR => G1: 5 * DIS # I7: 2,3 => CTR => I7: 6,7,8 * PRF # I3: 1,3 => SOL * DIS # C2: 1,3 => CTR => C2: 7,9 * DIS # I9: 1,3 => CTR => I9: 4,6,8 * DIS # C4: 3,8 => CTR => C4: 6 * DIS # C6: 6 => CTR => C6: 2,7 * DIS # F4: 5,6 => CTR => F4: 8 * DIS # E1: 5,6 => CTR => E1: 4,7,9 * DIS # C6: 2 => CTR => C6: 6,7 * DIS # I4: 1,2 => CTR => I4: 7 * DIS # C8: 5 => CTR => C8: 2,8 * DIS # H7: 2,8 => CTR => H7: 7 * DIS # I7: 2,8 => CTR => I7: 3,6,7 * DIS # C8: 5,8 => CTR => C8: 2 * DIS # H8: 7,8 => CTR => H8: 1,2,5 * DIS # E8: 4,7 => CTR => E8: 1 * DIS # F1: 4,7 => CTR => F1: 3,5,6,9 * DIS # I7: 2,3 => CTR => I7: 6,7,8 * DIS # G1: 2,3 => CTR => G1: 5 * CNT 22 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,C5,C9,D2,D6,D8,E4,F5,F8,G4,G7,I1,I2) * .8.1......2..8.46..6.2..7...4.9.....19.42.635.5..31849.145.....63....9..97...2... * PAIR D2: 3,7 BLK 2 F1: 3,7,4,5,6,9 # reduction candidate for 3,7 F1: 3,7 => CTR * 48.16.5...2.38.461.6124.7.8.4.9561.719.428635.56731849.145932.663.8749..97.6123.4 F2: 3,7,5,9 # reduction candidate for 3,7 F2: 3,7 => CTR * .8.1....3529.8.46136124.7.88439.....19742.635.5..31849.145....663.8.49..97...2..4 * RESTART * PAIR D2: 3,7 ROW 2 A2: 3,7,5 # reduction candidate for 3,7 A2: 3,7 # 21 pairs C2: 3,7,1,9 # reduction candidate for 3,7 C2: 3,7 # 21 pairs * PAIR I1: 2,3 BLK 3 G1: 2,3,5 # reduction candidate for 2,3 G1: 2,3 => CTR * .8.1......2..8.46..6.2..7..8439..1..19742.635.5..31849.145.....635...9..978..251. * PAIR I2: 1,3 BLK 3 I3: 1,3,8 # reduction candidate for 1,3 I3: 1,3 => SOLVED * 483176592729385461561249783346958127198427635257631849814593276632714958975862314 * DURATION: 0:00:05.827336 START: 23:29:59.299394 END: 23:30:05.126730 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060529-absurd-base-pr-001.dot * REASONING * DIS # F1: 3,7 => CTR => F1: 4,5,6,9 * DIS F1: 4,5,6,9 # F2: 3,7 => CTR => F2: 5,9 * DIS F1: 4,5,6,9 + F2: 5,9 # G1: 2,3 => CTR => G1: 5 * PRF F1: 4,5,6,9 + F2: 5,9 + G1: 5 # I3: 1,3 => SOL * STA F1: 4,5,6,9 + F2: 5,9 + G1: 5 + I3: 1,3 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060529, absurd
Solution
position: 483176592729385461561249783346958127198427635257631849814593276632714958975862314 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 # F1: 3,7 => CTR => F1: 4,5,6,9 * INC # F1: 4,5,6,9 => UNS * DIS # F2: 3,7 => CTR => F2: 5,9 * INC # F2: 5,9 => UNS * INC # A2: 3,7 => UNS * INC # C2: 3,7 => UNS * DIS # G1: 2,3 => CTR => G1: 5 * INC # G1: 5 => UNS * DIS # I7: 2,3 => CTR => I7: 6,7,8 * INC # I7: 6,7,8 => UNS * PRF # I3: 1,3 => SOL * INC # I3: 8 => UNS * DIS # C2: 1,3 => CTR => C2: 7,9 * INC # C2: 7,9 => UNS * DIS # I9: 1,3 => CTR => I9: 4,6,8 * INC # I9: 4,6,8 => UNS * DIS # C4: 3,8 => CTR => C4: 6 * INC # C4: 6 => UNS * INC # C6: 2,7 => UNS * DIS # C6: 6 => CTR => C6: 2,7 * DIS # F4: 5,6 => CTR => F4: 8 * INC # F4: 8 => UNS * DIS # E1: 5,6 => CTR => E1: 4,7,9 * INC # E1: 4,7,9 => UNS * INC # C6: 6,7 => UNS * DIS # C6: 2 => CTR => C6: 6,7 * INC # H4: 1,2 => UNS * DIS # I4: 1,2 => CTR => I4: 7 * INC # I4: 7 => UNS * INC # C8: 2,8 => UNS * DIS # C8: 5 => CTR => C8: 2,8 * DIS # H7: 2,8 => CTR => H7: 7 * INC # H7: 7 => UNS * DIS # I7: 2,8 => CTR => I7: 3,6,7 * INC # I7: 3,6,7 => UNS * DIS # C8: 5,8 => CTR => C8: 2 * INC # C8: 2 => UNS * INC # H9: 5,8 => UNS * INC # H9: 1 => UNS * DIS # H8: 7,8 => CTR => H8: 1,2,5 * INC # H8: 1,2,5 => UNS * INC # I8: 7,8 => UNS * DIS # E8: 4,7 => CTR => E8: 1 * INC # E8: 1 => UNS * INC # I8: 4,7 => UNS * INC # I8: 1,2,8 => UNS * DIS # F1: 4,7 => CTR => F1: 3,5,6,9 * INC # F1: 3,5,6,9 => UNS * DIS # I7: 2,3 => CTR => I7: 6,7,8 * INC # I7: 6,7,8 => UNS * DIS # G1: 2,3 => CTR => G1: 5 * INC # G1: 5 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F1: 3,7 => CTR => F1: 4,5,6,9 * DIS F1: 4,5,6,9 # F2: 3,7 => CTR => F2: 5,9 * INC F1: 4,5,6,9 + F2: 5,9 # A2: 3,7 => UNS * INC F1: 4,5,6,9 + F2: 5,9 # C2: 3,7 => UNS * DIS F1: 4,5,6,9 + F2: 5,9 # G1: 2,3 => CTR => G1: 5 * PRF F1: 4,5,6,9 + F2: 5,9 + G1: 5 # I3: 1,3 => SOL * STA F1: 4,5,6,9 + F2: 5,9 + G1: 5 + I3: 1,3 * CNT 6 HDP CHAINS / 6 HYP OPENED