Analysis of xx-top500-252-base.sdk
Contents
Original Sudoku
level: medium
position: ....2..346.1................4.53....7.....6.........8....6.75...3......7...1..... initial
Autosolve
position: .7..261346.1345...3.4.71.56846539..17532186492197643854.26.751313.4.2.67.671.34.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 8,9 => CTR => B3: 2 * DIS # G2: 2,8 => CTR => G2: 7,9 * DIS # B2: 9 => CTR => B2: 2,8 * DIS # G2: 8,9 => CTR => G2: 2,7 * DIS # H2: 2,7 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # B3: 8,9 => CTR => B3: 2 * PRF # E8: 5,8 => SOL * DIS # E8: 9 => CTR => E8: 5,8 * PRF # E9: 5,9 => SOL * DIS # E9: 8 => CTR => E9: 5,9 * DIS # E8: 8,9 => CTR => E8: 5 * PRF # E8: 5 => SOL * PRF # E9: 8,9 => SOL * DIS # E9: 5 => CTR => E9: 8,9 * DIS # E8: 8,9 => CTR => E8: 5 * PRF # E8: 5 => SOL * DIS # G2: 8,9 => CTR => G2: 2,7 * DIS # H2: 7 => CTR => H2: 2,9 * CNT 19 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 8,9 => CTR => B3: 2 * DIS B3: 2 # H2: 2,7 => CTR => H2: 9 * PRF B3: 2 + H2: 9 => SOL * STA B3: 2 + H2: 9 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....2..346.1................4.53....7.....6.........8....6.75...3......7...1..... | initial |
| .7..261346.1345...3.4.71.56846539..17532186492197643854.26.751313.4.2.67.671.34.. | autosolve |
| 975826134681345792324971856846539271753218649219764385492687513138452967567193428 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A1: 5,9 C1: 5,8 D1: 8,9 D3: 8,9 I2: 2,8 G4: 2,7 H4: 2,7 B7: 8,9 C8: 5,8 A9: 5,9 E7: 8,9 G8: 8,9 H9: 2,9 I9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 2.. / B2 = 2 => 0 pairs (X) / B3 = 2 => 17 pairs (_) G4,H4: 2.. / G4 = 2 => 15 pairs (_) / H4 = 2 => 0 pairs (X) H9,I9: 2.. / H9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) B3,G3: 2.. / B3 = 2 => 17 pairs (_) / G3 = 2 => 0 pairs (X) I2,I9: 2.. / I2 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) A1,C1: 5.. / A1 = 5 => 0 pairs (X) / C1 = 5 => 0 pairs (_) C8,A9: 5.. / C8 = 5 => 0 pairs (X) / A9 = 5 => 0 pairs (_) E8,E9: 5.. / E8 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) C8,E8: 5.. / C8 = 5 => 0 pairs (X) / E8 = 5 => 0 pairs (_) A9,E9: 5.. / A9 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) A1,A9: 5.. / A1 = 5 => 0 pairs (X) / A9 = 5 => 0 pairs (_) C1,C8: 5.. / C1 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) G2,H2: 7.. / G2 = 7 => 15 pairs (_) / H2 = 7 => 0 pairs (X) G4,H4: 7.. / G4 = 7 => 0 pairs (X) / H4 = 7 => 15 pairs (_) G2,G4: 7.. / G2 = 7 => 15 pairs (_) / G4 = 7 => 0 pairs (X) H2,H4: 7.. / H2 = 7 => 0 pairs (X) / H4 = 7 => 15 pairs (_) D1,D3: 8.. / D1 = 8 => 0 pairs (*) / D3 = 8 => 0 pairs (X) B7,C8: 8.. / B7 = 8 => 0 pairs (X) / C8 = 8 => 0 pairs (_) G8,I9: 8.. / G8 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) C1,D1: 8.. / C1 = 8 => 0 pairs (X) / D1 = 8 => 0 pairs (_) B7,E7: 8.. / B7 = 8 => 0 pairs (X) / E7 = 8 => 0 pairs (_) E9,I9: 8.. / E9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) C1,C8: 8.. / C1 = 8 => 0 pairs (X) / C8 = 8 => 0 pairs (_) I2,I9: 8.. / I2 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) D1,D3: 9.. / D1 = 9 => 0 pairs (X) / D3 = 9 => 0 pairs (_) B7,A9: 9.. / B7 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) G8,H9: 9.. / G8 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) A1,D1: 9.. / A1 = 9 => 0 pairs (*) / D1 = 9 => 0 pairs (X) B7,E7: 9.. / B7 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) E8,G8: 9.. / E8 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) A1,A9: 9.. / A1 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) H2,H9: 9.. / H2 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) * DURATION: 0:00:56.540752 START: 11:24:07.267833 END: 11:25:03.808585 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A9,B7,C1,C8,D1,D3,E7,G4,G8,H4,H9,I2,I9) * .7..261346.1345...3.4.71.56846539..17532186492197643854.26.751313.4.2.67.671.34.. * PAIR D3: 8,9 ROW 3 B3: 8,9,2 # reduction candidate for 8,9 B3: 8,9 => CTR * .7..26134621345..83.4.712568465397217532186492197643854.26.751313.4.2867.67183492 B3: 2 # 17 pairs G3: 8,9,2 # reduction candidate for 8,9 G3: 8,9 # 17 pairs * PAIR I2: 2,8 BLK 3 G2: 2,8,7,9 # reduction candidate for 2,8 G2: 2,8 => CTR * .7..261346.1345.7.3.4.719568465397217532186492197643854.26.751313.492867.671.34.. G2: 7,9 # 15 pairs G3: 2,8,9 # reduction candidate for 2,8 G3: 2,8 # 18 pairs * PAIR I2: 2,8 ROW 2 B2: 2,8,9 # reduction candidate for 2,8 B2: 9 => CTR * .7..26134691345...324.71956846539..1753218649219764385482697513135482.67.671.34.. B2: 2,8 # 18 pairs * PAIR G4: 2,7 COL G G2: 2,7,8,9 # reduction candidate for 2,7 G2: 8,9 => CTR * 97582613462134597838497125684653972175321864921976438549268751313.4.2.67.671.3492 G2: 2,7 # 17 pairs * PAIR H4: 2,7 COL H H2: 2,7,9 # reduction candidate for 2,7 H2: 2,7 => CTR * 9758261346.134597838497125684653972175321864921976438549268751313.4.2.67.671.3492 H2: 9 => SOLVED * 975826134681345792324971856846539271753218649219764385492687513138452967567193428 * PAIR B7: 8,9 COL B B2: 8,9,2 # reduction candidate for 8,9 B2: 8,9 # 17 pairs B3: 8,9,2 # reduction candidate for 8,9 B3: 8,9 => CTR * .7..26134621345..83.4.712568465397217532186492197643854.26.751313.4.2867.67183492 B3: 2 # 17 pairs * PAIR C8: 5,8 ROW 8 E8: 5,8,9 # reduction candidate for 5,8 E8: 5,8 => SOLVED * 975826134681345792324971856846539271753218649219764385492687513138452967567193428 E8: 9 => CTR * .7..261346.1345...3.4.71.56846539..17532186492197643854.26.75131354928679671.34.. * PAIR A9: 5,9 ROW 9 E9: 5,9,8 # reduction candidate for 5,9 E9: 5,9 => SOLVED * 975826134681345792324971856846539271753218649219764385492687513138452967567193428 E9: 8 => CTR * .7..261346.1345...3.4.71.56846539..17532186492197643854.26.751313.452967.671.34.. * PAIR E7: 8,9 BLK 8 E8: 8,9,5 # reduction candidate for 8,9 E8: 8,9 => CTR * 5789261346.13458..3.4.71.56846539..17532186492197643854.26.75131354.2.67967153428 E8: 5 => SOLVED * 975826134681345792324971856846539271753218649219764385492687513138452967567193428 E9: 8,9,5 # reduction candidate for 8,9 E9: 8,9 => SOLVED * 975826134681345792324971856846539271753218649219764385492687513138452967567193428 E9: 5 => CTR * 5789261346.1345872324871956846539..17532186492197643854.26.751313.4.2.67.671534.8 * PAIR G8: 8,9 ROW 8 E8: 8,9,5 # reduction candidate for 8,9 E8: 8,9 => CTR * 5789261346.13458..3.4.71.56846539..17532186492197643854.26.75131354.2.67967153428 E8: 5 => SOLVED * 975826134681345792324971856846539271753218649219764385492687513138452967567193428 * PAIR G8: 8,9 COL G G2: 8,9,2,7 # reduction candidate for 8,9 G2: 8,9 => CTR * 97582613462134597838497125684653972175321864921976438549268751313.4.2.67.671.3492 G2: 2,7 # 17 pairs G3: 8,9,2 # reduction candidate for 8,9 G3: 8,9 # 17 pairs * PAIR H9: 2,9 COL H H2: 2,9,7 # reduction candidate for 2,9 H2: 7 => CTR * 9758261346.134597838497125684653972175321864921976438549268751313.4.2.67.671.3492 H2: 2,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-252-base-pr-000.dot * REASONING * DIS # B3: 8,9 => CTR => B3: 2 * DIS # G2: 2,8 => CTR => G2: 7,9 * DIS # B2: 9 => CTR => B2: 2,8 * DIS # G2: 8,9 => CTR => G2: 2,7 * DIS # H2: 2,7 => CTR => H2: 9 * PRF # H2: 9 => SOL * DIS # B3: 8,9 => CTR => B3: 2 * PRF # E8: 5,8 => SOL * DIS # E8: 9 => CTR => E8: 5,8 * PRF # E9: 5,9 => SOL * DIS # E9: 8 => CTR => E9: 5,9 * DIS # E8: 8,9 => CTR => E8: 5 * PRF # E8: 5 => SOL * PRF # E9: 8,9 => SOL * DIS # E9: 5 => CTR => E9: 8,9 * DIS # E8: 8,9 => CTR => E8: 5 * PRF # E8: 5 => SOL * DIS # G2: 8,9 => CTR => G2: 2,7 * DIS # H2: 7 => CTR => H2: 2,9 * CNT 19 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A9,B7,C1,C8,D1,D3,E7,G4,G8,H4,H9,I2,I9) * .7..261346.1345...3.4.71.56846539..17532186492197643854.26.751313.4.2.67.671.34.. * PAIR D3: 8,9 ROW 3 B3: 8,9,2 # reduction candidate for 8,9 B3: 8,9 => CTR * .7..26134621345..83.4.712568465397217532186492197643854.26.751313.4.2867.67183492 * RESTART * PAIR RESTART * PAIR H4: 2,7 COL H H2: 2,7,9 # reduction candidate for 2,7 H2: 2,7 => CTR * .7..26134691345..8324871956846539..1753218649219764385482697513135482.67.671.34.. H2: 9 => SOLVED * 975826134681345792324971856846539271753218649219764385492687513138452967567193428 * DURATION: 0:00:04.315436 START: 11:25:35.910716 END: 11:25:40.226152 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-252-base-pr-001.dot * REASONING * DIS # B3: 8,9 => CTR => B3: 2 * DIS B3: 2 # H2: 2,7 => CTR => H2: 9 * PRF B3: 2 + H2: 9 => SOL * STA B3: 2 + H2: 9 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 252 solution: 975826134681345792324971856846539271753218649219764385492687513138452967567193428 info: 2075 FNBTWXY S8.f 3198 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 975826134681345792324971856846539271753218649219764385492687513138452967567193428 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 # B3: 8,9 => CTR => B3: 2 * INC # B3: 2 => UNS * INC # G3: 8,9 => UNS * DIS # G2: 2,8 => CTR => G2: 7,9 * INC # G2: 7,9 => UNS * INC # G3: 2,8 => UNS * INC # B2: 2,8 => UNS * DIS # B2: 9 => CTR => B2: 2,8 * INC # G2: 2,7 => UNS * DIS # G2: 8,9 => CTR => G2: 2,7 * DIS # H2: 2,7 => CTR => H2: 9 * PRF # H2: 9 => SOL * INC # B2: 8,9 => UNS * DIS # B3: 8,9 => CTR => B3: 2 * INC # B3: 2 => UNS * PRF # E8: 5,8 => SOL * DIS # E8: 9 => CTR => E8: 5,8 * PRF # E9: 5,9 => SOL * DIS # E9: 8 => CTR => E9: 5,9 * DIS # E8: 8,9 => CTR => E8: 5 * PRF # E8: 5 => SOL * PRF # E9: 8,9 => SOL * DIS # E9: 5 => CTR => E9: 8,9 * DIS # E8: 8,9 => CTR => E8: 5 * PRF # E8: 5 => SOL * DIS # G2: 8,9 => CTR => G2: 2,7 * INC # G2: 2,7 => UNS * INC # G3: 8,9 => UNS * INC # H2: 2,9 => UNS * DIS # H2: 7 => CTR => H2: 2,9 * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 8,9 => CTR => B3: 2 * DIS B3: 2 # H2: 2,7 => CTR => H2: 9 * PRF B3: 2 + H2: 9 => SOL * STA B3: 2 + H2: 9 * CNT 3 HDP CHAINS / 2 HYP OPENED