Analysis of xx-top500-091-base.sdk
Contents
Original Sudoku
level: medium
position: .4..1..........3.........7...35.2...6......1....7....43.....7...16.........8..5.. initial
Autosolve
position: 74.613.5..61...34..3.4..1761.35426.76743..215...761.343..1.476..16...4.34.78365.1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 2,9 => CTR => E2: 5,7,8 * DIS # A2: 2,9 => CTR => A2: 5,8 * PRF # I1: 8,9 => SOL * PRF # C1: 2 => SOL * DIS # B6: 8,9 => CTR => B6: 2,5 * DIS # B7: 8,9 => CTR => B7: 2,5 * PRF # H8: 8,9 => SOL * DIS # H8: 2 => CTR => H8: 8,9 * DIS # B6: 8,9 => CTR => B6: 2,5 * PRF # B7: 2,9 => SOL * DIS # A8: 2,9 => CTR => A8: 5,8 * DIS # B6: 2,9 => CTR => B6: 5,8 * PRF # E8: 2,9 => SOL * DIS # A8: 2,9 => CTR => A8: 5,8 * DIS # H8: 2,9 => CTR => H8: 8 * PRF # H8: 8 => SOL * PRF # H8: 8,9 => SOL * DIS # H8: 2 => CTR => H8: 8,9 * DIS # B7: 8,9 => CTR => B7: 2,5 * PRF # I1: 8,9 => SOL * DIS # H8: 2,9 => CTR => H8: 8 * PRF # H8: 8 => SOL * CNT 22 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 # E2: 2,9 => CTR => E2: 5,7,8 * DIS E2: 5,7,8 # A2: 2,9 => CTR => A2: 5,8 * DIS E2: 5,7,8 + A2: 5,8 # I2: 8 => CTR => I2: 2,9 * DIS E2: 5,7,8 + A2: 5,8 + I2: 2,9 # E3: 5,8 => CTR => E3: 2,9 * PRF E2: 5,7,8 + A2: 5,8 + I2: 2,9 + E3: 2,9 # I1: 8,9 => SOL * STA E2: 5,7,8 + A2: 5,8 + I2: 2,9 + E3: 2,9 + I1: 8,9 * CNT 5 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4..1..........3.........7...35.2...6......1....7....43.....7...16.........8..5.. | initial |
| 74.613.5..61...34..3.4..1761.35426.76743..215...761.343..1.476..16...4.34.78365.1 | autosolve |
| 742613958861975342935428176183542697674389215259761834328154769516297483497836521 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) D2: 2,9 G1: 8,9 B4: 8,9 E5: 8,9 F5: 8,9 H4: 8,9 G6: 8,9 B9: 2,9 D8: 2,9 I7: 8,9 H9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,I2: 2.. / I1 = 2 => 13 pairs (_) / I2 = 2 => 0 pairs (*) H8,H9: 2.. / H8 = 2 => 0 pairs (X) / H9 = 2 => 0 pairs (_) C1,I1: 2.. / C1 = 2 => 0 pairs (*) / I1 = 2 => 0 pairs (X) B9,H9: 2.. / B9 = 2 => 0 pairs (X) / H9 = 2 => 0 pairs (_) D2,D8: 2.. / D2 = 2 => 14 pairs (_) / D8 = 2 => 0 pairs (*) B6,B7: 5.. / B6 = 5 => 11 pairs (_) / B7 = 5 => 14 pairs (_) E2,F2: 7.. / E2 = 7 => 11 pairs (_) / F2 = 7 => 12 pairs (_) E8,F8: 7.. / E8 = 7 => 12 pairs (_) / F8 = 7 => 11 pairs (_) E2,E8: 7.. / E2 = 7 => 11 pairs (_) / E8 = 7 => 12 pairs (_) F2,F8: 7.. / F2 = 7 => 12 pairs (_) / F8 = 7 => 11 pairs (_) E5,F5: 8.. / E5 = 8 => 11 pairs (_) / F5 = 8 => 12 pairs (_) H4,G6: 8.. / H4 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) I7,H8: 8.. / I7 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) B4,H4: 8.. / B4 = 8 => 0 pairs (*) / H4 = 8 => 0 pairs (X) A8,H8: 8.. / A8 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) G1,G6: 8.. / G1 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) H4,H8: 8.. / H4 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) E5,F5: 9.. / E5 = 9 => 12 pairs (_) / F5 = 9 => 11 pairs (_) H4,G6: 9.. / H4 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) B4,H4: 9.. / B4 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) B9,H9: 9.. / B9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) D2,D8: 9.. / D2 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) G1,G6: 9.. / G1 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) * DURATION: 0:00:39.571521 START: 05:53:25.962712 END: 05:54:05.534233 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B9,D2,D8,E5,F5,G1,G6,H4,H9,I7) * 74.613.5..61...34..3.4..1761.35426.76743..215...761.343..1.476..16...4.34.78365.1 * PAIR D2: 2,9 BLK 2 E2: 2,9,5,7,8 # reduction candidate for 2,9 E2: 2,9 => CTR * 748613952561..7348.3.458176183542697674389215...7618343..124769216975483497836521 E2: 5,7,8 # 11 pairs E3: 2,9,5,8 # reduction candidate for 2,9 E3: 2,9 # 13 pairs * PAIR D2: 2,9 ROW 2 A2: 2,9,5,8 # reduction candidate for 2,9 A2: 2,9 => CTR * 748613952.61...348.3.4..1761835426976743..215...7618343..1.4769.16...483497836521 A2: 5,8 # 12 pairs I2: 2,9,8 # reduction candidate for 2,9 I2: 2,9 # 14 pairs * PAIR G1: 8,9 BLK 3 I1: 8,9,2 # reduction candidate for 8,9 I1: 8,9 => SOLVED * 742613958861975342935428176183542697674389215259761834328154769516297483497836521 I1: 2 # 13 pairs I2: 8,9,2 # reduction candidate for 8,9 I2: 8,9 # 13 pairs * PAIR G1: 8,9 ROW 1 C1: 8,9,2 # reduction candidate for 8,9 C1: 2 => SOLVED * 742613958861975342935428176183542697674389215259761834328154769516297483497836521 C1: 8,9 # 13 pairs * PAIR B4: 8,9 BLK 4 A6: 8,9,2,5 # reduction candidate for 8,9 A6: 8,9 # 14 pairs B6: 8,9,2,5 # reduction candidate for 8,9 B6: 8,9 => CTR * 74.61385..612..34993.4..1761935426876743..215.8.76193435.1247688169..423427836591 B6: 2,5 # 12 pairs C6: 8,9,2,5 # reduction candidate for 8,9 C6: 8,9 # 14 pairs * PAIR B4: 8,9 COL B B7: 8,9,2,5 # reduction candidate for 8,9 B7: 8,9 => CTR * 74.613.5..61...34..3.4..1761935426876743..215.5.76193438.1.476..16...4.3427836591 B7: 2,5 # 12 pairs * PAIR E5: 8,9 COL E E2: 8,9,2,5,7 # reduction candidate for 8,9 E2: 8,9 # 15 pairs E3: 8,9,2,5 # reduction candidate for 8,9 E3: 8,9 # 16 pairs * PAIR F5: 8,9 COL F F2: 8,9,5,7 # reduction candidate for 8,9 F2: 8,9 # 13 pairs F3: 8,9,5 # reduction candidate for 8,9 F3: 8,9 # 14 pairs * PAIR H4: 8,9 COL H H8: 8,9,2 # reduction candidate for 8,9 H8: 8,9 => SOLVED * 742613958861975342935428176183542697674389215259761834328154769516297483497836521 H8: 2 => CTR * 74.61385..612..34993.4..1761.35426876743..215...7619343..1.4768816...423427836591 * PAIR G6: 8,9 ROW 6 A6: 8,9,2,5 # reduction candidate for 8,9 A6: 8,9 # 14 pairs B6: 8,9,2,5 # reduction candidate for 8,9 B6: 8,9 => CTR * 74.61385..612..34993.4..1761935426876743..215.8.76193435.1247688169..423427836591 B6: 2,5 # 12 pairs C6: 8,9,2,5 # reduction candidate for 8,9 C6: 8,9 # 14 pairs * PAIR B9: 2,9 BLK 7 B7: 2,9,5,8 # reduction candidate for 2,9 B7: 2,9 => SOLVED * 742613958861975342935428176183542697674389215259761834328154769516297483497836521 B7: 5,8 # 12 pairs C7: 2,9,5,8 # reduction candidate for 2,9 C7: 2,9 # 14 pairs A8: 2,9,5,8 # reduction candidate for 2,9 A8: 2,9 => CTR * 74.613958.61...342.3.42.1761835426976743..215...7618343.81.4769.16...483497836521 A8: 5,8 # 12 pairs * PAIR B9: 2,9 COL B B6: 2,9,5,8 # reduction candidate for 2,9 B6: 2,9 => CTR * 742613958.612..34..3.4..1761835426976743..215.2.7618343581247692169..483497836521 B6: 5,8 # 12 pairs * PAIR D8: 2,9 BLK 8 E7: 2,9,5 # reduction candidate for 2,9 E7: 2,9 # 14 pairs E8: 2,9,5,7 # reduction candidate for 2,9 E8: 2,9 => SOLVED * 742613958861975342935428176183542697674389215259761834328154769516297483497836521 E8: 5,7 # 12 pairs * PAIR D8: 2,9 ROW 8 A8: 2,9,5,8 # reduction candidate for 2,9 A8: 2,9 => CTR * 74.613958.61...342.3.42.1761835426976743..215...7618343.81.4769.16...483497836521 A8: 5,8 # 12 pairs H8: 2,9,8 # reduction candidate for 2,9 H8: 2,9 => CTR * 742613859.612..34..384..1761935426876743..215.8.7619343591247688169..423427836591 H8: 8 => SOLVED * 742613958861975342935428176183542697674389215259761834328154769516297483497836521 * PAIR I7: 8,9 BLK 9 H8: 8,9,2 # reduction candidate for 8,9 H8: 8,9 => SOLVED * 742613958861975342935428176183542697674389215259761834328154769516297483497836521 H8: 2 => CTR * 74.61385..612..34993.4..1761.35426876743..215...7619343..1.4768816...423427836591 * PAIR I7: 8,9 ROW 7 B7: 8,9,2,5 # reduction candidate for 8,9 B7: 8,9 => CTR * 74.613.5..61...34..3.4..1761935426876743..215.5.76193438.1.476..16...4.3427836591 B7: 2,5 # 12 pairs C7: 8,9,2,5 # reduction candidate for 8,9 C7: 8,9 # 15 pairs * PAIR I7: 8,9 COL I I1: 8,9,2 # reduction candidate for 8,9 I1: 8,9 => SOLVED * 742613958861975342935428176183542697674389215259761834328154769516297483497836521 I1: 2 # 13 pairs I2: 8,9,2 # reduction candidate for 8,9 I2: 8,9 # 13 pairs * PAIR H9: 2,9 BLK 9 H8: 2,9,8 # reduction candidate for 2,9 H8: 2,9 => CTR * 742613859.612..34..384..1761935426876743..215.8.7619343591247688169..423427836591 H8: 8 => SOLVED * 742613958861975342935428176183542697674389215259761834328154769516297483497836521 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-091-base-pr-000.dot * REASONING * DIS # E2: 2,9 => CTR => E2: 5,7,8 * DIS # A2: 2,9 => CTR => A2: 5,8 * PRF # I1: 8,9 => SOL * PRF # C1: 2 => SOL * DIS # B6: 8,9 => CTR => B6: 2,5 * DIS # B7: 8,9 => CTR => B7: 2,5 * PRF # H8: 8,9 => SOL * DIS # H8: 2 => CTR => H8: 8,9 * DIS # B6: 8,9 => CTR => B6: 2,5 * PRF # B7: 2,9 => SOL * DIS # A8: 2,9 => CTR => A8: 5,8 * DIS # B6: 2,9 => CTR => B6: 5,8 * PRF # E8: 2,9 => SOL * DIS # A8: 2,9 => CTR => A8: 5,8 * DIS # H8: 2,9 => CTR => H8: 8 * PRF # H8: 8 => SOL * PRF # H8: 8,9 => SOL * DIS # H8: 2 => CTR => H8: 8,9 * DIS # B7: 8,9 => CTR => B7: 2,5 * PRF # I1: 8,9 => SOL * DIS # H8: 2,9 => CTR => H8: 8 * PRF # H8: 8 => SOL * CNT 22 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B9,D2,D8,E5,F5,G1,G6,H4,H9,I7) * 74.613.5..61...34..3.4..1761.35426.76743..215...761.343..1.476..16...4.34.78365.1 * PAIR D2: 2,9 BLK 2 E2: 2,9,5,7,8 # reduction candidate for 2,9 E2: 2,9 => CTR * 748613952561..7348.3.458176183542697674389215...7618343..124769216975483497836521 E3: 2,9,5,8 # reduction candidate for 2,9 E3: 2,9 # 13 pairs * RESTART * PAIR D2: 2,9 BLK 2 E3: 2,9,5,8 # reduction candidate for 2,9 E3: 5,8 # 14 pairs E3: 2,9 # 13 pairs * PAIR D2: 2,9 ROW 2 A2: 2,9,5,8 # reduction candidate for 2,9 A2: 2,9 => CTR * 748613952.61...348.3.4..1761835426976743..215...7618343..1.4769.16...483497836521 I2: 2,9,8 # reduction candidate for 2,9 I2: 2,9 # 14 pairs * RESTART * PAIR D2: 2,9 ROW 2 I2: 2,9,8 # reduction candidate for 2,9 I2: 8 => CTR * 748613952561279348.3.485176183542697674398215...7618343..1.4769216957483497836521 * PAIR RESTART * PAIR D2: 2,9 BLK 2 E3: 2,9,5,8 # reduction candidate for 2,9 E3: 5,8 => CTR * 74.613.5..612..349.3.4.91761.35426.7674398215...7619343..1.4768.16...4.34.78365.1 * PAIR G1: 8,9 BLK 3 I1: 8,9,2 # reduction candidate for 8,9 I1: 8,9 => SOLVED * 742613958861975342935428176183542697674389215259761834328154769516297483497836521 * DURATION: 0:00:11.643642 START: 05:54:53.091733 END: 05:55:04.735375 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-091-base-pr-001.dot * REASONING * DIS # E2: 2,9 => CTR => E2: 5,7,8 * DIS E2: 5,7,8 # A2: 2,9 => CTR => A2: 5,8 * DIS E2: 5,7,8 + A2: 5,8 # I2: 8 => CTR => I2: 2,9 * DIS E2: 5,7,8 + A2: 5,8 + I2: 2,9 # E3: 5,8 => CTR => E3: 2,9 * PRF E2: 5,7,8 + A2: 5,8 + I2: 2,9 + E3: 2,9 # I1: 8,9 => SOL * STA E2: 5,7,8 + A2: 5,8 + I2: 2,9 + E3: 2,9 + I1: 8,9 * CNT 5 HDP CHAINS / 11 HYP OPENED
Header Info
Top 500 Minimum 17 091 solution: 742613958861975342935428176183542697674389215259761834328154769516297483497836521 info: 1566 FNBTWXY S8.f 45336 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 742613958861975342935428176183542697674389215259761834328154769516297483497836521 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 # E2: 2,9 => CTR => E2: 5,7,8 * INC # E2: 5,7,8 => UNS * INC # E3: 2,9 => UNS * DIS # A2: 2,9 => CTR => A2: 5,8 * INC # A2: 5,8 => UNS * INC # I2: 2,9 => UNS * PRF # I1: 8,9 => SOL * INC # I1: 2 => UNS * INC # I2: 8,9 => UNS * INC # C1: 8,9 => UNS * PRF # C1: 2 => SOL * INC # A6: 8,9 => UNS * DIS # B6: 8,9 => CTR => B6: 2,5 * INC # B6: 2,5 => UNS * INC # C6: 8,9 => UNS * DIS # B7: 8,9 => CTR => B7: 2,5 * INC # B7: 2,5 => UNS * INC # E2: 8,9 => UNS * INC # E3: 8,9 => UNS * INC # F2: 8,9 => UNS * INC # F3: 8,9 => UNS * PRF # H8: 8,9 => SOL * DIS # H8: 2 => CTR => H8: 8,9 * INC # A6: 8,9 => UNS * DIS # B6: 8,9 => CTR => B6: 2,5 * INC # B6: 2,5 => UNS * INC # C6: 8,9 => UNS * PRF # B7: 2,9 => SOL * INC # B7: 5,8 => UNS * INC # C7: 2,9 => UNS * DIS # A8: 2,9 => CTR => A8: 5,8 * INC # A8: 5,8 => UNS * DIS # B6: 2,9 => CTR => B6: 5,8 * INC # B6: 5,8 => UNS * INC # E7: 2,9 => UNS * PRF # E8: 2,9 => SOL * INC # E8: 5,7 => UNS * DIS # A8: 2,9 => CTR => A8: 5,8 * INC # A8: 5,8 => UNS * DIS # H8: 2,9 => CTR => H8: 8 * PRF # H8: 8 => SOL * PRF # H8: 8,9 => SOL * DIS # H8: 2 => CTR => H8: 8,9 * DIS # B7: 8,9 => CTR => B7: 2,5 * INC # B7: 2,5 => UNS * INC # C7: 8,9 => UNS * PRF # I1: 8,9 => SOL * INC # I1: 2 => UNS * INC # I2: 8,9 => UNS * DIS # H8: 2,9 => CTR => H8: 8 * PRF # H8: 8 => SOL * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E2: 2,9 => CTR => E2: 5,7,8 * INC E2: 5,7,8 # E3: 2,9 => UNS * INC E2: 5,7,8 # E3: 2,9 => UNS * INC E2: 5,7,8 # E3: 5,8 => UNS * DIS E2: 5,7,8 # A2: 2,9 => CTR => A2: 5,8 * INC E2: 5,7,8 + A2: 5,8 # I2: 2,9 => UNS * INC E2: 5,7,8 + A2: 5,8 # I2: 2,9 => UNS * DIS E2: 5,7,8 + A2: 5,8 # I2: 8 => CTR => I2: 2,9 * INC E2: 5,7,8 + A2: 5,8 + I2: 2,9 # E3: 2,9 => UNS * DIS E2: 5,7,8 + A2: 5,8 + I2: 2,9 # E3: 5,8 => CTR => E3: 2,9 * PRF E2: 5,7,8 + A2: 5,8 + I2: 2,9 + E3: 2,9 # I1: 8,9 => SOL * STA E2: 5,7,8 + A2: 5,8 + I2: 2,9 + E3: 2,9 + I1: 8,9 * CNT 11 HDP CHAINS / 11 HYP OPENED