Analysis of xx-top500-082-base.sdk
Contents
Original Sudoku
level: medium
position: 7.48.....1.....5............3..562.......2..1..8......25.....9....41............. initial
Autosolve
position: 7.48.5.121.2.475..3.52.14..931756248.47.82..1.281.47..25367819487.41..2541.52.8.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 6,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 3 => CTR => G1: 6,9 * DIS # E1: 6 => CTR => E1: 3,9 * DIS # E1: 6,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * DIS # H5: 3 => CTR => H5: 5,6 * PRF # H6: 3 => SOL * DIS # G5: 6 => CTR => G5: 3,9 * PRF # I6: 6 => SOL * DIS # E1: 6 => CTR => E1: 3,9 * PRF # G1: 3,6 => SOL * DIS # G1: 9 => CTR => G1: 3,6 * DIS # G5: 3,6 => CTR => G5: 9 * PRF # G5: 9 => SOL * CNT 16 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 # E1: 6,9 => CTR => E1: 3 * PRF E1: 3 => SOL * STA E1: 3 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7.48.....1.....5............3..562.......2..1..8......25.....9....41............. | initial |
| 7.48.5.121.2.475..3.52.14..931756248.47.82..1.281.47..25367819487.41..2541.52.8.. | autosolve |
| 794835612162947583385261479931756248647382951528194736253678194876419325419523867 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B1: 6,9 D2: 3,9 E3: 6,9 A5: 5,6 A6: 5,6 D5: 3,9 E6: 3,9 C8: 6,9 C9: 6,9 F8: 3,9 F9: 3,9 G8: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,D2: 3.. / E1 = 3 => 0 pairs (*) / D2 = 3 => 0 pairs (X) D5,E6: 3.. / D5 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) F8,F9: 3.. / F8 = 3 => 12 pairs (_) / F9 = 3 => 0 pairs (*) E1,G1: 3.. / E1 = 3 => 0 pairs (*) / G1 = 3 => 0 pairs (X) F8,G8: 3.. / F8 = 3 => 12 pairs (_) / G8 = 3 => 0 pairs (*) D2,D5: 3.. / D2 = 3 => 0 pairs (X) / D5 = 3 => 0 pairs (_) E1,E6: 3.. / E1 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) A5,A6: 5.. / A5 = 5 => 12 pairs (_) / A6 = 5 => 12 pairs (_) H5,H6: 5.. / H5 = 5 => 12 pairs (_) / H6 = 5 => 12 pairs (_) A5,H5: 5.. / A5 = 5 => 12 pairs (_) / H5 = 5 => 12 pairs (_) A6,H6: 5.. / A6 = 5 => 12 pairs (_) / H6 = 5 => 12 pairs (_) E1,E3: 6.. / E1 = 6 => 0 pairs (X) / E3 = 6 => 15 pairs (_) A5,A6: 6.. / A5 = 6 => 12 pairs (_) / A6 = 6 => 12 pairs (_) C8,C9: 6.. / C8 = 6 => 0 pairs (*) / C9 = 6 => 0 pairs (X) C8,G8: 6.. / C8 = 6 => 0 pairs (*) / G8 = 6 => 0 pairs (X) H3,I3: 7.. / H3 = 7 => 15 pairs (_) / I3 = 7 => 14 pairs (_) H9,I9: 7.. / H9 = 7 => 14 pairs (_) / I9 = 7 => 15 pairs (_) H3,H9: 7.. / H3 = 7 => 15 pairs (_) / H9 = 7 => 14 pairs (_) I3,I9: 7.. / I3 = 7 => 14 pairs (_) / I9 = 7 => 15 pairs (_) B2,B3: 8.. / B2 = 8 => 16 pairs (_) / B3 = 8 => 14 pairs (_) H2,H3: 8.. / H2 = 8 => 14 pairs (_) / H3 = 8 => 16 pairs (_) B2,H2: 8.. / B2 = 8 => 16 pairs (_) / H2 = 8 => 14 pairs (_) B3,H3: 8.. / B3 = 8 => 14 pairs (_) / H3 = 8 => 16 pairs (_) D5,E6: 9.. / D5 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) G5,I6: 9.. / G5 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) C8,C9: 9.. / C8 = 9 => 12 pairs (_) / C9 = 9 => 0 pairs (*) F8,F9: 9.. / F8 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) D5,G5: 9.. / D5 = 9 => 0 pairs (X) / G5 = 9 => 0 pairs (_) E6,I6: 9.. / E6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) C8,F8: 9.. / C8 = 9 => 12 pairs (_) / F8 = 9 => 0 pairs (*) C9,F9: 9.. / C9 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) D2,D5: 9.. / D2 = 9 => 0 pairs (*) / D5 = 9 => 0 pairs (X) G1,G5: 9.. / G1 = 9 => 0 pairs (X) / G5 = 9 => 0 pairs (_) * DURATION: 0:00:52.917606 START: 05:35:37.516276 END: 05:36:30.433882 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B1,C8,C9,D2,D5,E3,E6,F8,F9,G8) * 7.48.5.121.2.475..3.52.14..931756248.47.82..1.281.47..25367819487.41..2541.52.8.. * PAIR B1: 6,9 BLK 1 B2: 6,9,8 # reduction candidate for 6,9 B2: 6,9 # 14 pairs B3: 6,9,8 # reduction candidate for 6,9 B3: 6,9 # 16 pairs * PAIR B1: 6,9 ROW 1 E1: 6,9,3 # reduction candidate for 6,9 E1: 6,9 => CTR * 7.48.53121.23475..3.52.14..931756248.479826.1.281.47..25367819487.41..2541.52.8.. E1: 3 => SOLVED * 794835612162947583385261479931756248647382951528194736253678194876419325419523867 G1: 6,9,3 # reduction candidate for 6,9 G1: 6,9 => SOLVED * 794835612162947583385261479931756248647382951528194736253678194876419325419523867 G1: 3 => CTR * 7.48.53121.23475..3.52.14..931756248.479826.1.281.47..25367819487.41..2541.52.8.. * PAIR D2: 3,9 BLK 2 E1: 3,9,6 # reduction candidate for 3,9 E1: 6 => CTR * 7.48653121.23475..3.52914..931756248.479826.1.281.47..25367819487.41..2541.52.8.. E1: 3,9 # 15 pairs * PAIR D2: 3,9 ROW 2 I2: 3,9,6 # reduction candidate for 3,9 I2: 6 # 20 pairs I2: 3,9 # 15 pairs * PAIR E3: 6,9 BLK 2 E1: 6,9,3 # reduction candidate for 6,9 E1: 6,9 => CTR * 7.48.53121.23475..3.52.14..931756248.479826.1.281.47..25367819487.41..2541.52.8.. E1: 3 => SOLVED * 794835612162947583385261479931756248647382951528194736253678194876419325419523867 * PAIR E3: 6,9 ROW 3 B3: 6,9,8 # reduction candidate for 6,9 B3: 6,9 # 16 pairs I3: 6,9,7 # reduction candidate for 6,9 I3: 6,9 # 15 pairs * PAIR A5: 5,6 ROW 5 H5: 5,6,3 # reduction candidate for 5,6 H5: 3 => CTR * 7.48.5.121.2.475..3.52.14..931756248547.8263162813475925367819487641932541.52.8.. H5: 5,6 # 14 pairs * PAIR A6: 5,6 ROW 6 H6: 5,6,3 # reduction candidate for 5,6 H6: 3 => SOLVED * 794835612162947583385261479931756248647382951528194736253678194876419325419523867 H6: 5,6 # 14 pairs * PAIR D5: 3,9 ROW 5 G5: 3,9,6 # reduction candidate for 3,9 G5: 6 => CTR * 7.48.59121.2.475..3.52.14..931756248.479826316281347592536781948764193254195238.. G5: 3,9 # 14 pairs * PAIR E6: 3,9 ROW 6 I6: 3,9,6 # reduction candidate for 3,9 I6: 6 => SOLVED * 794835612162947583385261479931756248647382951528194736253678194876419325419523867 I6: 3,9 # 14 pairs * PAIR E6: 3,9 COL E E1: 3,9,6 # reduction candidate for 3,9 E1: 6 => CTR * 7.48653121.23475..3.52914..931756248.479826.1.281.47..25367819487.41..2541.52.8.. E1: 3,9 # 15 pairs * PAIR G8: 3,6 BLK 9 H9: 3,6,7 # reduction candidate for 3,6 H9: 3,6 # 15 pairs I9: 3,6,7 # reduction candidate for 3,6 I9: 3,6 # 14 pairs * PAIR G8: 3,6 COL G G1: 3,6,9 # reduction candidate for 3,6 G1: 3,6 => SOLVED * 794835612162947583385261479931756248647382951528194736253678194876419325419523867 G1: 9 => CTR * 7.48359121.29475..3.52.14..931756248.47.82..1.281.47..25367819487.41..2541.52.8.. G5: 3,6,9 # reduction candidate for 3,6 G5: 3,6 => CTR * 7.48.59121.2.475..3.52.14..931756248.47982..1.281347.925367819487.41..2541.52.8.. G5: 9 => SOLVED * 794835612162947583385261479931756248647382951528194736253678194876419325419523867 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-082-base-pr-000.dot * REASONING * DIS # E1: 6,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 3 => CTR => G1: 6,9 * DIS # E1: 6 => CTR => E1: 3,9 * DIS # E1: 6,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * DIS # H5: 3 => CTR => H5: 5,6 * PRF # H6: 3 => SOL * DIS # G5: 6 => CTR => G5: 3,9 * PRF # I6: 6 => SOL * DIS # E1: 6 => CTR => E1: 3,9 * PRF # G1: 3,6 => SOL * DIS # G1: 9 => CTR => G1: 3,6 * DIS # G5: 3,6 => CTR => G5: 9 * PRF # G5: 9 => SOL * CNT 16 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B1,C8,C9,D2,D5,E3,E6,F8,F9,G8) * 7.48.5.121.2.475..3.52.14..931756248.47.82..1.281.47..25367819487.41..2541.52.8.. * PAIR B1: 6,9 BLK 1 B2: 6,9,8 # reduction candidate for 6,9 B2: 6,9 # 14 pairs B3: 6,9,8 # reduction candidate for 6,9 B3: 6,9 # 16 pairs * PAIR B1: 6,9 ROW 1 E1: 6,9,3 # reduction candidate for 6,9 E1: 6,9 => CTR * 7.48.53121.23475..3.52.14..931756248.479826.1.281.47..25367819487.41..2541.52.8.. E1: 3 => SOLVED * 794835612162947583385261479931756248647382951528194736253678194876419325419523867 * DURATION: 0:00:03.268536 START: 05:37:00.756206 END: 05:37:04.024742 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-082-base-pr-001.dot * REASONING * DIS # E1: 6,9 => CTR => E1: 3 * PRF E1: 3 => SOL * STA E1: 3 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 082 solution: 794835612162947583385261479931756248647382951528194736253678194876419325419523867 info: 1552 FNWXY S8.f 37374 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 794835612162947583385261479931756248647382951528194736253678194876419325419523867 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 # B2: 6,9 => UNS * INC # B3: 6,9 => UNS * DIS # E1: 6,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 3 => CTR => G1: 6,9 * INC # E1: 3,9 => UNS * DIS # E1: 6 => CTR => E1: 3,9 * INC # I2: 3,9 => UNS * INC # I2: 6 => UNS * DIS # E1: 6,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * INC # B3: 6,9 => UNS * INC # I3: 6,9 => UNS * INC # H5: 5,6 => UNS * DIS # H5: 3 => CTR => H5: 5,6 * INC # H6: 5,6 => UNS * PRF # H6: 3 => SOL * INC # G5: 3,9 => UNS * DIS # G5: 6 => CTR => G5: 3,9 * INC # I6: 3,9 => UNS * PRF # I6: 6 => SOL * INC # E1: 3,9 => UNS * DIS # E1: 6 => CTR => E1: 3,9 * INC # H9: 3,6 => UNS * INC # I9: 3,6 => UNS * PRF # G1: 3,6 => SOL * DIS # G1: 9 => CTR => G1: 3,6 * DIS # G5: 3,6 => CTR => G5: 9 * PRF # G5: 9 => SOL * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 6,9 => UNS * INC # B3: 6,9 => UNS * DIS # E1: 6,9 => CTR => E1: 3 * PRF E1: 3 => SOL * STA E1: 3 * CNT 4 HDP CHAINS / 3 HYP OPENED