Analysis of xx-top500-061-base.sdk
Contents
Original Sudoku
level: medium
position: ...6.5...2.....4............76....4....1..2.....83...........57.....4..61...2.... initial
Autosolve
position: ...6.57.225....46.6..4.25...76259.415..14627.4..837695....6..577..5.4.2616572.9.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I3: 8,9 => SOL * DIS # I3: 3 => CTR => I3: 8,9 * DIS # E2: 8,9 => CTR => E2: 1,7 * DIS # A1: 3,8 => CTR => A1: 9 * DIS # I3: 9 => CTR => I3: 3,8 * PRF # A7: 8 => SOL * CNT 6 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I3: 8,9 => SOL * STA I3: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6.5...2.....4............76....4....1..2.....83...........57.....4..61...2.... | initial |
| ...6.57.225....46.6..4.25...76259.415..14627.4..837695....6..577..5.4.2616572.9.4 | autosolve |
| 948615732251378469637492518376259841589146273412837695824961357793584126165723984 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) D2: 3,9 I2: 8,9 A4: 3,8 B6: 1,2 C6: 1,2 G4: 3,8 I5: 3,8 B7: 2,4 C7: 2,4 D7: 3,9 F9: 3,8 H9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H3: 1.. / H1 = 1 => 14 pairs (_) / H3 = 1 => 14 pairs (_) B6,C6: 1.. / B6 = 1 => 8 pairs (_) / C6 = 1 => 9 pairs (_) F7,E8: 1.. / F7 = 1 => 18 pairs (_) / E8 = 1 => 17 pairs (_) G7,G8: 1.. / G7 = 1 => 17 pairs (_) / G8 = 1 => 18 pairs (_) F7,G7: 1.. / F7 = 1 => 18 pairs (_) / G7 = 1 => 17 pairs (_) E8,G8: 1.. / E8 = 1 => 17 pairs (_) / G8 = 1 => 18 pairs (_) F2,F7: 1.. / F2 = 1 => 17 pairs (_) / F7 = 1 => 18 pairs (_) B6,C6: 2.. / B6 = 2 => 9 pairs (_) / C6 = 2 => 8 pairs (_) B7,C7: 2.. / B7 = 2 => 8 pairs (_) / C7 = 2 => 9 pairs (_) B6,B7: 2.. / B6 = 2 => 9 pairs (_) / B7 = 2 => 8 pairs (_) C6,C7: 2.. / C6 = 2 => 8 pairs (_) / C7 = 2 => 9 pairs (_) D2,F2: 3.. / D2 = 3 => 16 pairs (_) / F2 = 3 => 0 pairs (X) G4,I5: 3.. / G4 = 3 => 0 pairs (X) / I5 = 3 => 0 pairs (_) A4,G4: 3.. / A4 = 3 => 0 pairs (*) / G4 = 3 => 0 pairs (X) F9,H9: 3.. / F9 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) D2,D7: 3.. / D2 = 3 => 16 pairs (_) / D7 = 3 => 0 pairs (X) I3,I5: 3.. / I3 = 3 => 0 pairs (X) / I5 = 3 => 0 pairs (_) B1,C1: 4.. / B1 = 4 => 8 pairs (_) / C1 = 4 => 9 pairs (_) B7,C7: 4.. / B7 = 4 => 9 pairs (_) / C7 = 4 => 8 pairs (_) B1,B7: 4.. / B1 = 4 => 8 pairs (_) / B7 = 4 => 9 pairs (_) C1,C7: 4.. / C1 = 4 => 9 pairs (_) / C7 = 4 => 8 pairs (_) C2,C3: 7.. / C2 = 7 => 13 pairs (_) / C3 = 7 => 12 pairs (_) E2,E3: 7.. / E2 = 7 => 12 pairs (_) / E3 = 7 => 13 pairs (_) C2,E2: 7.. / C2 = 7 => 13 pairs (_) / E2 = 7 => 12 pairs (_) C3,E3: 7.. / C3 = 7 => 12 pairs (_) / E3 = 7 => 13 pairs (_) G4,I5: 8.. / G4 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) A4,G4: 8.. / A4 = 8 => 0 pairs (X) / G4 = 8 => 0 pairs (_) F9,H9: 8.. / F9 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) I2,I3: 9.. / I2 = 9 => 15 pairs (_) / I3 = 9 => 0 pairs (X) B5,C5: 9.. / B5 = 9 => 14 pairs (_) / C5 = 9 => 14 pairs (_) D7,E8: 9.. / D7 = 9 => 16 pairs (_) / E8 = 9 => 0 pairs (X) A7,D7: 9.. / A7 = 9 => 0 pairs (X) / D7 = 9 => 16 pairs (_) A1,A7: 9.. / A1 = 9 => 16 pairs (_) / A7 = 9 => 0 pairs (X) D2,D7: 9.. / D2 = 9 => 0 pairs (X) / D7 = 9 => 16 pairs (_) * DURATION: 0:01:01.816192 START: 04:45:04.716342 END: 04:46:06.532534 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B6,B7,C6,C7,D2,D7,F9,G4,H9,I2,I5) * ...6.57.225....46.6..4.25...76259.415..14627.4..837695....6..577..5.4.2616572.9.4 * PAIR I2: 8,9 BLK 3 I3: 8,9,3 # reduction candidate for 8,9 I3: 8,9 => SOLVED * 948615732251378469637492518376259841589146273412837695824961357793584126165723984 I3: 3 => CTR * 9..6.57.225.3..4696..4925.38762593415..1462784..8376953..96..577..5.4.26165728934 * PAIR I2: 8,9 ROW 2 C2: 8,9,1,7 # reduction candidate for 8,9 C2: 8,9 # 20 pairs E2: 8,9,1,7 # reduction candidate for 8,9 E2: 8,9 => CTR * 9..6857.22573914686..4725.9.762598415..1462734..8376958..9631577..51432616572.9.4 E2: 1,7 # 13 pairs * PAIR A4: 3,8 BLK 4 B5: 3,8,9 # reduction candidate for 3,8 B5: 3,8 # 14 pairs C5: 3,8,9 # reduction candidate for 3,8 C5: 3,8 # 14 pairs * PAIR A4: 3,8 COL A A1: 3,8,9 # reduction candidate for 3,8 A1: 3,8 => CTR * ...6.57.225.9.34686..4.25...76259.415..14627.4..8376959..36..577..594126165728934 A1: 9 # 16 pairs A7: 3,8,9 # reduction candidate for 3,8 A7: 3,8 # 16 pairs * PAIR G4: 3,8 COL G G7: 3,8,1 # reduction candidate for 3,8 G7: 3,8 # 18 pairs G8: 3,8,1 # reduction candidate for 3,8 G8: 3,8 # 17 pairs * PAIR I5: 3,8 ROW 5 B5: 3,8,9 # reduction candidate for 3,8 B5: 3,8 # 14 pairs C5: 3,8,9 # reduction candidate for 3,8 C5: 3,8 # 14 pairs * PAIR I5: 3,8 COL I I3: 3,8,9 # reduction candidate for 3,8 I3: 9 => CTR * ...6.57.225....4686..4.25.93762598415..1462734..837695....681577..514326165723984 I3: 3,8 # 15 pairs * PAIR D7: 3,9 ROW 7 A7: 3,9,8 # reduction candidate for 3,9 A7: 8 => SOLVED * 948615732251378469637492518376259841589146273412837695824961357793584126165723984 A7: 3,9 # 18 pairs * PAIR F9: 3,8 BLK 8 F7: 3,8,1 # reduction candidate for 3,8 F7: 1 # 18 pairs F7: 3,8 # 17 pairs * PAIR F9: 3,8 COL F F2: 3,8,1 # reduction candidate for 3,8 F2: 3,8 # 18 pairs F2: 1 # 17 pairs * PAIR H9: 3,8 BLK 9 G7: 3,8,1 # reduction candidate for 3,8 G7: 3,8 # 18 pairs G8: 3,8,1 # reduction candidate for 3,8 G8: 3,8 # 17 pairs * PAIR H9: 3,8 COL H H1: 3,8,1 # reduction candidate for 3,8 H1: 3,8 # 14 pairs H3: 3,8,1 # reduction candidate for 3,8 H3: 3,8 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-061-base-pr-000.dot * REASONING * PRF # I3: 8,9 => SOL * DIS # I3: 3 => CTR => I3: 8,9 * DIS # E2: 8,9 => CTR => E2: 1,7 * DIS # A1: 3,8 => CTR => A1: 9 * DIS # I3: 9 => CTR => I3: 3,8 * PRF # A7: 8 => SOL * CNT 6 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B6,B7,C6,C7,D2,D7,F9,G4,H9,I2,I5) * ...6.57.225....46.6..4.25...76259.415..14627.4..837695....6..577..5.4.2616572.9.4 * PAIR I2: 8,9 BLK 3 I3: 8,9,3 # reduction candidate for 8,9 I3: 8,9 => SOLVED * 948615732251378469637492518376259841589146273412837695824961357793584126165723984 * DURATION: 0:00:02.389461 START: 04:46:33.343413 END: 04:46:35.732874 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-061-base-pr-001.dot * REASONING * PRF # I3: 8,9 => SOL * STA I3: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 061 solution: 948615732251378469637492518376259841589146273412837695824961357793584126165723984 info: 1437 FNBHWX S8.f 10908 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 948615732251378469637492518376259841589146273412837695824961357793584126165723984 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:
* PRF # I3: 8,9 => SOL * DIS # I3: 3 => CTR => I3: 8,9 * INC # C2: 8,9 => UNS * DIS # E2: 8,9 => CTR => E2: 1,7 * INC # E2: 1,7 => UNS * INC # B5: 3,8 => UNS * INC # C5: 3,8 => UNS * DIS # A1: 3,8 => CTR => A1: 9 * INC # A1: 9 => UNS * INC # A7: 3,8 => UNS * INC # G7: 3,8 => UNS * INC # G8: 3,8 => UNS * INC # B5: 3,8 => UNS * INC # C5: 3,8 => UNS * INC # I3: 3,8 => UNS * DIS # I3: 9 => CTR => I3: 3,8 * INC # A7: 3,9 => UNS * PRF # A7: 8 => SOL * INC # F7: 3,8 => UNS * INC # F7: 1 => UNS * INC # F2: 3,8 => UNS * INC # F2: 1 => UNS * INC # G7: 3,8 => UNS * INC # G8: 3,8 => UNS * INC # H1: 3,8 => UNS * INC # H3: 3,8 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I3: 8,9 => SOL * STA I3: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED