Analysis of xx-top500-392-base.sdk
Contents
Original Sudoku
level: medium
position: 81..........5..3.....4....77.......5.....2.6.....1........6.12.5..7......4....... initial
Autosolve
position: 81.2.....4..5.63.1...4.12.77...4..151.4.5276.....17..2....651245.1724...24.1..57. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B4: 8,9 => CTR => B4: 2,3,6 * DIS # C4: 8,9 => CTR => C4: 2,3,6 * DIS # D4: 8,9 => CTR => D4: 3,6 * PRF # C9: 3,9 => SOL * PRF # C9: 3,9 => SOL * CNT 5 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B4: 8,9 => CTR => B4: 2,3,6 * DIS B4: 2,3,6 # C4: 8,9 => CTR => C4: 2,3,6 * DIS B4: 2,3,6 + C4: 2,3,6 # D4: 8,9 => CTR => D4: 3,6 * PRF B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # F9: 8 => SOL * STA B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 + F9: 8 * CNT 4 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 81..........5..3.....4....77.......5.....2.6.....1........6.12.5..7......4....... | initial |
| 81.2.....4..5.63.1...4.12.77...4..151.4.5276.....17..2....651245.1724...24.1..57. | autosolve |
| 815273649472596381936481257723649815194852763658317492387965124561724938249138576 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) F1: 3,9 I1: 6,9 H2: 8,9 G4: 8,9 A7: 3,9 E9: 3,9 H8: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 2.. / B2 = 2 => 8 pairs (_) / C2 = 2 => 8 pairs (_) B4,C4: 2.. / B4 = 2 => 8 pairs (_) / C4 = 2 => 8 pairs (_) B2,B4: 2.. / B2 = 2 => 8 pairs (_) / B4 = 2 => 8 pairs (_) C2,C4: 2.. / C2 = 2 => 8 pairs (_) / C4 = 2 => 8 pairs (_) I5,H6: 3.. / I5 = 3 => 10 pairs (_) / H6 = 3 => 15 pairs (_) H6,H8: 3.. / H6 = 3 => 15 pairs (_) / H8 = 3 => 10 pairs (_) G1,H1: 4.. / G1 = 4 => 19 pairs (_) / H1 = 4 => 12 pairs (_) G6,H6: 4.. / G6 = 4 => 12 pairs (_) / H6 = 4 => 19 pairs (_) G1,G6: 4.. / G1 = 4 => 19 pairs (_) / G6 = 4 => 12 pairs (_) H1,H6: 4.. / H1 = 4 => 12 pairs (_) / H6 = 4 => 19 pairs (_) H1,H3: 5.. / H1 = 5 => 19 pairs (_) / H3 = 5 => 11 pairs (_) B6,C6: 5.. / B6 = 5 => 7 pairs (_) / C6 = 5 => 0 pairs (X) C1,H1: 5.. / C1 = 5 => 11 pairs (_) / H1 = 5 => 19 pairs (_) B3,B6: 5.. / B3 = 5 => 0 pairs (X) / B6 = 5 => 7 pairs (_) G1,I1: 6.. / G1 = 6 => 14 pairs (_) / I1 = 6 => 8 pairs (_) D4,D6: 6.. / D4 = 6 => 7 pairs (_) / D6 = 6 => 11 pairs (_) B8,C9: 6.. / B8 = 6 => 16 pairs (_) / C9 = 6 => 7 pairs (_) C9,I9: 6.. / C9 = 6 => 7 pairs (_) / I9 = 6 => 16 pairs (_) A3,A6: 6.. / A3 = 6 => 8 pairs (_) / A6 = 6 => 8 pairs (_) G1,G8: 6.. / G1 = 6 => 14 pairs (_) / G8 = 6 => 8 pairs (_) E1,E2: 7.. / E1 = 7 => 10 pairs (_) / E2 = 7 => 19 pairs (_) B7,C7: 7.. / B7 = 7 => 8 pairs (_) / C7 = 7 => 8 pairs (_) C1,E1: 7.. / C1 = 7 => 19 pairs (_) / E1 = 7 => 10 pairs (_) B2,B7: 7.. / B2 = 7 => 8 pairs (_) / B7 = 7 => 8 pairs (_) E2,E3: 8.. / E2 = 8 => 20 pairs (_) / E3 = 8 => 8 pairs (_) H2,H3: 8.. / H2 = 8 => 8 pairs (_) / H3 = 8 => 20 pairs (_) D7,F9: 8.. / D7 = 8 => 18 pairs (_) / F9 = 8 => 11 pairs (_) E2,H2: 8.. / E2 = 8 => 20 pairs (_) / H2 = 8 => 8 pairs (_) E3,H3: 8.. / E3 = 8 => 8 pairs (_) / H3 = 8 => 20 pairs (_) F4,F9: 8.. / F4 = 8 => 18 pairs (_) / F9 = 8 => 11 pairs (_) * DURATION: 0:00:45.310084 START: 16:14:25.715122 END: 16:15:11.025206 2017-05-04 * CP COUNT: (30) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,E9,F1,G4,H2,H8,I1) * 81.2.....4..5.63.1...4.12.77...4..151.4.5276.....17..2....651245.1724...24.1..57. * PAIR F1: 3,9 BLK 2 E1: 3,9,7 # reduction candidate for 3,9 E1: 3,9 # 19 pairs E3: 3,9,8 # reduction candidate for 3,9 E3: 3,9 # 20 pairs * PAIR F1: 3,9 ROW 1 C1: 3,9,5,7 # reduction candidate for 3,9 C1: 3,9 # 22 pairs C1: 5,7 # 9 pairs * PAIR F1: 3,9 COL F F4: 3,9,8 # reduction candidate for 3,9 F4: 3,9 # 11 pairs F9: 3,9,8 # reduction candidate for 3,9 F9: 3,9 # 18 pairs * PAIR I1: 6,9 BLK 3 G1: 6,9,4 # reduction candidate for 6,9 G1: 4 # 19 pairs G1: 6,9 # 12 pairs * PAIR I1: 6,9 COL I I8: 6,9,3,8 # reduction candidate for 6,9 I8: 6,9 # 13 pairs I9: 6,9,3,8 # reduction candidate for 6,9 I9: 6,9 # 11 pairs * PAIR H2: 8,9 BLK 3 H3: 8,9,5 # reduction candidate for 8,9 H3: 8,9 # 19 pairs H3: 5 # 11 pairs * PAIR H2: 8,9 ROW 2 E2: 8,9,7 # reduction candidate for 8,9 E2: 7 # 19 pairs E2: 8,9 # 10 pairs * PAIR G4: 8,9 BLK 6 I5: 8,9,3 # reduction candidate for 8,9 I5: 8,9 # 15 pairs G6: 8,9,4 # reduction candidate for 8,9 G6: 8,9 # 19 pairs * PAIR G4: 8,9 ROW 4 B4: 8,9,2,3,6 # reduction candidate for 8,9 B4: 8,9 => CTR * 81.2.945642.5.63.1...4.12.77.2643.151.4.5276.....17..29783651245.17246.8246198573 B4: 2,3,6 # 7 pairs C4: 8,9,2,3,6 # reduction candidate for 8,9 C4: 8,9 => CTR * 81.2.94564.25.63.1...4.12.772.643.151.4.5276.....17..29..3651245.17246.8246198573 C4: 2,3,6 # 7 pairs D4: 8,9,3,6 # reduction candidate for 8,9 D4: 8,9 => CTR * 81.2.9..64..5.63.16..4.12.77...43.151.4.5276.3..617..29..3651245.172463.24.19857. D4: 3,6 # 8 pairs F4: 8,9,3 # reduction candidate for 8,9 F4: 8,9 # 10 pairs * PAIR G4: 8,9 COL G G8: 8,9,6 # reduction candidate for 8,9 G8: 8,9 # 14 pairs G8: 6 # 8 pairs * PAIR A7: 3,9 BLK 7 B7: 3,9,7,8 # reduction candidate for 3,9 B7: 3,9 # 21 pairs C7: 3,9,7,8 # reduction candidate for 3,9 C7: 3,9 # 20 pairs B8: 3,9,6,8 # reduction candidate for 3,9 B8: 3,9 # 15 pairs C9: 3,9,6,8 # reduction candidate for 3,9 C9: 3,9 => SOLVED * 815273649472596381936481257723649815194852763658317492387965124561724938249138576 C9: 6,8 # 8 pairs * PAIR A7: 3,9 ROW 7 D7: 3,9,8 # reduction candidate for 3,9 D7: 8 # 18 pairs D7: 3,9 # 11 pairs * PAIR A7: 3,9 COL A A3: 3,9,6 # reduction candidate for 3,9 A3: 3,9 # 8 pairs A6: 3,9,6 # reduction candidate for 3,9 A6: 3,9 # 8 pairs * PAIR E9: 3,9 BLK 8 D7: 3,9,8 # reduction candidate for 3,9 D7: 3,9 # 11 pairs F9: 3,9,8 # reduction candidate for 3,9 F9: 3,9 # 18 pairs * PAIR E9: 3,9 ROW 9 C9: 3,9,6,8 # reduction candidate for 3,9 C9: 3,9 => SOLVED * 815273649472596381936481257723649815194852763658317492387965124561724938249138576 C9: 6,8 # 8 pairs I9: 3,9,6,8 # reduction candidate for 3,9 I9: 3,9 # 15 pairs * PAIR E9: 3,9 COL E E1: 3,9,7 # reduction candidate for 3,9 E1: 3,9 # 19 pairs E3: 3,9,8 # reduction candidate for 3,9 E3: 3,9 # 20 pairs * PAIR H8: 3,9 BLK 9 I8: 3,9,6,8 # reduction candidate for 3,9 I8: 3,9 # 11 pairs I9: 3,9,6,8 # reduction candidate for 3,9 I9: 3,9 # 15 pairs * PAIR H8: 3,9 ROW 8 B8: 3,9,6,8 # reduction candidate for 3,9 B8: 3,9 # 15 pairs B8: 6,8 # 9 pairs * PAIR H8: 3,9 COL H H6: 3,9,4 # reduction candidate for 3,9 H6: 4 # 19 pairs H6: 3,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-392-base-pr-000.dot * REASONING * DIS # B4: 8,9 => CTR => B4: 2,3,6 * DIS # C4: 8,9 => CTR => C4: 2,3,6 * DIS # D4: 8,9 => CTR => D4: 3,6 * PRF # C9: 3,9 => SOL * PRF # C9: 3,9 => SOL * CNT 5 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,E9,F1,G4,H2,H8,I1) * 81.2.....4..5.63.1...4.12.77...4..151.4.5276.....17..2....651245.1724...24.1..57. * PAIR F1: 3,9 BLK 2 E1: 3,9,7 # reduction candidate for 3,9 E1: 3,9 # 19 pairs E3: 3,9,8 # reduction candidate for 3,9 E3: 3,9 # 20 pairs * PAIR F1: 3,9 ROW 1 C1: 3,9,5,7 # reduction candidate for 3,9 C1: 3,9 # 22 pairs C1: 5,7 # 9 pairs * PAIR F1: 3,9 COL F F4: 3,9,8 # reduction candidate for 3,9 F4: 3,9 # 11 pairs F9: 3,9,8 # reduction candidate for 3,9 F9: 3,9 # 18 pairs * PAIR I1: 6,9 BLK 3 G1: 6,9,4 # reduction candidate for 6,9 G1: 4 # 19 pairs G1: 6,9 # 12 pairs * PAIR I1: 6,9 COL I I8: 6,9,3,8 # reduction candidate for 6,9 I8: 6,9 # 13 pairs I9: 6,9,3,8 # reduction candidate for 6,9 I9: 6,9 # 11 pairs * PAIR H2: 8,9 BLK 3 H3: 8,9,5 # reduction candidate for 8,9 H3: 8,9 # 19 pairs H3: 5 # 11 pairs * PAIR H2: 8,9 ROW 2 E2: 8,9,7 # reduction candidate for 8,9 E2: 7 # 19 pairs E2: 8,9 # 10 pairs * PAIR G4: 8,9 BLK 6 I5: 8,9,3 # reduction candidate for 8,9 I5: 8,9 # 15 pairs G6: 8,9,4 # reduction candidate for 8,9 G6: 8,9 # 19 pairs * PAIR G4: 8,9 ROW 4 B4: 8,9,2,3,6 # reduction candidate for 8,9 B4: 8,9 => CTR * 81.2.945642.5.63.1...4.12.77.2643.151.4.5276.....17..29783651245.17246.8246198573 C4: 8,9,2,3,6 # reduction candidate for 8,9 C4: 8,9 => CTR * 81.2.94564.25.63.1...4.12.772.643.151.4.5276.....17..29..3651245.17246.8246198573 D4: 8,9,3,6 # reduction candidate for 8,9 D4: 8,9 => CTR * 81.2.9..64..5.63.16..4.12.77...43.151.4.5276.3..617..29..3651245.172463.24.19857. * RESTART * PAIR G4: 8,9 COL G G8: 8,9,6 # reduction candidate for 8,9 G8: 8,9 # 14 pairs G8: 6 # 14 pairs * PAIR RESTART * PAIR G4: 8,9 BLK 6 I5: 8,9,3 # reduction candidate for 8,9 I5: 8,9 # 15 pairs G6: 8,9,4 # reduction candidate for 8,9 G6: 8,9 # 19 pairs * PAIR G4: 8,9 COL G G8: 8,9,6 # reduction candidate for 8,9 G8: 8,9 # 14 pairs G8: 6 # 14 pairs * PAIR A7: 3,9 BLK 7 B7: 3,9,7,8 # reduction candidate for 3,9 B7: 3,9 # 21 pairs C7: 3,9,7,8 # reduction candidate for 3,9 C7: 3,9 # 20 pairs * PAIR A7: 3,9 COL A A3: 3,9,6 # reduction candidate for 3,9 A3: 3,9 # 13 pairs A6: 3,9,6 # reduction candidate for 3,9 A6: 3,9 # 11 pairs * PAIR E9: 3,9 BLK 8 F9: 3,9,8 # reduction candidate for 3,9 F9: 8 => SOLVED * 815273649472596381936481257723649815194852763658317492387965124561724938249138576 * DURATION: 0:00:29.381229 START: 16:15:50.722664 END: 16:16:20.103893 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-392-base-pr-001.dot * REASONING * DIS # B4: 8,9 => CTR => B4: 2,3,6 * DIS B4: 2,3,6 # C4: 8,9 => CTR => C4: 2,3,6 * DIS B4: 2,3,6 + C4: 2,3,6 # D4: 8,9 => CTR => D4: 3,6 * PRF B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # F9: 8 => SOL * STA B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 + F9: 8 * CNT 4 HDP CHAINS / 31 HYP OPENED
Header Info
Top 500 Minimum 17 392 solution: 815273649472596381936481257723649815194852763658317492387965124561724938249138576 info: 51242 FNBTXYK S8.f 38623 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 815273649472596381936481257723649815194852763658317492387965124561724938249138576 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 # E1: 3,9 => UNS * INC # E3: 3,9 => UNS * INC # C1: 3,9 => UNS * INC # C1: 5,7 => UNS * INC # F4: 3,9 => UNS * INC # F9: 3,9 => UNS * INC # G1: 6,9 => UNS * INC # G1: 4 => UNS * INC # I8: 6,9 => UNS * INC # I9: 6,9 => UNS * INC # H3: 8,9 => UNS * INC # H3: 5 => UNS * INC # E2: 8,9 => UNS * INC # E2: 7 => UNS * INC # I5: 8,9 => UNS * INC # G6: 8,9 => UNS * DIS # B4: 8,9 => CTR => B4: 2,3,6 * INC # B4: 2,3,6 => UNS * DIS # C4: 8,9 => CTR => C4: 2,3,6 * INC # C4: 2,3,6 => UNS * DIS # D4: 8,9 => CTR => D4: 3,6 * INC # D4: 3,6 => UNS * INC # F4: 8,9 => UNS * INC # G8: 8,9 => UNS * INC # G8: 6 => UNS * INC # B7: 3,9 => UNS * INC # C7: 3,9 => UNS * INC # B8: 3,9 => UNS * PRF # C9: 3,9 => SOL * INC # C9: 6,8 => UNS * INC # D7: 3,9 => UNS * INC # D7: 8 => UNS * INC # A3: 3,9 => UNS * INC # A6: 3,9 => UNS * INC # D7: 3,9 => UNS * INC # F9: 3,9 => UNS * PRF # C9: 3,9 => SOL * INC # C9: 6,8 => UNS * INC # I9: 3,9 => UNS * INC # E1: 3,9 => UNS * INC # E3: 3,9 => UNS * INC # I8: 3,9 => UNS * INC # I9: 3,9 => UNS * INC # B8: 3,9 => UNS * INC # B8: 6,8 => UNS * INC # H6: 3,9 => UNS * INC # H6: 4 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 3,9 => UNS * INC # E3: 3,9 => UNS * INC # C1: 3,9 => UNS * INC # C1: 5,7 => UNS * INC # F4: 3,9 => UNS * INC # F9: 3,9 => UNS * INC # G1: 6,9 => UNS * INC # G1: 4 => UNS * INC # I8: 6,9 => UNS * INC # I9: 6,9 => UNS * INC # H3: 8,9 => UNS * INC # H3: 5 => UNS * INC # E2: 8,9 => UNS * INC # E2: 7 => UNS * INC # I5: 8,9 => UNS * INC # G6: 8,9 => UNS * DIS # B4: 8,9 => CTR => B4: 2,3,6 * DIS B4: 2,3,6 # C4: 8,9 => CTR => C4: 2,3,6 * DIS B4: 2,3,6 + C4: 2,3,6 # D4: 8,9 => CTR => D4: 3,6 * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # G8: 8,9 => UNS * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # G8: 6 => UNS * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # I5: 8,9 => UNS * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # G6: 8,9 => UNS * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # G8: 8,9 => UNS * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # G8: 6 => UNS * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # B7: 3,9 => UNS * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # C7: 3,9 => UNS * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # A3: 3,9 => UNS * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # A6: 3,9 => UNS * INC B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # F9: 3,9 => UNS * PRF B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 # F9: 8 => SOL * STA B4: 2,3,6 + C4: 2,3,6 + D4: 3,6 + F9: 8 * CNT 31 HDP CHAINS / 31 HYP OPENED