Analysis of xx-top500-493-base.sdk
Contents
Original Sudoku
level: medium
position: .586..1...1.5....4.......2.7...2..3..6...................1..5..3...7....2........ initial
Autosolve
position: 4586.21..9125.7.64637....2578..25631.6....2...2..6....8.61.35.23.527..1.2.1.5.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I1: 3,9 => SOL * DIS # I1: 7 => CTR => I1: 3,9 * DIS # I1: 7,9 => CTR => I1: 3 * PRF # I1: 3 => SOL * DIS # H5: 7,9 => CTR => H5: 4,5,8 * DIS # H6: 7,9 => CTR => H6: 4,5,8 * DIS # H9: 7,9 => CTR => H9: 4,8 * DIS # E3: 8,9 => CTR => E3: 1,4 * DIS # F3: 8,9 => CTR => F3: 1,4 * DIS # C5: 4,9 => CTR => C5: 3 * DIS # E5: 4,9 => CTR => E5: 1,8 * PRF # F6: 4,9 => SOL * DIS # D3: 4,9 => CTR => D3: 8 * PRF # D3: 8 => SOL * PRF # D9: 4,9 => SOL * DIS # D9: 8 => CTR => D9: 4,9 * DIS # B7: 4,9 => CTR => B7: 7 * PRF # D9: 4,9 => SOL * DIS # D9: 8 => CTR => D9: 4,9 * DIS # F9: 4,9 => CTR => F9: 6,8 * PRF # F9: 6,8 => SOL * DIS # B7: 4,9 => CTR => B7: 7 * DIS # E3: 4,9 => CTR => E3: 1,8 * DIS # E5: 4,9 => CTR => E5: 1,8 * PRF # F9: 6,8 => SOL * DIS # F9: 4,9 => CTR => F9: 6,8 * DIS # G9: 4,9 => CTR => G9: 3,7 * DIS # H9: 4,9 => CTR => H9: 7,8 * DIS # G6: 4,9 => CTR => G6: 7 * PRF # G6: 7 => SOL * DIS # I9: 6,8 => CTR => I9: 3,7,9 * PRF # I9: 3,7,9 => SOL * CNT 32 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I1: 3,9 => SOL * STA I1: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .586..1...1.5....4.......2.7...2..3..6...................1..5..3...7....2........ | initial |
| 4586.21..9125.7.64637....2578..25631.6....2...2..6....8.61.35.23.527..1.2.1.5.... | autosolve |
| 458692173912537864637814925789425631563781249124369758876143592395278416241956387 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) E1: 3,9 E2: 3,8 H1: 7,9 G2: 3,8 G3: 8,9 C4: 4,9 A5: 1,5 A6: 1,5 D4: 4,9 D5: 3,7 D6: 3,7 B8: 4,9 E7: 4,9 F8: 6,8 G8: 4,9 I8: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 1.. / E3 = 1 => 16 pairs (_) / F3 = 1 => 0 pairs (X) A5,A6: 1.. / A5 = 1 => 16 pairs (_) / A6 = 1 => 14 pairs (_) A6,F6: 1.. / A6 = 1 => 14 pairs (_) / F6 = 1 => 16 pairs (_) E3,E5: 1.. / E3 = 1 => 16 pairs (_) / E5 = 1 => 0 pairs (X) E1,E2: 3.. / E1 = 3 => 0 pairs (X) / E2 = 3 => 0 pairs (_) I1,G2: 3.. / I1 = 3 => 0 pairs (*) / G2 = 3 => 0 pairs (X) C5,C6: 3.. / C5 = 3 => 16 pairs (_) / C6 = 3 => 0 pairs (X) D5,D6: 3.. / D5 = 3 => 0 pairs (X) / D6 = 3 => 16 pairs (_) G9,I9: 3.. / G9 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) E1,I1: 3.. / E1 = 3 => 0 pairs (X) / I1 = 3 => 0 pairs (_) E2,G2: 3.. / E2 = 3 => 0 pairs (*) / G2 = 3 => 0 pairs (X) C5,D5: 3.. / C5 = 3 => 16 pairs (_) / D5 = 3 => 0 pairs (X) C6,D6: 3.. / C6 = 3 => 0 pairs (X) / D6 = 3 => 16 pairs (_) G2,G9: 3.. / G2 = 3 => 0 pairs (X) / G9 = 3 => 0 pairs (_) I1,I9: 3.. / I1 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) C4,D4: 4.. / C4 = 4 => 18 pairs (_) / D4 = 4 => 20 pairs (_) B8,G8: 4.. / B8 = 4 => 0 pairs (X) / G8 = 4 => 0 pairs (_) A5,A6: 5.. / A5 = 5 => 14 pairs (_) / A6 = 5 => 16 pairs (_) H5,H6: 5.. / H5 = 5 => 16 pairs (_) / H6 = 5 => 14 pairs (_) A5,H5: 5.. / A5 = 5 => 14 pairs (_) / H5 = 5 => 16 pairs (_) A6,H6: 5.. / A6 = 5 => 16 pairs (_) / H6 = 5 => 14 pairs (_) F8,F9: 6.. / F8 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) I8,I9: 6.. / I8 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) F8,I8: 6.. / F8 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) F9,I9: 6.. / F9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) H1,I1: 7.. / H1 = 7 => 0 pairs (*) / I1 = 7 => 0 pairs (X) D5,D6: 7.. / D5 = 7 => 16 pairs (_) / D6 = 7 => 0 pairs (X) B7,B9: 7.. / B7 = 7 => 20 pairs (_) / B9 = 7 => 0 pairs (X) B7,H7: 7.. / B7 = 7 => 20 pairs (_) / H7 = 7 => 0 pairs (X) G6,G9: 7.. / G6 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) G2,G3: 8.. / G2 = 8 => 0 pairs (*) / G3 = 8 => 0 pairs (X) E2,G2: 8.. / E2 = 8 => 0 pairs (X) / G2 = 8 => 0 pairs (_) F8,I8: 8.. / F8 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) D3,D9: 8.. / D3 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) C4,D4: 9.. / C4 = 9 => 20 pairs (_) / D4 = 9 => 18 pairs (_) B8,G8: 9.. / B8 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) * DURATION: 0:01:11.891788 START: 19:30:09.027999 END: 19:31:20.919787 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B8,C4,D4,D5,D6,E1,E2,E7,F8,G2,G3,G8,H1,I8) * 4586.21..9125.7.64637....2578..25631.6....2...2..6....8.61.35.23.527..1.2.1.5.... * PAIR E1: 3,9 ROW 1 I1: 3,9,7 # reduction candidate for 3,9 I1: 3,9 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 I1: 7 => CTR * 458632197912587364637...82578..25631.6....2...2..6....8.61.35.23.527..1.2.185...3 * PAIR H1: 7,9 BLK 3 I1: 7,9,3 # reduction candidate for 7,9 I1: 7,9 => CTR * 4586321..912587364637...82578..25631.6....2...2..6....8.61.35.23.527..1.2.185...3 I1: 3 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 * PAIR H1: 7,9 COL H H5: 7,9,4,5,8 # reduction candidate for 7,9 H5: 7,9 => CTR * 4586.21..9125.7.646378..92578..2563156..812..12..6.45.8.61.35.23.527..1.2.1.5..8. H5: 4,5,8 # 16 pairs H6: 7,9,4,5,8 # reduction candidate for 7,9 H6: 7,9 => CTR * 4586321..912587364637.1.82578..2563116....25.52..614.8876193542345278916291456783 H6: 4,5,8 # 16 pairs H7: 7,9,4 # reduction candidate for 7,9 H7: 7,9 # 18 pairs H9: 7,9,4,8 # reduction candidate for 7,9 H9: 7,9 => CTR * 4586.21..9125.7.64637....2578..25631.6....2...2..6....8.61.35.23.527..1.2.1.5.... H9: 4,8 # 17 pairs * PAIR G3: 8,9 ROW 3 D3: 8,9,4 # reduction candidate for 8,9 D3: 8,9 # 19 pairs E3: 8,9,1,4 # reduction candidate for 8,9 E3: 8,9 => CTR * 4586.21.391253786463748192578492563156..1.28.12..6845.8.61435.23.527..1.2.1859..6 E3: 1,4 # 17 pairs F3: 8,9,1,4 # reduction candidate for 8,9 F3: 8,9 => CTR * 4586.21.3912537864637418925784925631.6..8.2...2..6..8.8.61435.2395276418241859376 F3: 1,4 # 17 pairs * PAIR C4: 4,9 BLK 4 C5: 4,9,3 # reduction candidate for 4,9 C5: 4,9 => CTR * 4586321..912587364637...82578..25631.6.3..2...2376....8761.35.23.527..162.185.7.3 C5: 3 # 16 pairs C6: 4,9,3 # reduction candidate for 4,9 C6: 4,9 # 16 pairs * PAIR D4: 4,9 BLK 5 E5: 4,9,1,8 # reduction candidate for 4,9 E5: 4,9 => CTR * 4586.21..912587364637.1.82578..25631.6....2...2..6....8.61.35.23.527..1.2.185...3 E5: 1,8 # 17 pairs F5: 4,9,1,8 # reduction candidate for 4,9 F5: 4,9 # 19 pairs F6: 4,9,1,8 # reduction candidate for 4,9 F6: 4,9 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 F6: 1,8 # 17 pairs * PAIR D4: 4,9 COL D D3: 4,9,8 # reduction candidate for 4,9 D3: 4,9 => CTR * 4586.21.3912537864637...92578.925631.6....2...2..6....8.61.35.23952764182.1859376 D3: 8 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 D9: 4,9,8 # reduction candidate for 4,9 D9: 4,9 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 D9: 8 => CTR * 4586.21.3912537864637...92578.925631.6....2...2..6....8.61.35.23952764182.1859376 * PAIR B8: 4,9 BLK 7 B7: 4,9,7 # reduction candidate for 4,9 B7: 4,9 => CTR * 4586.21979125.7364637...82578..25631.6.7..2...2.36.7..8.61.35723.527..1.27185..43 B7: 7 # 20 pairs B9: 4,9,7 # reduction candidate for 4,9 B9: 4,9 # 20 pairs * PAIR E7: 4,9 BLK 8 D9: 4,9,8 # reduction candidate for 4,9 D9: 4,9 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 D9: 8 => CTR * 4586.21.3912537864637...92578.925631.6....2...2..6....8.61.35.23952764182.1859376 F9: 4,9,6,8 # reduction candidate for 4,9 F9: 4,9 => CTR * 4586.21.3912537864637...92578.925631.6....2...2..6....8.61.35.23952764182.1859376 F9: 6,8 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 * PAIR E7: 4,9 ROW 7 B7: 4,9,7 # reduction candidate for 4,9 B7: 4,9 => CTR * 4586.21979125.7364637...82578..25631.6.7..2...2.36.7..8.61.35723.527..1.27185..43 B7: 7 # 20 pairs H7: 4,9,7 # reduction candidate for 4,9 H7: 4,9 # 20 pairs * PAIR E7: 4,9 COL E E3: 4,9,1,8 # reduction candidate for 4,9 E3: 4,9 => CTR * 4586.21..912587364637..182578..2563156..1.2..12..6..5.8.61.35.23.527..1.2.185...3 E3: 1,8 # 17 pairs E5: 4,9,1,8 # reduction candidate for 4,9 E5: 4,9 => CTR * 4586.21..912587364637.1.82578..25631.6....2...2..6....8.61.35.23.527..1.2.185...3 E5: 1,8 # 17 pairs * PAIR F8: 6,8 BLK 8 F9: 6,8,4,9 # reduction candidate for 6,8 F9: 6,8 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 F9: 4,9 => CTR * 4586.21.3912537864637...92578.925631.6....2...2..6....8.61.35.23952764182.1859376 * PAIR G8: 4,9 BLK 9 H7: 4,9,7 # reduction candidate for 4,9 H7: 4,9 # 20 pairs G9: 4,9,3,7 # reduction candidate for 4,9 G9: 4,9 => CTR * 4586.21..9125.7364637...82578..25631.6....2...2..6.7..8.61.35.23.527..1.2.185...3 G9: 3,7 # 17 pairs H9: 4,9,7,8 # reduction candidate for 4,9 H9: 4,9 => CTR * 4586.21..9125.7.64637....2578..25631.6....2...2..6....8.61.35.23.527..1.2.1.5.... H9: 7,8 # 17 pairs * PAIR G8: 4,9 COL G G6: 4,9,7 # reduction candidate for 4,9 G6: 4,9 => CTR * 4586321..912587364637...82578..25631.6....2...2..6....8761.35.23.527..162.185.7.3 G6: 7 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 * PAIR I8: 6,8 BLK 9 I9: 6,8,3,7,9 # reduction candidate for 6,8 I9: 6,8 => CTR * 458692173912537864637...92578..25631.6....2...2..6.7..87614359239527.41.241.5.386 I9: 3,7,9 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-493-base-pr-000.dot * REASONING * PRF # I1: 3,9 => SOL * DIS # I1: 7 => CTR => I1: 3,9 * DIS # I1: 7,9 => CTR => I1: 3 * PRF # I1: 3 => SOL * DIS # H5: 7,9 => CTR => H5: 4,5,8 * DIS # H6: 7,9 => CTR => H6: 4,5,8 * DIS # H9: 7,9 => CTR => H9: 4,8 * DIS # E3: 8,9 => CTR => E3: 1,4 * DIS # F3: 8,9 => CTR => F3: 1,4 * DIS # C5: 4,9 => CTR => C5: 3 * DIS # E5: 4,9 => CTR => E5: 1,8 * PRF # F6: 4,9 => SOL * DIS # D3: 4,9 => CTR => D3: 8 * PRF # D3: 8 => SOL * PRF # D9: 4,9 => SOL * DIS # D9: 8 => CTR => D9: 4,9 * DIS # B7: 4,9 => CTR => B7: 7 * PRF # D9: 4,9 => SOL * DIS # D9: 8 => CTR => D9: 4,9 * DIS # F9: 4,9 => CTR => F9: 6,8 * PRF # F9: 6,8 => SOL * DIS # B7: 4,9 => CTR => B7: 7 * DIS # E3: 4,9 => CTR => E3: 1,8 * DIS # E5: 4,9 => CTR => E5: 1,8 * PRF # F9: 6,8 => SOL * DIS # F9: 4,9 => CTR => F9: 6,8 * DIS # G9: 4,9 => CTR => G9: 3,7 * DIS # H9: 4,9 => CTR => H9: 7,8 * DIS # G6: 4,9 => CTR => G6: 7 * PRF # G6: 7 => SOL * DIS # I9: 6,8 => CTR => I9: 3,7,9 * PRF # I9: 3,7,9 => SOL * CNT 32 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B8,C4,D4,D5,D6,E1,E2,E7,F8,G2,G3,G8,H1,I8) * 4586.21..9125.7.64637....2578..25631.6....2...2..6....8.61.35.23.527..1.2.1.5.... * PAIR E1: 3,9 ROW 1 I1: 3,9,7 # reduction candidate for 3,9 I1: 3,9 => SOLVED * 458692173912537864637814925789425631563781249124369758876143592395278416241956387 * DURATION: 0:00:02.584656 START: 19:32:23.892083 END: 19:32:26.476739 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-493-base-pr-001.dot * REASONING * PRF # I1: 3,9 => SOL * STA I1: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 493 solution: 458692173912537864637814925789425631563781249124369758876143592395278416241956387 info: 96272 FNBTHXK S8.f 20734 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 458692173912537864637814925789425631563781249124369758876143592395278416241956387 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 # I1: 3,9 => SOL * DIS # I1: 7 => CTR => I1: 3,9 * DIS # I1: 7,9 => CTR => I1: 3 * PRF # I1: 3 => SOL * DIS # H5: 7,9 => CTR => H5: 4,5,8 * INC # H5: 4,5,8 => UNS * DIS # H6: 7,9 => CTR => H6: 4,5,8 * INC # H6: 4,5,8 => UNS * INC # H7: 7,9 => UNS * DIS # H9: 7,9 => CTR => H9: 4,8 * INC # H9: 4,8 => UNS * INC # D3: 8,9 => UNS * DIS # E3: 8,9 => CTR => E3: 1,4 * INC # E3: 1,4 => UNS * DIS # F3: 8,9 => CTR => F3: 1,4 * INC # F3: 1,4 => UNS * DIS # C5: 4,9 => CTR => C5: 3 * INC # C5: 3 => UNS * INC # C6: 4,9 => UNS * DIS # E5: 4,9 => CTR => E5: 1,8 * INC # E5: 1,8 => UNS * INC # F5: 4,9 => UNS * PRF # F6: 4,9 => SOL * INC # F6: 1,8 => UNS * DIS # D3: 4,9 => CTR => D3: 8 * PRF # D3: 8 => SOL * PRF # D9: 4,9 => SOL * DIS # D9: 8 => CTR => D9: 4,9 * DIS # B7: 4,9 => CTR => B7: 7 * INC # B7: 7 => UNS * INC # B9: 4,9 => UNS * PRF # D9: 4,9 => SOL * DIS # D9: 8 => CTR => D9: 4,9 * DIS # F9: 4,9 => CTR => F9: 6,8 * PRF # F9: 6,8 => SOL * DIS # B7: 4,9 => CTR => B7: 7 * INC # B7: 7 => UNS * INC # H7: 4,9 => UNS * DIS # E3: 4,9 => CTR => E3: 1,8 * INC # E3: 1,8 => UNS * DIS # E5: 4,9 => CTR => E5: 1,8 * INC # E5: 1,8 => UNS * PRF # F9: 6,8 => SOL * DIS # F9: 4,9 => CTR => F9: 6,8 * INC # H7: 4,9 => UNS * DIS # G9: 4,9 => CTR => G9: 3,7 * INC # G9: 3,7 => UNS * DIS # H9: 4,9 => CTR => H9: 7,8 * INC # H9: 7,8 => UNS * DIS # G6: 4,9 => CTR => G6: 7 * PRF # G6: 7 => SOL * DIS # I9: 6,8 => CTR => I9: 3,7,9 * PRF # I9: 3,7,9 => SOL * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I1: 3,9 => SOL * STA I1: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED