Analysis of xx-top500-105-base.sdk
Contents
Original Sudoku
level: medium
position: .9..7..2.....3.6..............5.1.9.3.....8.76........8.....3...5.9........4..... initial
Autosolve
position: .93675.28.8.13967..6.84293..78561.933152948676.9387...8..7.63.9.5.9.3.8.93.4.8... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A8: 1,4 => CTR => A8: 2,7 * DIS # A2: 2,4 => CTR => A2: 5 * PRF # A2: 5 => SOL * DIS # C7: 2,4 => CTR => C7: 1 * PRF # A3: 1,7 => SOL * DIS # A3: 5 => CTR => A3: 1,7 * DIS # C8: 1,7 => CTR => C8: 2,4,6 * DIS # C9: 1,7 => CTR => C9: 2,6 * DIS # G6: 1,4 => CTR => G6: 2,5 * DIS # G8: 1,4 => CTR => G8: 2,7 * PRF # A2: 4,5 => SOL * DIS # A2: 2 => CTR => A2: 4,5 * DIS # A3: 7 => CTR => A3: 1,5 * DIS # A2: 2,4 => CTR => A2: 5 * PRF # A2: 5 => SOL * DIS # A8: 2,4 => CTR => A8: 1,7 * DIS # G6: 2,4 => CTR => G6: 1,5 * PRF # I6: 2,4 => SOL * DIS # I6: 1 => CTR => I6: 2,4 * DIS # G6: 2,4 => CTR => G6: 1,5 * PRF # I6: 2,4 => SOL * DIS # I6: 1 => CTR => I6: 2,4 * PRF # G8: 2,4 => SOL * DIS # C7: 2,4 => CTR => C7: 1 * DIS # A8: 2,4 => CTR => A8: 1,7 * DIS # E7: 1,2 => CTR => E7: 5 * DIS # A8: 1,2 => CTR => A8: 4,7 * DIS # C8: 1,2 => CTR => C8: 4,6,7 * DIS # I8: 1,2 => CTR => I8: 4,6 * DIS # H7: 1,5 => CTR => H7: 4 * PRF # H7: 4 => SOL * DIS # G9: 1,5 => CTR => G9: 2,7 * PRF # E9: 2 => SOL * PRF # H6: 1,5 => SOL * DIS # H6: 4 => CTR => H6: 1,5 * CNT 35 HDP CHAINS / 58 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A8: 1,4 => CTR => A8: 2,7 * DIS A8: 2,7 # A2: 2,4 => CTR => A2: 5 * PRF A8: 2,7 + A2: 5 => SOL * STA A8: 2,7 + A2: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .9..7..2.....3.6..............5.1.9.3.....8.76........8.....3...5.9........4..... | initial |
| .93675.28.8.13967..6.84293..78561.933152948676.9387...8..7.63.9.5.9.3.8.93.4.8... | autosolve |
| 493675128582139674167842935278561493315294867649387512821756349754913286936428751 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A1: 1,4 C2: 2,4 C3: 1,7 G1: 1,4 I2: 4,5 I3: 1,5 A4: 2,4 B6: 2,4 G4: 2,4 B7: 2,4 E8: 1,2 H9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,I3: 1.. / G1 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) A1,G1: 1.. / A1 = 1 => 0 pairs (X) / G1 = 1 => 0 pairs (_) A2,C2: 2.. / A2 = 2 => 0 pairs (X) / C2 = 2 => 0 pairs (_) A4,B6: 2.. / A4 = 2 => 0 pairs (*) / B6 = 2 => 0 pairs (X) A4,G4: 2.. / A4 = 2 => 0 pairs (*) / G4 = 2 => 0 pairs (X) B6,B7: 2.. / B6 = 2 => 0 pairs (X) / B7 = 2 => 0 pairs (_) G1,I2: 4.. / G1 = 4 => 0 pairs (X) / I2 = 4 => 0 pairs (_) A4,B6: 4.. / A4 = 4 => 0 pairs (X) / B6 = 4 => 0 pairs (_) A1,G1: 4.. / A1 = 4 => 0 pairs (*) / G1 = 4 => 0 pairs (X) A4,G4: 4.. / A4 = 4 => 0 pairs (X) / G4 = 4 => 0 pairs (_) B6,B7: 4.. / B6 = 4 => 0 pairs (*) / B7 = 4 => 0 pairs (X) H6,H7: 4.. / H6 = 4 => 0 pairs (X) / H7 = 4 => 0 pairs (_) A2,A3: 5.. / A2 = 5 => 0 pairs (*) / A3 = 5 => 0 pairs (X) I2,I3: 5.. / I2 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) G6,H6: 5.. / G6 = 5 => 13 pairs (_) / H6 = 5 => 0 pairs (X) E7,E9: 5.. / E7 = 5 => 14 pairs (_) / E9 = 5 => 0 pairs (X) A2,I2: 5.. / A2 = 5 => 0 pairs (*) / I2 = 5 => 0 pairs (X) A3,I3: 5.. / A3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) E7,H7: 5.. / E7 = 5 => 14 pairs (_) / H7 = 5 => 0 pairs (X) G6,G9: 5.. / G6 = 5 => 13 pairs (_) / G9 = 5 => 0 pairs (X) C8,C9: 6.. / C8 = 6 => 12 pairs (_) / C9 = 6 => 14 pairs (_) I8,I9: 6.. / I8 = 6 => 14 pairs (_) / I9 = 6 => 12 pairs (_) C8,I8: 6.. / C8 = 6 => 12 pairs (_) / I8 = 6 => 14 pairs (_) C9,I9: 6.. / C9 = 6 => 14 pairs (_) / I9 = 6 => 12 pairs (_) A3,C3: 7.. / A3 = 7 => 0 pairs (X) / C3 = 7 => 13 pairs (_) G8,G9: 7.. / G8 = 7 => 0 pairs (X) / G9 = 7 => 13 pairs (_) C9,G9: 7.. / C9 = 7 => 0 pairs (X) / G9 = 7 => 13 pairs (_) A3,A8: 7.. / A3 = 7 => 0 pairs (X) / A8 = 7 => 13 pairs (_) * DURATION: 0:00:47.480792 START: 06:21:18.597184 END: 06:22:06.077976 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B6,B7,C2,C3,E8,G1,G4,H9,I2,I3) * .93675.28.8.13967..6.84293..78561.933152948676.9387...8..7.63.9.5.9.3.8.93.4.8... * PAIR A1: 1,4 COL A A8: 1,4,2,7 # reduction candidate for 1,4 A8: 1,4 => CTR * 493675128582139674761842935278561493315294867649387...8247.63.915.92378693.4.8... A8: 2,7 # 13 pairs * PAIR C2: 2,4 BLK 1 A2: 2,4,5 # reduction candidate for 2,4 A2: 2,4 => CTR * 193675428.8.13967556784293147856129331529486762938751484.7.635975.9.3.8.93.4.87.. A2: 5 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 * PAIR C2: 2,4 COL C C7: 2,4,1 # reduction candidate for 2,4 C7: 2,4 => CTR * .9367512828413967..6.84293..78561.933152948676.93875418427.63.9.5.9.3.8.93.4.8... C7: 1 # 16 pairs C8: 2,4,1,6,7 # reduction candidate for 2,4 C8: 2,4 # 17 pairs * PAIR C3: 1,7 BLK 1 A3: 1,7,5 # reduction candidate for 1,7 A3: 1,7 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 A3: 5 => CTR * 193675428.8.13967556784293147856129331529486762938751484.7.635975.9.3.8.93.4.87.. * PAIR C3: 1,7 COL C C8: 1,7,2,4,6 # reduction candidate for 1,7 C8: 1,7 => CTR * .93675128.8.139674.6.842935.78561.933152948676.93875..8.47.63.9.5.9234869364.87.2 C8: 2,4,6 # 12 pairs C9: 1,7,2,6 # reduction candidate for 1,7 C9: 1,7 => CTR * .9367512828413967..6.84293..78561.933152948676.93875418427.63.9.569.3.8293.428.56 C9: 2,6 # 14 pairs * PAIR G1: 1,4 COL G G6: 1,4,2,5 # reduction candidate for 1,4 G6: 1,4 => CTR * .93675.28.8.13967..6.84293..78561.93315294867649387152821756349.5.913.8.93.4.851. G6: 2,5 # 13 pairs G8: 1,4,2,7 # reduction candidate for 1,4 G8: 1,4 => CTR * .93675.28.841396755678429314785612933152948676293875..84.7.63.9.5.9.3.8.93.4.87.. G8: 2,7 # 13 pairs * PAIR I2: 4,5 ROW 2 A2: 4,5,2 # reduction candidate for 4,5 A2: 4,5 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 A2: 2 => CTR * .93675.28284139675567842931478561293315294867629387..484.7.63.975.9.348.93.4.8... * PAIR I3: 1,5 ROW 3 A3: 1,5,7 # reduction candidate for 1,5 A3: 7 => CTR * .93675.28582139674761842935.78561.933152948676.9387...8.47.63.915.9234869364.87.2 A3: 1,5 # 13 pairs * PAIR A4: 2,4 COL A A2: 2,4,5 # reduction candidate for 2,4 A2: 2,4 => CTR * 193675428.8.13967556784293147856129331529486762938751484.7.635975.9.3.8.93.4.87.. A2: 5 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 A8: 2,4,1,7 # reduction candidate for 2,4 A8: 2,4 => CTR * .93675.28.8.13967.761842935.78561.933152948676.9387...8..7.63.9.5.9.3.8.93.4.8... A8: 1,7 # 13 pairs * PAIR B6: 2,4 ROW 6 G6: 2,4,1,5 # reduction candidate for 2,4 G6: 2,4 => CTR * .93675128.8.139674.6.842935.78561.93315294867649387251821756349.5491378.93.4.851. G6: 1,5 # 13 pairs I6: 2,4,1 # reduction candidate for 2,4 I6: 2,4 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 I6: 1 => CTR * 493675128582139674.6.84293527856149331529486764938725182.756349.549.378693.4.8... * PAIR G4: 2,4 BLK 6 G6: 2,4,1,5 # reduction candidate for 2,4 G6: 2,4 => CTR * .93675128.8.139674.6.842935.78561.93315294867649387251821756349.5491378.93.4.851. G6: 1,5 # 13 pairs I6: 2,4,1 # reduction candidate for 2,4 I6: 2,4 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 I6: 1 => CTR * 493675128582139674.6.84293527856149331529486764938725182.756349.549.378693.4.8... * PAIR G4: 2,4 COL G G8: 2,4,1,7 # reduction candidate for 2,4 G8: 2,4 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 G8: 1,7 # 13 pairs * PAIR B7: 2,4 BLK 7 C7: 2,4,1 # reduction candidate for 2,4 C7: 2,4 => CTR * .9367512828413967..6.84293..78561.933152948676.93875418427.63.9.5.9.3.8.93.4.8... C7: 1 # 16 pairs A8: 2,4,1,7 # reduction candidate for 2,4 A8: 2,4 => CTR * .93675.28.8.13967.761842935.78561.933152948676.9387...8..7.63.9.5.9.3.8.93.4.8... A8: 1,7 # 13 pairs C8: 2,4,1,6,7 # reduction candidate for 2,4 C8: 2,4 # 17 pairs * PAIR E8: 1,2 BLK 8 E7: 1,2,5 # reduction candidate for 1,2 E7: 1,2 => CTR * .93675128.8413967..6.84293..78561.933152948676.938754184.7.6359.5.9.3.8.93.458.1. E7: 5 # 14 pairs E9: 1,2,5 # reduction candidate for 1,2 E9: 1,2 # 14 pairs * PAIR E8: 1,2 ROW 8 A8: 1,2,4,7 # reduction candidate for 1,2 A8: 1,2 => CTR * 493675128582139674761842935278561493315294867649387...8247.63.915.92378693.4.8... A8: 4,7 # 13 pairs C8: 1,2,4,6,7 # reduction candidate for 1,2 C8: 1,2 => CTR * 493675128.82139674167842935278561.933152948676.93875..8..7.63.975.9.34869364.87.2 C8: 4,6,7 # 12 pairs G8: 1,2,4,7 # reduction candidate for 1,2 G8: 1,2 # 16 pairs I8: 1,2,4,6 # reduction candidate for 1,2 I8: 1,2 => CTR * 493675128.82139674167842935278561.933152948676.9387...8..7.63.97569.348.93.4.87.6 I8: 4,6 # 13 pairs * PAIR H9: 1,5 BLK 9 H7: 1,5,4 # reduction candidate for 1,5 H7: 1,5 => CTR * .93675.28.841396755678429314785612933152948676.9387.4.84.7.63.9.5.9.3.8.93.4.8... H7: 4 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 G9: 1,5,2,7 # reduction candidate for 1,5 G9: 1,5 => CTR * .93675.28.8.13967.761842935.78561.933152948676.9387...8..7.63.915692378.9374.8..6 G9: 2,7 # 14 pairs * PAIR H9: 1,5 ROW 9 E9: 1,5,2 # reduction candidate for 1,5 E9: 2 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 E9: 1,5 # 16 pairs * PAIR H9: 1,5 COL H H6: 1,5,4 # reduction candidate for 1,5 H6: 1,5 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 H6: 4 => CTR * .93675128.8413967..6.84293..78561.933152948676.938754184.7.63.9.5.9.3.8.93.4.8... * INCONCLUSIVE * SAVE PR GRAPH xx-top500-105-base-pr-000.dot * REASONING * DIS # A8: 1,4 => CTR => A8: 2,7 * DIS # A2: 2,4 => CTR => A2: 5 * PRF # A2: 5 => SOL * DIS # C7: 2,4 => CTR => C7: 1 * PRF # A3: 1,7 => SOL * DIS # A3: 5 => CTR => A3: 1,7 * DIS # C8: 1,7 => CTR => C8: 2,4,6 * DIS # C9: 1,7 => CTR => C9: 2,6 * DIS # G6: 1,4 => CTR => G6: 2,5 * DIS # G8: 1,4 => CTR => G8: 2,7 * PRF # A2: 4,5 => SOL * DIS # A2: 2 => CTR => A2: 4,5 * DIS # A3: 7 => CTR => A3: 1,5 * DIS # A2: 2,4 => CTR => A2: 5 * PRF # A2: 5 => SOL * DIS # A8: 2,4 => CTR => A8: 1,7 * DIS # G6: 2,4 => CTR => G6: 1,5 * PRF # I6: 2,4 => SOL * DIS # I6: 1 => CTR => I6: 2,4 * DIS # G6: 2,4 => CTR => G6: 1,5 * PRF # I6: 2,4 => SOL * DIS # I6: 1 => CTR => I6: 2,4 * PRF # G8: 2,4 => SOL * DIS # C7: 2,4 => CTR => C7: 1 * DIS # A8: 2,4 => CTR => A8: 1,7 * DIS # E7: 1,2 => CTR => E7: 5 * DIS # A8: 1,2 => CTR => A8: 4,7 * DIS # C8: 1,2 => CTR => C8: 4,6,7 * DIS # I8: 1,2 => CTR => I8: 4,6 * DIS # H7: 1,5 => CTR => H7: 4 * PRF # H7: 4 => SOL * DIS # G9: 1,5 => CTR => G9: 2,7 * PRF # E9: 2 => SOL * PRF # H6: 1,5 => SOL * DIS # H6: 4 => CTR => H6: 1,5 * CNT 35 HDP CHAINS / 58 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B6,B7,C2,C3,E8,G1,G4,H9,I2,I3) * .93675.28.8.13967..6.84293..78561.933152948676.9387...8..7.63.9.5.9.3.8.93.4.8... * PAIR A1: 1,4 COL A A8: 1,4,2,7 # reduction candidate for 1,4 A8: 1,4 => CTR * 493675128582139674761842935278561493315294867649387...8247.63.915.92378693.4.8... * PAIR RESTART * PAIR C2: 2,4 BLK 1 A2: 2,4,5 # reduction candidate for 2,4 A2: 2,4 => CTR * .93675.28.8.139675567842931.78561.933152948676.938751.8..7.63497549.3186936418752 A2: 5 => SOLVED * 493675128582139674167842935278561493315294867649387512821756349754913286936428751 * DURATION: 0:00:05.085684 START: 06:23:01.795277 END: 06:23:06.880961 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-105-base-pr-001.dot * REASONING * DIS # A8: 1,4 => CTR => A8: 2,7 * DIS A8: 2,7 # A2: 2,4 => CTR => A2: 5 * PRF A8: 2,7 + A2: 5 => SOL * STA A8: 2,7 + A2: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 105 solution: 493675128582139674167842935278561493315294867649387512821756349754913286936428751 info: 1621 FNBHWXY S8.f 24487 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 493675128582139674167842935278561493315294867649387512821756349754913286936428751 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 # A8: 1,4 => CTR => A8: 2,7 * INC # A8: 2,7 => UNS * DIS # A2: 2,4 => CTR => A2: 5 * PRF # A2: 5 => SOL * DIS # C7: 2,4 => CTR => C7: 1 * INC # C7: 1 => UNS * INC # C8: 2,4 => UNS * PRF # A3: 1,7 => SOL * DIS # A3: 5 => CTR => A3: 1,7 * DIS # C8: 1,7 => CTR => C8: 2,4,6 * INC # C8: 2,4,6 => UNS * DIS # C9: 1,7 => CTR => C9: 2,6 * INC # C9: 2,6 => UNS * DIS # G6: 1,4 => CTR => G6: 2,5 * INC # G6: 2,5 => UNS * DIS # G8: 1,4 => CTR => G8: 2,7 * INC # G8: 2,7 => UNS * PRF # A2: 4,5 => SOL * DIS # A2: 2 => CTR => A2: 4,5 * INC # A3: 1,5 => UNS * DIS # A3: 7 => CTR => A3: 1,5 * DIS # A2: 2,4 => CTR => A2: 5 * PRF # A2: 5 => SOL * DIS # A8: 2,4 => CTR => A8: 1,7 * INC # A8: 1,7 => UNS * DIS # G6: 2,4 => CTR => G6: 1,5 * INC # G6: 1,5 => UNS * PRF # I6: 2,4 => SOL * DIS # I6: 1 => CTR => I6: 2,4 * DIS # G6: 2,4 => CTR => G6: 1,5 * INC # G6: 1,5 => UNS * PRF # I6: 2,4 => SOL * DIS # I6: 1 => CTR => I6: 2,4 * PRF # G8: 2,4 => SOL * INC # G8: 1,7 => UNS * DIS # C7: 2,4 => CTR => C7: 1 * INC # C7: 1 => UNS * DIS # A8: 2,4 => CTR => A8: 1,7 * INC # A8: 1,7 => UNS * INC # C8: 2,4 => UNS * DIS # E7: 1,2 => CTR => E7: 5 * INC # E7: 5 => UNS * INC # E9: 1,2 => UNS * DIS # A8: 1,2 => CTR => A8: 4,7 * INC # A8: 4,7 => UNS * DIS # C8: 1,2 => CTR => C8: 4,6,7 * INC # C8: 4,6,7 => UNS * INC # G8: 1,2 => UNS * DIS # I8: 1,2 => CTR => I8: 4,6 * INC # I8: 4,6 => UNS * DIS # H7: 1,5 => CTR => H7: 4 * PRF # H7: 4 => SOL * DIS # G9: 1,5 => CTR => G9: 2,7 * INC # G9: 2,7 => UNS * INC # E9: 1,5 => UNS * PRF # E9: 2 => SOL * PRF # H6: 1,5 => SOL * DIS # H6: 4 => CTR => H6: 1,5 * CNT 58 HDP CHAINS / 58 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A8: 1,4 => CTR => A8: 2,7 * DIS A8: 2,7 # A2: 2,4 => CTR => A2: 5 * PRF A8: 2,7 + A2: 5 => SOL * STA A8: 2,7 + A2: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED