Analysis of xx-top500-086-base.sdk
Contents
Original Sudoku
level: medium
position: .1.53....46....2........8...7.....1.8....2..........6.2.....4.....67.......1..... initial
Autosolve
position: 9125386474687912..7..246891.7486..128.6.127.412.457.682.1.8.476.8.67412.64712..8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B5: 3,5 => SOL * DIS # B5: 9 => CTR => B5: 3,5 * DIS # B7: 3,5 => CTR => B7: 9 * PRF # B7: 9 => SOL * PRF # C8: 3,5 => SOL * DIS # C8: 9 => CTR => C8: 3,5 * DIS # I8: 3,5 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # I9: 3,5 => SOL * DIS # I9: 9 => CTR => I9: 3,5 * PRF # B5: 3,5 => SOL * DIS # B5: 9 => CTR => B5: 3,5 * DIS # G4: 3,5 => CTR => G4: 9 * PRF # G4: 9 => SOL * PRF # B5: 3,9 => SOL * DIS # B5: 5 => CTR => B5: 3,9 * PRF # C8: 5 => SOL * PRF # G4: 3,9 => SOL * DIS # G4: 5 => CTR => G4: 3,9 * DIS # F7: 3,9 => CTR => F7: 5 * PRF # B5: 3,9 => SOL * DIS # B5: 5 => CTR => B5: 3,9 * DIS # G4: 3,5 => CTR => G4: 9 * PRF # G4: 9 => SOL * PRF # B5: 3,5 => SOL * DIS # B5: 9 => CTR => B5: 3,5 * PRF # G4: 3,9 => SOL * DIS # G4: 5 => CTR => G4: 3,9 * DIS # B7: 3,5 => CTR => B7: 9 * PRF # B7: 9 => SOL * PRF # C8: 3,5 => SOL * DIS # C8: 9 => CTR => C8: 3,5 * DIS # I8: 3,5 => CTR => I8: 9 * PRF # I8: 9 => SOL * DIS # F7: 3,9 => CTR => F7: 5 * DIS # B7: 5 => CTR => B7: 3,9 * DIS # I8: 3,5 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # I9: 3,5 => SOL * DIS # I9: 9 => CTR => I9: 3,5 * DIS # F9: 3,5 => CTR => F9: 9 * PRF # F9: 9 => SOL * DIS # G4: 3,5 => CTR => G4: 9 * PRF # G4: 9 => SOL * CNT 44 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B5: 3,5 => SOL * STA B5: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1.53....46....2........8...7.....1.8....2..........6.2.....4.....67.......1..... | initial |
| 9125386474687912..7..246891.7486..128.6.127.412.457.682.1.8.476.8.67412.64712..8. | autosolve |
| 912538647468791235753246891574863912836912754129457368291385476385674129647129583 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B3: 3,5 C3: 3,5 H2: 3,5 I2: 3,5 A4: 3,5 C6: 3,9 F4: 3,9 D5: 3,9 H5: 3,5 G6: 3,9 A8: 3,5 D7: 3,9 G9: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 3.. / B3 = 3 => 16 pairs (_) / C3 = 3 => 0 pairs (*) H2,I2: 3.. / H2 = 3 => 0 pairs (*) / I2 = 3 => 0 pairs (X) F4,D5: 3.. / F4 = 3 => 0 pairs (*) / D5 = 3 => 0 pairs (X) C6,G6: 3.. / C6 = 3 => 0 pairs (X) / G6 = 3 => 0 pairs (_) A4,A8: 3.. / A4 = 3 => 0 pairs (X) / A8 = 3 => 0 pairs (_) D5,D7: 3.. / D5 = 3 => 0 pairs (X) / D7 = 3 => 0 pairs (_) H2,H5: 3.. / H2 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) B3,C3: 5.. / B3 = 5 => 0 pairs (*) / C3 = 5 => 0 pairs (X) H2,I2: 5.. / H2 = 5 => 0 pairs (X) / I2 = 5 => 0 pairs (_) A4,B5: 5.. / A4 = 5 => 0 pairs (*) / B5 = 5 => 0 pairs (X) G4,H5: 5.. / G4 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) F7,F9: 5.. / F7 = 5 => 16 pairs (_) / F9 = 5 => 0 pairs (X) A4,G4: 5.. / A4 = 5 => 0 pairs (*) / G4 = 5 => 0 pairs (X) B5,H5: 5.. / B5 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) B7,F7: 5.. / B7 = 5 => 0 pairs (X) / F7 = 5 => 16 pairs (_) A4,A8: 5.. / A4 = 5 => 0 pairs (*) / A8 = 5 => 0 pairs (X) C3,C8: 5.. / C3 = 5 => 16 pairs (_) / C8 = 5 => 0 pairs (*) G4,G9: 5.. / G4 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) H2,H5: 5.. / H2 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) B5,C6: 9.. / B5 = 9 => 0 pairs (X) / C6 = 9 => 0 pairs (_) F4,D5: 9.. / F4 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) G4,G6: 9.. / G4 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) B7,C8: 9.. / B7 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) I8,I9: 9.. / I8 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) F4,G4: 9.. / F4 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) B5,D5: 9.. / B5 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) C6,G6: 9.. / C6 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) C8,I8: 9.. / C8 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) F9,I9: 9.. / F9 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) B5,B7: 9.. / B5 = 9 => 0 pairs (X) / B7 = 9 => 0 pairs (_) C6,C8: 9.. / C6 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) D5,D7: 9.. / D5 = 9 => 0 pairs (*) / D7 = 9 => 0 pairs (X) * DURATION: 0:00:54.399320 START: 05:43:19.936995 END: 05:44:14.336315 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B3,C3,C6,D5,D7,F4,G6,G9,H2,H5,I2) * 9125386474687912..7..246891.7486..128.6.127.412.457.682.1.8.476.8.67412.64712..8. * PAIR B3: 3,5 COL B B5: 3,5,9 # reduction candidate for 3,5 B5: 3,5 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 B5: 9 => CTR * 9125386474687912..7..24689157486..128963127541234579682.198.47638967412564712538. B7: 3,5,9 # reduction candidate for 3,5 B7: 3,5 => CTR * 9125386474687912..7..246891.7486..128963127541234579682.198.47638967412564712538. B7: 9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 * PAIR C3: 3,5 COL C C8: 3,5,9 # reduction candidate for 3,5 C8: 3,5 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 C8: 9 => CTR * 9125386474687912..7.5246891.7486..128.6.127.41234579682.1.8.476389674125647125389 * PAIR I2: 3,5 COL I I8: 3,5,9 # reduction candidate for 3,5 I8: 3,5 => CTR * 9125386474687912..7.5246891.7486..1289631275412345796825198347638967412564712..89 I8: 9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 I9: 3,5,9 # reduction candidate for 3,5 I9: 3,5 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 I9: 9 => CTR * 9125386474687912..7.5246891.7486..1289631275412345796825198347638967412564712..89 * PAIR A4: 3,5 BLK 4 B5: 3,5,9 # reduction candidate for 3,5 B5: 3,5 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 B5: 9 => CTR * 9125386474687912..7..24689157486..128963127541234579682.198.47638967412564712538. * PAIR A4: 3,5 ROW 4 G4: 3,5,9 # reduction candidate for 3,5 G4: 3,5 => CTR * 9125386474687912..7..246891.74869.128963127541234579682.198.47638967412564712538. G4: 9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 * PAIR C6: 3,9 BLK 4 B5: 3,9,5 # reduction candidate for 3,9 B5: 3,9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 B5: 5 => CTR * 9125386474687912..7..246891.7486..1285691273412.457.682.1.8.476.8.67412.64712..8. * PAIR C6: 3,9 COL C C8: 3,9,5 # reduction candidate for 3,9 C8: 5 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 C8: 3,9 # 16 pairs * PAIR F4: 3,9 ROW 4 G4: 3,9,5 # reduction candidate for 3,9 G4: 3,9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 G4: 5 => CTR * 9125386474687912..7..246891.748695128.6.127.412.457.682.1.8.476.8.67412.64712..8. * PAIR F4: 3,9 COL F F7: 3,9,5 # reduction candidate for 3,9 F7: 3,9 => CTR * 9125386474687912..7..246891.7486..128.6.127.412.457.68251.8.476389674125647125389 F7: 5 # 16 pairs F9: 3,9,5 # reduction candidate for 3,9 F9: 3,9 # 16 pairs * PAIR D5: 3,9 ROW 5 B5: 3,9,5 # reduction candidate for 3,9 B5: 3,9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 B5: 5 => CTR * 9125386474687912..7..246891.7486..1285691273412.457.682.1.8.476.8.67412.64712..8. * PAIR H5: 3,5 BLK 6 G4: 3,5,9 # reduction candidate for 3,5 G4: 3,5 => CTR * 9125386474687912..7..246891.74869.128963127541234579682.198.47638967412564712538. G4: 9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 * PAIR H5: 3,5 ROW 5 B5: 3,5,9 # reduction candidate for 3,5 B5: 3,5 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 B5: 9 => CTR * 9125386474687912..7..24689157486..128963127541234579682.198.47638967412564712538. * PAIR G6: 3,9 BLK 6 G4: 3,9,5 # reduction candidate for 3,9 G4: 3,9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 G4: 5 => CTR * 9125386474687912..7..246891.748695128.6.127.412.457.682.1.8.476.8.67412.64712..8. * PAIR A8: 3,5 BLK 7 B7: 3,5,9 # reduction candidate for 3,5 B7: 3,5 => CTR * 9125386474687912..7..246891.7486..128963127541234579682.198.47638967412564712538. B7: 9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 C8: 3,5,9 # reduction candidate for 3,5 C8: 3,5 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 C8: 9 => CTR * 9125386474687912..7.5246891.7486..128.6.127.41234579682.1.8.476389674125647125389 * PAIR A8: 3,5 ROW 8 I8: 3,5,9 # reduction candidate for 3,5 I8: 3,5 => CTR * 9125386474687912..7.5246891.7486..1289631275412345796825198347638967412564712..89 I8: 9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 * PAIR D7: 3,9 BLK 8 F7: 3,9,5 # reduction candidate for 3,9 F7: 3,9 => CTR * 9125386474687912..7..246891.7486..128.6.127.412.457.68251.8.476389674125647125389 F7: 5 # 16 pairs F9: 3,9,5 # reduction candidate for 3,9 F9: 3,9 # 16 pairs * PAIR D7: 3,9 ROW 7 B7: 3,9,5 # reduction candidate for 3,9 B7: 5 => CTR * 9125386474687912..7..246891.7486..1289631275412345796825198347638967412564712538. B7: 3,9 # 16 pairs * PAIR G9: 3,5 BLK 9 I8: 3,5,9 # reduction candidate for 3,5 I8: 3,5 => CTR * 9125386474687912..7.5246891.7486..1289631275412345796825198347638967412564712..89 I8: 9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 I9: 3,5,9 # reduction candidate for 3,5 I9: 3,5 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 I9: 9 => CTR * 9125386474687912..7.5246891.7486..1289631275412345796825198347638967412564712..89 * PAIR G9: 3,5 ROW 9 F9: 3,5,9 # reduction candidate for 3,5 F9: 3,5 => CTR * 9125386474687912..7.5246891.7486..1289631275412345796825198347638967412564712..89 F9: 9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 * PAIR G9: 3,5 COL G G4: 3,5,9 # reduction candidate for 3,5 G4: 3,5 => CTR * 9125386474687912..7..246891.74869.128963127541234579682.198.47638967412564712538. G4: 9 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-086-base-pr-000.dot * REASONING * PRF # B5: 3,5 => SOL * DIS # B5: 9 => CTR => B5: 3,5 * DIS # B7: 3,5 => CTR => B7: 9 * PRF # B7: 9 => SOL * PRF # C8: 3,5 => SOL * DIS # C8: 9 => CTR => C8: 3,5 * DIS # I8: 3,5 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # I9: 3,5 => SOL * DIS # I9: 9 => CTR => I9: 3,5 * PRF # B5: 3,5 => SOL * DIS # B5: 9 => CTR => B5: 3,5 * DIS # G4: 3,5 => CTR => G4: 9 * PRF # G4: 9 => SOL * PRF # B5: 3,9 => SOL * DIS # B5: 5 => CTR => B5: 3,9 * PRF # C8: 5 => SOL * PRF # G4: 3,9 => SOL * DIS # G4: 5 => CTR => G4: 3,9 * DIS # F7: 3,9 => CTR => F7: 5 * PRF # B5: 3,9 => SOL * DIS # B5: 5 => CTR => B5: 3,9 * DIS # G4: 3,5 => CTR => G4: 9 * PRF # G4: 9 => SOL * PRF # B5: 3,5 => SOL * DIS # B5: 9 => CTR => B5: 3,5 * PRF # G4: 3,9 => SOL * DIS # G4: 5 => CTR => G4: 3,9 * DIS # B7: 3,5 => CTR => B7: 9 * PRF # B7: 9 => SOL * PRF # C8: 3,5 => SOL * DIS # C8: 9 => CTR => C8: 3,5 * DIS # I8: 3,5 => CTR => I8: 9 * PRF # I8: 9 => SOL * DIS # F7: 3,9 => CTR => F7: 5 * DIS # B7: 5 => CTR => B7: 3,9 * DIS # I8: 3,5 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # I9: 3,5 => SOL * DIS # I9: 9 => CTR => I9: 3,5 * DIS # F9: 3,5 => CTR => F9: 9 * PRF # F9: 9 => SOL * DIS # G4: 3,5 => CTR => G4: 9 * PRF # G4: 9 => SOL * CNT 44 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B3,C3,C6,D5,D7,F4,G6,G9,H2,H5,I2) * 9125386474687912..7..246891.7486..128.6.127.412.457.682.1.8.476.8.67412.64712..8. * PAIR B3: 3,5 COL B B5: 3,5,9 # reduction candidate for 3,5 B5: 3,5 => SOLVED * 912538647468791235753246891574863912836912754129457368291385476385674129647129583 * DURATION: 0:00:01.897773 START: 05:45:09.260163 END: 05:45:11.157936 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-086-base-pr-001.dot * REASONING * PRF # B5: 3,5 => SOL * STA B5: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 086 solution: 912538647468791235753246891574863912836912754129457368291385476385674129647129583 info: 1559 FNBWXY S8.f 15621 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 912538647468791235753246891574863912836912754129457368291385476385674129647129583 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 # B5: 3,5 => SOL * DIS # B5: 9 => CTR => B5: 3,5 * DIS # B7: 3,5 => CTR => B7: 9 * PRF # B7: 9 => SOL * PRF # C8: 3,5 => SOL * DIS # C8: 9 => CTR => C8: 3,5 * DIS # I8: 3,5 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # I9: 3,5 => SOL * DIS # I9: 9 => CTR => I9: 3,5 * PRF # B5: 3,5 => SOL * DIS # B5: 9 => CTR => B5: 3,5 * DIS # G4: 3,5 => CTR => G4: 9 * PRF # G4: 9 => SOL * PRF # B5: 3,9 => SOL * DIS # B5: 5 => CTR => B5: 3,9 * INC # C8: 3,9 => UNS * PRF # C8: 5 => SOL * PRF # G4: 3,9 => SOL * DIS # G4: 5 => CTR => G4: 3,9 * DIS # F7: 3,9 => CTR => F7: 5 * INC # F7: 5 => UNS * INC # F9: 3,9 => UNS * PRF # B5: 3,9 => SOL * DIS # B5: 5 => CTR => B5: 3,9 * DIS # G4: 3,5 => CTR => G4: 9 * PRF # G4: 9 => SOL * PRF # B5: 3,5 => SOL * DIS # B5: 9 => CTR => B5: 3,5 * PRF # G4: 3,9 => SOL * DIS # G4: 5 => CTR => G4: 3,9 * DIS # B7: 3,5 => CTR => B7: 9 * PRF # B7: 9 => SOL * PRF # C8: 3,5 => SOL * DIS # C8: 9 => CTR => C8: 3,5 * DIS # I8: 3,5 => CTR => I8: 9 * PRF # I8: 9 => SOL * DIS # F7: 3,9 => CTR => F7: 5 * INC # F7: 5 => UNS * INC # F9: 3,9 => UNS * INC # B7: 3,9 => UNS * DIS # B7: 5 => CTR => B7: 3,9 * DIS # I8: 3,5 => CTR => I8: 9 * PRF # I8: 9 => SOL * PRF # I9: 3,5 => SOL * DIS # I9: 9 => CTR => I9: 3,5 * DIS # F9: 3,5 => CTR => F9: 9 * PRF # F9: 9 => SOL * DIS # G4: 3,5 => CTR => G4: 9 * PRF # G4: 9 => SOL * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B5: 3,5 => SOL * STA B5: 3,5 * CNT 1 HDP CHAINS / 1 HYP OPENED