Analysis of xx-top500-022-base.sdk
Contents
Original Sudoku
level: medium
position: .89...7.....2.1............51.3...6.....9.4..2........1......2.3...7.......4..... initial
Autosolve
position: 6895347127352.1...4219.7...517348269863792451294615...1.685..2.3.217....9.842.1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G2: 6,8 => SOL * DIS # G2: 9 => CTR => G2: 6,8 * DIS # I2: 6,8 => CTR => I2: 4 * PRF # I2: 4 => SOL * DIS # G3: 6,8 => CTR => G3: 3,5 * DIS # I3: 6,8 => CTR => I3: 3,5 * DIS # G3: 3,8 => CTR => G3: 5,6 * DIS # H6: 3,8 => CTR => H6: 7 * PRF # H6: 7 => SOL * DIS # H6: 3,8 => CTR => H6: 7 * PRF # H6: 7 => SOL * PRF # I6: 3,8 => SOL * DIS # I6: 7 => CTR => I6: 3,8 * DIS # G3: 3,8 => CTR => G3: 5,6 * DIS # I8: 4,5 => CTR => I8: 6,8 * PRF # I9: 5,7 => SOL * DIS # I9: 3,6 => CTR => I9: 5,7 * DIS # G8: 6,9 => CTR => G8: 5,8 * DIS # I9: 3,6 => CTR => I9: 5,7 * PRF # I9: 5,7 => SOL * DIS # I9: 3,7 => CTR => I9: 5,6 * DIS # H6: 8 => CTR => H6: 3,7 * CNT 22 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G2: 6,8 => SOL * STA G2: 6,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .89...7.....2.1............51.3...6.....9.4..2........1......2.3...7.......4..... | initial |
| 6895347127352.1...4219.7...517348269863792451294615...1.685..2.3.217....9.842.1.. | autosolve |
| 689534712735281694421967583517348269863792451294615378146853927352179846978426135 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) E2: 6,8 E3: 6,8 H2: 4,9 H3: 3,8 G6: 3,8 B7: 4,7 B8: 4,5 B9: 5,7 F7: 3,9 F8: 6,9 F9: 3,6 G7: 3,9 I7: 4,7 H8: 4,9 H9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F7,F9: 3.. / F7 = 3 => 0 pairs (*) / F9 = 3 => 0 pairs (X) F7,G7: 3.. / F7 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) H2,I2: 4.. / H2 = 4 => 0 pairs (X) / I2 = 4 => 0 pairs (_) B7,B8: 4.. / B7 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) B7,I7: 4.. / B7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) H2,H8: 4.. / H2 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) G3,I3: 5.. / G3 = 5 => 15 pairs (_) / I3 = 5 => 0 pairs (X) B8,B9: 5.. / B8 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) B9,I9: 5.. / B9 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) G3,G8: 5.. / G3 = 5 => 15 pairs (_) / G8 = 5 => 0 pairs (X) E2,E3: 6.. / E2 = 6 => 0 pairs (X) / E3 = 6 => 15 pairs (_) F8,F9: 6.. / F8 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) F9,I9: 6.. / F9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) H6,I6: 7.. / H6 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) B7,B9: 7.. / B7 = 7 => 0 pairs (X) / B9 = 7 => 0 pairs (_) B7,I7: 7.. / B7 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) H6,H9: 7.. / H6 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) E2,E3: 8.. / E2 = 8 => 15 pairs (_) / E3 = 8 => 0 pairs (X) G8,I8: 8.. / G8 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) H3,H6: 8.. / H3 = 8 => 17 pairs (_) / H6 = 8 => 0 pairs (X) G2,H2: 9.. / G2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) F7,F8: 9.. / F7 = 9 => 0 pairs (X) / F8 = 9 => 0 pairs (_) F7,G7: 9.. / F7 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) H2,H8: 9.. / H2 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) * DURATION: 0:00:56.689682 START: 03:20:09.781589 END: 03:21:06.471271 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B8,B9,E2,E3,F7,F8,F9,G6,G7,H2,H3,H8,H9,I7) * 6895347127352.1...4219.7...517348269863792451294615...1.685..2.3.217....9.842.1.. * PAIR E2: 6,8 ROW 2 G2: 6,8,9 # reduction candidate for 6,8 G2: 6,8 => SOLVED * 689534712735281694421967583517348269863792451294615378146853927352179846978426135 G2: 9 => CTR * 689534712735261948421987635517348269863792451294615...1.685932.3.2176.9.9.8423176 I2: 6,8,4 # reduction candidate for 6,8 I2: 6,8 => CTR * 689534712735261948421987635517348269863792451294615...1.685932.3.2176.9.9.8423176 I2: 4 => SOLVED * 689534712735281694421967583517348269863792451294615378146853927352179846978426135 * PAIR E3: 6,8 ROW 3 G3: 6,8,3,5 # reduction candidate for 6,8 G3: 6,8 => CTR * 6895347127352.1..44219.7.35517348269863792451294615.8.1.685..2.3.217.5.895842.1.6 G3: 3,5 # 16 pairs I3: 6,8,3,5 # reduction candidate for 6,8 I3: 6,8 => CTR * 6895347127352.1...4219.753.517348269863792451294615.8717685..2434217..9595842.173 I3: 3,5 # 16 pairs * PAIR H3: 3,8 BLK 3 G3: 3,8,5,6 # reduction candidate for 3,8 G3: 3,8 => CTR * 6895347127352.1694421967..5517348269863792451294615..31.685..2.3.217.5.895842.1.6 G3: 5,6 # 16 pairs I3: 3,8,5,6 # reduction candidate for 3,8 I3: 3,8 # 16 pairs * PAIR H3: 3,8 COL H H6: 3,8,7 # reduction candidate for 3,8 H6: 3,8 => CTR * 68953471273526194842198763.517348269863792451294615..7176859324342176.9.958423176 H6: 7 => SOLVED * 689534712735281694421967583517348269863792451294615378146853927352179846978426135 * PAIR G6: 3,8 BLK 6 H6: 3,8,7 # reduction candidate for 3,8 H6: 3,8 => CTR * 68953471273526194842198763.517348269863792451294615..7176859324342176.9.958423176 H6: 7 => SOLVED * 689534712735281694421967583517348269863792451294615378146853927352179846978426135 I6: 3,8,7 # reduction candidate for 3,8 I6: 3,8 => SOLVED * 689534712735281694421967583517348269863792451294615378146853927352179846978426135 I6: 7 => CTR * 68953471273526194842198763.517348269863792451294615..7176859324342176.9.958423176 * PAIR G6: 3,8 COL G G3: 3,8,5,6 # reduction candidate for 3,8 G3: 3,8 => CTR * 6895347127352.1694421967..5517348269863792451294615..31.685..2.3.217.5.895842.1.6 G3: 5,6 # 16 pairs * PAIR B8: 4,5 ROW 8 I8: 4,5,6,8 # reduction candidate for 4,5 I8: 4,5 => CTR * 6895347127352.1...4219.75..5173482698637924512946153..1.6853.2.3.217.8..9.842.1.6 I8: 6,8 # 16 pairs * PAIR B9: 5,7 ROW 9 I9: 5,7,3,6 # reduction candidate for 5,7 I9: 5,7 => SOLVED * 689534712735281694421967583517348269863792451294615378146853927352179846978426135 I9: 3,6 => CTR * 68953471273526194842198763.517348269863792451294615..7176859324342176.9.958423176 * PAIR F8: 6,9 ROW 8 G8: 6,9,5,8 # reduction candidate for 6,9 G8: 6,9 => CTR * 6895347127352.1.944219.758.517348269863792451294615...1.685..2.35217.648978426135 G8: 5,8 # 17 pairs * PAIR F9: 3,6 ROW 9 I9: 3,6,5,7 # reduction candidate for 3,6 I9: 3,6 => CTR * 68953471273526194842198763.517348269863792451294615..7176859324342176.9.958423176 I9: 5,7 => SOLVED * 689534712735281694421967583517348269863792451294615378146853927352179846978426135 * PAIR H9: 3,7 BLK 9 I9: 3,7,5,6 # reduction candidate for 3,7 I9: 3,7 => CTR * 6895347127352.1...4219.7...517348269863792451294615...1768539243.217....9584261.. I9: 5,6 # 16 pairs * PAIR H9: 3,7 COL H H6: 3,7,8 # reduction candidate for 3,7 H6: 8 => CTR * 6895347127352.1...4219.7...517348269863792451294615.8717685..2434217..9.95842.17. H6: 3,7 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-022-base-pr-000.dot * REASONING * PRF # G2: 6,8 => SOL * DIS # G2: 9 => CTR => G2: 6,8 * DIS # I2: 6,8 => CTR => I2: 4 * PRF # I2: 4 => SOL * DIS # G3: 6,8 => CTR => G3: 3,5 * DIS # I3: 6,8 => CTR => I3: 3,5 * DIS # G3: 3,8 => CTR => G3: 5,6 * DIS # H6: 3,8 => CTR => H6: 7 * PRF # H6: 7 => SOL * DIS # H6: 3,8 => CTR => H6: 7 * PRF # H6: 7 => SOL * PRF # I6: 3,8 => SOL * DIS # I6: 7 => CTR => I6: 3,8 * DIS # G3: 3,8 => CTR => G3: 5,6 * DIS # I8: 4,5 => CTR => I8: 6,8 * PRF # I9: 5,7 => SOL * DIS # I9: 3,6 => CTR => I9: 5,7 * DIS # G8: 6,9 => CTR => G8: 5,8 * DIS # I9: 3,6 => CTR => I9: 5,7 * PRF # I9: 5,7 => SOL * DIS # I9: 3,7 => CTR => I9: 5,6 * DIS # H6: 8 => CTR => H6: 3,7 * CNT 22 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B8,B9,E2,E3,F7,F8,F9,G6,G7,H2,H3,H8,H9,I7) * 6895347127352.1...4219.7...517348269863792451294615...1.685..2.3.217....9.842.1.. * PAIR E2: 6,8 ROW 2 G2: 6,8,9 # reduction candidate for 6,8 G2: 6,8 => SOLVED * 689534712735281694421967583517348269863792451294615378146853927352179846978426135 * DURATION: 0:00:02.344359 START: 03:21:53.745460 END: 03:21:56.089819 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-022-base-pr-001.dot * REASONING * PRF # G2: 6,8 => SOL * STA G2: 6,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 022 solution: 689534712735281694421967583517348269863792451294615378146853927352179846978426135 info: 1313 FNBTHY S8.f 42959 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 689534712735281694421967583517348269863792451294615378146853927352179846978426135 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 # G2: 6,8 => SOL * DIS # G2: 9 => CTR => G2: 6,8 * DIS # I2: 6,8 => CTR => I2: 4 * PRF # I2: 4 => SOL * DIS # G3: 6,8 => CTR => G3: 3,5 * INC # G3: 3,5 => UNS * DIS # I3: 6,8 => CTR => I3: 3,5 * INC # I3: 3,5 => UNS * DIS # G3: 3,8 => CTR => G3: 5,6 * INC # G3: 5,6 => UNS * INC # I3: 3,8 => UNS * DIS # H6: 3,8 => CTR => H6: 7 * PRF # H6: 7 => SOL * DIS # H6: 3,8 => CTR => H6: 7 * PRF # H6: 7 => SOL * PRF # I6: 3,8 => SOL * DIS # I6: 7 => CTR => I6: 3,8 * DIS # G3: 3,8 => CTR => G3: 5,6 * INC # G3: 5,6 => UNS * DIS # I8: 4,5 => CTR => I8: 6,8 * INC # I8: 6,8 => UNS * PRF # I9: 5,7 => SOL * DIS # I9: 3,6 => CTR => I9: 5,7 * DIS # G8: 6,9 => CTR => G8: 5,8 * INC # G8: 5,8 => UNS * DIS # I9: 3,6 => CTR => I9: 5,7 * PRF # I9: 5,7 => SOL * DIS # I9: 3,7 => CTR => I9: 5,6 * INC # I9: 5,6 => UNS * INC # H6: 3,7 => UNS * DIS # H6: 8 => CTR => H6: 3,7 * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # G2: 6,8 => SOL * STA G2: 6,8 * CNT 1 HDP CHAINS / 1 HYP OPENED