Analysis of xx-top500-359-base.sdk
Contents
Original Sudoku
level: medium
position: 7.....4.98..2...........6......48.5.9............1.......3.7....4.....2..6.9..... initial
Autosolve
position: 726...4.98.4296.7..9.47.6826.274895.9..632.4.4..51926.2..367.94349...726.67924... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C3: 1,3 => SOL * DIS # C3: 5 => CTR => C3: 1,3 * DIS # G2: 5 => CTR => G2: 1,3 * DIS # C3: 1,5 => CTR => C3: 3 * PRF # C3: 3 => SOL * DIS # F1: 5 => CTR => F1: 1,3 * PRF # C3: 1,3 => SOL * DIS # C3: 5 => CTR => C3: 1,3 * DIS # G2: 5 => CTR => G2: 1,3 * DIS # F1: 5 => CTR => F1: 1,3 * DIS # G2: 1,5 => CTR => G2: 3 * PRF # G2: 3 => SOL * DIS # I9: 1,5 => CTR => I9: 8 * DIS # B5: 7,8 => CTR => B5: 5 * DIS # I6: 7,8 => CTR => I6: 3 * PRF # I6: 3 => SOL * DIS # I6: 7 => CTR => I6: 3,8 * DIS # I5: 1,8 => CTR => I5: 7 * DIS # C5: 5 => CTR => C5: 1,8 * DIS # G9: 1,8 => CTR => G9: 3,5 * PRF # C7: 5,8 => SOL * DIS # C7: 1 => CTR => C7: 5,8 * DIS # B5: 7 => CTR => B5: 5,8 * DIS # C7: 8 => CTR => C7: 1,5 * PRF # G9: 1,5 => SOL * DIS # I9: 1,5 => CTR => I9: 8 * DIS # F1: 1,5 => CTR => F1: 3 * PRF # F1: 3 => SOL * PRF # G9: 1,5 => SOL * DIS # I9: 1,5 => CTR => I9: 8 * DIS # C7: 8 => CTR => C7: 1,5 * DIS # G2: 1,5 => CTR => G2: 3 * PRF # G2: 3 => SOL * DIS # G9: 1,3 => CTR => G9: 5,8 * PRF # G9: 5,8 => SOL * CNT 35 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C3: 1,3 => SOL * STA C3: 1,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7.....4.98..2...........6......48.5.9............1.......3.7....4.....2..6.9..... | initial |
| 726...4.98.4296.7..9.47.6826.274895.9..632.4.4..51926.2..367.94349...726.67924... | autosolve |
| 726853419814296375593471682632748951951632847478519263285367194349185726167924538 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B2: 1,3 A3: 1,5 D1: 1,8 E1: 5,8 F3: 1,3 H1: 1,3 I2: 1,5 B4: 1,3 B6: 7,8 C6: 3,8 I4: 1,3 G5: 1,8 B7: 5,8 A9: 1,5 D8: 1,8 E8: 5,8 F8: 1,5 G7: 1,5 H9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,C5: 1.. / B4 = 1 => 0 pairs (X) / C5 = 1 => 0 pairs (_) C7,A9: 1.. / C7 = 1 => 0 pairs (X) / A9 = 1 => 0 pairs (_) D8,F8: 1.. / D8 = 1 => 15 pairs (_) / F8 = 1 => 0 pairs (X) B4,I4: 1.. / B4 = 1 => 0 pairs (X) / I4 = 1 => 0 pairs (_) C7,G7: 1.. / C7 = 1 => 0 pairs (X) / G7 = 1 => 0 pairs (_) A3,A9: 1.. / A3 = 1 => 0 pairs (X) / A9 = 1 => 0 pairs (_) B2,B4: 1.. / B2 = 1 => 0 pairs (*) / B4 = 1 => 0 pairs (X) D1,D8: 1.. / D1 = 1 => 0 pairs (X) / D8 = 1 => 15 pairs (_) H1,H9: 1.. / H1 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) B2,C3: 3.. / B2 = 3 => 0 pairs (X) / C3 = 3 => 0 pairs (_) F1,F3: 3.. / F1 = 3 => 0 pairs (*) / F3 = 3 => 0 pairs (X) H1,G2: 3.. / H1 = 3 => 0 pairs (X) / G2 = 3 => 0 pairs (_) B4,C6: 3.. / B4 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) I4,I6: 3.. / I4 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) G9,H9: 3.. / G9 = 3 => 0 pairs (X) / H9 = 3 => 0 pairs (_) F1,H1: 3.. / F1 = 3 => 0 pairs (*) / H1 = 3 => 0 pairs (X) B2,G2: 3.. / B2 = 3 => 0 pairs (X) / G2 = 3 => 0 pairs (_) C3,F3: 3.. / C3 = 3 => 0 pairs (*) / F3 = 3 => 0 pairs (X) B4,I4: 3.. / B4 = 3 => 0 pairs (*) / I4 = 3 => 0 pairs (X) C6,I6: 3.. / C6 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) B2,B4: 3.. / B2 = 3 => 0 pairs (X) / B4 = 3 => 0 pairs (_) C3,C6: 3.. / C3 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) G2,G9: 3.. / G2 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) H1,H9: 3.. / H1 = 3 => 0 pairs (X) / H9 = 3 => 0 pairs (_) A3,C3: 5.. / A3 = 5 => 0 pairs (*) / C3 = 5 => 0 pairs (X) E1,F1: 5.. / E1 = 5 => 15 pairs (_) / F1 = 5 => 0 pairs (X) G2,I2: 5.. / G2 = 5 => 0 pairs (X) / I2 = 5 => 20 pairs (_) B5,C5: 5.. / B5 = 5 => 20 pairs (_) / C5 = 5 => 0 pairs (X) E8,F8: 5.. / E8 = 5 => 0 pairs (X) / F8 = 5 => 15 pairs (_) A3,A9: 5.. / A3 = 5 => 0 pairs (*) / A9 = 5 => 0 pairs (X) B5,B7: 5.. / B5 = 5 => 20 pairs (_) / B7 = 5 => 0 pairs (X) E1,E8: 5.. / E1 = 5 => 15 pairs (_) / E8 = 5 => 0 pairs (X) F1,F8: 5.. / F1 = 5 => 0 pairs (X) / F8 = 5 => 15 pairs (_) I2,I9: 5.. / I2 = 5 => 20 pairs (_) / I9 = 5 => 0 pairs (X) B5,B6: 7.. / B5 = 7 => 0 pairs (X) / B6 = 7 => 20 pairs (_) I5,I6: 7.. / I5 = 7 => 20 pairs (_) / I6 = 7 => 0 pairs (X) B5,I5: 7.. / B5 = 7 => 0 pairs (X) / I5 = 7 => 20 pairs (_) B6,I6: 7.. / B6 = 7 => 20 pairs (_) / I6 = 7 => 0 pairs (X) D1,E1: 8.. / D1 = 8 => 15 pairs (_) / E1 = 8 => 0 pairs (X) B7,C7: 8.. / B7 = 8 => 20 pairs (_) / C7 = 8 => 0 pairs (X) D8,E8: 8.. / D8 = 8 => 0 pairs (X) / E8 = 8 => 15 pairs (_) G9,I9: 8.. / G9 = 8 => 0 pairs (X) / I9 = 8 => 22 pairs (_) D1,D8: 8.. / D1 = 8 => 15 pairs (_) / D8 = 8 => 0 pairs (X) E1,E8: 8.. / E1 = 8 => 0 pairs (X) / E8 = 8 => 15 pairs (_) G5,G9: 8.. / G5 = 8 => 22 pairs (_) / G9 = 8 => 0 pairs (X) * DURATION: 0:01:26.176567 START: 15:01:56.197850 END: 15:03:22.374417 2017-05-04 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B2,B4,B6,B7,C6,D1,D8,E1,E8,F3,F8,G5,G7,H1,H9,I2,I4) * 726...4.98.4296.7..9.47.6826.274895.9..632.4.4..51926.2..367.94349...726.67924... * PAIR B2: 1,3 BLK 1 C3: 1,3,5 # reduction candidate for 1,3 C3: 1,3 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 C3: 5 => CTR * 726...4.9834296.7.19547368261274895395863214.4..51926.2..367.94349...726.67924... * PAIR B2: 1,3 ROW 2 G2: 1,3,5 # reduction candidate for 1,3 G2: 5 => CTR * 726...439834296571.9.4736826127489539..63214.4..51926.2..367.94349...726.67924... G2: 1,3 # 20 pairs * PAIR A3: 1,5 BLK 1 C3: 1,5,3 # reduction candidate for 1,5 C3: 1,5 => CTR * 726...439834296.75195473682612748953958632.4.4.351926.2..367.94349...726.67924318 C3: 3 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 * PAIR F3: 1,3 BLK 2 F1: 1,3,5 # reduction candidate for 1,3 F1: 5 => CTR * 726185439834296.75195473682612748953958632.4.4.351926.2..367.94349.51726.67924318 F1: 1,3 # 15 pairs * PAIR F3: 1,3 ROW 3 C3: 1,3,5 # reduction candidate for 1,3 C3: 1,3 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 C3: 5 => CTR * 726...4.9834296.7.19547368261274895395863214.4..51926.2..367.94349...726.67924... * PAIR H1: 1,3 BLK 3 G2: 1,3,5 # reduction candidate for 1,3 G2: 5 => CTR * 726...439834296571.9.4736826127489539..63214.4..51926.2..367.94349...726.67924... G2: 1,3 # 20 pairs * PAIR H1: 1,3 ROW 1 F1: 1,3,5 # reduction candidate for 1,3 F1: 5 => CTR * 726185439834296.75195473682612748953958632.4.4.351926.2..367.94349.51726.67924318 F1: 1,3 # 15 pairs * PAIR I2: 1,5 BLK 3 G2: 1,5,3 # reduction candidate for 1,5 G2: 1,5 => CTR * 726...439834296.75195473682612748953958632.4.4.351926.2..367.94349...726.67924318 G2: 3 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 * PAIR I2: 1,5 COL I I9: 1,5,8 # reduction candidate for 1,5 I9: 1,5 => CTR * 726..341981429637559.47.6826.274895.9..632.4.4..51926.2..367.94349...726.6792483. I9: 8 # 22 pairs * PAIR B6: 7,8 BLK 4 B5: 7,8,5 # reduction candidate for 7,8 B5: 7,8 => CTR * 726..3419814296.7..9.47.6826.274895.9.5632.4.4..51926.258367194349...726167924.3. B5: 5 # 20 pairs * PAIR B6: 7,8 ROW 6 I6: 7,8,3 # reduction candidate for 7,8 I6: 7,8 => CTR * 726...439834296.75195473682612748953958632.4.4.351926.2..367.94349...726.67924318 I6: 3 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 * PAIR C6: 3,8 ROW 6 I6: 3,8,7 # reduction candidate for 3,8 I6: 7 => CTR * 726...4.9834296.7..9.473682612748953975632.4.483519267258367194349...7261679243.. I6: 3,8 # 20 pairs * PAIR G5: 1,8 BLK 6 I5: 1,8,7 # reduction candidate for 1,8 I5: 1,8 => CTR * 726..34198.4296.7..9.47.6826.274895.975632.4.483519267258367194349...726167924.3. I5: 7 # 20 pairs * PAIR G5: 1,8 ROW 5 C5: 1,8,5 # reduction candidate for 1,8 C5: 5 => CTR * 726..341983429657..9.47.6826127489539.5632.4.4.351926.258367194349...726167924.3. C5: 1,8 # 20 pairs * PAIR G5: 1,8 COL G G9: 1,8,3,5 # reduction candidate for 1,8 G9: 1,8 => CTR * 726...4.98.4296375.934716826327489519.163284.4..51926.2..367.94349...726.67924... G9: 3,5 # 23 pairs * PAIR B7: 5,8 BLK 7 C7: 5,8,1 # reduction candidate for 5,8 C7: 5,8 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 C7: 1 => CTR * 726...4.98.4296.75195473682612748953958632147473519268281367594349...72656792483. * PAIR B7: 5,8 COL B B5: 5,8,7 # reduction candidate for 5,8 B5: 7 => CTR * 726..34198.4296.7..9.47.6826.274895.975632.4.483519267258367194349...726167924.3. B5: 5,8 # 20 pairs * PAIR A9: 1,5 BLK 7 C7: 1,5,8 # reduction candidate for 1,5 C7: 8 => CTR * 726..341981429637559347.6826.274895.9..632.4.4..51926.2.8367194349...726167924.3. C7: 1,5 # 20 pairs * PAIR A9: 1,5 ROW 9 G9: 1,5,3,8 # reduction candidate for 1,5 G9: 1,5 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 G9: 3,8 # 20 pairs I9: 1,5,8 # reduction candidate for 1,5 I9: 1,5 => CTR * 726..341981429637559.47.6826.274895.9..632.4.4..51926.2..367.94349...726.6792483. I9: 8 # 22 pairs * PAIR F8: 1,5 COL F F1: 1,5,3 # reduction candidate for 1,5 F1: 1,5 => CTR * 726...439834296.75195473682612748953958632.4.4.351926.2..367.94349...726.67924318 F1: 3 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 * PAIR G7: 1,5 BLK 9 G9: 1,5,3,8 # reduction candidate for 1,5 G9: 1,5 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 G9: 3,8 # 20 pairs I9: 1,5,8 # reduction candidate for 1,5 I9: 1,5 => CTR * 726..341981429637559.47.6826.274895.9..632.4.4..51926.2..367.94349...726.6792483. I9: 8 # 22 pairs * PAIR G7: 1,5 ROW 7 C7: 1,5,8 # reduction candidate for 1,5 C7: 8 => CTR * 726..341981429637559347.6826.274895.9..632.4.4..51926.2.8367194349...726167924.3. C7: 1,5 # 20 pairs * PAIR G7: 1,5 COL G G2: 1,5,3 # reduction candidate for 1,5 G2: 1,5 => CTR * 726...439834296.75195473682612748953958632.4.4.351926.2..367.94349...726.67924318 G2: 3 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 * PAIR H9: 1,3 BLK 9 G9: 1,3,5,8 # reduction candidate for 1,3 G9: 1,3 => CTR * 726...4.98.4296.7519547368261274895.9..63284.4..51926.2..367594349...726567924..8 G9: 5,8 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-359-base-pr-000.dot * REASONING * PRF # C3: 1,3 => SOL * DIS # C3: 5 => CTR => C3: 1,3 * DIS # G2: 5 => CTR => G2: 1,3 * DIS # C3: 1,5 => CTR => C3: 3 * PRF # C3: 3 => SOL * DIS # F1: 5 => CTR => F1: 1,3 * PRF # C3: 1,3 => SOL * DIS # C3: 5 => CTR => C3: 1,3 * DIS # G2: 5 => CTR => G2: 1,3 * DIS # F1: 5 => CTR => F1: 1,3 * DIS # G2: 1,5 => CTR => G2: 3 * PRF # G2: 3 => SOL * DIS # I9: 1,5 => CTR => I9: 8 * DIS # B5: 7,8 => CTR => B5: 5 * DIS # I6: 7,8 => CTR => I6: 3 * PRF # I6: 3 => SOL * DIS # I6: 7 => CTR => I6: 3,8 * DIS # I5: 1,8 => CTR => I5: 7 * DIS # C5: 5 => CTR => C5: 1,8 * DIS # G9: 1,8 => CTR => G9: 3,5 * PRF # C7: 5,8 => SOL * DIS # C7: 1 => CTR => C7: 5,8 * DIS # B5: 7 => CTR => B5: 5,8 * DIS # C7: 8 => CTR => C7: 1,5 * PRF # G9: 1,5 => SOL * DIS # I9: 1,5 => CTR => I9: 8 * DIS # F1: 1,5 => CTR => F1: 3 * PRF # F1: 3 => SOL * PRF # G9: 1,5 => SOL * DIS # I9: 1,5 => CTR => I9: 8 * DIS # C7: 8 => CTR => C7: 1,5 * DIS # G2: 1,5 => CTR => G2: 3 * PRF # G2: 3 => SOL * DIS # G9: 1,3 => CTR => G9: 5,8 * PRF # G9: 5,8 => SOL * CNT 35 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B2,B4,B6,B7,C6,D1,D8,E1,E8,F3,F8,G5,G7,H1,H9,I2,I4) * 726...4.98.4296.7..9.47.6826.274895.9..632.4.4..51926.2..367.94349...726.67924... * PAIR B2: 1,3 BLK 1 C3: 1,3,5 # reduction candidate for 1,3 C3: 1,3 => SOLVED * 726853419814296375593471682632748951951632847478519263285367194349185726167924538 * DURATION: 0:00:02.130154 START: 15:04:19.581050 END: 15:04:21.711204 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-359-base-pr-001.dot * REASONING * PRF # C3: 1,3 => SOL * STA C3: 1,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 359 solution: 726853419814296375593471682632748951951632847478519263285367194349185726167924538 info: 4898 FNBTWY S8.f 43240 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 726853419814296375593471682632748951951632847478519263285367194349185726167924538 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 # C3: 1,3 => SOL * DIS # C3: 5 => CTR => C3: 1,3 * INC # G2: 1,3 => UNS * DIS # G2: 5 => CTR => G2: 1,3 * DIS # C3: 1,5 => CTR => C3: 3 * PRF # C3: 3 => SOL * INC # F1: 1,3 => UNS * DIS # F1: 5 => CTR => F1: 1,3 * PRF # C3: 1,3 => SOL * DIS # C3: 5 => CTR => C3: 1,3 * INC # G2: 1,3 => UNS * DIS # G2: 5 => CTR => G2: 1,3 * INC # F1: 1,3 => UNS * DIS # F1: 5 => CTR => F1: 1,3 * DIS # G2: 1,5 => CTR => G2: 3 * PRF # G2: 3 => SOL * DIS # I9: 1,5 => CTR => I9: 8 * INC # I9: 8 => UNS * DIS # B5: 7,8 => CTR => B5: 5 * INC # B5: 5 => UNS * DIS # I6: 7,8 => CTR => I6: 3 * PRF # I6: 3 => SOL * INC # I6: 3,8 => UNS * DIS # I6: 7 => CTR => I6: 3,8 * DIS # I5: 1,8 => CTR => I5: 7 * INC # I5: 7 => UNS * INC # C5: 1,8 => UNS * DIS # C5: 5 => CTR => C5: 1,8 * DIS # G9: 1,8 => CTR => G9: 3,5 * INC # G9: 3,5 => UNS * PRF # C7: 5,8 => SOL * DIS # C7: 1 => CTR => C7: 5,8 * INC # B5: 5,8 => UNS * DIS # B5: 7 => CTR => B5: 5,8 * INC # C7: 1,5 => UNS * DIS # C7: 8 => CTR => C7: 1,5 * PRF # G9: 1,5 => SOL * INC # G9: 3,8 => UNS * DIS # I9: 1,5 => CTR => I9: 8 * INC # I9: 8 => UNS * DIS # F1: 1,5 => CTR => F1: 3 * PRF # F1: 3 => SOL * PRF # G9: 1,5 => SOL * INC # G9: 3,8 => UNS * DIS # I9: 1,5 => CTR => I9: 8 * INC # I9: 8 => UNS * INC # C7: 1,5 => UNS * DIS # C7: 8 => CTR => C7: 1,5 * DIS # G2: 1,5 => CTR => G2: 3 * PRF # G2: 3 => SOL * DIS # G9: 1,3 => CTR => G9: 5,8 * PRF # G9: 5,8 => SOL * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C3: 1,3 => SOL * STA C3: 1,3 * CNT 1 HDP CHAINS / 1 HYP OPENED