Analysis of xx-top500-358-base.sdk
Contents
Original Sudoku
level: medium
position: ....57.1..1....9......2.......4..63.5..8.....2........8...9...5.3.6.............. initial
Autosolve
position: 38.95721..123..95795712....7984156325..8.279.2..7.95..87.29...5.3567..29.295...7. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 8 => CTR => F2: 4,6 * DIS # A9: 1 => CTR => A9: 4,6 * DIS # F2: 4,8 => CTR => F2: 6 * PRF # F2: 6 => SOL * DIS # F2: 8 => CTR => F2: 4,6 * DIS # H3: 4,6 => CTR => H3: 8 * PRF # H3: 8 => SOL * PRF # I3: 4,6 => SOL * DIS # H3: 4,6 => CTR => H3: 8 * PRF # H3: 8 => SOL * PRF # I3: 4,6 => SOL * DIS # I9: 4,6 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * DIS # I6: 1,4 => CTR => I6: 8 * PRF # I6: 8 => SOL * DIS # I6: 1 => CTR => I6: 4,8 * PRF # H3: 4,8 => SOL * DIS # H3: 6 => CTR => H3: 4,8 * DIS # A9: 1 => CTR => A9: 4,6 * DIS # A9: 1,4 => CTR => A9: 6 * PRF # A9: 6 => SOL * DIS # F9: 4,8 => CTR => F9: 1,3 * DIS # F9: 4,8 => CTR => F9: 1,3 * DIS # I9: 4,8 => CTR => I9: 3,6 * DIS # I9: 4,6 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * DIS # H3: 4,6 => CTR => H3: 8 * PRF # H3: 8 => SOL * CNT 28 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 8 => CTR => F2: 4,6 * DIS F2: 4,6 # H3: 4,6 => CTR => H3: 8 * PRF F2: 4,6 + H3: 8 => SOL * STA F2: 4,6 + H3: 8 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....57.1..1....9......2.......4..63.5..8.....2........8...9...5.3.6.............. | initial |
| 38.95721..123..95795712....7984156325..8.279.2..7.95..87.29...5.3567..29.295...7. | autosolve |
| 386957214412386957957124386798415632543862791261739548874293165135678429629541873 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C1: 4,6 A2: 4,6 E2: 4,8 F3: 4,6 I1: 4,6 B5: 4,6 C5: 1,3 B6: 4,6 C6: 1,3 E5: 3,6 E6: 3,6 I5: 1,4 H6: 4,8 C7: 4,6 A8: 1,4 F7: 1,3 E9: 4,8 G7: 1,3 H7: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C5,C6: 1.. / C5 = 1 => 0 pairs (X) / C6 = 1 => 13 pairs (_) I5,I6: 1.. / I5 = 1 => 13 pairs (_) / I6 = 1 => 0 pairs (X) A8,A9: 1.. / A8 = 1 => 22 pairs (_) / A9 = 1 => 0 pairs (X) C5,I5: 1.. / C5 = 1 => 0 pairs (X) / I5 = 1 => 13 pairs (_) C6,I6: 1.. / C6 = 1 => 13 pairs (_) / I6 = 1 => 0 pairs (X) F7,G7: 1.. / F7 = 1 => 19 pairs (_) / G7 = 1 => 18 pairs (_) G3,I3: 3.. / G3 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) C5,C6: 3.. / C5 = 3 => 13 pairs (_) / C6 = 3 => 0 pairs (X) E5,E6: 3.. / E5 = 3 => 0 pairs (X) / E6 = 3 => 13 pairs (_) F7,F9: 3.. / F7 = 3 => 18 pairs (_) / F9 = 3 => 19 pairs (_) C5,E5: 3.. / C5 = 3 => 13 pairs (_) / E5 = 3 => 0 pairs (X) C6,E6: 3.. / C6 = 3 => 0 pairs (X) / E6 = 3 => 13 pairs (_) F7,G7: 3.. / F7 = 3 => 18 pairs (_) / G7 = 3 => 19 pairs (_) I3,I9: 3.. / I3 = 3 => 20 pairs (_) / I9 = 3 => 0 pairs (*) C1,A2: 4.. / C1 = 4 => 0 pairs (X) / A2 = 4 => 0 pairs (_) B5,B6: 4.. / B5 = 4 => 13 pairs (_) / B6 = 4 => 0 pairs (X) C1,I1: 4.. / C1 = 4 => 0 pairs (X) / I1 = 4 => 0 pairs (_) B5,I5: 4.. / B5 = 4 => 13 pairs (_) / I5 = 4 => 0 pairs (X) C7,H7: 4.. / C7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) C1,C7: 4.. / C1 = 4 => 0 pairs (X) / C7 = 4 => 0 pairs (_) E2,E9: 4.. / E2 = 4 => 0 pairs (X) / E9 = 4 => 20 pairs (_) C1,A2: 6.. / C1 = 6 => 0 pairs (*) / A2 = 6 => 0 pairs (X) F2,F3: 6.. / F2 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) B5,B6: 6.. / B5 = 6 => 0 pairs (X) / B6 = 6 => 13 pairs (_) E5,E6: 6.. / E5 = 6 => 13 pairs (_) / E6 = 6 => 0 pairs (X) C7,A9: 6.. / C7 = 6 => 0 pairs (X) / A9 = 6 => 0 pairs (_) H7,I9: 6.. / H7 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) C1,I1: 6.. / C1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) A2,F2: 6.. / A2 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) B5,E5: 6.. / B5 = 6 => 0 pairs (X) / E5 = 6 => 13 pairs (_) B6,E6: 6.. / B6 = 6 => 13 pairs (_) / E6 = 6 => 0 pairs (X) C7,H7: 6.. / C7 = 6 => 0 pairs (X) / H7 = 6 => 0 pairs (_) A9,I9: 6.. / A9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) A2,A9: 6.. / A2 = 6 => 0 pairs (X) / A9 = 6 => 0 pairs (_) C1,C7: 6.. / C1 = 6 => 0 pairs (*) / C7 = 6 => 0 pairs (X) H3,H7: 6.. / H3 = 6 => 0 pairs (X) / H7 = 6 => 0 pairs (_) E2,F2: 8.. / E2 = 8 => 20 pairs (_) / F2 = 8 => 0 pairs (X) H6,I6: 8.. / H6 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) F8,G8: 8.. / F8 = 8 => 21 pairs (_) / G8 = 8 => 21 pairs (_) E2,E9: 8.. / E2 = 8 => 20 pairs (_) / E9 = 8 => 0 pairs (X) H3,H6: 8.. / H3 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) * DURATION: 0:01:25.429824 START: 14:59:17.813789 END: 15:00:43.243613 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B5,B6,C1,C5,C6,C7,E2,E5,E6,E9,F3,F7,G7,H6,H7,I1,I5) * 38.95721..123..95795712....7984156325..8.279.2..7.95..87.29...5.3567..29.295...7. * PAIR A2: 4,6 ROW 2 F2: 4,6,8 # reduction candidate for 4,6 F2: 8 => CTR * 38.95721.612348957957126...7984156325..8.279.2..7.95..87629..45.3567.829.2958..76 F2: 4,6 # 20 pairs * PAIR A2: 4,6 COL A A9: 4,6,1 # reduction candidate for 4,6 A9: 1 => CTR * 38.95721.6123..957957126...7984156325..8.279.2..7.95..87629..4543567..291295...76 A9: 4,6 # 22 pairs * PAIR E2: 4,8 BLK 2 F2: 4,8,6 # reduction candidate for 4,8 F2: 4,8 => CTR * 38.95721.6123..957957126...7984156325..8.279.2..7.95..87629..45.3567..29.295...76 F2: 6 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 * PAIR F3: 4,6 BLK 2 F2: 4,6,8 # reduction candidate for 4,6 F2: 8 => CTR * 38.95721.612348957957126...7984156325..8.279.2..7.95..87629..45.3567.829.2958..76 F2: 4,6 # 20 pairs * PAIR F3: 4,6 ROW 3 H3: 4,6,8 # reduction candidate for 4,6 H3: 4,6 => CTR * 3849572166123..957957126.4.7984156325..8.279.2..7.958.87.29...5.3567..29.295...7. H3: 8 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 I3: 4,6,3,8 # reduction candidate for 4,6 I3: 4,6 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 I3: 3,8 # 20 pairs * PAIR I1: 4,6 BLK 3 H3: 4,6,8 # reduction candidate for 4,6 H3: 4,6 => CTR * 3849572166123..957957126.4.7984156325..8.279.2..7.958.87.29...5.3567..29.295...7. H3: 8 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 I3: 4,6,3,8 # reduction candidate for 4,6 I3: 4,6 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 I3: 3,8 # 20 pairs * PAIR I1: 4,6 COL I I9: 4,6,3,8 # reduction candidate for 4,6 I9: 4,6 => CTR * 38.95721..123..95795712..837984156325..8.27912.173954887429..6513567..296295...74 I9: 3,8 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 * PAIR I5: 1,4 BLK 6 I6: 1,4,8 # reduction candidate for 1,4 I6: 1,4 => CTR * 3849572166123..957957126.4.7984156325..8.279.2..7.958.87.29...5.3567..29.295...7. I6: 8 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 * PAIR H6: 4,8 BLK 6 I6: 4,8,1 # reduction candidate for 4,8 I6: 1 => CTR * 3849572166123..957957126.4.7984156325.183279424376958187.29...5.3567..29.295...7. I6: 4,8 # 13 pairs * PAIR H6: 4,8 COL H H3: 4,8,6 # reduction candidate for 4,8 H3: 4,8 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 H3: 6 => CTR * 38.95721..123..95795712..6.7984156325..8.279.2..7.958.87629..45.3567..29.295...76 * PAIR C7: 4,6 BLK 7 A9: 4,6,1 # reduction candidate for 4,6 A9: 1 => CTR * 38.95721.6123..957957126...7984156325..8.279.2..7.95..87629..4543567..291295...76 A9: 4,6 # 22 pairs * PAIR A8: 1,4 BLK 7 A9: 1,4,6 # reduction candidate for 1,4 A9: 1,4 => CTR * 38.95721.6123..957957126...7984156325..8.279.2..7.95..87629..45.3567..29.295...76 A9: 6 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 * PAIR A8: 1,4 ROW 8 F8: 1,4,8 # reduction candidate for 1,4 F8: 1,4 # 21 pairs G8: 1,4,8 # reduction candidate for 1,4 G8: 1,4 # 21 pairs * PAIR F7: 1,3 BLK 8 F9: 1,3,4,8 # reduction candidate for 1,3 F9: 4,8 => CTR * 3869572144123..95795712....7984156325..8.279.2..7.95..87.2931.5.356718291295...76 F9: 1,3 # 21 pairs * PAIR E9: 4,8 BLK 8 F8: 4,8,1 # reduction candidate for 4,8 F8: 4,8 # 21 pairs F9: 4,8,1,3 # reduction candidate for 4,8 F9: 4,8 => CTR * 3869572144123..95795712....7984156325..8.279.2..7.95..87.2931.5.356718291295...76 F9: 1,3 # 21 pairs * PAIR E9: 4,8 ROW 9 G9: 4,8,1,3 # reduction candidate for 4,8 G9: 4,8 # 25 pairs I9: 4,8,3,6 # reduction candidate for 4,8 I9: 4,8 => CTR * 38695721441238.95795712...37984156325..8.279.2..7.95..87.29..65.3567..296295...7. I9: 3,6 # 21 pairs * PAIR G7: 1,3 BLK 9 G9: 1,3,4,8 # reduction candidate for 1,3 G9: 4,8 # 25 pairs G9: 1,3 # 22 pairs * PAIR H7: 4,6 BLK 9 I9: 4,6,3,8 # reduction candidate for 4,6 I9: 4,6 => CTR * 38.95721..123..95795712..837984156325..8.27912.173954887429..6513567..296295...74 I9: 3,8 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 * PAIR H7: 4,6 COL H H3: 4,6,8 # reduction candidate for 4,6 H3: 4,6 => CTR * 3849572166123..957957126.4.7984156325..8.279.2..7.958.87.29...5.3567..29.295...7. H3: 8 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-358-base-pr-000.dot * REASONING * DIS # F2: 8 => CTR => F2: 4,6 * DIS # A9: 1 => CTR => A9: 4,6 * DIS # F2: 4,8 => CTR => F2: 6 * PRF # F2: 6 => SOL * DIS # F2: 8 => CTR => F2: 4,6 * DIS # H3: 4,6 => CTR => H3: 8 * PRF # H3: 8 => SOL * PRF # I3: 4,6 => SOL * DIS # H3: 4,6 => CTR => H3: 8 * PRF # H3: 8 => SOL * PRF # I3: 4,6 => SOL * DIS # I9: 4,6 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * DIS # I6: 1,4 => CTR => I6: 8 * PRF # I6: 8 => SOL * DIS # I6: 1 => CTR => I6: 4,8 * PRF # H3: 4,8 => SOL * DIS # H3: 6 => CTR => H3: 4,8 * DIS # A9: 1 => CTR => A9: 4,6 * DIS # A9: 1,4 => CTR => A9: 6 * PRF # A9: 6 => SOL * DIS # F9: 4,8 => CTR => F9: 1,3 * DIS # F9: 4,8 => CTR => F9: 1,3 * DIS # I9: 4,8 => CTR => I9: 3,6 * DIS # I9: 4,6 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * DIS # H3: 4,6 => CTR => H3: 8 * PRF # H3: 8 => SOL * CNT 28 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B5,B6,C1,C5,C6,C7,E2,E5,E6,E9,F3,F7,G7,H6,H7,I1,I5) * 38.95721..123..95795712....7984156325..8.279.2..7.95..87.29...5.3567..29.295...7. * PAIR A2: 4,6 ROW 2 F2: 4,6,8 # reduction candidate for 4,6 F2: 8 => CTR * 38.95721.612348957957126...7984156325..8.279.2..7.95..87629..45.3567.829.2958..76 * PAIR RESTART * PAIR F3: 4,6 ROW 3 H3: 4,6,8 # reduction candidate for 4,6 H3: 4,6 => CTR * 384957216612384957957126.4.7984156325..8.279.2..7.958.87.29...5.3567..29.2954..7. H3: 8 => SOLVED * 386957214412386957957124386798415632543862791261739548874293165135678429629541873 * DURATION: 0:00:04.283444 START: 15:01:36.688043 END: 15:01:40.971487 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-358-base-pr-001.dot * REASONING * DIS # F2: 8 => CTR => F2: 4,6 * DIS F2: 4,6 # H3: 4,6 => CTR => H3: 8 * PRF F2: 4,6 + H3: 8 => SOL * STA F2: 4,6 + H3: 8 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 358 solution: 386957214412386957957124386798415632543862791261739548874293165135678429629541873 info: 4897 FNBTWX S8.f 5063 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 386957214412386957957124386798415632543862791261739548874293165135678429629541873 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:
* INC # F2: 4,6 => UNS * DIS # F2: 8 => CTR => F2: 4,6 * INC # A9: 4,6 => UNS * DIS # A9: 1 => CTR => A9: 4,6 * DIS # F2: 4,8 => CTR => F2: 6 * PRF # F2: 6 => SOL * INC # F2: 4,6 => UNS * DIS # F2: 8 => CTR => F2: 4,6 * DIS # H3: 4,6 => CTR => H3: 8 * PRF # H3: 8 => SOL * PRF # I3: 4,6 => SOL * INC # I3: 3,8 => UNS * DIS # H3: 4,6 => CTR => H3: 8 * PRF # H3: 8 => SOL * PRF # I3: 4,6 => SOL * INC # I3: 3,8 => UNS * DIS # I9: 4,6 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * DIS # I6: 1,4 => CTR => I6: 8 * PRF # I6: 8 => SOL * INC # I6: 4,8 => UNS * DIS # I6: 1 => CTR => I6: 4,8 * PRF # H3: 4,8 => SOL * DIS # H3: 6 => CTR => H3: 4,8 * INC # A9: 4,6 => UNS * DIS # A9: 1 => CTR => A9: 4,6 * DIS # A9: 1,4 => CTR => A9: 6 * PRF # A9: 6 => SOL * INC # F8: 1,4 => UNS * INC # G8: 1,4 => UNS * INC # F9: 1,3 => UNS * DIS # F9: 4,8 => CTR => F9: 1,3 * INC # F8: 4,8 => UNS * DIS # F9: 4,8 => CTR => F9: 1,3 * INC # F9: 1,3 => UNS * INC # G9: 4,8 => UNS * DIS # I9: 4,8 => CTR => I9: 3,6 * INC # I9: 3,6 => UNS * INC # G9: 1,3 => UNS * INC # G9: 4,8 => UNS * DIS # I9: 4,6 => CTR => I9: 3,8 * PRF # I9: 3,8 => SOL * DIS # H3: 4,6 => CTR => H3: 8 * PRF # H3: 8 => SOL * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F2: 4,6 => UNS * DIS # F2: 8 => CTR => F2: 4,6 * DIS F2: 4,6 # H3: 4,6 => CTR => H3: 8 * PRF F2: 4,6 + H3: 8 => SOL * STA F2: 4,6 + H3: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED