Analysis of xx-top500-128-base.sdk
Contents
Original Sudoku
level: medium
position: ..4.....1.3..8.......3......7..2.6..1......4...2...........42........58.6..1..... initial
Autosolve
position: .642..831.31486.2.82.31.46.473.216.81.6.3..42..264.1.33..8.421621..635846481523.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 5,9 => SOL * DIS # A1: 7 => CTR => A1: 5,9 * DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * PRF # F3: 5,9 => SOL * DIS # F3: 7 => CTR => F3: 5,9 * DIS # I3: 5,9 => CTR => I3: 7 * PRF # I3: 7 => SOL * DIS # C7: 5,9 => CTR => C7: 7 * PRF # C7: 7 => SOL * DIS # F1: 7,9 => CTR => F1: 5 * DIS # A1: 5 => CTR => A1: 7,9 * DIS # I2: 7,9 => CTR => I2: 5 * DIS # A2: 5 => CTR => A2: 7,9 * DIS # B6: 5,9 => CTR => B6: 8 * PRF # H6: 5,9 => SOL * DIS # H6: 7 => CTR => H6: 5,9 * PRF # A1: 5,9 => SOL * DIS # A1: 7 => CTR => A1: 5,9 * DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * PRF # D5: 5,9 => SOL * DIS # D5: 7 => CTR => D5: 5,9 * PRF # H6: 5,9 => SOL * DIS # H6: 7 => CTR => H6: 5,9 * PRF # H6: 7,9 => SOL * DIS # H6: 5 => CTR => H6: 7,9 * DIS # D5: 7,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * DIS # F5: 7,9 => CTR => F5: 8 * DIS # C7: 5,9 => CTR => C7: 7 * PRF # C7: 7 => SOL * DIS # B6: 5,9 => CTR => B6: 8 * PRF # C7: 7,9 => SOL * DIS # C7: 5 => CTR => C7: 7,9 * PRF # C7: 7,9 => SOL * DIS # C7: 5 => CTR => C7: 7,9 * DIS # D5: 7,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * PRF # H6: 7,9 => SOL * DIS # H6: 5 => CTR => H6: 7,9 * DIS # I2: 7,9 => CTR => I2: 5 * CNT 42 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 5,9 => SOL * STA A1: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..4.....1.3..8.......3......7..2.6..1......4...2...........42........58.6..1..... | initial |
| .642..831.31486.2.82.31.46.473.216.81.6.3..42..264.1.33..8.421621..635846481523.. | autosolve |
| 964275831731486925825319467473921658196538742582647193357894216219763584648152379 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C3: 5,9 E1: 7,9 G2: 7,9 A6: 5,9 D4: 5,9 H4: 5,9 G5: 7,9 B7: 5,9 C8: 7,9 E7: 7,9 D8: 7,9 H9: 7,9 I9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F3: 5.. / F1 = 5 => 15 pairs (_) / F3 = 5 => 0 pairs (X) I2,I3: 5.. / I2 = 5 => 15 pairs (_) / I3 = 5 => 0 pairs (X) D4,D5: 5.. / D4 = 5 => 0 pairs (X) / D5 = 5 => 0 pairs (_) H4,H6: 5.. / H4 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) B7,C7: 5.. / B7 = 5 => 0 pairs (*) / C7 = 5 => 0 pairs (X) A1,F1: 5.. / A1 = 5 => 0 pairs (X) / F1 = 5 => 15 pairs (_) A2,I2: 5.. / A2 = 5 => 0 pairs (X) / I2 = 5 => 15 pairs (_) D4,H4: 5.. / D4 = 5 => 0 pairs (X) / H4 = 5 => 0 pairs (_) B5,D5: 5.. / B5 = 5 => 0 pairs (X) / D5 = 5 => 0 pairs (_) C3,C7: 5.. / C3 = 5 => 0 pairs (*) / C7 = 5 => 0 pairs (X) A1,A2: 7.. / A1 = 7 => 0 pairs (X) / A2 = 7 => 0 pairs (_) G5,H6: 7.. / G5 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) C7,C8: 7.. / C7 = 7 => 0 pairs (*) / C8 = 7 => 0 pairs (X) E7,D8: 7.. / E7 = 7 => 0 pairs (X) / D8 = 7 => 0 pairs (_) H9,I9: 7.. / H9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) F3,I3: 7.. / F3 = 7 => 0 pairs (X) / I3 = 7 => 0 pairs (_) F6,H6: 7.. / F6 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) C7,E7: 7.. / C7 = 7 => 0 pairs (*) / E7 = 7 => 0 pairs (X) C8,D8: 7.. / C8 = 7 => 0 pairs (X) / D8 = 7 => 0 pairs (_) D5,D8: 7.. / D5 = 7 => 0 pairs (X) / D8 = 7 => 0 pairs (_) E1,E7: 7.. / E1 = 7 => 0 pairs (*) / E7 = 7 => 0 pairs (X) G2,G5: 7.. / G2 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) H6,H9: 7.. / H6 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) B5,B6: 8.. / B5 = 8 => 0 pairs (X) / B6 = 8 => 15 pairs (_) F5,F6: 8.. / F5 = 8 => 15 pairs (_) / F6 = 8 => 0 pairs (X) B5,F5: 8.. / B5 = 8 => 0 pairs (X) / F5 = 8 => 15 pairs (_) B6,F6: 8.. / B6 = 8 => 15 pairs (_) / F6 = 8 => 0 pairs (X) E7,D8: 9.. / E7 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) H9,I9: 9.. / H9 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) D4,H4: 9.. / D4 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) C8,D8: 9.. / C8 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) E1,E7: 9.. / E1 = 9 => 0 pairs (X) / E7 = 9 => 0 pairs (_) G2,G5: 9.. / G2 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) * DURATION: 0:00:55.021984 START: 07:08:12.584752 END: 07:09:07.606736 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,C3,C8,D4,D8,E1,E7,G2,G5,H4,H9,I9) * .642..831.31486.2.82.31.46.473.216.81.6.3..42..264.1.33..8.421621..635846481523.. * PAIR C3: 5,9 BLK 1 A1: 5,9,7 # reduction candidate for 5,9 A1: 5,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 A1: 7 => CTR * 764295831.31486.2.82.31746.473.216.81.673.942..26491.33..8.421621..635846481523.. A2: 5,9,7 # reduction candidate for 5,9 A2: 5,9 => CTR * 764295831.31486.2.82.31746.473.216.81.673.942..26491.33..8.421621..635846481523.. A2: 7 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 * PAIR C3: 5,9 ROW 3 F3: 5,9,7 # reduction candidate for 5,9 F3: 5,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 F3: 7 => CTR * .642.5831.31486.2.82.31746.473.216.81.673.942..26491.33..8.421621..635846481523.. I3: 5,9,7 # reduction candidate for 5,9 I3: 5,9 => CTR * .642..831.31486.2.82.31746.473.216.81.673.942..264.1733..8742162179635846481523.. I3: 7 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 * PAIR C3: 5,9 COL C C7: 5,9,7 # reduction candidate for 5,9 C7: 5,9 => CTR * .6429.831.31486.2.82.31.46.47352169815673..42..264.1.33..8742162179635846481523.. C7: 7 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 * PAIR E1: 7,9 BLK 2 F1: 7,9,5 # reduction candidate for 7,9 F1: 7,9 => CTR * 5642..831731486925829315467473.216.81.6.3.7429.264715339587421621..635846481523.. F1: 5 # 15 pairs F3: 7,9,5 # reduction candidate for 7,9 F3: 7,9 # 15 pairs * PAIR E1: 7,9 ROW 1 A1: 7,9,5 # reduction candidate for 7,9 A1: 5 => CTR * 5642..831731486925829315467473.216.81.6.3.7429.264715339587421621..635846481523.. A1: 7,9 # 15 pairs * PAIR G2: 7,9 BLK 3 I2: 7,9,5 # reduction candidate for 7,9 I2: 7,9 => CTR * 764295831531486.2.8293174654735216981.6.3..429.264.1.33958742162179635846481523.. I2: 5 # 15 pairs I3: 7,9,5 # reduction candidate for 7,9 I3: 7,9 # 15 pairs * PAIR G2: 7,9 ROW 2 A2: 7,9,5 # reduction candidate for 7,9 A2: 5 => CTR * 764295831531486.2.829317465473.216.81.673.9429.26481.33..8.421621..635846481523.. A2: 7,9 # 15 pairs * PAIR A6: 5,9 BLK 4 B5: 5,9,8 # reduction candidate for 5,9 B5: 5,9 # 15 pairs B6: 5,9,8 # reduction candidate for 5,9 B6: 5,9 => CTR * .6427.83173148692.82.31.46.473.216.818653..42..26481733..8.421621.763584648152397 B6: 8 # 15 pairs * PAIR A6: 5,9 ROW 6 H6: 5,9,7 # reduction candidate for 5,9 H6: 5,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 H6: 7 => CTR * .6427.831731486.2.82.31.46.473.216581.653.942..264.1733..8.421621.763584648152397 * PAIR A6: 5,9 COL A A1: 5,9,7 # reduction candidate for 5,9 A1: 5,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 A1: 7 => CTR * 764295831.31486.2.82.31746.473.216.81.673.942..26491.33..8.421621..635846481523.. A2: 5,9,7 # reduction candidate for 5,9 A2: 5,9 => CTR * 764295831.31486.2.82.31746.473.216.81.673.942..26491.33..8.421621..635846481523.. A2: 7 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 * PAIR D4: 5,9 BLK 5 D5: 5,9,7 # reduction candidate for 5,9 D5: 5,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 D5: 7 => CTR * .642..831.31486.2.82.31.46.47352169815673..42..264.1.33..8.421621..635846481523.. * PAIR H4: 5,9 BLK 6 H6: 5,9,7 # reduction candidate for 5,9 H6: 5,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 H6: 7 => CTR * .6427.831731486.2.82.31.46.473.216581.653.942..264.1733..8.421621.763584648152397 * PAIR G5: 7,9 BLK 6 H6: 7,9,5 # reduction candidate for 7,9 H6: 7,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 H6: 5 => CTR * .6427.83173148692582.31.46747352169815693874298264715339.8.421621.763584648152379 * PAIR G5: 7,9 ROW 5 D5: 7,9,5 # reduction candidate for 7,9 D5: 7,9 => CTR * .642..831.31486.2.82.31.46.473521698156.3874298264715339587421621..635846481523.. D5: 5 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 F5: 7,9,8 # reduction candidate for 7,9 F5: 7,9 => CTR * .6427.83173148692.82.31.46.473.216.818653..42..26481733..8.421621.763584648152397 F5: 8 # 15 pairs * PAIR B7: 5,9 BLK 7 C7: 5,9,7 # reduction candidate for 5,9 C7: 5,9 => CTR * .6429.831.31486.2.82.31.46.47352169815673..42..264.1.33..8742162179635846481523.. C7: 7 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 * PAIR B7: 5,9 COL B B5: 5,9,8 # reduction candidate for 5,9 B5: 5,9 # 15 pairs B6: 5,9,8 # reduction candidate for 5,9 B6: 5,9 => CTR * .6427.83173148692.82.31.46.473.216.818653..42..26481733..8.421621.763584648152397 B6: 8 # 15 pairs * PAIR C8: 7,9 BLK 7 C7: 7,9,5 # reduction candidate for 7,9 C7: 7,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 C7: 5 => CTR * .6429.831.31486.2.82931.46.47352169815673..42..264.1.33.58742162179635846481523.. * PAIR E7: 7,9 ROW 7 C7: 7,9,5 # reduction candidate for 7,9 C7: 7,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 C7: 5 => CTR * .6429.831.31486.2.82931.46.47352169815673..42..264.1.33.58742162179635846481523.. * PAIR D8: 7,9 COL D D5: 7,9,5 # reduction candidate for 7,9 D5: 7,9 => CTR * .642..831.31486.2.82.31.46.473521698156.3874298264715339587421621..635846481523.. D5: 5 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 * PAIR H9: 7,9 COL H H6: 7,9,5 # reduction candidate for 7,9 H6: 7,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 H6: 5 => CTR * .6427.83173148692582.31.46747352169815693874298264715339.8.421621.763584648152379 * PAIR I9: 7,9 COL I I2: 7,9,5 # reduction candidate for 7,9 I2: 7,9 => CTR * 764295831531486.2.8293174654735216981.6.3..429.264.1.33958742162179635846481523.. I2: 5 # 15 pairs I3: 7,9,5 # reduction candidate for 7,9 I3: 7,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-128-base-pr-000.dot * REASONING * PRF # A1: 5,9 => SOL * DIS # A1: 7 => CTR => A1: 5,9 * DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * PRF # F3: 5,9 => SOL * DIS # F3: 7 => CTR => F3: 5,9 * DIS # I3: 5,9 => CTR => I3: 7 * PRF # I3: 7 => SOL * DIS # C7: 5,9 => CTR => C7: 7 * PRF # C7: 7 => SOL * DIS # F1: 7,9 => CTR => F1: 5 * DIS # A1: 5 => CTR => A1: 7,9 * DIS # I2: 7,9 => CTR => I2: 5 * DIS # A2: 5 => CTR => A2: 7,9 * DIS # B6: 5,9 => CTR => B6: 8 * PRF # H6: 5,9 => SOL * DIS # H6: 7 => CTR => H6: 5,9 * PRF # A1: 5,9 => SOL * DIS # A1: 7 => CTR => A1: 5,9 * DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * PRF # D5: 5,9 => SOL * DIS # D5: 7 => CTR => D5: 5,9 * PRF # H6: 5,9 => SOL * DIS # H6: 7 => CTR => H6: 5,9 * PRF # H6: 7,9 => SOL * DIS # H6: 5 => CTR => H6: 7,9 * DIS # D5: 7,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * DIS # F5: 7,9 => CTR => F5: 8 * DIS # C7: 5,9 => CTR => C7: 7 * PRF # C7: 7 => SOL * DIS # B6: 5,9 => CTR => B6: 8 * PRF # C7: 7,9 => SOL * DIS # C7: 5 => CTR => C7: 7,9 * PRF # C7: 7,9 => SOL * DIS # C7: 5 => CTR => C7: 7,9 * DIS # D5: 7,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * PRF # H6: 7,9 => SOL * DIS # H6: 5 => CTR => H6: 7,9 * DIS # I2: 7,9 => CTR => I2: 5 * CNT 42 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,C3,C8,D4,D8,E1,E7,G2,G5,H4,H9,I9) * .642..831.31486.2.82.31.46.473.216.81.6.3..42..264.1.33..8.421621..635846481523.. * PAIR C3: 5,9 BLK 1 A1: 5,9,7 # reduction candidate for 5,9 A1: 5,9 => SOLVED * 964275831731486925825319467473921658196538742582647193357894216219763584648152379 * DURATION: 0:00:02.028244 START: 07:10:04.643989 END: 07:10:06.672233 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-128-base-pr-001.dot * REASONING * PRF # A1: 5,9 => SOL * STA A1: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 128 solution: 964275831731486925825319467473921658196538742582647193357894216219763584648152379 info: 1810 FNBWY S8.f 49074 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 964275831731486925825319467473921658196538742582647193357894216219763584648152379 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 # A1: 5,9 => SOL * DIS # A1: 7 => CTR => A1: 5,9 * DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * PRF # F3: 5,9 => SOL * DIS # F3: 7 => CTR => F3: 5,9 * DIS # I3: 5,9 => CTR => I3: 7 * PRF # I3: 7 => SOL * DIS # C7: 5,9 => CTR => C7: 7 * PRF # C7: 7 => SOL * DIS # F1: 7,9 => CTR => F1: 5 * INC # F1: 5 => UNS * INC # F3: 7,9 => UNS * INC # A1: 7,9 => UNS * DIS # A1: 5 => CTR => A1: 7,9 * DIS # I2: 7,9 => CTR => I2: 5 * INC # I2: 5 => UNS * INC # I3: 7,9 => UNS * INC # A2: 7,9 => UNS * DIS # A2: 5 => CTR => A2: 7,9 * INC # B5: 5,9 => UNS * DIS # B6: 5,9 => CTR => B6: 8 * INC # B6: 8 => UNS * PRF # H6: 5,9 => SOL * DIS # H6: 7 => CTR => H6: 5,9 * PRF # A1: 5,9 => SOL * DIS # A1: 7 => CTR => A1: 5,9 * DIS # A2: 5,9 => CTR => A2: 7 * PRF # A2: 7 => SOL * PRF # D5: 5,9 => SOL * DIS # D5: 7 => CTR => D5: 5,9 * PRF # H6: 5,9 => SOL * DIS # H6: 7 => CTR => H6: 5,9 * PRF # H6: 7,9 => SOL * DIS # H6: 5 => CTR => H6: 7,9 * DIS # D5: 7,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * DIS # F5: 7,9 => CTR => F5: 8 * INC # F5: 8 => UNS * DIS # C7: 5,9 => CTR => C7: 7 * PRF # C7: 7 => SOL * INC # B5: 5,9 => UNS * DIS # B6: 5,9 => CTR => B6: 8 * INC # B6: 8 => UNS * PRF # C7: 7,9 => SOL * DIS # C7: 5 => CTR => C7: 7,9 * PRF # C7: 7,9 => SOL * DIS # C7: 5 => CTR => C7: 7,9 * DIS # D5: 7,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * PRF # H6: 7,9 => SOL * DIS # H6: 5 => CTR => H6: 7,9 * DIS # I2: 7,9 => CTR => I2: 5 * INC # I2: 5 => UNS * INC # I3: 7,9 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 5,9 => SOL * STA A1: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED