Analysis of xx-top500-445-base.sdk
Contents
Original Sudoku
level: medium
position: 1....5.9.....1...4..............615...49......2........8.47....5.....8.....2..... initial
Autosolve
position: 14...529...5.12..42...94.15..9.46152.54921....215.74.9.8647.5215.216.84.41.2589.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 3,8 => CTR => D1: 6,7 * DIS # I1: 3,8 => CTR => I1: 6,7 * PRF # A4: 8 => SOL * DIS # B2: 3,7 => CTR => B2: 6,9 * DIS # B3: 3,7 => CTR => B3: 6 * PRF # A4: 3,8 => SOL * DIS # D1: 3,8 => CTR => D1: 6,7 * PRF # B8: 3,9 => SOL * DIS # B8: 7 => CTR => B8: 3,9 * PRF # A2: 7 => SOL * DIS # B8: 9 => CTR => B8: 3,7 * PRF # C3: 3,7 => SOL * PRF # B8: 3,9 => SOL * DIS # B8: 7 => CTR => B8: 3,9 * DIS # B8: 9 => CTR => B8: 3,7 * DIS # I5: 3,7 => CTR => I5: 6,8 * CNT 16 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 3,8 => CTR => D1: 6,7 * DIS D1: 6,7 # I1: 3,8 => CTR => I1: 6,7 * DIS D1: 6,7 + I1: 6,7 # D3: 6,7 => CTR => D3: 3,8 * DIS D1: 6,7 + I1: 6,7 + D3: 3,8 # A4: 3,7 => CTR => A4: 8 * PRF D1: 6,7 + I1: 6,7 + D3: 3,8 + A4: 8 => SOL * STA D1: 6,7 + I1: 6,7 + D3: 3,8 + A4: 8 * CNT 5 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1....5.9.....1...4..............615...49......2........8.47....5.....8.....2..... | initial |
| 14...529...5.12..42...94.15..9.46152.54921....215.74.9.8647.5215.216.84.41.2589.. | autosolve |
| 148735296795612384263894715879346152354921678621587439986473521532169847417258963 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) E1: 3,8 B4: 3,7 D4: 3,8 E6: 3,8 A7: 3,9 C9: 3,7 F7: 3,9 F8: 3,9 I8: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,E6: 3.. / D4 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) F7,F8: 3.. / F7 = 3 => 9 pairs (_) / F8 = 3 => 0 pairs (X) A7,F7: 3.. / A7 = 3 => 0 pairs (X) / F7 = 3 => 9 pairs (_) E1,E6: 3.. / E1 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) B2,B3: 6.. / B2 = 6 => 0 pairs (X) / B3 = 6 => 10 pairs (_) A5,A6: 6.. / A5 = 6 => 12 pairs (_) / A6 = 6 => 11 pairs (_) H9,I9: 6.. / H9 = 6 => 14 pairs (_) / I9 = 6 => 10 pairs (_) D1,I1: 6.. / D1 = 6 => 9 pairs (_) / I1 = 6 => 0 pairs (*) A6,H6: 6.. / A6 = 6 => 11 pairs (_) / H6 = 6 => 12 pairs (_) A4,B4: 7.. / A4 = 7 => 15 pairs (_) / B4 = 7 => 0 pairs (*) B8,C9: 7.. / B8 = 7 => 0 pairs (X) / C9 = 7 => 0 pairs (_) B8,I8: 7.. / B8 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) A2,A4: 7.. / A2 = 7 => 0 pairs (*) / A4 = 7 => 0 pairs (X) C1,C3: 8.. / C1 = 8 => 0 pairs (*) / C3 = 8 => 0 pairs (X) I1,H2: 8.. / I1 = 8 => 0 pairs (X) / H2 = 8 => 11 pairs (_) D4,E6: 8.. / D4 = 8 => 14 pairs (_) / E6 = 8 => 0 pairs (*) D2,H2: 8.. / D2 = 8 => 0 pairs (X) / H2 = 8 => 11 pairs (_) C3,D3: 8.. / C3 = 8 => 10 pairs (_) / D3 = 8 => 0 pairs (*) A4,D4: 8.. / A4 = 8 => 0 pairs (*) / D4 = 8 => 0 pairs (X) E1,E6: 8.. / E1 = 8 => 14 pairs (_) / E6 = 8 => 0 pairs (*) I1,I5: 8.. / I1 = 8 => 0 pairs (X) / I5 = 8 => 11 pairs (_) A2,B2: 9.. / A2 = 9 => 0 pairs (X) / B2 = 9 => 9 pairs (_) A7,B8: 9.. / A7 = 9 => 9 pairs (_) / B8 = 9 => 0 pairs (X) F7,F8: 9.. / F7 = 9 => 0 pairs (X) / F8 = 9 => 9 pairs (_) A7,F7: 9.. / A7 = 9 => 9 pairs (_) / F7 = 9 => 0 pairs (X) B8,F8: 9.. / B8 = 9 => 0 pairs (X) / F8 = 9 => 9 pairs (_) A2,A7: 9.. / A2 = 9 => 0 pairs (X) / A7 = 9 => 9 pairs (_) B2,B8: 9.. / B2 = 9 => 9 pairs (_) / B8 = 9 => 0 pairs (X) * DURATION: 0:00:49.969684 START: 17:57:10.624238 END: 17:58:00.593922 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B4,C9,D4,E1,E6,F7,F8,I8) * 14...529...5.12..42...94.15..9.46152.54921....215.74.9.8647.5215.216.84.41.2589.. * PAIR E1: 3,8 BLK 2 D1: 3,8,6,7 # reduction candidate for 3,8 D1: 3,8 => CTR * 147835296..5.12.842.8.94.15..9.46152.549216.8621587439.8647.5215.216.84.41.25896. D1: 6,7 # 10 pairs D2: 3,8,6,7 # reduction candidate for 3,8 D2: 3,8 # 13 pairs D3: 3,8,6,7 # reduction candidate for 3,8 D3: 3,8 # 14 pairs * PAIR E1: 3,8 ROW 1 C1: 3,8,7 # reduction candidate for 3,8 C1: 3,8 # 16 pairs I1: 3,8,6,7 # reduction candidate for 3,8 I1: 3,8 => CTR * 1476.529...5.12..42.8.94.15739846152.54921....215374.9.8647.5215721698434132589.. I1: 6,7 # 14 pairs * PAIR B4: 3,7 BLK 4 A4: 3,7,8 # reduction candidate for 3,7 A4: 8 => SOLVED * 148735296795612384263894715879346152354921678621587439986473521532169847417258963 A4: 3,7 # 14 pairs * PAIR B4: 3,7 COL B B2: 3,7,6,9 # reduction candidate for 3,7 B2: 3,7 => CTR * 14.785296975612384268394715739846152.549216...215374.93864795215921638474172589.. B2: 6,9 # 10 pairs B3: 3,7,6 # reduction candidate for 3,7 B3: 3,7 => CTR * 14.7.5296965.12.8427.694315739846152.5492167..215.74.9.8647.5215921638474172589.. B3: 6 # 10 pairs B8: 3,7,9 # reduction candidate for 3,7 B8: 3,7 # 9 pairs * PAIR D4: 3,8 ROW 4 A4: 3,8,7 # reduction candidate for 3,8 A4: 3,8 => SOLVED * 148735296795612384263894715879346152354921678621587439986473521532169847417258963 A4: 7 # 15 pairs * PAIR D4: 3,8 COL D D1: 3,8,6,7 # reduction candidate for 3,8 D1: 3,8 => CTR * 147835296..5.12.842.8.94.15..9.46152.549216.8621587439.8647.5215.216.84.41.25896. D1: 6,7 # 10 pairs D2: 3,8,6,7 # reduction candidate for 3,8 D2: 3,8 # 13 pairs D3: 3,8,6,7 # reduction candidate for 3,8 D3: 3,8 # 14 pairs * PAIR E6: 3,8 ROW 6 A6: 3,8,6 # reduction candidate for 3,8 A6: 3,8 # 12 pairs H6: 3,8,6 # reduction candidate for 3,8 H6: 3,8 # 11 pairs * PAIR A7: 3,9 BLK 7 B8: 3,9,7 # reduction candidate for 3,9 B8: 3,9 => SOLVED * 148735296795612384263894715879346152354921678621587439986473521532169847417258963 B8: 7 => CTR * 14.385296395612784268794315739846152.549216...215374.99864735215721698434132589.. * PAIR A7: 3,9 COL A A2: 3,9,7 # reduction candidate for 3,9 A2: 7 => SOLVED * 148735296795612384263894715879346152354921678621587439986473521532169847417258963 A2: 3,9 # 15 pairs * PAIR C9: 3,7 BLK 7 B8: 3,7,9 # reduction candidate for 3,7 B8: 9 => CTR * 14.7.52969.5.12.842...94.15739846152.5492167..215.74.9.8647.5215921638474172589.. B8: 3,7 # 9 pairs * PAIR C9: 3,7 ROW 9 H9: 3,7,6 # reduction candidate for 3,7 H9: 3,7 # 10 pairs I9: 3,7,6 # reduction candidate for 3,7 I9: 3,7 # 14 pairs * PAIR C9: 3,7 COL C C1: 3,7,8 # reduction candidate for 3,7 C1: 3,7 # 10 pairs C3: 3,7,8 # reduction candidate for 3,7 C3: 3,7 => SOLVED * 148735296795612384263894715879346152354921678621587439986473521532169847417258963 C3: 8 # 10 pairs * PAIR F8: 3,9 ROW 8 B8: 3,9,7 # reduction candidate for 3,9 B8: 3,9 => SOLVED * 148735296795612384263894715879346152354921678621587439986473521532169847417258963 B8: 7 => CTR * 14.385296395612784268794315739846152.549216...215374.99864735215721698434132589.. * PAIR I8: 3,7 BLK 9 H9: 3,7,6 # reduction candidate for 3,7 H9: 3,7 # 10 pairs I9: 3,7,6 # reduction candidate for 3,7 I9: 3,7 # 14 pairs * PAIR I8: 3,7 ROW 8 B8: 3,7,9 # reduction candidate for 3,7 B8: 9 => CTR * 14.7.52969.5.12.842...94.15739846152.5492167..215.74.9.8647.5215921638474172589.. B8: 3,7 # 9 pairs * PAIR I8: 3,7 COL I I1: 3,7,6,8 # reduction candidate for 3,7 I1: 3,7 # 15 pairs I5: 3,7,6,8 # reduction candidate for 3,7 I5: 3,7 => CTR * 14...5298..5812..42.8.94.15879346152.54921.8..215874.9.8647.5215.216.8474172589.6 I5: 6,8 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-445-base-pr-000.dot * REASONING * DIS # D1: 3,8 => CTR => D1: 6,7 * DIS # I1: 3,8 => CTR => I1: 6,7 * PRF # A4: 8 => SOL * DIS # B2: 3,7 => CTR => B2: 6,9 * DIS # B3: 3,7 => CTR => B3: 6 * PRF # A4: 3,8 => SOL * DIS # D1: 3,8 => CTR => D1: 6,7 * PRF # B8: 3,9 => SOL * DIS # B8: 7 => CTR => B8: 3,9 * PRF # A2: 7 => SOL * DIS # B8: 9 => CTR => B8: 3,7 * PRF # C3: 3,7 => SOL * PRF # B8: 3,9 => SOL * DIS # B8: 7 => CTR => B8: 3,9 * DIS # B8: 9 => CTR => B8: 3,7 * DIS # I5: 3,7 => CTR => I5: 6,8 * CNT 16 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B4,C9,D4,E1,E6,F7,F8,I8) * 14...529...5.12..42...94.15..9.46152.54921....215.74.9.8647.5215.216.84.41.2589.. * PAIR E1: 3,8 BLK 2 D1: 3,8,6,7 # reduction candidate for 3,8 D1: 3,8 => CTR * 147835296..5.12.842.8.94.15..9.46152.549216.8621587439.8647.5215.216.84.41.25896. D2: 3,8,6,7 # reduction candidate for 3,8 D2: 3,8 # 13 pairs D3: 3,8,6,7 # reduction candidate for 3,8 D3: 3,8 # 14 pairs * PAIR E1: 3,8 ROW 1 C1: 3,8,7 # reduction candidate for 3,8 C1: 3,8 # 16 pairs I1: 3,8,6,7 # reduction candidate for 3,8 I1: 3,8 => CTR * 1476.529...5.12..42.8.94.15739846152.54921....215374.9.8647.5215721698434132589.. * RESTART * PAIR RESTART * PAIR E1: 3,8 BLK 2 D3: 3,8,6,7 # reduction candidate for 3,8 D3: 6,7 => CTR * 14..8529...5312.842.8.94315..9846152.54921..8821537469.8647.5215.216.84.4172589.. * PAIR B4: 3,7 BLK 4 A4: 3,7,8 # reduction candidate for 3,7 A4: 3,7 => CTR * 14...529...5.12.842...94.15..9846152.54921..8821537469.8647.5215.216.84.41.258976 A4: 8 => SOLVED * 148735296795612384263894715879346152354921678621587439986473521532169847417258963 * DURATION: 0:00:10.298091 START: 17:58:42.318147 END: 17:58:52.616238 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-445-base-pr-001.dot * REASONING * DIS # D1: 3,8 => CTR => D1: 6,7 * DIS D1: 6,7 # I1: 3,8 => CTR => I1: 6,7 * DIS D1: 6,7 + I1: 6,7 # D3: 6,7 => CTR => D3: 3,8 * DIS D1: 6,7 + I1: 6,7 + D3: 3,8 # A4: 3,7 => CTR => A4: 8 * PRF D1: 6,7 + I1: 6,7 + D3: 3,8 + A4: 8 => SOL * STA D1: 6,7 + I1: 6,7 + D3: 3,8 + A4: 8 * CNT 5 HDP CHAINS / 8 HYP OPENED
Header Info
Top 500 Minimum 17 445 solution: 148735296795612384263894715879346152354921678621587439986473521532169847417258963 info: 95318 FNBXYK S8.f 25166 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 148735296795612384263894715879346152354921678621587439986473521532169847417258963 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:
* DIS # D1: 3,8 => CTR => D1: 6,7 * INC # D1: 6,7 => UNS * INC # D2: 3,8 => UNS * INC # D3: 3,8 => UNS * INC # C1: 3,8 => UNS * DIS # I1: 3,8 => CTR => I1: 6,7 * INC # I1: 6,7 => UNS * INC # A4: 3,7 => UNS * PRF # A4: 8 => SOL * DIS # B2: 3,7 => CTR => B2: 6,9 * INC # B2: 6,9 => UNS * DIS # B3: 3,7 => CTR => B3: 6 * INC # B3: 6 => UNS * INC # B8: 3,7 => UNS * PRF # A4: 3,8 => SOL * INC # A4: 7 => UNS * DIS # D1: 3,8 => CTR => D1: 6,7 * INC # D1: 6,7 => UNS * INC # D2: 3,8 => UNS * INC # D3: 3,8 => UNS * INC # A6: 3,8 => UNS * INC # H6: 3,8 => UNS * PRF # B8: 3,9 => SOL * DIS # B8: 7 => CTR => B8: 3,9 * INC # A2: 3,9 => UNS * PRF # A2: 7 => SOL * INC # B8: 3,7 => UNS * DIS # B8: 9 => CTR => B8: 3,7 * INC # H9: 3,7 => UNS * INC # I9: 3,7 => UNS * INC # C1: 3,7 => UNS * PRF # C3: 3,7 => SOL * INC # C3: 8 => UNS * PRF # B8: 3,9 => SOL * DIS # B8: 7 => CTR => B8: 3,9 * INC # H9: 3,7 => UNS * INC # I9: 3,7 => UNS * INC # B8: 3,7 => UNS * DIS # B8: 9 => CTR => B8: 3,7 * INC # I1: 3,7 => UNS * DIS # I5: 3,7 => CTR => I5: 6,8 * INC # I5: 6,8 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 3,8 => CTR => D1: 6,7 * INC D1: 6,7 # D2: 3,8 => UNS * INC D1: 6,7 # D3: 3,8 => UNS * INC D1: 6,7 # C1: 3,8 => UNS * DIS D1: 6,7 # I1: 3,8 => CTR => I1: 6,7 * INC D1: 6,7 + I1: 6,7 # D3: 3,8 => UNS * DIS D1: 6,7 + I1: 6,7 # D3: 6,7 => CTR => D3: 3,8 * DIS D1: 6,7 + I1: 6,7 + D3: 3,8 # A4: 3,7 => CTR => A4: 8 * PRF D1: 6,7 + I1: 6,7 + D3: 3,8 + A4: 8 => SOL * STA D1: 6,7 + I1: 6,7 + D3: 3,8 + A4: 8 * CNT 9 HDP CHAINS / 8 HYP OPENED