Analysis of xx-top500-264-base.sdk
Contents
Original Sudoku
level: medium
position: .53..8.7..4....2....1......6...4............1.......9.2...6.4.....1.9......3..... initial
Autosolve
position: 953218674.46..321..214.69..6.5.413..3.26...411.4.32.9621..6.4..43.1.9.6.56.3.41.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E2: 5,7 => SOL * DIS # E5: 5,7 => CTR => E5: 8,9 * DIS # I3: 5,8 => CTR => I3: 3 * DIS # I3: 8 => CTR => I3: 3,5 * PRF # B5: 7,8 => SOL * DIS # G6: 7,8 => CTR => G6: 5 * DIS # E5: 5,7 => CTR => E5: 8,9 * DIS # G5: 8 => CTR => G5: 5,7 * PRF # I9: 2,7 => SOL * PRF # C7: 7,8 => SOL * PRF # D7: 5,7 => SOL * DIS # I7: 5,7 => CTR => I7: 3,9 * DIS # I7: 3,5 => CTR => I7: 7,9 * PRF # I7: 7,9 => SOL * DIS # G6: 7,8 => CTR => G6: 5 * DIS # E9: 7 => CTR => E9: 2,8 * CNT 16 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E2: 5,7 => SOL * STA E2: 5,7 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .53..8.7..4....2....1......6...4............1.......9.2...6.4.....1.9......3..... | initial |
| 953218674.46..321..214.69..6.5.413..3.26...411.4.32.9621..6.4..43.1.9.6.56.3.41.. | autosolve |
| 953218674746953218821476953695741382382695741174832596218567439437129865569384127 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A2: 7,8 A3: 7,8 E3: 5,7 I2: 5,8 H3: 3,5 B6: 7,8 F5: 5,7 H4: 2,8 I4: 2,7 C8: 7,8 F7: 5,7 E8: 2,5 H7: 3,5 G8: 7,8 I8: 2,5 H9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H4,I4: 2.. / H4 = 2 => 0 pairs (X) / I4 = 2 => 0 pairs (_) E8,E9: 2.. / E8 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) E8,I8: 2.. / E8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) H4,H9: 2.. / H4 = 2 => 0 pairs (X) / H9 = 2 => 0 pairs (_) H3,I3: 3.. / H3 = 3 => 0 pairs (X) / I3 = 3 => 17 pairs (_) H7,I7: 3.. / H7 = 3 => 17 pairs (_) / I7 = 3 => 0 pairs (X) H3,H7: 3.. / H3 = 3 => 0 pairs (X) / H7 = 3 => 17 pairs (_) I3,I7: 3.. / I3 = 3 => 17 pairs (_) / I7 = 3 => 0 pairs (X) G5,G6: 5.. / G5 = 5 => 0 pairs (X) / G6 = 5 => 18 pairs (_) D6,G6: 5.. / D6 = 5 => 0 pairs (X) / G6 = 5 => 18 pairs (_) E8,I8: 5.. / E8 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) F5,F7: 5.. / F5 = 5 => 21 pairs (_) / F7 = 5 => 0 pairs (X) H3,H7: 5.. / H3 = 5 => 17 pairs (_) / H7 = 5 => 0 pairs (X) A2,A3: 7.. / A2 = 7 => 19 pairs (_) / A3 = 7 => 0 pairs (X) A3,E3: 7.. / A3 = 7 => 0 pairs (X) / E3 = 7 => 19 pairs (_) C8,G8: 7.. / C8 = 7 => 0 pairs (*) / G8 = 7 => 0 pairs (X) F5,F7: 7.. / F5 = 7 => 0 pairs (X) / F7 = 7 => 21 pairs (_) A2,A3: 8.. / A2 = 8 => 0 pairs (X) / A3 = 8 => 19 pairs (_) I2,I3: 8.. / I2 = 8 => 19 pairs (_) / I3 = 8 => 0 pairs (X) D7,E9: 8.. / D7 = 8 => 22 pairs (_) / E9 = 8 => 0 pairs (*) G8,H9: 8.. / G8 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) A2,I2: 8.. / A2 = 8 => 0 pairs (X) / I2 = 8 => 19 pairs (_) A3,I3: 8.. / A3 = 8 => 19 pairs (_) / I3 = 8 => 0 pairs (X) C7,D7: 8.. / C7 = 8 => 0 pairs (*) / D7 = 8 => 0 pairs (X) C8,G8: 8.. / C8 = 8 => 0 pairs (X) / G8 = 8 => 0 pairs (_) E5,E9: 8.. / E5 = 8 => 22 pairs (_) / E9 = 8 => 0 pairs (*) H4,H9: 8.. / H4 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) D2,E2: 9.. / D2 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) B4,B5: 9.. / B4 = 9 => 0 pairs (*) / B5 = 9 => 0 pairs (X) D4,E5: 9.. / D4 = 9 => 18 pairs (_) / E5 = 9 => 0 pairs (*) C7,C9: 9.. / C7 = 9 => 22 pairs (_) / C9 = 9 => 0 pairs (*) I7,I9: 9.. / I7 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) B4,D4: 9.. / B4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) B5,E5: 9.. / B5 = 9 => 18 pairs (_) / E5 = 9 => 0 pairs (*) C7,I7: 9.. / C7 = 9 => 22 pairs (_) / I7 = 9 => 0 pairs (*) C9,I9: 9.. / C9 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) D2,D4: 9.. / D2 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) E2,E5: 9.. / E2 = 9 => 18 pairs (_) / E5 = 9 => 0 pairs (*) * DURATION: 0:01:16.201693 START: 11:53:15.479928 END: 11:54:31.681621 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B6,C8,E3,E8,F5,F7,G8,H3,H4,H7,H9,I2,I4,I8) * 953218674.46..321..214.69..6.5.413..3.26...411.4.32.9621..6.4..43.1.9.6.56.3.41.. * PAIR E3: 5,7 BLK 2 D2: 5,7,9 # reduction candidate for 5,7 D2: 5,7 # 18 pairs E2: 5,7,9 # reduction candidate for 5,7 E2: 5,7 => SOLVED * 953218674746953218821476953695741382382695741174832596218567439437129865569384127 E2: 9 # 18 pairs * PAIR E3: 5,7 COL E E5: 5,7,8,9 # reduction candidate for 5,7 E5: 5,7 => CTR * 953218674.46.9321..214.69..6.59413..3926..8411.4832596218.6.4.94371.9.6.56.3.41.. E5: 8,9 # 17 pairs * PAIR I2: 5,8 BLK 3 I3: 5,8,3 # reduction candidate for 5,8 I3: 5,8 => CTR * 953218674.465932188214769356.594132739268..411.4.32.9621..6.45343.159.6256.324189 I3: 3 # 17 pairs * PAIR H3: 3,5 BLK 3 I3: 3,5,8 # reduction candidate for 3,5 I3: 8 => CTR * 953218674.46..321..214.69386.5.413..3.26...411.4.32.9621..6.45343.159.6256.324189 I3: 3,5 # 19 pairs * PAIR B6: 7,8 BLK 4 B4: 7,8,9 # reduction candidate for 7,8 B4: 7,8 # 18 pairs B5: 7,8,9 # reduction candidate for 7,8 B5: 7,8 => SOLVED * 953218674746953218821476953695741382382695741174832596218567439437129865569384127 B5: 9 # 18 pairs * PAIR B6: 7,8 ROW 6 D6: 7,8,5 # reduction candidate for 7,8 D6: 7,8 # 18 pairs G6: 7,8,5 # reduction candidate for 7,8 G6: 7,8 => CTR * 953218674.46.532188214769536.5.413..3.26975411.4532.9621.76543943.129.65569384127 G6: 5 # 18 pairs * PAIR F5: 5,7 BLK 5 E5: 5,7,8,9 # reduction candidate for 5,7 E5: 5,7 => CTR * 953218674.46.9321..214.69..6.59413..3926..8411.4832596218.6.4.94371.9.6.56.3.41.. E5: 8,9 # 17 pairs D6: 5,7,8 # reduction candidate for 5,7 D6: 5,7 # 19 pairs * PAIR F5: 5,7 ROW 5 G5: 5,7,8 # reduction candidate for 5,7 G5: 8 => CTR * 953218674.46..321..214.69..6.5.413..3.26..8411.4.3259621..6.4..4381.976.56.38412. G5: 5,7 # 19 pairs * PAIR I4: 2,7 COL I I9: 2,7,9 # reduction candidate for 2,7 I9: 2,7 => SOLVED * 953218674746953218821476953695741382382695741174832596218567439437129865569384127 I9: 9 # 22 pairs * PAIR C8: 7,8 BLK 7 C7: 7,8,9 # reduction candidate for 7,8 C7: 7,8 => SOLVED * 953218674746953218821476953695741382382695741174832596218567439437129865569384127 C7: 9 # 22 pairs C9: 7,8,9 # reduction candidate for 7,8 C9: 7,8 # 22 pairs * PAIR F7: 5,7 BLK 8 D7: 5,7,8 # reduction candidate for 5,7 D7: 5,7 => SOLVED * 953218674746953218821476953695741382382695741174832596218567439437129865569384127 D7: 8 # 22 pairs * PAIR F7: 5,7 ROW 7 I7: 5,7,3,9 # reduction candidate for 5,7 I7: 5,7 => CTR * 953218674.46..32188214769536.5.413..3.268..411.4.32.9621986743543.159762567324189 I7: 3,9 # 17 pairs * PAIR H7: 3,5 BLK 9 I7: 3,5,7,9 # reduction candidate for 3,5 I7: 3,5 => CTR * 953218674.465932188214769..68594132.3.26...411.4.32.962198674..43.159.6256.324189 I7: 7,9 => SOLVED * 953218674746953218821476953695741382382695741174832596218567439437129865569384127 * PAIR G8: 7,8 COL G G5: 7,8,5 # reduction candidate for 7,8 G5: 7,8 # 18 pairs G6: 7,8,5 # reduction candidate for 7,8 G6: 7,8 => CTR * 953218674.46.532188214769536.5.413..3.26975411.4532.9621.76543943.129.65569384127 G6: 5 # 18 pairs * PAIR H9: 2,8 ROW 9 E9: 2,8,7 # reduction candidate for 2,8 E9: 7 => CTR * 953218674.467.321..214.69..6.5.413..3.268..411.4.32.9621.86.4..43.129.6556.3741.. E9: 2,8 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-264-base-pr-000.dot * REASONING * PRF # E2: 5,7 => SOL * DIS # E5: 5,7 => CTR => E5: 8,9 * DIS # I3: 5,8 => CTR => I3: 3 * DIS # I3: 8 => CTR => I3: 3,5 * PRF # B5: 7,8 => SOL * DIS # G6: 7,8 => CTR => G6: 5 * DIS # E5: 5,7 => CTR => E5: 8,9 * DIS # G5: 8 => CTR => G5: 5,7 * PRF # I9: 2,7 => SOL * PRF # C7: 7,8 => SOL * PRF # D7: 5,7 => SOL * DIS # I7: 5,7 => CTR => I7: 3,9 * DIS # I7: 3,5 => CTR => I7: 7,9 * PRF # I7: 7,9 => SOL * DIS # G6: 7,8 => CTR => G6: 5 * DIS # E9: 7 => CTR => E9: 2,8 * CNT 16 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B6,C8,E3,E8,F5,F7,G8,H3,H4,H7,H9,I2,I4,I8) * 953218674.46..321..214.69..6.5.413..3.26...411.4.32.9621..6.4..43.1.9.6.56.3.41.. * PAIR E3: 5,7 BLK 2 D2: 5,7,9 # reduction candidate for 5,7 D2: 5,7 # 18 pairs E2: 5,7,9 # reduction candidate for 5,7 E2: 5,7 => SOLVED * 953218674746953218821476953695741382382695741174832596218567439437129865569384127 * DURATION: 0:00:03.430986 START: 11:55:14.091355 END: 11:55:17.522341 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-264-base-pr-001.dot * REASONING * PRF # E2: 5,7 => SOL * STA E2: 5,7 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 264 solution: 953218674746953218821476953695741382382695741174832596218567439437129865569384127 info: 2117 FNBTWXY S8.f 20601 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 953218674746953218821476953695741382382695741174832596218567439437129865569384127 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 # D2: 5,7 => UNS * PRF # E2: 5,7 => SOL * INC # E2: 9 => UNS * DIS # E5: 5,7 => CTR => E5: 8,9 * INC # E5: 8,9 => UNS * DIS # I3: 5,8 => CTR => I3: 3 * INC # I3: 3 => UNS * INC # I3: 3,5 => UNS * DIS # I3: 8 => CTR => I3: 3,5 * INC # B4: 7,8 => UNS * PRF # B5: 7,8 => SOL * INC # B5: 9 => UNS * INC # D6: 7,8 => UNS * DIS # G6: 7,8 => CTR => G6: 5 * INC # G6: 5 => UNS * DIS # E5: 5,7 => CTR => E5: 8,9 * INC # E5: 8,9 => UNS * INC # D6: 5,7 => UNS * INC # G5: 5,7 => UNS * DIS # G5: 8 => CTR => G5: 5,7 * PRF # I9: 2,7 => SOL * INC # I9: 9 => UNS * PRF # C7: 7,8 => SOL * INC # C7: 9 => UNS * INC # C9: 7,8 => UNS * PRF # D7: 5,7 => SOL * INC # D7: 8 => UNS * DIS # I7: 5,7 => CTR => I7: 3,9 * INC # I7: 3,9 => UNS * DIS # I7: 3,5 => CTR => I7: 7,9 * PRF # I7: 7,9 => SOL * INC # G5: 7,8 => UNS * DIS # G6: 7,8 => CTR => G6: 5 * INC # G6: 5 => UNS * INC # E9: 2,8 => UNS * DIS # E9: 7 => CTR => E9: 2,8 * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 5,7 => UNS * PRF # E2: 5,7 => SOL * STA E2: 5,7 * CNT 2 HDP CHAINS / 2 HYP OPENED