Analysis of xx-top500-247-base.sdk
Contents
Original Sudoku
level: medium
position: 7......1....5.8....3.......6..27.....4....3.....1.....1.2.....9....348........... initial
Autosolve
position: 7.43.2.1821.5.874383.4172..6.82731.4.41...37232714..8.1.2...439....348214.3.21..7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 6,9 => CTR => B1: 5 * PRF # B1: 5 => SOL * PRF # C3: 6,9 => SOL * DIS # C3: 5 => CTR => C3: 6,9 * DIS # C8: 6,9 => CTR => C8: 5 * PRF # C8: 5 => SOL * DIS # B1: 6,9 => CTR => B1: 5 * PRF # B1: 5 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 5 => CTR => G1: 6,9 * PRF # G1: 5,6 => SOL * DIS # G1: 9 => CTR => G1: 5,6 * DIS # H3: 5,6 => CTR => H3: 9 * PRF # H3: 9 => SOL * PRF # C3: 5,6 => SOL * DIS # C3: 9 => CTR => C3: 5,6 * DIS # B8: 5,9 => CTR => B8: 6,7 * DIS # F5: 6 => CTR => F5: 5,9 * DIS # F5: 6 => CTR => F5: 5,9 * PRF # G6: 5,9 => SOL * DIS # G6: 6 => CTR => G6: 5,9 * PRF # G6: 5,9 => SOL * DIS # G6: 6 => CTR => G6: 5,9 * PRF # H3: 5,9 => SOL * DIS # H3: 6 => CTR => H3: 5,9 * DIS # G6: 5,6 => CTR => G6: 9 * PRF # G6: 9 => SOL * DIS # B8: 5,9 => CTR => B8: 6,7 * DIS # F5: 5,6 => CTR => F5: 9 * PRF # F5: 9 => SOL * PRF # G1: 5,6 => SOL * DIS # G1: 9 => CTR => G1: 5,6 * DIS # G6: 5,6 => CTR => G6: 9 * PRF # G6: 9 => SOL * DIS # H3: 5,6 => CTR => H3: 9 * PRF # H3: 9 => SOL * CNT 36 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 # B1: 6,9 => CTR => B1: 5 * PRF B1: 5 => SOL * STA B1: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7......1....5.8....3.......6..27.....4....3.....1.....1.2.....9....348........... | initial |
| 7.43.2.1821.5.874383.4172..6.82731.4.41...37232714..8.1.2...439....348214.3.21..7 | autosolve |
| 754392618219568743836417295698273154541689372327145986172856439965734821483921567 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) C2: 6,9 E1: 6,9 E2: 6,9 I3: 5,6 B4: 5,9 A5: 5,9 D5: 6,8 E5: 5,8 F6: 5,9 H4: 5,9 I6: 5,6 A8: 5,9 B9: 8,9 E7: 5,8 F7: 5,6 D9: 8,9 G9: 5,6 H9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C3: 5.. / B1 = 5 => 0 pairs (*) / C3 = 5 => 0 pairs (X) B4,A5: 5.. / B4 = 5 => 0 pairs (X) / A5 = 5 => 0 pairs (_) E7,F7: 5.. / E7 = 5 => 18 pairs (_) / F7 = 5 => 0 pairs (X) G9,H9: 5.. / G9 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) B1,G1: 5.. / B1 = 5 => 0 pairs (*) / G1 = 5 => 0 pairs (X) B4,H4: 5.. / B4 = 5 => 0 pairs (X) / H4 = 5 => 0 pairs (_) A5,A8: 5.. / A5 = 5 => 0 pairs (*) / A8 = 5 => 0 pairs (X) C3,C8: 5.. / C3 = 5 => 0 pairs (X) / C8 = 5 => 0 pairs (_) E5,E7: 5.. / E5 = 5 => 0 pairs (X) / E7 = 5 => 18 pairs (_) I3,I6: 5.. / I3 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) E1,E2: 6.. / E1 = 6 => 20 pairs (_) / E2 = 6 => 0 pairs (*) D5,F5: 6.. / D5 = 6 => 18 pairs (_) / F5 = 6 => 0 pairs (X) G6,I6: 6.. / G6 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) G9,H9: 6.. / G9 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) C2,E2: 6.. / C2 = 6 => 20 pairs (_) / E2 = 6 => 0 pairs (*) F5,F7: 6.. / F5 = 6 => 0 pairs (X) / F7 = 6 => 18 pairs (_) H3,H9: 6.. / H3 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) I3,I6: 6.. / I3 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) B7,B8: 7.. / B7 = 7 => 17 pairs (_) / B8 = 7 => 20 pairs (_) D7,D8: 7.. / D7 = 7 => 20 pairs (_) / D8 = 7 => 17 pairs (_) B7,D7: 7.. / B7 = 7 => 17 pairs (_) / D7 = 7 => 20 pairs (_) B8,D8: 7.. / B8 = 7 => 20 pairs (_) / D8 = 7 => 17 pairs (_) D5,E5: 8.. / D5 = 8 => 0 pairs (X) / E5 = 8 => 18 pairs (_) B7,B9: 8.. / B7 = 8 => 0 pairs (X) / B9 = 8 => 18 pairs (_) B9,D9: 8.. / B9 = 8 => 18 pairs (_) / D9 = 8 => 0 pairs (X) E5,E7: 8.. / E5 = 8 => 18 pairs (_) / E7 = 8 => 0 pairs (X) E1,E2: 9.. / E1 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) G1,H3: 9.. / G1 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B4,A5: 9.. / B4 = 9 => 0 pairs (*) / A5 = 9 => 0 pairs (X) F5,F6: 9.. / F5 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) H4,G6: 9.. / H4 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) D8,D9: 9.. / D8 = 9 => 0 pairs (X) / D9 = 9 => 18 pairs (_) C2,E2: 9.. / C2 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) C3,H3: 9.. / C3 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B4,H4: 9.. / B4 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) A5,F5: 9.. / A5 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) F6,G6: 9.. / F6 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) B9,D9: 9.. / B9 = 9 => 0 pairs (X) / D9 = 9 => 18 pairs (_) A5,A8: 9.. / A5 = 9 => 0 pairs (X) / A8 = 9 => 0 pairs (_) G1,G6: 9.. / G1 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) H3,H4: 9.. / H3 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) * DURATION: 0:01:15.473047 START: 11:13:34.153201 END: 11:14:49.626248 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B4,B9,C2,D5,D9,E1,E2,E5,E7,F6,F7,G9,H4,H9,I3,I6) * 7.43.2.1821.5.874383.4172..6.82731.4.41...37232714..8.1.2...439....348214.3.21..7 * PAIR C2: 6,9 BLK 1 B1: 6,9,5 # reduction candidate for 6,9 B1: 6,9 => CTR * 7.43.251821.5.8743835417296698273154.41...37232714..8.1.2...439....348214.3.21..7 B1: 5 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 C3: 6,9,5 # reduction candidate for 6,9 C3: 6,9 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 C3: 5 => CTR * 7.43.2.1821.5.8743835417296698273154.41...37232714..8.1.2...439....348214.3.21..7 * PAIR C2: 6,9 COL C C8: 6,9,5 # reduction candidate for 6,9 C8: 6,9 => CTR * 7.43.2.1821.5.8743835417296698273154.41...37232714..8.1.2...439....348214.3.21..7 C8: 5 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 * PAIR E1: 6,9 ROW 1 B1: 6,9,5 # reduction candidate for 6,9 B1: 6,9 => CTR * 7.43.251821.5.8743835417296698273154.41...37232714..8.1.2...439....348214.3.21..7 B1: 5 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 G1: 6,9,5 # reduction candidate for 6,9 G1: 6,9 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 G1: 5 => CTR * 7.43.251821.5.8743835417296698273154.41...37232714..8.1.2...439....348214.3.21..7 * PAIR I3: 5,6 BLK 3 G1: 5,6,9 # reduction candidate for 5,6 G1: 5,6 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 G1: 9 => CTR * 7543629182165987438394172..6982731.4.41...37232714..8.1.2...439....348214.3.21..7 H3: 5,6,9 # reduction candidate for 5,6 H3: 5,6 => CTR * 7.43.291821.5987438394172..6.8273194941...372327149.8.1.2...4395.6.348214.3.21..7 H3: 9 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 * PAIR I3: 5,6 ROW 3 C3: 5,6,9 # reduction candidate for 5,6 C3: 5,6 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 C3: 9 => CTR * 7543.2.182165987438394172..6982731.4.41...37232714..8.1.2...439....348214.3.21..7 * PAIR B4: 5,9 COL B B1: 5,9,6 # reduction candidate for 5,9 B1: 5,9 # 21 pairs B8: 5,9,6,7 # reduction candidate for 5,9 B8: 5,9 => CTR * 764392518219568743835417296698273154.41...37232714..8.172...439..6734821483921..7 B8: 6,7 # 19 pairs * PAIR A5: 5,9 ROW 5 F5: 5,9,6 # reduction candidate for 5,9 F5: 6 => CTR * 7.43.291821.59874383.4172..6.82731.4941.56372327149.8.1.2.854395...34821483921..7 F5: 5,9 # 18 pairs * PAIR D5: 6,8 COL D D7: 6,8,7 # reduction candidate for 6,8 D7: 7 # 20 pairs D7: 6,8 # 17 pairs * PAIR F6: 5,9 BLK 5 F5: 5,9,6 # reduction candidate for 5,9 F5: 6 => CTR * 7.43.291821.59874383.4172..6.82731.4941.56372327149.8.1.2.854395...34821483921..7 F5: 5,9 # 18 pairs * PAIR F6: 5,9 ROW 6 G6: 5,9,6 # reduction candidate for 5,9 G6: 5,9 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 G6: 6 => CTR * 7.43.291821.5987438394172..6.8273194941...3723271496851.2...4395.6.348214.3.21..7 * PAIR H4: 5,9 BLK 6 G6: 5,9,6 # reduction candidate for 5,9 G6: 5,9 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 G6: 6 => CTR * 7.43.291821.5987438394172..6.8273194941...3723271496851.2...4395.6.348214.3.21..7 * PAIR H4: 5,9 COL H H3: 5,9,6 # reduction candidate for 5,9 H3: 5,9 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 H3: 6 => CTR * 7.43.291821.5987438394172656.8273194941...3723271495861.2...4395.6.348214.3.21..7 * PAIR I6: 5,6 BLK 6 G6: 5,6,9 # reduction candidate for 5,6 G6: 5,6 => CTR * 7.43.291821.5987438394172..6.8273194941...372327149.8.1.2...4395.6.348214.3.21..7 G6: 9 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 * PAIR A8: 5,9 BLK 7 B8: 5,9,6,7 # reduction candidate for 5,9 B8: 5,9 => CTR * 764392518219568743835417296698273154.41...37232714..8.172...439..6734821483921..7 B8: 6,7 # 19 pairs C8: 5,9,6 # reduction candidate for 5,9 C8: 5,9 # 21 pairs * PAIR F7: 5,6 COL F F5: 5,6,9 # reduction candidate for 5,6 F5: 5,6 => CTR * 7.43.291821.59874383.4172..6.82731.4941...372327149.8.1.2...4395...348214.3.21..7 F5: 9 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 * PAIR G9: 5,6 COL G G1: 5,6,9 # reduction candidate for 5,6 G1: 5,6 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 G1: 9 => CTR * 7543629182165987438394172..6982731.4.41...37232714..8.1.2...439....348214.3.21..7 G6: 5,6,9 # reduction candidate for 5,6 G6: 5,6 => CTR * 7.43.291821.5987438394172..6.8273194941...372327149.8.1.2...4395.6.348214.3.21..7 G6: 9 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 * PAIR H9: 5,6 COL H H3: 5,6,9 # reduction candidate for 5,6 H3: 5,6 => CTR * 7.43.291821.5987438394172..6.8273194941...372327149.8.1.2...4395.6.348214.3.21..7 H3: 9 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-247-base-pr-000.dot * REASONING * DIS # B1: 6,9 => CTR => B1: 5 * PRF # B1: 5 => SOL * PRF # C3: 6,9 => SOL * DIS # C3: 5 => CTR => C3: 6,9 * DIS # C8: 6,9 => CTR => C8: 5 * PRF # C8: 5 => SOL * DIS # B1: 6,9 => CTR => B1: 5 * PRF # B1: 5 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 5 => CTR => G1: 6,9 * PRF # G1: 5,6 => SOL * DIS # G1: 9 => CTR => G1: 5,6 * DIS # H3: 5,6 => CTR => H3: 9 * PRF # H3: 9 => SOL * PRF # C3: 5,6 => SOL * DIS # C3: 9 => CTR => C3: 5,6 * DIS # B8: 5,9 => CTR => B8: 6,7 * DIS # F5: 6 => CTR => F5: 5,9 * DIS # F5: 6 => CTR => F5: 5,9 * PRF # G6: 5,9 => SOL * DIS # G6: 6 => CTR => G6: 5,9 * PRF # G6: 5,9 => SOL * DIS # G6: 6 => CTR => G6: 5,9 * PRF # H3: 5,9 => SOL * DIS # H3: 6 => CTR => H3: 5,9 * DIS # G6: 5,6 => CTR => G6: 9 * PRF # G6: 9 => SOL * DIS # B8: 5,9 => CTR => B8: 6,7 * DIS # F5: 5,6 => CTR => F5: 9 * PRF # F5: 9 => SOL * PRF # G1: 5,6 => SOL * DIS # G1: 9 => CTR => G1: 5,6 * DIS # G6: 5,6 => CTR => G6: 9 * PRF # G6: 9 => SOL * DIS # H3: 5,6 => CTR => H3: 9 * PRF # H3: 9 => SOL * CNT 36 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B4,B9,C2,D5,D9,E1,E2,E5,E7,F6,F7,G9,H4,H9,I3,I6) * 7.43.2.1821.5.874383.4172..6.82731.4.41...37232714..8.1.2...439....348214.3.21..7 * PAIR C2: 6,9 BLK 1 B1: 6,9,5 # reduction candidate for 6,9 B1: 6,9 => CTR * 7.43.251821.5.8743835417296698273154.41...37232714..8.1.2...439....348214.3.21..7 B1: 5 => SOLVED * 754392618219568743836417295698273154541689372327145986172856439965734821483921567 * DURATION: 0:00:01.654732 START: 11:15:40.346689 END: 11:15:42.001421 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-247-base-pr-001.dot * REASONING * DIS # B1: 6,9 => CTR => B1: 5 * PRF B1: 5 => SOL * STA B1: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 247 solution: 754392618219568743836417295698273154541689372327145986172856439965734821483921567 info: 2072 FNBWXY S8.f 36232 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 754392618219568743836417295698273154541689372327145986172856439965734821483921567 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 # B1: 6,9 => CTR => B1: 5 * PRF # B1: 5 => SOL * PRF # C3: 6,9 => SOL * DIS # C3: 5 => CTR => C3: 6,9 * DIS # C8: 6,9 => CTR => C8: 5 * PRF # C8: 5 => SOL * DIS # B1: 6,9 => CTR => B1: 5 * PRF # B1: 5 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 5 => CTR => G1: 6,9 * PRF # G1: 5,6 => SOL * DIS # G1: 9 => CTR => G1: 5,6 * DIS # H3: 5,6 => CTR => H3: 9 * PRF # H3: 9 => SOL * PRF # C3: 5,6 => SOL * DIS # C3: 9 => CTR => C3: 5,6 * INC # B1: 5,9 => UNS * DIS # B8: 5,9 => CTR => B8: 6,7 * INC # B8: 6,7 => UNS * INC # F5: 5,9 => UNS * DIS # F5: 6 => CTR => F5: 5,9 * INC # D7: 6,8 => UNS * INC # D7: 7 => UNS * INC # F5: 5,9 => UNS * DIS # F5: 6 => CTR => F5: 5,9 * PRF # G6: 5,9 => SOL * DIS # G6: 6 => CTR => G6: 5,9 * PRF # G6: 5,9 => SOL * DIS # G6: 6 => CTR => G6: 5,9 * PRF # H3: 5,9 => SOL * DIS # H3: 6 => CTR => H3: 5,9 * DIS # G6: 5,6 => CTR => G6: 9 * PRF # G6: 9 => SOL * DIS # B8: 5,9 => CTR => B8: 6,7 * INC # B8: 6,7 => UNS * INC # C8: 5,9 => UNS * DIS # F5: 5,6 => CTR => F5: 9 * PRF # F5: 9 => SOL * PRF # G1: 5,6 => SOL * DIS # G1: 9 => CTR => G1: 5,6 * DIS # G6: 5,6 => CTR => G6: 9 * PRF # G6: 9 => SOL * DIS # H3: 5,6 => CTR => H3: 9 * PRF # H3: 9 => SOL * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 6,9 => CTR => B1: 5 * PRF B1: 5 => SOL * STA B1: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED