Analysis of xx-top500-272-base.sdk
Contents
Original Sudoku
level: medium
position: .1......2....4..8....6...4.5.7.3....4...8..........1..3.....8.....1..6.....2..... initial
Autosolve
position: .148..3626..342.812..61..4.567431298421.8..36....261.43.2.6481..4.1..62.1.62..4.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 5 => CTR => B2: 7,9 * DIS # F1: 7,9 => CTR => F1: 5 * DIS # A8: 8 => CTR => A8: 7,9 * DIS # B2: 5,9 => CTR => B2: 7 * DIS # F1: 7,9 => CTR => F1: 5 * DIS # G3: 5 => CTR => G3: 7,9 * DIS # F5: 5 => CTR => F5: 7,9 * DIS # G3: 5 => CTR => G3: 7,9 * DIS # B2: 5 => CTR => B2: 7,9 * DIS # G3: 9 => CTR => G3: 5,7 * DIS # A8: 8,9 => CTR => A8: 7 * DIS # D5: 5,7 => CTR => D5: 9 * DIS # D7: 9 => CTR => D7: 5,7 * DIS # D5: 5,7 => CTR => D5: 9 * DIS # G3: 9 => CTR => G3: 5,7 * CNT 15 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 5 => CTR => B2: 7,9 * DIS B2: 7,9 # F1: 7,9 => CTR => F1: 5 * DIS B2: 7,9 + F1: 5 # A8: 8 => CTR => A8: 7,9 * DIS B2: 7,9 + F1: 5 + A8: 7,9 # G3: 5 => CTR => G3: 7,9 * PRF B2: 7,9 + F1: 5 + A8: 7,9 + G3: 7,9 # B9: 8 => SOL * STA B2: 7,9 + F1: 5 + A8: 7,9 + G3: 7,9 + B9: 8 * CNT 5 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1......2....4..8....6...4.5.7.3....4...8..........1..3.....8.....1..6.....2..... | initial |
| .148..3626..342.812..61..4.567431298421.8..36....261.43.2.6481..4.1..62.1.62..4.. | autosolve |
| 914875362675342981238619745567431298421987536893526174352764819749158623186293457 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A1: 7,9 C2: 5,9 B3: 3,8 C3: 3,8 F3: 7,9 G2: 7,9 I3: 5,7 A6: 8,9 D6: 5,7 G5: 5,7 H6: 5,7 F8: 3,8 F9: 3,8 H9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 3.. / B3 = 3 => 14 pairs (_) / C3 = 3 => 11 pairs (_) B6,C6: 3.. / B6 = 3 => 11 pairs (_) / C6 = 3 => 14 pairs (_) F8,F9: 3.. / F8 = 3 => 13 pairs (_) / F9 = 3 => 14 pairs (_) I8,I9: 3.. / I8 = 3 => 14 pairs (_) / I9 = 3 => 13 pairs (_) F8,I8: 3.. / F8 = 3 => 13 pairs (_) / I8 = 3 => 14 pairs (_) F9,I9: 3.. / F9 = 3 => 14 pairs (_) / I9 = 3 => 13 pairs (_) B3,B6: 3.. / B3 = 3 => 14 pairs (_) / B6 = 3 => 11 pairs (_) C3,C6: 3.. / C3 = 3 => 11 pairs (_) / C6 = 3 => 14 pairs (_) B2,C2: 5.. / B2 = 5 => 0 pairs (X) / C2 = 5 => 15 pairs (_) E1,F1: 5.. / E1 = 5 => 0 pairs (X) / F1 = 5 => 17 pairs (_) G3,I3: 5.. / G3 = 5 => 0 pairs (X) / I3 = 5 => 17 pairs (_) G5,H6: 5.. / G5 = 5 => 17 pairs (_) / H6 = 5 => 0 pairs (X) D6,H6: 5.. / D6 = 5 => 17 pairs (_) / H6 = 5 => 0 pairs (X) C2,C8: 5.. / C2 = 5 => 15 pairs (_) / C8 = 5 => 0 pairs (X) F1,F5: 5.. / F1 = 5 => 17 pairs (_) / F5 = 5 => 0 pairs (X) G3,G5: 5.. / G3 = 5 => 0 pairs (X) / G5 = 5 => 17 pairs (_) H6,H9: 5.. / H6 = 5 => 0 pairs (X) / H9 = 5 => 17 pairs (_) A1,B2: 7.. / A1 = 7 => 0 pairs (X) / B2 = 7 => 19 pairs (_) G5,H6: 7.. / G5 = 7 => 0 pairs (X) / H6 = 7 => 17 pairs (_) B2,G2: 7.. / B2 = 7 => 19 pairs (_) / G2 = 7 => 0 pairs (X) D6,H6: 7.. / D6 = 7 => 0 pairs (X) / H6 = 7 => 17 pairs (_) A1,A8: 7.. / A1 = 7 => 0 pairs (X) / A8 = 7 => 19 pairs (_) H6,H9: 7.. / H6 = 7 => 17 pairs (_) / H9 = 7 => 0 pairs (X) B3,C3: 8.. / B3 = 8 => 11 pairs (_) / C3 = 8 => 14 pairs (_) F8,F9: 8.. / F8 = 8 => 14 pairs (_) / F9 = 8 => 13 pairs (_) B9,F9: 8.. / B9 = 8 => 14 pairs (_) / F9 = 8 => 13 pairs (_) A6,A8: 8.. / A6 = 8 => 16 pairs (_) / A8 = 8 => 0 pairs (X) G2,G3: 9.. / G2 = 9 => 19 pairs (_) / G3 = 9 => 0 pairs (X) D5,F5: 9.. / D5 = 9 => 17 pairs (_) / F5 = 9 => 0 pairs (X) F3,G3: 9.. / F3 = 9 => 19 pairs (_) / G3 = 9 => 0 pairs (X) D5,D7: 9.. / D5 = 9 => 17 pairs (_) / D7 = 9 => 0 pairs (X) * DURATION: 0:01:01.921017 START: 12:12:46.299280 END: 12:13:48.220297 2017-05-04 * CP COUNT: (31) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B3,C2,C3,D6,F3,F8,F9,G2,G5,H6,H9,I3) * .148..3626..342.812..61..4.567431298421.8..36....261.43.2.6481..4.1..62.1.62..4.. * PAIR A1: 7,9 BLK 1 B2: 7,9,5 # reduction candidate for 7,9 B2: 5 => CTR * 7148..3626593427812..617945567431298421789536...5261.43.2.6481..4.1..62.1.62..4.. B2: 7,9 # 15 pairs * PAIR A1: 7,9 ROW 1 E1: 7,9,5 # reduction candidate for 7,9 E1: 7,9 # 17 pairs F1: 7,9,5 # reduction candidate for 7,9 F1: 7,9 => CTR * .1485.3626753429812..619547567431298421985736...72615439256481..4.1..62.1.62..47. F1: 5 # 17 pairs * PAIR A1: 7,9 COL A A8: 7,9,8 # reduction candidate for 7,9 A8: 8 => CTR * 7148..3626..3427812..6179455674312984217895369..52617435296481784.1..62.1.62..4.. A8: 7,9 # 16 pairs * PAIR C2: 5,9 BLK 1 B2: 5,9,7 # reduction candidate for 5,9 B2: 5,9 => CTR * 7148..3626..3427812..617945567431298421789536...526174352964817.4.1..62.1.62..4.. B2: 7 # 19 pairs * PAIR C2: 5,9 COL C C8: 5,9,8 # reduction candidate for 5,9 C8: 5,9 # 16 pairs C8: 8 # 10 pairs * PAIR B3: 3,8 COL B B6: 3,8,9 # reduction candidate for 3,8 B6: 9 # 14 pairs B6: 3,8 # 13 pairs * PAIR C3: 3,8 COL C C6: 3,8,9 # reduction candidate for 3,8 C6: 3,8 # 16 pairs C6: 9 # 10 pairs * PAIR F3: 7,9 BLK 2 E1: 7,9,5 # reduction candidate for 7,9 E1: 7,9 # 17 pairs F1: 7,9,5 # reduction candidate for 7,9 F1: 7,9 => CTR * .1485.3626753429812..619547567431298421985736...72615439256481..4.1..62.1.62..47. F1: 5 # 17 pairs * PAIR F3: 7,9 ROW 3 G3: 7,9,5 # reduction candidate for 7,9 G3: 5 => CTR * .148..3626..3429812..619547567431298421985736...726154372564819.4.17.62.1.629.47. G3: 7,9 # 17 pairs * PAIR F3: 7,9 COL F F5: 7,9,5 # reduction candidate for 7,9 F5: 5 => CTR * .1485.3626753429812..619547567431298421985736...72615439256481..4.1..62.1.62..47. F5: 7,9 # 17 pairs * PAIR G2: 7,9 BLK 3 G3: 7,9,5 # reduction candidate for 7,9 G3: 5 => CTR * .148..3626..3429812..619547567431298421985736...726154372564819.4.17.62.1.629.47. G3: 7,9 # 17 pairs * PAIR G2: 7,9 ROW 2 B2: 7,9,5 # reduction candidate for 7,9 B2: 5 => CTR * 7148..3626593427812..617945567431298421789536...5261.43.2.6481..4.1..62.1.62..4.. B2: 7,9 # 15 pairs * PAIR I3: 5,7 BLK 3 G3: 5,7,9 # reduction candidate for 5,7 G3: 9 => CTR * .148.53626.53427812..617945567431298421789536...52617435296481774.15.62.1.627.45. G3: 5,7 # 19 pairs * PAIR I3: 5,7 COL I I7: 5,7,9 # reduction candidate for 5,7 I7: 5,7 # 17 pairs I8: 5,7,3,9 # reduction candidate for 5,7 I8: 5,7 # 18 pairs I9: 5,7,3,9 # reduction candidate for 5,7 I9: 5,7 # 18 pairs * PAIR A6: 8,9 BLK 4 B6: 8,9,3 # reduction candidate for 8,9 B6: 8,9 # 14 pairs C6: 8,9,3 # reduction candidate for 8,9 C6: 8,9 # 11 pairs * PAIR A6: 8,9 COL A A8: 8,9,7 # reduction candidate for 8,9 A8: 8,9 => CTR * 7148..3626..3427812..617945567431298421789536...526174352964817.4.1..62.1.62..4.. A8: 7 # 19 pairs * PAIR D6: 5,7 BLK 5 D5: 5,7,9 # reduction candidate for 5,7 D5: 5,7 => CTR * 7148953626953427812..617945567431298421789536...526174352964817.4.15.62.186273459 D5: 9 # 17 pairs F5: 5,7,9 # reduction candidate for 5,7 F5: 5,7 # 17 pairs * PAIR D6: 5,7 COL D D7: 5,7,9 # reduction candidate for 5,7 D7: 9 => CTR * 7148953626953427812..617945567431298421789536...526174352964817.4.15.62.186273459 D7: 5,7 # 17 pairs * PAIR G5: 5,7 ROW 5 D5: 5,7,9 # reduction candidate for 5,7 D5: 5,7 => CTR * 7148953626953427812..617945567431298421789536...526174352964817.4.15.62.186273459 D5: 9 # 17 pairs F5: 5,7,9 # reduction candidate for 5,7 F5: 5,7 # 17 pairs * PAIR G5: 5,7 COL G G3: 5,7,9 # reduction candidate for 5,7 G3: 9 => CTR * .148.53626.53427812..617945567431298421789536...52617435296481774.15.62.1.627.45. G3: 5,7 # 19 pairs * PAIR H9: 5,7 BLK 9 I7: 5,7,9 # reduction candidate for 5,7 I7: 5,7 # 17 pairs I8: 5,7,3,9 # reduction candidate for 5,7 I8: 5,7 # 18 pairs I9: 5,7,3,9 # reduction candidate for 5,7 I9: 5,7 # 18 pairs * PAIR H9: 5,7 ROW 9 B9: 5,7,8,9 # reduction candidate for 5,7 B9: 5,7 # 18 pairs E9: 5,7,9 # reduction candidate for 5,7 E9: 5,7 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-272-base-pr-000.dot * REASONING * DIS # B2: 5 => CTR => B2: 7,9 * DIS # F1: 7,9 => CTR => F1: 5 * DIS # A8: 8 => CTR => A8: 7,9 * DIS # B2: 5,9 => CTR => B2: 7 * DIS # F1: 7,9 => CTR => F1: 5 * DIS # G3: 5 => CTR => G3: 7,9 * DIS # F5: 5 => CTR => F5: 7,9 * DIS # G3: 5 => CTR => G3: 7,9 * DIS # B2: 5 => CTR => B2: 7,9 * DIS # G3: 9 => CTR => G3: 5,7 * DIS # A8: 8,9 => CTR => A8: 7 * DIS # D5: 5,7 => CTR => D5: 9 * DIS # D7: 9 => CTR => D7: 5,7 * DIS # D5: 5,7 => CTR => D5: 9 * DIS # G3: 9 => CTR => G3: 5,7 * CNT 15 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B3,C2,C3,D6,F3,F8,F9,G2,G5,H6,H9,I3) * .148..3626..342.812..61..4.567431298421.8..36....261.43.2.6481..4.1..62.1.62..4.. * PAIR A1: 7,9 BLK 1 B2: 7,9,5 # reduction candidate for 7,9 B2: 5 => CTR * 7148..3626593427812..617945567431298421789536...5261.43.2.6481..4.1..62.1.62..4.. * PAIR A1: 7,9 ROW 1 E1: 7,9,5 # reduction candidate for 7,9 E1: 7,9 # 18 pairs F1: 7,9,5 # reduction candidate for 7,9 F1: 7,9 => CTR * .1485.3626753429812..619547567431298421985736...72615439256481..4.1..6251562.8473 * RESTART * PAIR A1: 7,9 COL A A8: 7,9,8 # reduction candidate for 7,9 A8: 8 => CTR * 7148953626953427812..6179455674312984217895369..52617435296481784.1..62.1.62..4.. * PAIR RESTART * PAIR F3: 7,9 ROW 3 G3: 7,9,5 # reduction candidate for 7,9 G3: 5 => CTR * .148.53626.53429812..619547567431298421.8..368...261.43.2.6481..4.1..62.1.62..4.. * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A8,B2,B3,B6,C3,C6,C8,D5,D7,E1,E9,F3,F5,F8,F9,G2,G3,I7) * .148.53626.5342.812..61..45567431298421.8.5368..526174352.6481..4.15.62.1.62..45. * PAIR B2: 7,9 COL B B9: 7,9,8 # reduction candidate for 7,9 B9: 8 => SOLVED * 914875362675342981238619745567431298421987536893526174352764819749158623186293457 * DURATION: 0:00:13.359245 START: 12:14:41.629962 END: 12:14:54.989207 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-272-base-pr-001.dot * REASONING * DIS # B2: 5 => CTR => B2: 7,9 * DIS B2: 7,9 # F1: 7,9 => CTR => F1: 5 * DIS B2: 7,9 + F1: 5 # A8: 8 => CTR => A8: 7,9 * DIS B2: 7,9 + F1: 5 + A8: 7,9 # G3: 5 => CTR => G3: 7,9 * PRF B2: 7,9 + F1: 5 + A8: 7,9 + G3: 7,9 # B9: 8 => SOL * STA B2: 7,9 + F1: 5 + A8: 7,9 + G3: 7,9 + B9: 8 * CNT 5 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 272 solution: 914875362675342981238619745567431298421987536893526174352764819749158623186293457 info: 2200 FNBHWXY S8.f 44996 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 914875362675342981238619745567431298421987536893526174352764819749158623186293457 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 # B2: 7,9 => UNS * DIS # B2: 5 => CTR => B2: 7,9 * INC # E1: 7,9 => UNS * DIS # F1: 7,9 => CTR => F1: 5 * INC # F1: 5 => UNS * INC # A8: 7,9 => UNS * DIS # A8: 8 => CTR => A8: 7,9 * DIS # B2: 5,9 => CTR => B2: 7 * INC # B2: 7 => UNS * INC # C8: 5,9 => UNS * INC # C8: 8 => UNS * INC # B6: 3,8 => UNS * INC # B6: 9 => UNS * INC # C6: 3,8 => UNS * INC # C6: 9 => UNS * INC # E1: 7,9 => UNS * DIS # F1: 7,9 => CTR => F1: 5 * INC # F1: 5 => UNS * INC # G3: 7,9 => UNS * DIS # G3: 5 => CTR => G3: 7,9 * INC # F5: 7,9 => UNS * DIS # F5: 5 => CTR => F5: 7,9 * INC # G3: 7,9 => UNS * DIS # G3: 5 => CTR => G3: 7,9 * INC # B2: 7,9 => UNS * DIS # B2: 5 => CTR => B2: 7,9 * INC # G3: 5,7 => UNS * DIS # G3: 9 => CTR => G3: 5,7 * INC # I7: 5,7 => UNS * INC # I8: 5,7 => UNS * INC # I9: 5,7 => UNS * INC # B6: 8,9 => UNS * INC # C6: 8,9 => UNS * DIS # A8: 8,9 => CTR => A8: 7 * INC # A8: 7 => UNS * DIS # D5: 5,7 => CTR => D5: 9 * INC # D5: 9 => UNS * INC # F5: 5,7 => UNS * INC # D7: 5,7 => UNS * DIS # D7: 9 => CTR => D7: 5,7 * DIS # D5: 5,7 => CTR => D5: 9 * INC # D5: 9 => UNS * INC # F5: 5,7 => UNS * INC # G3: 5,7 => UNS * DIS # G3: 9 => CTR => G3: 5,7 * INC # I7: 5,7 => UNS * INC # I8: 5,7 => UNS * INC # I9: 5,7 => UNS * INC # B9: 5,7 => UNS * INC # E9: 5,7 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 7,9 => UNS * DIS # B2: 5 => CTR => B2: 7,9 * INC B2: 7,9 # E1: 7,9 => UNS * DIS B2: 7,9 # F1: 7,9 => CTR => F1: 5 * INC B2: 7,9 + F1: 5 # A8: 7,9 => UNS * DIS B2: 7,9 + F1: 5 # A8: 8 => CTR => A8: 7,9 * INC B2: 7,9 + F1: 5 + A8: 7,9 # G3: 7,9 => UNS * DIS B2: 7,9 + F1: 5 + A8: 7,9 # G3: 5 => CTR => G3: 7,9 * INC B2: 7,9 + F1: 5 + A8: 7,9 + G3: 7,9 # B9: 7,9 => UNS * PRF B2: 7,9 + F1: 5 + A8: 7,9 + G3: 7,9 # B9: 8 => SOL * STA B2: 7,9 + F1: 5 + A8: 7,9 + G3: 7,9 + B9: 8 * CNT 10 HDP CHAINS / 10 HYP OPENED