Analysis of xx-top500-340-base.sdk
Contents
Original Sudoku
level: medium
position: 17..........8...2..45..........14..53......6.....7.1........4.72..3.............. initial
Autosolve
position: 172.........8...2.845..........14..53......6.....731........4.72..3.............. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A4: 6,9 => SOL * DIS # A4: 7 => CTR => A4: 6,9 * DIS # A6: 6,9 => CTR => A6: 4,5 * DIS # A7: 6,9 => CTR => A7: 5 * DIS # A9: 6,9 => CTR => A9: 4,5,7 * DIS # E1: 4,5 => CTR => E1: 3,6,9 * DIS # E9: 4,5 => CTR => E9: 6,8,9 * PRF # F2: 5,7 => SOL * DIS # F2: 1 => CTR => F2: 5,7 * CNT 9 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A4: 6,9 => SOL * STA A4: 6,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 17..........8...2..45..........14..53......6.....7.1........4.72..3.............. | initial |
| 172.........8...2.845..........14..53......6.....731........4.72..3.............. | autosolve |
| 172936548693845721845721693928614375317598264456273189569182437284357916731469852 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) A2: 6,9 E2: 4,5 G2: 5,7 I2: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,C5: 1.. / B5 = 1 => 4 pairs (_) / C5 = 1 => 0 pairs (X) F2,I2: 1.. / F2 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) G9,I9: 2.. / G9 = 2 => 5 pairs (_) / I9 = 2 => 7 pairs (_) B2,C2: 3.. / B2 = 3 => 5 pairs (_) / C2 = 3 => 5 pairs (_) E1,E3: 3.. / E1 = 3 => 4 pairs (_) / E3 = 3 => 5 pairs (_) G4,H4: 3.. / G4 = 3 => 4 pairs (_) / H4 = 3 => 0 pairs (X) E2,I2: 4.. / E2 = 4 => 0 pairs (*) / I2 = 4 => 0 pairs (X) C5,I5: 4.. / C5 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) C8,E8: 4.. / C8 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) A6,A9: 4.. / A6 = 4 => 0 pairs (*) / A9 = 4 => 0 pairs (X) D1,D9: 4.. / D1 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) H1,H6: 4.. / H1 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) D4,D6: 6.. / D4 = 6 => 5 pairs (_) / D6 = 6 => 5 pairs (_) F2,G2: 7.. / F2 = 7 => 0 pairs (X) / G2 = 7 => 0 pairs (_) C5,G5: 7.. / C5 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) C8,F8: 7.. / C8 = 7 => 0 pairs (X) / F8 = 7 => 0 pairs (_) A4,A9: 7.. / A4 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) D3,D9: 7.. / D3 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) H3,H4: 7.. / H3 = 7 => 0 pairs (X) / H4 = 7 => 0 pairs (_) E5,F5: 8.. / E5 = 8 => 4 pairs (_) / F5 = 8 => 4 pairs (_) * DURATION: 0:00:30.082804 START: 14:22:17.873904 END: 14:22:47.956708 2017-05-04 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E2,G2,I2) * 172.........8...2.845..........14..53......6.....731........4.72..3.............. * PAIR A2: 6,9 BLK 1 B2: 6,9,3 # reduction candidate for 6,9 B2: 6,9 # 5 pairs C2: 6,9,3 # reduction candidate for 6,9 C2: 6,9 # 5 pairs * PAIR A2: 6,9 COL A A4: 6,9,7 # reduction candidate for 6,9 A4: 6,9 => SOLVED * 172936548693845721845721693928614375317598264456273189569182437284357916731469852 A4: 7 => CTR * 172.........8.7521845....7.7...14..53.....76.....731........4.72.734............. A6: 6,9,4,5 # reduction candidate for 6,9 A6: 6,9 => CTR * 1724........85.724845......7...14..53......6.....731........4.72..3.....4........ A6: 4,5 # 5 pairs A7: 6,9,5 # reduction candidate for 6,9 A7: 6,9 => CTR * 172.........8.7521845....7.7...14..53.....76.....731........4.72.734............. A7: 5 # 4 pairs A9: 6,9,4,5,7 # reduction candidate for 6,9 A9: 6,9 => CTR * 172....4....847521845....7.7...14..53.....7644...731..5.....4.72..3.............. A9: 4,5,7 # 4 pairs * PAIR E2: 4,5 BLK 2 D1: 4,5,9 # reduction candidate for 4,5 D1: 4,5 # 7 pairs E1: 4,5,3,6,9 # reduction candidate for 4,5 E1: 4,5 => CTR * 1729.6......8.1724845732.......14.753.7....6.4...731.....12.4.72.43.7...7.14..... E1: 3,6,9 # 4 pairs * PAIR E2: 4,5 COL E E8: 4,5,6,8,9 # reduction candidate for 4,5 E8: 4,5 # 5 pairs E9: 4,5,6,8,9 # reduction candidate for 4,5 E9: 4,5 => CTR * 172....4....8457218457.1.......143753175...6445..731..5.....4.72.43.7.1.7..45.... E9: 6,8,9 # 4 pairs * PAIR G2: 5,7 ROW 2 F2: 5,7,1 # reduction candidate for 5,7 F2: 5,7 => SOLVED * 172936548693845721845721693928614375317598264456273189569182437284357916731469852 F2: 1 => CTR * 172.........8.1724845..........14.753......6.....731........4.72..3.............. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-340-base-pr-000.dot * REASONING * PRF # A4: 6,9 => SOL * DIS # A4: 7 => CTR => A4: 6,9 * DIS # A6: 6,9 => CTR => A6: 4,5 * DIS # A7: 6,9 => CTR => A7: 5 * DIS # A9: 6,9 => CTR => A9: 4,5,7 * DIS # E1: 4,5 => CTR => E1: 3,6,9 * DIS # E9: 4,5 => CTR => E9: 6,8,9 * PRF # F2: 5,7 => SOL * DIS # F2: 1 => CTR => F2: 5,7 * CNT 9 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E2,G2,I2) * 172.........8...2.845..........14..53......6.....731........4.72..3.............. * PAIR A2: 6,9 BLK 1 B2: 6,9,3 # reduction candidate for 6,9 B2: 6,9 # 5 pairs C2: 6,9,3 # reduction candidate for 6,9 C2: 6,9 # 5 pairs * PAIR A2: 6,9 COL A A4: 6,9,7 # reduction candidate for 6,9 A4: 6,9 => SOLVED * 172936548693845721845721693928614375317598264456273189569182437284357916731469852 * DURATION: 0:00:03.866397 START: 14:23:01.873215 END: 14:23:05.739612 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-340-base-pr-001.dot * REASONING * PRF # A4: 6,9 => SOL * STA A4: 6,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 340 solution: 172936548693845721845721693928614375317598264456273189569182437284357916731469852 info: 3225 FNBHWXY S8.f 26568 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 172936548693845721845721693928614375317598264456273189569182437284357916731469852 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: 6,9 => UNS * INC # C2: 6,9 => UNS * PRF # A4: 6,9 => SOL * DIS # A4: 7 => CTR => A4: 6,9 * DIS # A6: 6,9 => CTR => A6: 4,5 * INC # A6: 4,5 => UNS * DIS # A7: 6,9 => CTR => A7: 5 * INC # A7: 5 => UNS * DIS # A9: 6,9 => CTR => A9: 4,5,7 * INC # A9: 4,5,7 => UNS * INC # D1: 4,5 => UNS * DIS # E1: 4,5 => CTR => E1: 3,6,9 * INC # E1: 3,6,9 => UNS * INC # E8: 4,5 => UNS * DIS # E9: 4,5 => CTR => E9: 6,8,9 * INC # E9: 6,8,9 => UNS * PRF # F2: 5,7 => SOL * DIS # F2: 1 => CTR => F2: 5,7 * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 6,9 => UNS * INC # C2: 6,9 => UNS * PRF # A4: 6,9 => SOL * STA A4: 6,9 * CNT 3 HDP CHAINS / 3 HYP OPENED