Analysis of xx-top500-347-base.sdk
Contents
Original Sudoku
level: medium
position: .2....4.....5.7......3.....5.....713.8..2.............1...6..8.3.7.........4..... initial
Autosolve
position: .2....4.....5.7......3.2...5.2...713.8..2.............1...6..8.3.7.5....2.84..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 1,3 => CTR => C1: 5,9 * DIS # C2: 1,3 => CTR => C2: 4,6,9 * PRF # B6: 7 => SOL * DIS # B6: 3 => CTR => B6: 1,7 * PRF # A5: 4,9 => SOL * DIS # C5: 4,9 => CTR => C5: 1,3,6 * DIS # F4: 6,8 => CTR => F4: 4,9 * PRF # B7: 4,9 => SOL * DIS # D4: 8,9 => CTR => D4: 6 * DIS # F4: 8,9 => CTR => F4: 4,6 * DIS # E1: 8,9 => CTR => E1: 1 * DIS # B6: 1 => CTR => B6: 3,7 * PRF # B7: 4,9 => SOL * DIS # I7: 4,9 => CTR => I7: 2,5,7 * DIS # C5: 4,9 => CTR => C5: 1,3,6 * PRF # F9: 3,9 => SOL * DIS # G7: 3,9 => CTR => G7: 2,5 * PRF # G7: 2,5 => SOL * DIS # F5: 3,9 => CTR => F5: 1,4,5 * DIS # F6: 3,9 => CTR => F6: 1,4,5 * CNT 20 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 1,3 => CTR => C1: 5,9 * DIS C1: 5,9 # C2: 1,3 => CTR => C2: 4,6,9 * PRF C1: 5,9 + C2: 4,6,9 # A5: 4,9 => SOL * STA C1: 5,9 + C2: 4,6,9 + A5: 4,9 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2....4.....5.7......3.....5.....713.8..2.............1...6..8.3.7.........4..... | initial |
| .2....4.....5.7......3.2...5.2...713.8..2.............1...6..8.3.7.5....2.84..... | autosolve |
| 725816439936547128814392675592684713483721956671935842149263587367158294258479361 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B2: 1,3 B3: 1,7 B4: 4,9 E4: 8,9 E6: 3,7 C7: 4,9 F7: 3,9 E9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D7,D8: 2.. / D7 = 2 => 0 pairs (*) / D8 = 2 => 0 pairs (X) C1,H1: 3.. / C1 = 3 => 0 pairs (X) / H1 = 3 => 8 pairs (_) C5,F5: 3.. / C5 = 3 => 9 pairs (_) / F5 = 3 => 0 pairs (X) F7,G7: 3.. / F7 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) B2,B6: 3.. / B2 = 3 => 8 pairs (_) / B6 = 3 => 0 pairs (X) E6,E9: 3.. / E6 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) E2,E3: 4.. / E2 = 4 => 8 pairs (_) / E3 = 4 => 8 pairs (_) B4,F4: 4.. / B4 = 4 => 0 pairs (X) / F4 = 4 => 0 pairs (_) C1,C3: 5.. / C1 = 5 => 8 pairs (_) / C3 = 5 => 8 pairs (_) F5,F6: 5.. / F5 = 5 => 0 pairs (X) / F6 = 5 => 8 pairs (_) B7,B9: 5.. / B7 = 5 => 9 pairs (_) / B9 = 5 => 0 pairs (*) D1,F1: 6.. / D1 = 6 => 0 pairs (X) / F1 = 6 => 9 pairs (_) D4,F4: 6.. / D4 = 6 => 9 pairs (_) / F4 = 6 => 0 pairs (X) B8,B9: 6.. / B8 = 6 => 9 pairs (_) / B9 = 6 => 9 pairs (_) D1,D4: 6.. / D1 = 6 => 0 pairs (X) / D4 = 6 => 9 pairs (_) F1,F4: 6.. / F1 = 6 => 9 pairs (_) / F4 = 6 => 0 pairs (X) D7,E9: 7.. / D7 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) A5,D5: 7.. / A5 = 7 => 12 pairs (_) / D5 = 7 => 0 pairs (*) D7,I7: 7.. / D7 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) B3,B6: 7.. / B3 = 7 => 11 pairs (_) / B6 = 7 => 0 pairs (*) E6,E9: 7.. / E6 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) G6,I6: 8.. / G6 = 8 => 8 pairs (_) / I6 = 8 => 8 pairs (_) D8,F8: 8.. / D8 = 8 => 0 pairs (X) / F8 = 8 => 11 pairs (_) * DURATION: 0:00:42.281612 START: 14:35:45.246531 END: 14:36:27.528143 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B4,C7,E4,E6,E9,F7) * .2....4.....5.7......3.2...5.2...713.8..2.............1...6..8.3.7.5....2.84..... * PAIR B2: 1,3 BLK 1 C1: 1,3,5,9 # reduction candidate for 1,3 C1: 1,3 => CTR * .23.164...1.5.7.3..753.2...5.268471378..23....3..75.2.1547693823.7258...2.8431... C1: 5,9 # 9 pairs C2: 1,3,4,6,9 # reduction candidate for 1,3 C2: 1,3 => CTR * .25.16437...5.7....7.3.2...5.268471378..2........7....1547693823.7258...2.8431.7. C2: 4,6,9 # 8 pairs * PAIR B2: 1,3 ROW 2 G2: 1,3,2,6,8,9 # reduction candidate for 1,3 G2: 1,3 # 9 pairs G2: 2,6,8,9 # 8 pairs * PAIR B2: 1,3 COL B B6: 1,3,7 # reduction candidate for 1,3 B6: 7 => SOLVED * 725816439936547128814392675592684713483721956671935842149263587367158294258479361 B6: 1,3 # 11 pairs * PAIR B3: 1,7 ROW 3 I3: 1,7,5,6,8,9 # reduction candidate for 1,7 I3: 1,7 # 9 pairs I3: 5,6,8,9 # 8 pairs * PAIR B3: 1,7 COL B B6: 1,7,3 # reduction candidate for 1,7 B6: 3 => CTR * .2...64...1.5.7....7.3.2...5.268471378..23....3..75...1547693823.7258...2.8431... B6: 1,7 # 8 pairs * PAIR B4: 4,9 BLK 4 A5: 4,9,6,7 # reduction candidate for 4,9 A5: 4,9 => SOLVED * 725816439936547128814392675592684713483721956671935842149263587367158294258479361 A5: 6,7 # 9 pairs C5: 4,9,1,3,6 # reduction candidate for 4,9 C5: 4,9 => CTR * .2...64.....5.7....7.3.2...5.268471378.123......975...1547693823.7258...2.8431... C5: 1,3,6 # 8 pairs A6: 4,9,6,7 # reduction candidate for 4,9 A6: 4,9 # 10 pairs C6: 4,9,1,3,6 # reduction candidate for 4,9 C6: 4,9 # 15 pairs * PAIR B4: 4,9 ROW 4 F4: 4,9,6,8 # reduction candidate for 4,9 F4: 6,8 => CTR * .2....43..3.5.7....7.3.2...542...71378312.....1.73....1.4.6..873.7.5....2.847.... F4: 4,9 # 10 pairs * PAIR B4: 4,9 COL B B7: 4,9,5 # reduction candidate for 4,9 B7: 4,9 => SOLVED * 725816439936547128814392675592684713483721956671935842149263587367158294258479361 B7: 5 # 9 pairs B8: 4,9,6 # reduction candidate for 4,9 B8: 4,9 # 9 pairs * PAIR E4: 8,9 BLK 5 D4: 8,9,6 # reduction candidate for 8,9 D4: 8,9 => CTR * .2.6..43..3.5.7....7.3.2...542..671378312.....1.73....1.4.6..873.7.5....2.847.... D4: 6 # 9 pairs F4: 8,9,4,6 # reduction candidate for 8,9 F4: 8,9 => CTR * .2...643..3.5.7....7.3.2...5426..71378312.....1.73....1.4.6..873.7.5....2.847.... F4: 4,6 # 9 pairs * PAIR E4: 8,9 COL E E1: 8,9,1 # reduction candidate for 8,9 E1: 8,9 => CTR * 725.96431.3.517....1.342.7.592684713.83721....71935...1.9263.873.7158...2.847.1.. E1: 1 # 8 pairs E2: 8,9,1,4 # reduction candidate for 8,9 E2: 8,9 # 9 pairs E3: 8,9,1,4 # reduction candidate for 8,9 E3: 8,9 # 9 pairs * PAIR E6: 3,7 ROW 6 B6: 3,7,1 # reduction candidate for 3,7 B6: 1 => CTR * 925816437.3.5.7....7.3.2...59268471378.12.....1.97....154769382367258...2.8431.7. B6: 3,7 # 10 pairs * PAIR C7: 4,9 BLK 7 B7: 4,9,5 # reduction candidate for 4,9 B7: 4,9 => SOLVED * 725816439936547128814392675592684713483721956671935842149263587367158294258479361 B7: 5 # 9 pairs B8: 4,9,6 # reduction candidate for 4,9 B8: 4,9 # 9 pairs * PAIR C7: 4,9 ROW 7 I7: 4,9,2,5,7 # reduction candidate for 4,9 I7: 4,9 => CTR * .2....4.....5.7......3.2...5.2...713.8..2.............1..76.28.3.7258...2.8431... I7: 2,5,7 # 9 pairs * PAIR C7: 4,9 COL C C2: 4,9,1,3,6 # reduction candidate for 4,9 C2: 4,9 # 9 pairs C3: 4,9,1,5,6 # reduction candidate for 4,9 C3: 4,9 # 9 pairs C5: 4,9,1,3,6 # reduction candidate for 4,9 C5: 4,9 => CTR * .2...64.....5.7....7.3.2...5.268471378.123......975...1547693823.7258...2.8431... C5: 1,3,6 # 8 pairs C6: 4,9,1,3,6 # reduction candidate for 4,9 C6: 4,9 # 15 pairs * PAIR F7: 3,9 BLK 8 F9: 3,9,1 # reduction candidate for 3,9 F9: 3,9 => SOLVED * 725816439936547128814392675592684713483721956671935842149263587367158294258479361 F9: 1 # 9 pairs * PAIR F7: 3,9 ROW 7 G7: 3,9,2,5 # reduction candidate for 3,9 G7: 3,9 => CTR * .2....43..3.5.7....7.3.2...542...71378312.....1.73....15426..873.7.5....2.847.... G7: 2,5 => SOLVED * 725816439936547128814392675592684713483721956671935842149263587367158294258479361 * PAIR F7: 3,9 COL F F5: 3,9,1,4,5 # reduction candidate for 3,9 F5: 3,9 => CTR * .2.8.643..3.5.7....7.3.2...5926847137831296...1.735...149263587367958...2584713.. F5: 1,4,5 # 9 pairs F6: 3,9,1,4,5 # reduction candidate for 3,9 F6: 3,9 => CTR * .2.8.6437.3.5.7....7.3.2...592684713783125....1.739...1.92635843.7.58...2.84713.. F6: 1,4,5 # 8 pairs * PAIR E9: 3,7 ROW 9 H9: 3,7,5,6,9 # reduction candidate for 3,7 H9: 3,7 # 10 pairs H9: 5,6,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-347-base-pr-000.dot * REASONING * DIS # C1: 1,3 => CTR => C1: 5,9 * DIS # C2: 1,3 => CTR => C2: 4,6,9 * PRF # B6: 7 => SOL * DIS # B6: 3 => CTR => B6: 1,7 * PRF # A5: 4,9 => SOL * DIS # C5: 4,9 => CTR => C5: 1,3,6 * DIS # F4: 6,8 => CTR => F4: 4,9 * PRF # B7: 4,9 => SOL * DIS # D4: 8,9 => CTR => D4: 6 * DIS # F4: 8,9 => CTR => F4: 4,6 * DIS # E1: 8,9 => CTR => E1: 1 * DIS # B6: 1 => CTR => B6: 3,7 * PRF # B7: 4,9 => SOL * DIS # I7: 4,9 => CTR => I7: 2,5,7 * DIS # C5: 4,9 => CTR => C5: 1,3,6 * PRF # F9: 3,9 => SOL * DIS # G7: 3,9 => CTR => G7: 2,5 * PRF # G7: 2,5 => SOL * DIS # F5: 3,9 => CTR => F5: 1,4,5 * DIS # F6: 3,9 => CTR => F6: 1,4,5 * CNT 20 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B4,C7,E4,E6,E9,F7) * .2....4.....5.7......3.2...5.2...713.8..2.............1...6..8.3.7.5....2.84..... * PAIR B2: 1,3 BLK 1 C1: 1,3,5,9 # reduction candidate for 1,3 C1: 1,3 => CTR * .23.164...1.5.7.3..753.2...5.268471378..23....3..75.2.1547693823.7258...2.8431... C2: 1,3,4,6,9 # reduction candidate for 1,3 C2: 1,3 => CTR * .25.16437...5.7....7.3.2...5.268471378..2........7....1547693823.7258...2.8431.7. * PAIR B4: 4,9 BLK 4 A5: 4,9,6,7 # reduction candidate for 4,9 A5: 4,9 => SOLVED * 725816439936547128814392675592684713483721956671935842149263587367158294258479361 * DURATION: 0:00:05.268244 START: 14:37:18.017005 END: 14:37:23.285249 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-347-base-pr-001.dot * REASONING * DIS # C1: 1,3 => CTR => C1: 5,9 * DIS C1: 5,9 # C2: 1,3 => CTR => C2: 4,6,9 * PRF C1: 5,9 + C2: 4,6,9 # A5: 4,9 => SOL * STA C1: 5,9 + C2: 4,6,9 + A5: 4,9 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 347 solution: 725816439936547128814392675592684713483721956671935842149263587367158294258479361 info: 3682 FNBHXY S8.f 47303 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 725816439936547128814392675592684713483721956671935842149263587367158294258479361 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 # C1: 1,3 => CTR => C1: 5,9 * INC # C1: 5,9 => UNS * DIS # C2: 1,3 => CTR => C2: 4,6,9 * INC # C2: 4,6,9 => UNS * INC # G2: 1,3 => UNS * INC # G2: 2,6,8,9 => UNS * INC # B6: 1,3 => UNS * PRF # B6: 7 => SOL * INC # I3: 1,7 => UNS * INC # I3: 5,6,8,9 => UNS * INC # B6: 1,7 => UNS * DIS # B6: 3 => CTR => B6: 1,7 * PRF # A5: 4,9 => SOL * INC # A5: 6,7 => UNS * DIS # C5: 4,9 => CTR => C5: 1,3,6 * INC # C5: 1,3,6 => UNS * INC # A6: 4,9 => UNS * INC # C6: 4,9 => UNS * INC # F4: 4,9 => UNS * DIS # F4: 6,8 => CTR => F4: 4,9 * PRF # B7: 4,9 => SOL * INC # B7: 5 => UNS * INC # B8: 4,9 => UNS * DIS # D4: 8,9 => CTR => D4: 6 * INC # D4: 6 => UNS * DIS # F4: 8,9 => CTR => F4: 4,6 * INC # F4: 4,6 => UNS * DIS # E1: 8,9 => CTR => E1: 1 * INC # E1: 1 => UNS * INC # E2: 8,9 => UNS * INC # E3: 8,9 => UNS * INC # B6: 3,7 => UNS * DIS # B6: 1 => CTR => B6: 3,7 * PRF # B7: 4,9 => SOL * INC # B7: 5 => UNS * INC # B8: 4,9 => UNS * DIS # I7: 4,9 => CTR => I7: 2,5,7 * INC # I7: 2,5,7 => UNS * INC # C2: 4,9 => UNS * INC # C3: 4,9 => UNS * DIS # C5: 4,9 => CTR => C5: 1,3,6 * INC # C5: 1,3,6 => UNS * INC # C6: 4,9 => UNS * PRF # F9: 3,9 => SOL * INC # F9: 1 => UNS * DIS # G7: 3,9 => CTR => G7: 2,5 * PRF # G7: 2,5 => SOL * DIS # F5: 3,9 => CTR => F5: 1,4,5 * INC # F5: 1,4,5 => UNS * DIS # F6: 3,9 => CTR => F6: 1,4,5 * INC # F6: 1,4,5 => UNS * INC # H9: 3,7 => UNS * INC # H9: 5,6,9 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 1,3 => CTR => C1: 5,9 * DIS C1: 5,9 # C2: 1,3 => CTR => C2: 4,6,9 * PRF C1: 5,9 + C2: 4,6,9 # A5: 4,9 => SOL * STA C1: 5,9 + C2: 4,6,9 + A5: 4,9 * CNT 3 HDP CHAINS / 3 HYP OPENED