Analysis of xx-top500-113-base.sdk
Contents
Original Sudoku
level: medium
position: ....35.8.2.1...............7..2......8.....3......6...6..1..2...5..8..........4.7 initial
Autosolve
position: ....351822.1..........21...7..2......82....3......6.2.6..1..2.8.5..82....2....4.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 4,9 => CTR => C1: 6,7 * DIS # A5: 4,9 => CTR => A5: 5 * PRF # A5: 5 => SOL * PRF # A6: 4,9 => SOL * DIS # A8: 4,9 => CTR => A8: 1 * PRF # A8: 1 => SOL * PRF # F7: 3,9 => SOL * DIS # F7: 4,7 => CTR => F7: 3,9 * DIS # D9: 3,9 => CTR => D9: 5,6 * PRF # D9: 5,6 => SOL * PRF # A9: 3,9 => SOL * DIS # A9: 1,8 => CTR => A9: 3,9 * DIS # C9: 3,9 => CTR => C9: 8 * DIS # H9: 5,9 => CTR => H9: 1,6 * DIS # E7: 5,9 => CTR => E7: 4,7 * CNT 15 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 4,9 => CTR => C1: 6,7 * DIS C1: 6,7 # A5: 4,9 => CTR => A5: 5 * PRF C1: 6,7 + A5: 5 => SOL * STA C1: 6,7 + A5: 5 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....35.8.2.1...............7..2......8.....3......6...6..1..2...5..8..........4.7 | initial |
| ....351822.1..........21...7..2......82....3......6.2.6..1..2.8.5..82....2....4.7 | autosolve |
| 976435182231897564845621379763258941582914736419376825697143258154782693328569417 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A1: 4,9 A3: 5,8 C3: 5,8 F4: 3,8 D6: 3,8 F9: 3,9 H7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,B6: 1.. / B4 = 1 => 0 pairs (X) / B6 = 1 => 7 pairs (_) A8,A9: 1.. / A8 = 1 => 0 pairs (*) / A9 = 1 => 0 pairs (X) E5,I5: 1.. / E5 = 1 => 7 pairs (_) / I5 = 1 => 0 pairs (X) A9,H9: 1.. / A9 = 1 => 0 pairs (X) / H9 = 1 => 0 pairs (_) B2,B3: 3.. / B2 = 3 => 7 pairs (_) / B3 = 3 => 10 pairs (_) F4,D6: 3.. / F4 = 3 => 0 pairs (X) / D6 = 3 => 0 pairs (_) G8,I8: 3.. / G8 = 3 => 8 pairs (_) / I8 = 3 => 9 pairs (_) C4,F4: 3.. / C4 = 3 => 0 pairs (*) / F4 = 3 => 0 pairs (X) C7,F7: 3.. / C7 = 3 => 0 pairs (X) / F7 = 3 => 0 pairs (_) A6,A9: 3.. / A6 = 3 => 0 pairs (X) / A9 = 3 => 0 pairs (_) D6,D9: 3.. / D6 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) A3,C3: 5.. / A3 = 5 => 0 pairs (X) / C3 = 5 => 5 pairs (_) G2,I2: 5.. / G2 = 5 => 8 pairs (_) / I2 = 5 => 9 pairs (_) H7,H9: 5.. / H7 = 5 => 6 pairs (_) / H9 = 5 => 0 pairs (X) E7,H7: 5.. / E7 = 5 => 0 pairs (X) / H7 = 5 => 6 pairs (_) D5,D9: 5.. / D5 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) B4,C4: 6.. / B4 = 6 => 8 pairs (_) / C4 = 6 => 0 pairs (X) G5,I5: 6.. / G5 = 6 => 0 pairs (X) / I5 = 6 => 7 pairs (_) C1,C4: 6.. / C1 = 6 => 8 pairs (_) / C4 = 6 => 0 pairs (X) E2,E9: 6.. / E2 = 6 => 8 pairs (_) / E9 = 6 => 7 pairs (_) H2,H3: 7.. / H2 = 7 => 8 pairs (_) / H3 = 7 => 7 pairs (_) G5,G6: 7.. / G5 = 7 => 8 pairs (_) / G6 = 7 => 0 pairs (X) E6,G6: 7.. / E6 = 7 => 8 pairs (_) / G6 = 7 => 0 pairs (X) C8,D8: 7.. / C8 = 7 => 8 pairs (_) / D8 = 7 => 9 pairs (_) A3,C3: 8.. / A3 = 8 => 5 pairs (_) / C3 = 8 => 0 pairs (X) D2,F2: 8.. / D2 = 8 => 0 pairs (*) / F2 = 8 => 0 pairs (X) F4,D6: 8.. / F4 = 8 => 0 pairs (*) / D6 = 8 => 0 pairs (X) G4,G6: 8.. / G4 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) A9,C9: 8.. / A9 = 8 => 0 pairs (X) / C9 = 8 => 5 pairs (_) F4,G4: 8.. / F4 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) D6,G6: 8.. / D6 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) A3,A9: 8.. / A3 = 8 => 5 pairs (_) / A9 = 8 => 0 pairs (X) C3,C9: 8.. / C3 = 8 => 0 pairs (X) / C9 = 8 => 5 pairs (_) D2,D6: 8.. / D2 = 8 => 0 pairs (*) / D6 = 8 => 0 pairs (X) F2,F4: 8.. / F2 = 8 => 0 pairs (X) / F4 = 8 => 0 pairs (_) * DURATION: 0:00:58.360485 START: 06:37:33.786205 END: 06:38:32.146690 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,C3,D6,F4,F9,H7) * ....351822.1..........21...7..2......82....3......6.2.6..1..2.8.5..82....2....4.7 * PAIR A1: 4,9 BLK 1 B1: 4,9,6,7 # reduction candidate for 4,9 B1: 4,9 # 10 pairs C1: 4,9,6,7 # reduction candidate for 4,9 C1: 4,9 => CTR * ....351822.1..8.......21...7.62.38...825...3.3.58.6.2.6.31..2.8.57.82....283.94.7 C1: 6,7 # 8 pairs B2: 4,9,3,6,7 # reduction candidate for 4,9 B2: 4,9 # 14 pairs B3: 4,9,3,6,7 # reduction candidate for 4,9 B3: 4,9 # 11 pairs * PAIR A1: 4,9 ROW 1 D1: 4,9,6,7 # reduction candidate for 4,9 D1: 4,9 # 10 pairs D1: 6,7 # 8 pairs * PAIR A1: 4,9 COL A A5: 4,9,5 # reduction candidate for 4,9 A5: 4,9 => CTR * ..6.351822.18.7...8.5.21.7.7632.8....82.147365..37682.6..143258154782...328..9417 A5: 5 => SOLVED * 976435182231897564845621379763258941582914736419376825697143258154782693328569417 A6: 4,9,3,5 # reduction candidate for 4,9 A6: 4,9 => SOLVED * 976435182231897564845621379763258941582914736419376825697143258154782693328569417 A6: 3,5 # 8 pairs A8: 4,9,1 # reduction candidate for 4,9 A8: 4,9 => CTR * ....351822.1..8...8.5.21...7..2.38..582....3.3..8.6.2.6.31..2.8.5..82...1283.94.7 A8: 1 => SOLVED * 976435182231897564845621379763258941582914736419376825697143258154782693328569417 * PAIR F9: 3,9 BLK 8 F7: 3,9,4,7 # reduction candidate for 3,9 F7: 3,9 => SOLVED * 976435182231897564845621379763258941582914736419376825697143258154782693328569417 F7: 4,7 => CTR * ....351822.1..8.......21...7..2.38...825...3.3..8.6.2.6.31..2.8.5..82....283.94.7 D9: 3,9,5,6 # reduction candidate for 3,9 D9: 3,9 => CTR * ....351822.1..........21...7..2......825...3......6.2.6..1..2.8.5..82....2....4.7 D9: 5,6 => SOLVED * 976435182231897564845621379763258941582914736419376825697143258154782693328569417 * PAIR F9: 3,9 ROW 9 A9: 3,9,1,8 # reduction candidate for 3,9 A9: 3,9 => SOLVED * 976435182231897564845621379763258941582914736419376825697143258154782693328569417 A9: 1,8 => CTR * ....351822.1..8.......21...7..2.38...825...3.3..8.6.2.6.31..2.8.5..82....283.94.7 C9: 3,9,8 # reduction candidate for 3,9 C9: 3,9 => CTR * ....351822.1......5.8.21...7..2......82....3.3..8.6.2.6..1..25815..82...82.3..417 C9: 8 # 5 pairs * PAIR H7: 5,9 BLK 9 H9: 5,9,1,6 # reduction candidate for 5,9 H9: 5,9 => CTR * ....351822.1..8...8.5.21...7..2.38..582....3.3..8.6.2.6.315.298.5..82...128369457 H9: 1,6 # 9 pairs * PAIR H7: 5,9 ROW 7 E7: 5,9,4,7 # reduction candidate for 5,9 E7: 5,9 => CTR * ....351822.1..8.......21...7..2.38...825...3.3..8.6.2.6.315.298.5..82...128369457 E7: 4,7 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-113-base-pr-000.dot * REASONING * DIS # C1: 4,9 => CTR => C1: 6,7 * DIS # A5: 4,9 => CTR => A5: 5 * PRF # A5: 5 => SOL * PRF # A6: 4,9 => SOL * DIS # A8: 4,9 => CTR => A8: 1 * PRF # A8: 1 => SOL * PRF # F7: 3,9 => SOL * DIS # F7: 4,7 => CTR => F7: 3,9 * DIS # D9: 3,9 => CTR => D9: 5,6 * PRF # D9: 5,6 => SOL * PRF # A9: 3,9 => SOL * DIS # A9: 1,8 => CTR => A9: 3,9 * DIS # C9: 3,9 => CTR => C9: 8 * DIS # H9: 5,9 => CTR => H9: 1,6 * DIS # E7: 5,9 => CTR => E7: 4,7 * CNT 15 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,C3,D6,F4,F9,H7) * ....351822.1..........21...7..2......82....3......6.2.6..1..2.8.5..82....2....4.7 * PAIR A1: 4,9 BLK 1 B1: 4,9,6,7 # reduction candidate for 4,9 B1: 4,9 # 10 pairs C1: 4,9,6,7 # reduction candidate for 4,9 C1: 4,9 => CTR * ....351822.1..8.......21...7.62.38...825...3.3.58.6.2.6.31..2.8.57.82....283.94.7 B2: 4,9,3,6,7 # reduction candidate for 4,9 B2: 4,9 # 14 pairs B3: 4,9,3,6,7 # reduction candidate for 4,9 B3: 4,9 # 11 pairs * PAIR A1: 4,9 ROW 1 D1: 4,9,6,7 # reduction candidate for 4,9 D1: 6,7 # 10 pairs D1: 4,9 # 10 pairs * PAIR A1: 4,9 COL A A5: 4,9,5 # reduction candidate for 4,9 A5: 4,9 => CTR * ..6.351822.18.7...8.5.21.7.7632.8....82.147365..37682.6..143258154782...328..9417 A5: 5 => SOLVED * 976435182231897564845621379763258941582914736419376825697143258154782693328569417 * DURATION: 0:00:07.239964 START: 06:38:57.882252 END: 06:39:05.122216 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-113-base-pr-001.dot * REASONING * DIS # C1: 4,9 => CTR => C1: 6,7 * DIS C1: 6,7 # A5: 4,9 => CTR => A5: 5 * PRF C1: 6,7 + A5: 5 => SOL * STA C1: 6,7 + A5: 5 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 113 solution: 976435182231897564845621379763258941582914736419376825697143258154782693328569417 info: 1686 FNBHWY S8.f 4066 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 976435182231897564845621379763258941582914736419376825697143258154782693328569417 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 # B1: 4,9 => UNS * DIS # C1: 4,9 => CTR => C1: 6,7 * INC # C1: 6,7 => UNS * INC # B2: 4,9 => UNS * INC # B3: 4,9 => UNS * INC # D1: 4,9 => UNS * INC # D1: 6,7 => UNS * DIS # A5: 4,9 => CTR => A5: 5 * PRF # A5: 5 => SOL * PRF # A6: 4,9 => SOL * INC # A6: 3,5 => UNS * DIS # A8: 4,9 => CTR => A8: 1 * PRF # A8: 1 => SOL * PRF # F7: 3,9 => SOL * DIS # F7: 4,7 => CTR => F7: 3,9 * DIS # D9: 3,9 => CTR => D9: 5,6 * PRF # D9: 5,6 => SOL * PRF # A9: 3,9 => SOL * DIS # A9: 1,8 => CTR => A9: 3,9 * DIS # C9: 3,9 => CTR => C9: 8 * INC # C9: 8 => UNS * DIS # H9: 5,9 => CTR => H9: 1,6 * INC # H9: 1,6 => UNS * DIS # E7: 5,9 => CTR => E7: 4,7 * INC # E7: 4,7 => UNS * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 4,9 => UNS * DIS # C1: 4,9 => CTR => C1: 6,7 * INC C1: 6,7 # B2: 4,9 => UNS * INC C1: 6,7 # B3: 4,9 => UNS * INC C1: 6,7 # D1: 4,9 => UNS * INC C1: 6,7 # D1: 6,7 => UNS * DIS C1: 6,7 # A5: 4,9 => CTR => A5: 5 * PRF C1: 6,7 + A5: 5 => SOL * STA C1: 6,7 + A5: 5 * CNT 8 HDP CHAINS / 7 HYP OPENED