Analysis of xx-top500-492-base.sdk
Contents
Original Sudoku
level: medium
position: ...4..6....1......5...............35.7.8...........21.2...53.......1...7.6....4.. initial
Autosolve
position: ...4..6....1......5..............735.7.8..9........2182...53.......14..7.6....4.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A9: 7 => CTR => A9: 1,3 * DIS # C5: 2,3 => CTR => C5: 5 * PRF # C5: 5 => SOL * DIS # B7: 1,8 => CTR => B7: 4 * PRF # B7: 4 => SOL * DIS # G3: 3 => CTR => G3: 1,8 * CNT 6 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A9: 7 => CTR => A9: 1,3 * DIS A9: 1,3 # C5: 2,3 => CTR => C5: 5 * PRF A9: 1,3 + C5: 5 => SOL * STA A9: 1,3 + C5: 5 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...4..6....1......5...............35.7.8...........21.2...53.......1...7.6....4.. | initial |
| ...4..6....1......5..............735.7.8..9........2182...53.......14..7.6....4.. | autosolve |
| 739485621681372594524169873812946735375821946496537218247653189958214367163798452 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A5: 1,3 E5: 2,3 H5: 4,6 I5: 4,6 D8: 2,6 G7: 1,8 H8: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B7,A9: 1.. / B7 = 1 => 0 pairs (X) / A9 = 1 => 0 pairs (_) F1,I1: 1.. / F1 = 1 => 0 pairs (X) / I1 = 1 => 0 pairs (_) A5,F5: 1.. / A5 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) A9,I9: 1.. / A9 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) B4,B7: 1.. / B4 = 1 => 0 pairs (*) / B7 = 1 => 0 pairs (X) D3,D4: 1.. / D3 = 1 => 0 pairs (*) / D4 = 1 => 0 pairs (X) G3,G7: 1.. / G3 = 1 => 0 pairs (X) / G7 = 1 => 0 pairs (_) D8,H8: 2.. / D8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) G8,I9: 3.. / G8 = 3 => 0 pairs (*) / I9 = 3 => 0 pairs (X) E4,E6: 4.. / E4 = 4 => 7 pairs (_) / E6 = 4 => 7 pairs (_) H5,I5: 4.. / H5 = 4 => 6 pairs (_) / I5 = 4 => 6 pairs (_) B7,C7: 4.. / B7 = 4 => 0 pairs (*) / C7 = 4 => 0 pairs (X) G8,H9: 5.. / G8 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) F1,H1: 5.. / F1 = 5 => 0 pairs (*) / H1 = 5 => 0 pairs (X) C5,F5: 5.. / C5 = 5 => 0 pairs (*) / F5 = 5 => 0 pairs (X) C9,H9: 5.. / C9 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) B6,B8: 5.. / B6 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) D2,D6: 5.. / D2 = 5 => 0 pairs (X) / D6 = 5 => 0 pairs (_) G2,G8: 5.. / G2 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) A2,C3: 6.. / A2 = 6 => 7 pairs (_) / C3 = 6 => 7 pairs (_) H5,I5: 6.. / H5 = 6 => 6 pairs (_) / I5 = 6 => 6 pairs (_) D7,D8: 6.. / D7 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) D8,H8: 6.. / D8 = 6 => 7 pairs (_) / H8 = 6 => 0 pairs (*) I5,I7: 6.. / I5 = 6 => 6 pairs (_) / I7 = 6 => 6 pairs (_) C7,D7: 7.. / C7 = 7 => 0 pairs (*) / D7 = 7 => 0 pairs (X) E9,F9: 8.. / E9 = 8 => 7 pairs (_) / F9 = 8 => 7 pairs (_) * DURATION: 0:00:41.791994 START: 19:28:56.160333 END: 19:29:37.952327 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,D8,E5,G7,H5,H8,I5) * ...4..6....1......5..............735.7.8..9........2182...53.......14..7.6....4.. * PAIR A5: 1,3 COL A A9: 1,3,7 # reduction candidate for 1,3 A9: 7 => CTR * ...4.165...1...3..5..............735.7.8..9........2182147538.....614.2776....4.1 A9: 1,3 # 9 pairs * PAIR E5: 2,3 ROW 5 C5: 2,3,5 # reduction candidate for 2,3 C5: 2,3 => CTR * ...4..65...15.....5..............73517.8.59........2182147538.....614527.6....4.. C5: 5 => SOLVED * 739485621681372594524169873812946735375821946496537218247653189958214367163798452 * PAIR E5: 2,3 COL E E1: 2,3,7,8,9 # reduction candidate for 2,3 E1: 2,3 # 8 pairs E2: 2,3,6,7,8,9 # reduction candidate for 2,3 E2: 2,3 # 8 pairs E3: 2,3,6,7,8,9 # reduction candidate for 2,3 E3: 2,3 # 8 pairs * PAIR G7: 1,8 ROW 7 B7: 1,8,4 # reduction candidate for 1,8 B7: 1,8 => CTR * ...4.56.1..1...5..5.....3...129.67353758219.....5372182847531..9536148271672..453 B7: 4 => SOLVED * 739485621681372594524169873812946735375821946496537218247653189958214367163798452 * PAIR G7: 1,8 COL G G3: 1,8,3 # reduction candidate for 1,8 G3: 3 => CTR * ...4.56.1..1...5..5..1..3..8129467353758219.....5372182..7531..9536148271672..453 G3: 1,8 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-492-base-pr-000.dot * REASONING * DIS # A9: 7 => CTR => A9: 1,3 * DIS # C5: 2,3 => CTR => C5: 5 * PRF # C5: 5 => SOL * DIS # B7: 1,8 => CTR => B7: 4 * PRF # B7: 4 => SOL * DIS # G3: 3 => CTR => G3: 1,8 * CNT 6 HDP CHAINS / 11 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,D8,E5,G7,H5,H8,I5) * ...4..6....1......5..............735.7.8..9........2182...53.......14..7.6....4.. * PAIR A5: 1,3 COL A A9: 1,3,7 # reduction candidate for 1,3 A9: 7 => CTR * ...4.165...1...3..5..............735.7.8..9........2182147538.....614.2776....4.1 * PAIR RESTART * PAIR E5: 2,3 ROW 5 C5: 2,3,5 # reduction candidate for 2,3 C5: 2,3 => CTR * ...4..65...15.....5..............73517.8.59........2182147538.....614527.6....4.. C5: 5 => SOLVED * 739485621681372594524169873812946735375821946496537218247653189958214367163798452 * DURATION: 0:00:04.982270 START: 19:29:48.056023 END: 19:29:53.038293 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-492-base-pr-001.dot * REASONING * DIS # A9: 7 => CTR => A9: 1,3 * DIS A9: 1,3 # C5: 2,3 => CTR => C5: 5 * PRF A9: 1,3 + C5: 5 => SOL * STA A9: 1,3 + C5: 5 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 492 solution: 739485621681372594524169873812946735375821946496537218247653189958214367163798452 info: 96258 FNBHWYK S8.f 9141 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 739485621681372594524169873812946735375821946496537218247653189958214367163798452 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 # A9: 1,3 => UNS * DIS # A9: 7 => CTR => A9: 1,3 * DIS # C5: 2,3 => CTR => C5: 5 * PRF # C5: 5 => SOL * INC # E1: 2,3 => UNS * INC # E2: 2,3 => UNS * INC # E3: 2,3 => UNS * DIS # B7: 1,8 => CTR => B7: 4 * PRF # B7: 4 => SOL * INC # G3: 1,8 => UNS * DIS # G3: 3 => CTR => G3: 1,8 * CNT 11 HDP CHAINS / 11 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A9: 1,3 => UNS * DIS # A9: 7 => CTR => A9: 1,3 * DIS A9: 1,3 # C5: 2,3 => CTR => C5: 5 * PRF A9: 1,3 + C5: 5 => SOL * STA A9: 1,3 + C5: 5 * CNT 4 HDP CHAINS / 3 HYP OPENED