Analysis of xx-top95-091-base.sdk
Contents
Original Sudoku
level: medium
position: ...658.....4......12............96.7...3..5....2.8...3..19..8..3.6.....4....473.. initial
Autosolve
position: ...658.....4....3.12............96.7...3..5....2.8...3..19..8..3.68.5..4....473.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 7,9 => CTR => B1: 3 * DIS # A5: 7,9 => CTR => A5: 4,6,8 * DIS # I3: 5,8 => CTR => I3: 6 * DIS # C4: 5,8 => CTR => C4: 3 * DIS # E3: 7,9 => CTR => E3: 3 * DIS # F5: 4,6 => CTR => F5: 1,2 * DIS # H1: 1,2 => CTR => H1: 4 * DIS # I5: 1,2 => CTR => I5: 8,9 * DIS # I9: 1,2 => CTR => I9: 5,6,9 * DIS # I3: 5,8 => CTR => I3: 6 * DIS # E3: 7,9 => CTR => E3: 3 * DIS # D6: 7 => CTR => D6: 4,5 * DIS # F5: 4,6 => CTR => F5: 1,2 * DIS # H4: 4,8 => CTR => H4: 1,2 * DIS # H4: 1,4 => CTR => H4: 2,8 * PRF # H5: 1,4 => SOL * DIS # H6: 1,4 => CTR => H6: 9 * PRF # H6: 9 => SOL * PRF # B6: 1,4 => SOL * DIS # F6: 1,4 => CTR => F6: 6 * DIS # G1: 1,4 => CTR => G1: 2 * PRF # G1: 2 => SOL * DIS # B1: 7,9 => CTR => B1: 3 * DIS # H9: 1,2 => CTR => H9: 5,6,9 * DIS # I9: 1,2 => CTR => I9: 5,6,9 * PRF # H7: 2,5 => SOL * DIS # H7: 7 => CTR => H7: 2,5 * DIS # H9: 2,5 => CTR => H9: 1,6,9 * DIS # I9: 2,5 => CTR => I9: 1,6,9 * DIS # A7: 2,5 => CTR => A7: 4,7 * PRF # A7: 4,7 => SOL * DIS # H9: 1,2 => CTR => H9: 5,6,9 * DIS # I9: 1,2 => CTR => I9: 5,6,9 * DIS # G1: 4 => CTR => G1: 1,2 * CNT 34 HDP CHAINS / 78 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 7,9 => CTR => B1: 3 * DIS B1: 3 # A5: 7,9 => CTR => A5: 4,6,8 * DIS B1: 3 + A5: 4,6,8 # I3: 5,8 => CTR => I3: 6 * DIS B1: 3 + A5: 4,6,8 + I3: 6 # C9: 9 => CTR => C9: 5,8 * DIS B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 # E3: 7,9 => CTR => E3: 3 * PRF B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 + E3: 3 => SOL * STA B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 + E3: 3 * CNT 6 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...658.....4......12............96.7...3..5....2.8...3..19..8..3.6.....4....473.. | initial |
| ...658.....4....3.12............96.7...3..5....2.8...3..19..8..3.68.5..4....473.. | autosolve |
| 937658241864291735125734986583419627649372518712586493471963852396825174258147369 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (23) A1: 7,9 C3: 5,8 D2: 1,2 E2: 7,9 F2: 1,2 D3: 4,7 F3: 3,4 I1: 1,2 G2: 7,9 I2: 5,8 G3: 7,9 D4: 4,5 E4: 1,2 E5: 6,7 G6: 1,4 B8: 7,9 E7: 3,6 F7: 3,6 E8: 1,2 D9: 1,2 I7: 2,5 G8: 1,2 H8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,F2: 1.. / D2 = 1 => 0 pairs (X) / F2 = 1 => 0 pairs (_) E8,D9: 1.. / E8 = 1 => 0 pairs (X) / D9 = 1 => 0 pairs (_) E8,G8: 1.. / E8 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) D2,D9: 1.. / D2 = 1 => 0 pairs (X) / D9 = 1 => 0 pairs (_) E4,E8: 1.. / E4 = 1 => 0 pairs (*) / E8 = 1 => 0 pairs (X) D2,F2: 2.. / D2 = 2 => 0 pairs (*) / F2 = 2 => 0 pairs (X) E4,F5: 2.. / E4 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) A7,A9: 2.. / A7 = 2 => 0 pairs (X) / A9 = 2 => 0 pairs (_) E8,D9: 2.. / E8 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) E4,H4: 2.. / E4 = 2 => 0 pairs (X) / H4 = 2 => 0 pairs (_) E8,G8: 2.. / E8 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) D2,D9: 2.. / D2 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) E4,E8: 2.. / E4 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) F2,F5: 2.. / F2 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) G1,G8: 2.. / G1 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) B1,C1: 3.. / B1 = 3 => 24 pairs (_) / C1 = 3 => 0 pairs (X) E3,F3: 3.. / E3 = 3 => 17 pairs (_) / F3 = 3 => 0 pairs (X) B4,C4: 3.. / B4 = 3 => 0 pairs (X) / C4 = 3 => 24 pairs (_) E7,F7: 3.. / E7 = 3 => 0 pairs (X) / F7 = 3 => 17 pairs (_) B1,B4: 3.. / B1 = 3 => 24 pairs (_) / B4 = 3 => 0 pairs (X) C1,C4: 3.. / C1 = 3 => 0 pairs (X) / C4 = 3 => 24 pairs (_) E3,E7: 3.. / E3 = 3 => 17 pairs (_) / E7 = 3 => 0 pairs (X) F3,F7: 3.. / F3 = 3 => 0 pairs (X) / F7 = 3 => 17 pairs (_) D3,F3: 4.. / D3 = 4 => 0 pairs (X) / F3 = 4 => 17 pairs (_) G1,H1: 4.. / G1 = 4 => 0 pairs (X) / H1 = 4 => 26 pairs (_) A7,B7: 4.. / A7 = 4 => 0 pairs (*) / B7 = 4 => 0 pairs (X) G1,G6: 4.. / G1 = 4 => 0 pairs (X) / G6 = 4 => 26 pairs (_) D4,D6: 5.. / D4 = 5 => 25 pairs (_) / D6 = 5 => 16 pairs (_) A2,B2: 6.. / A2 = 6 => 24 pairs (_) / B2 = 6 => 24 pairs (_) H3,I3: 6.. / H3 = 6 => 0 pairs (X) / I3 = 6 => 24 pairs (_) E7,F7: 6.. / E7 = 6 => 17 pairs (_) / F7 = 6 => 0 pairs (X) H9,I9: 6.. / H9 = 6 => 24 pairs (_) / I9 = 6 => 0 pairs (X) E5,E7: 6.. / E5 = 6 => 0 pairs (X) / E7 = 6 => 17 pairs (_) H3,H9: 6.. / H3 = 6 => 0 pairs (X) / H9 = 6 => 24 pairs (_) I3,I9: 6.. / I3 = 6 => 24 pairs (_) / I9 = 6 => 0 pairs (X) G2,G3: 7.. / G2 = 7 => 21 pairs (_) / G3 = 7 => 0 pairs (X) E5,D6: 7.. / E5 = 7 => 17 pairs (_) / D6 = 7 => 0 pairs (X) H7,H8: 7.. / H7 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) E2,G2: 7.. / E2 = 7 => 0 pairs (X) / G2 = 7 => 21 pairs (_) B8,H8: 7.. / B8 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) C1,C5: 7.. / C1 = 7 => 23 pairs (_) / C5 = 7 => 0 pairs (X) D3,D6: 7.. / D3 = 7 => 17 pairs (_) / D6 = 7 => 0 pairs (X) E2,E3: 9.. / E2 = 9 => 21 pairs (_) / E3 = 9 => 0 pairs (X) G2,G3: 9.. / G2 = 9 => 0 pairs (X) / G3 = 9 => 21 pairs (_) E2,G2: 9.. / E2 = 9 => 21 pairs (_) / G2 = 9 => 0 pairs (X) E3,G3: 9.. / E3 = 9 => 0 pairs (X) / G3 = 9 => 21 pairs (_) B8,H8: 9.. / B8 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) I5,I9: 9.. / I5 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) * DURATION: 0:01:53.368045 START: 01:05:21.925855 END: 01:07:15.293900 2017-05-04 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B8,C3,D2,D3,D4,D9,E2,E4,E5,E7,E8,F2,F3,F7,G2,G3,G6,G8,H8,I1,I2,I7) * ...658.....4....3.12............96.7...3..5....2.8...3..19..8..3.68.5..4....473.. * PAIR A1: 7,9 BLK 1 B1: 7,9,3 # reduction candidate for 7,9 B1: 7,9 => CTR * 793658.....4....3.1254.3....385.96.74.736.5.9..278...3..19368..3768.5.94..9.473.. B1: 3 # 24 pairs C1: 7,9,3 # reduction candidate for 7,9 C1: 7,9 # 24 pairs * PAIR A1: 7,9 COL A A5: 7,9,4,6,8 # reduction candidate for 7,9 A5: 7,9 => CTR * .3.658241..42.1.3.12.4.3..68435196.7...36.5....278..934719368..3968.51742..147369 A5: 4,6,8 # 23 pairs A6: 7,9,4,5,6 # reduction candidate for 7,9 A6: 7,9 # 25 pairs * PAIR C3: 5,8 BLK 1 A2: 5,8,6 # reduction candidate for 5,8 A2: 5,8 # 24 pairs B2: 5,8,6 # reduction candidate for 5,8 B2: 5,8 # 24 pairs * PAIR C3: 5,8 ROW 3 H3: 5,8,6 # reduction candidate for 5,8 H3: 5,8 # 24 pairs I3: 5,8,6 # reduction candidate for 5,8 I3: 5,8 => CTR * ...658241..42.1.3.12...4.6....419627.17362589..2.8.413..19..8.23.68251.42..1473.6 I3: 6 # 24 pairs * PAIR C3: 5,8 COL C C4: 5,8,3 # reduction candidate for 5,8 C4: 5,8 => CTR * 793658.....4....3.1254.3....385.96.74.736.5.9..278...3..19368..3768.5.94..9.473.. C4: 3 # 24 pairs C9: 5,8,9 # reduction candidate for 5,8 C9: 5,8 # 26 pairs * PAIR E2: 7,9 BLK 2 E3: 7,9,3 # reduction candidate for 7,9 E3: 7,9 => CTR * ...658241..42.1.3.12.4.3..6...519627.1.36258...278..93..19368..3968.5174...147369 E3: 3 # 17 pairs * PAIR F2: 1,2 COL F F5: 1,2,4,6 # reduction candidate for 1,2 F5: 4,6 => CTR * ...658.....4..2.3.12...........296.7...3..5....2.81493..19..8..396815274...2473.9 F5: 1,2 # 25 pairs * PAIR D3: 4,7 COL D D6: 4,7,5 # reduction candidate for 4,7 D6: 4,7 # 25 pairs D6: 5 # 16 pairs * PAIR I1: 1,2 BLK 3 G1: 1,2,4 # reduction candidate for 1,2 G1: 1,2 # 26 pairs H1: 1,2,4 # reduction candidate for 1,2 H1: 1,2 => CTR * .39658412..41.2.38128..4.56.134296874873615.9..2.8.1432419..875376815294..5247361 H1: 4 # 26 pairs * PAIR I1: 1,2 COL I I5: 1,2,8,9 # reduction candidate for 1,2 I5: 1,2 => CTR * ...658.....4....38128....56.....96.7...3..5....2.8...3..19..825396825174285147369 I5: 8,9 # 26 pairs I9: 1,2,5,6,9 # reduction candidate for 1,2 I9: 1,2 => CTR * 739658.....4....381284.3.56..35.96.7..736.5.9..278...32419368753768.5.94..5.4736. I9: 5,6,9 # 23 pairs * PAIR I2: 5,8 BLK 3 H3: 5,8,6 # reduction candidate for 5,8 H3: 5,8 # 24 pairs I3: 5,8,6 # reduction candidate for 5,8 I3: 5,8 => CTR * ...658241..42.1.3.12...4.6....419627.17362589..2.8.413..19..8.23.68251.42..1473.6 I3: 6 # 24 pairs * PAIR I2: 5,8 ROW 2 A2: 5,8,6 # reduction candidate for 5,8 A2: 5,8 # 24 pairs B2: 5,8,6 # reduction candidate for 5,8 B2: 5,8 # 24 pairs * PAIR G3: 7,9 ROW 3 E3: 7,9,3 # reduction candidate for 7,9 E3: 7,9 => CTR * ...658241..42.1.3.12.4.3..6...519627.1.36258...278..93..19368..3968.5174...147369 E3: 3 # 17 pairs * PAIR D4: 4,5 BLK 5 D6: 4,5,7 # reduction candidate for 4,5 D6: 7 => CTR * ...658241..42.1.3.12.4.3..6...519627.1.36258...278..93..19368..3968.5174...147369 D6: 4,5 # 17 pairs * PAIR D4: 4,5 ROW 4 A4: 4,5,8 # reduction candidate for 4,5 A4: 4,5 # 25 pairs B4: 4,5,1,3,8 # reduction candidate for 4,5 B4: 4,5 # 29 pairs * PAIR E4: 1,2 BLK 5 F5: 1,2,4,6 # reduction candidate for 1,2 F5: 4,6 => CTR * ...658.....4..2.3.12...........296.7...3..5....2.81493..19..8..396815274...2473.9 F5: 1,2 # 25 pairs * PAIR E4: 1,2 ROW 4 H4: 1,2,4,8 # reduction candidate for 1,2 H4: 4,8 => CTR * 739658..2..41.2.381284.3.56.13529687.87361529..27841.3241936875376815294..5247361 H4: 1,2 # 25 pairs * PAIR E5: 6,7 ROW 5 A5: 6,7,4,8,9 # reduction candidate for 6,7 A5: 6,7 # 24 pairs B5: 6,7,1,4,8,9 # reduction candidate for 6,7 B5: 6,7 # 25 pairs * PAIR G6: 1,4 BLK 6 H4: 1,4,2,8 # reduction candidate for 1,4 H4: 1,4 => CTR * ...658.....41.2.38128....56....296.7...3..58...2.8...32419..875376815294...2473.. H4: 2,8 # 24 pairs H5: 1,4,2,8,9 # reduction candidate for 1,4 H5: 1,4 => SOLVED * 937658241864291735125734986583419627649372518712586493471963852396825174258147369 H5: 2,8,9 # 23 pairs H6: 1,4,9 # reduction candidate for 1,4 H6: 1,4 => CTR * 937658..2..41927351257349..513429687..83715.9792586..3..19638..376815294..92473.. H6: 9 => SOLVED * 937658241864291735125734986583419627649372518712586493471963852396825174258147369 * PAIR G6: 1,4 ROW 6 B6: 1,4,5,6,7,9 # reduction candidate for 1,4 B6: 1,4 => SOLVED * 937658241864291735125734986583419627649372518712586493471963852396825174258147369 B6: 5,6,7,9 # 23 pairs F6: 1,4,6 # reduction candidate for 1,4 F6: 1,4 => CTR * ...658241..42.1.3.12......6....19627.1.3.258...2.8..93..19..8..3968.5174...147369 F6: 6 # 17 pairs * PAIR G6: 1,4 COL G G1: 1,4,2 # reduction candidate for 1,4 G1: 1,4 => CTR * 7.9658..2..41.2.381284.3.564135296878.736.529..278...3241936875376815294..5247361 G1: 2 => SOLVED * 937658241864291735125734986583419627649372518712586493471963852396825174258147369 * PAIR B8: 7,9 COL B B1: 7,9,3 # reduction candidate for 7,9 B1: 7,9 => CTR * 793658.....4....3.1254.3....385.96.74.736.5.9..278...3..19368..3768.5.94..9.473.. B1: 3 # 24 pairs B5: 7,9,1,4,6,8 # reduction candidate for 7,9 B5: 7,9 # 27 pairs B6: 7,9,1,4,5,6 # reduction candidate for 7,9 B6: 7,9 # 27 pairs * PAIR D9: 1,2 ROW 9 H9: 1,2,5,6,9 # reduction candidate for 1,2 H9: 1,2 => CTR * ...658.....4....3.12.....6......96.7...3..5....2.8...3..19..8523.68251.4....473.. H9: 5,6,9 # 23 pairs I9: 1,2,5,6,9 # reduction candidate for 1,2 I9: 1,2 => CTR * 739658.....4....381284.3.56..35.96.7..736.5.9..278...32419368753768.5.94..5.4736. I9: 5,6,9 # 23 pairs * PAIR I7: 2,5 BLK 9 H7: 2,5,7 # reduction candidate for 2,5 H7: 2,5 => SOLVED * 937658241864291735125734986583419627649372518712586493471963852396825174258147369 H7: 7 => CTR * 937658.....4.9273.125734968513429687..8371529792586..3..196387.376815294..9.473.. H9: 2,5,1,6,9 # reduction candidate for 2,5 H9: 2,5 => CTR * ...658241..42.1.3.12...4.6....419627.17362589..2.8.413..19..8723768251942..147356 H9: 1,6,9 # 23 pairs I9: 2,5,1,6,9 # reduction candidate for 2,5 I9: 2,5 => CTR * ...658241..42.1.381284.3.56...519627..7362589..2784..3..19368..3.68.5194...14736. I9: 1,6,9 # 23 pairs * PAIR I7: 2,5 ROW 7 A7: 2,5,4,7 # reduction candidate for 2,5 A7: 2,5 => CTR * 937658..26.419273.12.7349.6.13429687468371529792586..324196387537681529485.2473.1 A7: 4,7 => SOLVED * 937658241864291735125734986583419627649372518712586493471963852396825174258147369 * PAIR G8: 1,2 BLK 9 H9: 1,2,5,6,9 # reduction candidate for 1,2 H9: 1,2 => CTR * ...658.....4....3.12.....6......96.7...3..5....2.8...3..19..8523.68251.4....473.. H9: 5,6,9 # 23 pairs I9: 1,2,5,6,9 # reduction candidate for 1,2 I9: 1,2 => CTR * 739658.....4....381284.3.56..35.96.7..736.5.9..278...32419368753768.5.94..5.4736. I9: 5,6,9 # 23 pairs * PAIR G8: 1,2 COL G G1: 1,2,4 # reduction candidate for 1,2 G1: 4 => CTR * .39658412..41.2.38128..4.56.134296874873615.9..2.8.1432419..875376815294..5247361 G1: 1,2 # 26 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-091-base-pr-000.dot * REASONING * DIS # B1: 7,9 => CTR => B1: 3 * DIS # A5: 7,9 => CTR => A5: 4,6,8 * DIS # I3: 5,8 => CTR => I3: 6 * DIS # C4: 5,8 => CTR => C4: 3 * DIS # E3: 7,9 => CTR => E3: 3 * DIS # F5: 4,6 => CTR => F5: 1,2 * DIS # H1: 1,2 => CTR => H1: 4 * DIS # I5: 1,2 => CTR => I5: 8,9 * DIS # I9: 1,2 => CTR => I9: 5,6,9 * DIS # I3: 5,8 => CTR => I3: 6 * DIS # E3: 7,9 => CTR => E3: 3 * DIS # D6: 7 => CTR => D6: 4,5 * DIS # F5: 4,6 => CTR => F5: 1,2 * DIS # H4: 4,8 => CTR => H4: 1,2 * DIS # H4: 1,4 => CTR => H4: 2,8 * PRF # H5: 1,4 => SOL * DIS # H6: 1,4 => CTR => H6: 9 * PRF # H6: 9 => SOL * PRF # B6: 1,4 => SOL * DIS # F6: 1,4 => CTR => F6: 6 * DIS # G1: 1,4 => CTR => G1: 2 * PRF # G1: 2 => SOL * DIS # B1: 7,9 => CTR => B1: 3 * DIS # H9: 1,2 => CTR => H9: 5,6,9 * DIS # I9: 1,2 => CTR => I9: 5,6,9 * PRF # H7: 2,5 => SOL * DIS # H7: 7 => CTR => H7: 2,5 * DIS # H9: 2,5 => CTR => H9: 1,6,9 * DIS # I9: 2,5 => CTR => I9: 1,6,9 * DIS # A7: 2,5 => CTR => A7: 4,7 * PRF # A7: 4,7 => SOL * DIS # H9: 1,2 => CTR => H9: 5,6,9 * DIS # I9: 1,2 => CTR => I9: 5,6,9 * DIS # G1: 4 => CTR => G1: 1,2 * CNT 34 HDP CHAINS / 78 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B8,C3,D2,D3,D4,D9,E2,E4,E5,E7,E8,F2,F3,F7,G2,G3,G6,G8,H8,I1,I2,I7) * ...658.....4....3.12............96.7...3..5....2.8...3..19..8..3.68.5..4....473.. * PAIR A1: 7,9 BLK 1 B1: 7,9,3 # reduction candidate for 7,9 B1: 7,9 => CTR * 793658.....4....3.1254.3....385.96.74.736.5.9..278...3..19368..3768.5.94..9.473.. * RESTART * PAIR A1: 7,9 COL A A5: 7,9,4,6,8 # reduction candidate for 7,9 A5: 7,9 => CTR * .3.658241..42.1.3.12.4.3..68435196.7...36.5....278..934719368..3968.51742..147369 A6: 7,9,4,5,6 # reduction candidate for 7,9 A6: 7,9 # 25 pairs * RESTART * PAIR A1: 7,9 COL A A6: 7,9,4,5,6 # reduction candidate for 7,9 A6: 4,5,6 # 29 pairs A6: 7,9 # 25 pairs * PAIR RESTART * PAIR A1: 7,9 COL A A6: 7,9,4,5,6 # reduction candidate for 7,9 A6: 4,5,6 # 29 pairs A6: 7,9 # 25 pairs * PAIR C3: 5,8 BLK 1 A2: 5,8,6 # reduction candidate for 5,8 A2: 5,8 # 25 pairs B2: 5,8,6 # reduction candidate for 5,8 B2: 5,8 # 26 pairs * PAIR C3: 5,8 ROW 3 H3: 5,8,6 # reduction candidate for 5,8 H3: 5,8 # 25 pairs I3: 5,8,6 # reduction candidate for 5,8 I3: 5,8 => CTR * .3.658241..42.1.3.12...4.6...3419627.17362589..2.8.413..19..8.23.68251.42..1473.6 * RESTART * PAIR C3: 5,8 COL C C9: 5,8,9 # reduction candidate for 5,8 C9: 9 => CTR * .3.658.....4....3.125....86..3..96.7..83..5....2.8...3..19..8523.68251742...4736. * PAIR RESTART * PAIR C3: 5,8 BLK 1 A2: 5,8,6 # reduction candidate for 5,8 A2: 5,8 # 28 pairs B2: 5,8,6 # reduction candidate for 5,8 B2: 5,8 # 29 pairs * PAIR E2: 7,9 BLK 2 E3: 7,9,3 # reduction candidate for 7,9 E3: 7,9 => CTR * .3.658.....4....3.12.4.3..6.135296.7...36.5....278..93.419368..3968152.4....4736. E3: 3 => SOLVED * 937658241864291735125734986583419627649372518712586493471963852396825174258147369 * DURATION: 0:00:21.510382 START: 01:08:46.010268 END: 01:09:07.520650 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-091-base-pr-001.dot * REASONING * DIS # B1: 7,9 => CTR => B1: 3 * DIS B1: 3 # A5: 7,9 => CTR => A5: 4,6,8 * DIS B1: 3 + A5: 4,6,8 # I3: 5,8 => CTR => I3: 6 * DIS B1: 3 + A5: 4,6,8 + I3: 6 # C9: 9 => CTR => C9: 5,8 * DIS B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 # E3: 7,9 => CTR => E3: 3 * PRF B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 + E3: 3 => SOL * STA B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 + E3: 3 * CNT 6 HDP CHAINS / 16 HYP OPENED
Header Info
Top 95 Sudokus 091 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 937658241864291735125734986583419627649372518712586493471963852396825174258147369 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 # B1: 7,9 => CTR => B1: 3 * INC # B1: 3 => UNS * INC # C1: 7,9 => UNS * DIS # A5: 7,9 => CTR => A5: 4,6,8 * INC # A5: 4,6,8 => UNS * INC # A6: 7,9 => UNS * INC # A2: 5,8 => UNS * INC # B2: 5,8 => UNS * INC # H3: 5,8 => UNS * DIS # I3: 5,8 => CTR => I3: 6 * INC # I3: 6 => UNS * DIS # C4: 5,8 => CTR => C4: 3 * INC # C4: 3 => UNS * INC # C9: 5,8 => UNS * DIS # E3: 7,9 => CTR => E3: 3 * INC # E3: 3 => UNS * INC # F5: 1,2 => UNS * DIS # F5: 4,6 => CTR => F5: 1,2 * INC # D6: 4,7 => UNS * INC # D6: 5 => UNS * INC # G1: 1,2 => UNS * DIS # H1: 1,2 => CTR => H1: 4 * INC # H1: 4 => UNS * DIS # I5: 1,2 => CTR => I5: 8,9 * INC # I5: 8,9 => UNS * DIS # I9: 1,2 => CTR => I9: 5,6,9 * INC # I9: 5,6,9 => UNS * INC # H3: 5,8 => UNS * DIS # I3: 5,8 => CTR => I3: 6 * INC # I3: 6 => UNS * INC # A2: 5,8 => UNS * INC # B2: 5,8 => UNS * DIS # E3: 7,9 => CTR => E3: 3 * INC # E3: 3 => UNS * INC # D6: 4,5 => UNS * DIS # D6: 7 => CTR => D6: 4,5 * INC # A4: 4,5 => UNS * INC # B4: 4,5 => UNS * INC # F5: 1,2 => UNS * DIS # F5: 4,6 => CTR => F5: 1,2 * INC # H4: 1,2 => UNS * DIS # H4: 4,8 => CTR => H4: 1,2 * INC # A5: 6,7 => UNS * INC # B5: 6,7 => UNS * DIS # H4: 1,4 => CTR => H4: 2,8 * INC # H4: 2,8 => UNS * PRF # H5: 1,4 => SOL * INC # H5: 2,8,9 => UNS * DIS # H6: 1,4 => CTR => H6: 9 * PRF # H6: 9 => SOL * PRF # B6: 1,4 => SOL * INC # B6: 5,6,7,9 => UNS * DIS # F6: 1,4 => CTR => F6: 6 * INC # F6: 6 => UNS * DIS # G1: 1,4 => CTR => G1: 2 * PRF # G1: 2 => SOL * DIS # B1: 7,9 => CTR => B1: 3 * INC # B1: 3 => UNS * INC # B5: 7,9 => UNS * INC # B6: 7,9 => UNS * DIS # H9: 1,2 => CTR => H9: 5,6,9 * INC # H9: 5,6,9 => UNS * DIS # I9: 1,2 => CTR => I9: 5,6,9 * INC # I9: 5,6,9 => UNS * PRF # H7: 2,5 => SOL * DIS # H7: 7 => CTR => H7: 2,5 * DIS # H9: 2,5 => CTR => H9: 1,6,9 * INC # H9: 1,6,9 => UNS * DIS # I9: 2,5 => CTR => I9: 1,6,9 * INC # I9: 1,6,9 => UNS * DIS # A7: 2,5 => CTR => A7: 4,7 * PRF # A7: 4,7 => SOL * DIS # H9: 1,2 => CTR => H9: 5,6,9 * INC # H9: 5,6,9 => UNS * DIS # I9: 1,2 => CTR => I9: 5,6,9 * INC # I9: 5,6,9 => UNS * INC # G1: 1,2 => UNS * DIS # G1: 4 => CTR => G1: 1,2 * CNT 78 HDP CHAINS / 78 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 7,9 => CTR => B1: 3 * DIS B1: 3 # A5: 7,9 => CTR => A5: 4,6,8 * INC B1: 3 + A5: 4,6,8 # A6: 7,9 => UNS * INC B1: 3 + A5: 4,6,8 # A6: 7,9 => UNS * INC B1: 3 + A5: 4,6,8 # A6: 4,5,6 => UNS * INC B1: 3 + A5: 4,6,8 # A6: 7,9 => UNS * INC B1: 3 + A5: 4,6,8 # A6: 4,5,6 => UNS * INC B1: 3 + A5: 4,6,8 # A2: 5,8 => UNS * INC B1: 3 + A5: 4,6,8 # B2: 5,8 => UNS * INC B1: 3 + A5: 4,6,8 # H3: 5,8 => UNS * DIS B1: 3 + A5: 4,6,8 # I3: 5,8 => CTR => I3: 6 * INC B1: 3 + A5: 4,6,8 + I3: 6 # C9: 5,8 => UNS * DIS B1: 3 + A5: 4,6,8 + I3: 6 # C9: 9 => CTR => C9: 5,8 * INC B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 # A2: 5,8 => UNS * INC B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 # B2: 5,8 => UNS * DIS B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 # E3: 7,9 => CTR => E3: 3 * PRF B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 + E3: 3 => SOL * STA B1: 3 + A5: 4,6,8 + I3: 6 + C9: 5,8 + E3: 3 * CNT 17 HDP CHAINS / 16 HYP OPENED