Analysis of zz-menneske-no-06912949-base.sdk
Contents
Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=06912949
level: medium
position: ....7.6.8.5..........1...2.5.6........28....7...93...1.1.....3......48..9.7.6.... initial
Autosolve
position: ....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 2,4 => SOL * PRF # D1: 3,5 => SOL * PRF # C7: 4,8 => SOL * DIS # F6: 5,6 => CTR => F6: 2 * DIS # H5: 5,6 => CTR => H5: 4,9 * DIS # F6: 6 => CTR => F6: 2,5 * DIS # G7: 2,5 => CTR => G7: 4,7,9 * DIS # H5: 5,6 => CTR => H5: 4,9 * DIS # F6: 5,6 => CTR => F6: 2 * PRF # A7: 2,6 => SOL * PRF # I8: 2,6 => SOL * CNT 11 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 2,4 => SOL * STA A1: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....7.6.8.5..........1...2.5.6........28....7...93...1.1.....3......48..9.7.6.... | initial |
| ....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6.... | autosolve |
| 241573698853629174769148325596417283132856947478932561614285739325794816987361452 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 2,4 B4: 3,9 B5: 3,9 C6: 4,8 E5: 4,5 F5: 5,6 G6: 2,5 H6: 5,6 B8: 2,6 C8: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C2: 1.. / C1 = 1 => 10 pairs (_) / C2 = 1 => 0 pairs (X) E4,F4: 1.. / E4 = 1 => 20 pairs (_) / F4 = 1 => 19 pairs (_) E8,F9: 1.. / E8 = 1 => 19 pairs (_) / F9 = 1 => 20 pairs (_) C1,H1: 1.. / C1 = 1 => 10 pairs (_) / H1 = 1 => 0 pairs (X) E8,H8: 1.. / E8 = 1 => 19 pairs (_) / H8 = 1 => 20 pairs (_) E4,E8: 1.. / E4 = 1 => 20 pairs (_) / E8 = 1 => 19 pairs (_) F4,F9: 1.. / F4 = 1 => 19 pairs (_) / F9 = 1 => 20 pairs (_) G2,G9: 1.. / G2 = 1 => 10 pairs (_) / G9 = 1 => 0 pairs (X) F6,G6: 2.. / F6 = 2 => 10 pairs (_) / G6 = 2 => 0 pairs (X) B4,B5: 3.. / B4 = 3 => 8 pairs (_) / B5 = 3 => 8 pairs (_) A8,C8: 3.. / A8 = 3 => 0 pairs (*) / C8 = 3 => 0 pairs (X) D9,F9: 3.. / D9 = 3 => 10 pairs (_) / F9 = 3 => 0 pairs (X) B5,G5: 3.. / B5 = 3 => 8 pairs (_) / G5 = 3 => 8 pairs (_) D1,D9: 3.. / D1 = 3 => 0 pairs (X) / D9 = 3 => 10 pairs (_) D1,D4: 4.. / D1 = 4 => 19 pairs (_) / D4 = 4 => 0 pairs (*) C7,C8: 5.. / C7 = 5 => 15 pairs (_) / C8 = 5 => 0 pairs (*) A3,B3: 6.. / A3 = 6 => 10 pairs (_) / B3 = 6 => 0 pairs (*) F5,F6: 6.. / F5 = 6 => 9 pairs (_) / F6 = 6 => 0 pairs (X) H5,H6: 6.. / H5 = 6 => 0 pairs (X) / H6 = 6 => 9 pairs (_) I7,I8: 6.. / I7 = 6 => 10 pairs (_) / I8 = 6 => 0 pairs (*) F5,H5: 6.. / F5 = 6 => 9 pairs (_) / H5 = 6 => 0 pairs (X) F6,H6: 6.. / F6 = 6 => 0 pairs (X) / H6 = 6 => 9 pairs (_) A7,I7: 6.. / A7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) B3,B8: 6.. / B3 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) A6,B6: 7.. / A6 = 7 => 11 pairs (_) / B6 = 7 => 11 pairs (_) D4,F4: 7.. / D4 = 7 => 19 pairs (_) / F4 = 7 => 20 pairs (_) G7,H8: 7.. / G7 = 7 => 20 pairs (_) / H8 = 7 => 19 pairs (_) D8,H8: 7.. / D8 = 7 => 20 pairs (_) / H8 = 7 => 19 pairs (_) B3,B6: 7.. / B3 = 7 => 11 pairs (_) / B6 = 7 => 11 pairs (_) F4,F7: 7.. / F4 = 7 => 20 pairs (_) / F7 = 7 => 19 pairs (_) H2,H8: 7.. / H2 = 7 => 20 pairs (_) / H8 = 7 => 19 pairs (_) B9,F9: 8.. / B9 = 8 => 12 pairs (_) / F9 = 8 => 19 pairs (_) B4,B5: 9.. / B4 = 9 => 8 pairs (_) / B5 = 9 => 8 pairs (_) * DURATION: 0:00:49.896795 START: 07:05:23.340236 END: 07:06:13.237031 2017-05-01 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B4,B5,B8,C6,C8,E5,F5,G6,H6) * ....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6.... * PAIR B1: 2,4 BLK 1 A1: 2,4,3 # reduction candidate for 2,4 A1: 2,4 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 A1: 3 # 15 pairs A2: 2,4,3,7,8 # reduction candidate for 2,4 A2: 2,4 # 21 pairs * PAIR B1: 2,4 ROW 1 D1: 2,4,3,5 # reduction candidate for 2,4 D1: 3,5 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 D1: 2,4 # 19 pairs * PAIR B1: 2,4 COL B B9: 2,4,8 # reduction candidate for 2,4 B9: 2,4 # 19 pairs B9: 8 # 12 pairs * PAIR B4: 3,9 ROW 4 G4: 3,9,2,4 # reduction candidate for 3,9 G4: 3,9 # 12 pairs I4: 3,9,2,4 # reduction candidate for 3,9 I4: 3,9 # 12 pairs * PAIR B5: 3,9 ROW 5 G5: 3,9,4,5 # reduction candidate for 3,9 G5: 3,9 # 11 pairs G5: 4,5 # 8 pairs * PAIR C6: 4,8 BLK 4 A6: 4,8,7 # reduction candidate for 4,8 A6: 4,8 # 11 pairs B6: 4,8,7 # reduction candidate for 4,8 B6: 4,8 # 11 pairs * PAIR C6: 4,8 COL C C2: 4,8,1,3,9 # reduction candidate for 4,8 C2: 4,8 # 16 pairs C3: 4,8,3,9 # reduction candidate for 4,8 C3: 4,8 # 18 pairs C7: 4,8,5 # reduction candidate for 4,8 C7: 4,8 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 C7: 5 # 15 pairs * PAIR E5: 4,5 ROW 5 G5: 4,5,3,9 # reduction candidate for 4,5 G5: 4,5 # 8 pairs H5: 4,5,6,9 # reduction candidate for 4,5 H5: 4,5 # 11 pairs * PAIR E5: 4,5 COL E E3: 4,5,8,9 # reduction candidate for 4,5 E3: 4,5 # 12 pairs E3: 8,9 # 11 pairs * PAIR F5: 5,6 BLK 5 F6: 5,6,2 # reduction candidate for 5,6 F6: 5,6 => CTR * 321479658.5.62....6..15..2.59621..8.132846597...935261.1.....3..6...48..9.7362..5 F6: 2 # 10 pairs * PAIR F5: 5,6 ROW 5 H5: 5,6,4,9 # reduction candidate for 5,6 H5: 5,6 => CTR * ....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6.... H5: 4,9 # 10 pairs * PAIR G6: 2,5 ROW 6 F6: 2,5,6 # reduction candidate for 2,5 F6: 6 => CTR * ...57.6.8.5.6........1...2.5.64...8.1.28.5.67...936251.1.....3......48..9.7.6.... F6: 2,5 # 9 pairs * PAIR G6: 2,5 COL G G7: 2,5,4,7,9 # reduction candidate for 2,5 G7: 2,5 => CTR * .2.47.6.8.5.6........1...2.5.67.1.8.1.28....7...93...1.1..97.36.6..14879947368... G7: 4,7,9 # 10 pairs G9: 2,5,1,4 # reduction candidate for 2,5 G9: 2,5 # 11 pairs * PAIR H6: 5,6 BLK 6 H5: 5,6,4,9 # reduction candidate for 5,6 H5: 5,6 => CTR * ....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6.... H5: 4,9 # 10 pairs * PAIR H6: 5,6 ROW 6 F6: 5,6,2 # reduction candidate for 5,6 F6: 5,6 => CTR * 321479658.5.62....6..15..2.59621..8.132846597...935261.1.....3..6...48..9.7362..5 F6: 2 # 10 pairs * PAIR B8: 2,6 BLK 7 A7: 2,6,4,8 # reduction candidate for 2,6 A7: 2,6 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 A7: 4,8 # 11 pairs A8: 2,6,3 # reduction candidate for 2,6 A8: 2,6 # 15 pairs * PAIR B8: 2,6 ROW 8 I8: 2,6,5,9 # reduction candidate for 2,6 I8: 2,6 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 I8: 5,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06912949-base-pr-000.dot * REASONING * PRF # A1: 2,4 => SOL * PRF # D1: 3,5 => SOL * PRF # C7: 4,8 => SOL * DIS # F6: 5,6 => CTR => F6: 2 * DIS # H5: 5,6 => CTR => H5: 4,9 * DIS # F6: 6 => CTR => F6: 2,5 * DIS # G7: 2,5 => CTR => G7: 4,7,9 * DIS # H5: 5,6 => CTR => H5: 4,9 * DIS # F6: 5,6 => CTR => F6: 2 * PRF # A7: 2,6 => SOL * PRF # I8: 2,6 => SOL * CNT 11 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B4,B5,B8,C6,C8,E5,F5,G6,H6) * ....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6.... * PAIR B1: 2,4 BLK 1 A1: 2,4,3 # reduction candidate for 2,4 A1: 2,4 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 * DURATION: 0:00:02.593505 START: 07:06:44.344071 END: 07:06:46.937576 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06912949-base-pr-001.dot * REASONING * PRF # A1: 2,4 => SOL * STA A1: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=06912949 umulig ----------------------------- Positions ----------------------------- ===================================================================================== ========= ``....7.6.8.5..........1...2.5.6........28....7...93...1.1.....3......48..9.7.6....`` initial ``....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6....`` autosolve ``241573698853629174769148325596417283132856947478932561614285739325794816987361452`` solved ===================================================================================== ========= ---------------------------------- Classification ---------------------------------- level: medium ------------------------------------ Pairing Analysis ------------------------------------ -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B4,B5,B8,C6,C8,E5,F5,G6,H6) * ....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6.... * PAIR B1: 2,4 BLK 1 A1: 2,4,3 # reduction candidate for 2,4 A1: 2,4 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 A1: 3 # 15 pairs A2: 2,4,3,7,8 # reduction candidate for 2,4 A2: 2,4 # 21 pairs * PAIR B1: 2,4 ROW 1 D1: 2,4,3,5 # reduction candidate for 2,4 D1: 3,5 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 D1: 2,4 # 19 pairs * PAIR B1: 2,4 COL B B9: 2,4,8 # reduction candidate for 2,4 B9: 2,4 # 19 pairs B9: 8 # 12 pairs * PAIR B4: 3,9 ROW 4 G4: 3,9,2,4 # reduction candidate for 3,9 G4: 3,9 # 12 pairs I4: 3,9,2,4 # reduction candidate for 3,9 I4: 3,9 # 12 pairs * PAIR B5: 3,9 ROW 5 G5: 3,9,4,5 # reduction candidate for 3,9 G5: 3,9 # 11 pairs G5: 4,5 # 8 pairs * PAIR C6: 4,8 BLK 4 A6: 4,8,7 # reduction candidate for 4,8 A6: 4,8 # 11 pairs B6: 4,8,7 # reduction candidate for 4,8 B6: 4,8 # 11 pairs * PAIR C6: 4,8 COL C C2: 4,8,1,3,9 # reduction candidate for 4,8 C2: 4,8 # 16 pairs C3: 4,8,3,9 # reduction candidate for 4,8 C3: 4,8 # 18 pairs C7: 4,8,5 # reduction candidate for 4,8 C7: 4,8 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 C7: 5 # 15 pairs * PAIR E5: 4,5 ROW 5 G5: 4,5,3,9 # reduction candidate for 4,5 G5: 4,5 # 8 pairs H5: 4,5,6,9 # reduction candidate for 4,5 H5: 4,5 # 11 pairs * PAIR E5: 4,5 COL E E3: 4,5,8,9 # reduction candidate for 4,5 E3: 4,5 # 12 pairs E3: 8,9 # 11 pairs * PAIR F5: 5,6 BLK 5 F6: 5,6,2 # reduction candidate for 5,6 F6: 5,6 => CTR * 321479658.5.62....6..15..2.59621..8.132846597...935261.1.....3..6...48..9.7362..5 F6: 2 # 10 pairs * PAIR F5: 5,6 ROW 5 H5: 5,6,4,9 # reduction candidate for 5,6 H5: 5,6 => CTR * ....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6.... H5: 4,9 # 10 pairs * PAIR G6: 2,5 ROW 6 F6: 2,5,6 # reduction candidate for 2,5 F6: 6 => CTR * ...57.6.8.5.6........1...2.5.64...8.1.28.5.67...936251.1.....3......48..9.7.6.... F6: 2,5 # 9 pairs * PAIR G6: 2,5 COL G G7: 2,5,4,7,9 # reduction candidate for 2,5 G7: 2,5 => CTR * .2.47.6.8.5.6........1...2.5.67.1.8.1.28....7...93...1.1..97.36.6..14879947368... G7: 4,7,9 # 10 pairs G9: 2,5,1,4 # reduction candidate for 2,5 G9: 2,5 # 11 pairs * PAIR H6: 5,6 BLK 6 H5: 5,6,4,9 # reduction candidate for 5,6 H5: 5,6 => CTR * ....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6.... H5: 4,9 # 10 pairs * PAIR H6: 5,6 ROW 6 F6: 5,6,2 # reduction candidate for 5,6 F6: 5,6 => CTR * 321479658.5.62....6..15..2.59621..8.132846597...935261.1.....3..6...48..9.7362..5 F6: 2 # 10 pairs * PAIR B8: 2,6 BLK 7 A7: 2,6,4,8 # reduction candidate for 2,6 A7: 2,6 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 A7: 4,8 # 11 pairs A8: 2,6,3 # reduction candidate for 2,6 A8: 2,6 # 15 pairs * PAIR B8: 2,6 ROW 8 I8: 2,6,5,9 # reduction candidate for 2,6 I8: 2,6 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 I8: 5,9 # 11 pairs * UNSOLVED! * SAVE PR GRAPH zz-menneske-no-06912949-base-pr-000.dot -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B4,B5,B8,C6,C8,E5,F5,G6,H6) * ....7.6.8.5.6........1...2.5.6....8.1.28....7...93...1.1.....3......48..9.7.6.... * PAIR B1: 2,4 BLK 1 A1: 2,4,3 # reduction candidate for 2,4 A1: 2,4 => SOLVED * 241573698853629174769148325596417283132856947478932561614285739325794816987361452 * SOLVED! * SAVE PR GRAPH zz-menneske-no-06912949-base-pr-001.dot
Solution
position: 241573698853629174769148325596417283132856947478932561614285739325794816987361452 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:
* PRF # A1: 2,4 => SOL * INC # A1: 3 => UNS * INC # A2: 2,4 => UNS * INC # D1: 2,4 => UNS * PRF # D1: 3,5 => SOL * INC # B9: 2,4 => UNS * INC # B9: 8 => UNS * INC # G4: 3,9 => UNS * INC # I4: 3,9 => UNS * INC # G5: 3,9 => UNS * INC # G5: 4,5 => UNS * INC # A6: 4,8 => UNS * INC # B6: 4,8 => UNS * INC # C2: 4,8 => UNS * INC # C3: 4,8 => UNS * PRF # C7: 4,8 => SOL * INC # C7: 5 => UNS * INC # G5: 4,5 => UNS * INC # H5: 4,5 => UNS * INC # E3: 4,5 => UNS * INC # E3: 8,9 => UNS * DIS # F6: 5,6 => CTR => F6: 2 * INC # F6: 2 => UNS * DIS # H5: 5,6 => CTR => H5: 4,9 * INC # H5: 4,9 => UNS * INC # F6: 2,5 => UNS * DIS # F6: 6 => CTR => F6: 2,5 * DIS # G7: 2,5 => CTR => G7: 4,7,9 * INC # G7: 4,7,9 => UNS * INC # G9: 2,5 => UNS * DIS # H5: 5,6 => CTR => H5: 4,9 * INC # H5: 4,9 => UNS * DIS # F6: 5,6 => CTR => F6: 2 * INC # F6: 2 => UNS * PRF # A7: 2,6 => SOL * INC # A7: 4,8 => UNS * INC # A8: 2,6 => UNS * PRF # I8: 2,6 => SOL * INC # I8: 5,9 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 2,4 => SOL * STA A1: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED