Analysis of zz-menneske-no-06912919-base.sdk
Contents
Original Sudoku
level: medium
position: 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52.........65...71..... initial
Autosolve
position: 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52...2.9...6515.71..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H2: 3,9 => CTR => H2: 1,8 * DIS # H9: 3,9 => CTR => H9: 2,8 * DIS # B9: 4 => CTR => B9: 3,6 * DIS # D7: 9 => CTR => D7: 3,6 * DIS # B9: 3,4 => CTR => B9: 6 * DIS # D5: 3,7 => CTR => D5: 2,5,6 * CNT 6 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H2: 3,9 => CTR => H2: 1,8 * DIS H2: 1,8 # H9: 3,9 => CTR => H9: 2,8 * DIS H2: 1,8 + H9: 2,8 # H7: 7 => CTR => H7: 3,9 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 # G4: 5 => CTR => G4: 3,9 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 # B9: 4 => CTR => B9: 3,6 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 # A2: 8 => CTR => A2: 3,6 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 # B3: 7 => CTR => B3: 3,8 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 # I1: 3,8 => CTR => I1: 5 * PRF H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5 => SOL * STA H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5 * CNT 9 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52.........65...71..... | initial |
| 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52...2.9...6515.71..... | autosolve |
| 984361275652978413731425869125846937896537142473219586318652794249783651567194328 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) D2: 2,9 E3: 2,9 A5: 7,8 B6: 7,8 H4: 3,9 A7: 3,6 B8: 3,4 D8: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H2: 1.. / H1 = 1 => 0 pairs (X) / H2 = 1 => 8 pairs (_) C6,E6: 1.. / C6 = 1 => 14 pairs (_) / E6 = 1 => 8 pairs (_) C2,C3: 2.. / C2 = 2 => 15 pairs (_) / C3 = 2 => 0 pairs (X) D2,E3: 2.. / D2 = 2 => 0 pairs (X) / E3 = 2 => 15 pairs (_) H9,I9: 2.. / H9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) C2,D2: 2.. / C2 = 2 => 15 pairs (_) / D2 = 2 => 0 pairs (X) C3,E3: 2.. / C3 = 2 => 0 pairs (X) / E3 = 2 => 15 pairs (_) H6,H9: 2.. / H6 = 2 => 8 pairs (_) / H9 = 2 => 0 pairs (*) C1,C2: 4.. / C1 = 4 => 8 pairs (_) / C2 = 4 => 0 pairs (X) E4,F4: 4.. / E4 = 4 => 9 pairs (_) / F4 = 4 => 9 pairs (_) B8,B9: 4.. / B8 = 4 => 11 pairs (_) / B9 = 4 => 0 pairs (X) G7,I7: 4.. / G7 = 4 => 0 pairs (X) / I7 = 4 => 8 pairs (_) C1,I1: 4.. / C1 = 4 => 8 pairs (_) / I1 = 4 => 0 pairs (X) G2,G7: 4.. / G2 = 4 => 8 pairs (_) / G7 = 4 => 0 pairs (X) I5,I6: 6.. / I5 = 6 => 0 pairs (X) / I6 = 6 => 8 pairs (_) A7,B9: 6.. / A7 = 6 => 0 pairs (X) / B9 = 6 => 11 pairs (_) A7,D7: 6.. / A7 = 6 => 0 pairs (X) / D7 = 6 => 11 pairs (_) B1,B9: 6.. / B1 = 6 => 0 pairs (X) / B9 = 6 => 11 pairs (_) H1,G3: 7.. / H1 = 7 => 11 pairs (_) / G3 = 7 => 0 pairs (X) A5,B6: 7.. / A5 = 7 => 11 pairs (_) / B6 = 7 => 16 pairs (_) D8,F8: 7.. / D8 = 7 => 15 pairs (_) / F8 = 7 => 10 pairs (_) G7,H7: 7.. / G7 = 7 => 11 pairs (_) / H7 = 7 => 0 pairs (X) B1,H1: 7.. / B1 = 7 => 0 pairs (X) / H1 = 7 => 11 pairs (_) B6,D6: 7.. / B6 = 7 => 16 pairs (_) / D6 = 7 => 11 pairs (_) A3,A5: 7.. / A3 = 7 => 16 pairs (_) / A5 = 7 => 11 pairs (_) F5,F8: 7.. / F5 = 7 => 15 pairs (_) / F8 = 7 => 10 pairs (_) G3,G7: 7.. / G3 = 7 => 0 pairs (X) / G7 = 7 => 11 pairs (_) H1,H7: 7.. / H1 = 7 => 11 pairs (_) / H7 = 7 => 0 pairs (X) A5,B6: 8.. / A5 = 8 => 16 pairs (_) / B6 = 8 => 11 pairs (_) E8,F8: 8.. / E8 = 8 => 8 pairs (_) / F8 = 8 => 22 pairs (_) A5,I5: 8.. / A5 = 8 => 16 pairs (_) / I5 = 8 => 11 pairs (_) E1,E8: 8.. / E1 = 8 => 22 pairs (_) / E8 = 8 => 8 pairs (_) D2,E3: 9.. / D2 = 9 => 15 pairs (_) / E3 = 9 => 0 pairs (X) G4,H4: 9.. / G4 = 9 => 13 pairs (_) / H4 = 9 => 9 pairs (_) D7,E9: 9.. / D7 = 9 => 0 pairs (X) / E9 = 9 => 15 pairs (_) D2,D7: 9.. / D2 = 9 => 15 pairs (_) / D7 = 9 => 0 pairs (X) E3,E9: 9.. / E3 = 9 => 0 pairs (X) / E9 = 9 => 15 pairs (_) * DURATION: 0:00:55.239364 START: 07:03:29.372930 END: 07:04:24.612294 2017-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,B6,B8,D2,D8,E3,H4) * 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52...2.9...6515.71..... * PAIR A5: 7,8 COL A A3: 7,8,1,3 # reduction candidate for 7,8 A3: 1,3 # 15 pairs A3: 7,8 # 9 pairs * PAIR B6: 7,8 COL B B1: 7,8,3,6 # reduction candidate for 7,8 B1: 7,8 # 13 pairs B3: 7,8,3 # reduction candidate for 7,8 B3: 7,8 # 13 pairs * PAIR H4: 3,9 BLK 6 G4: 3,9,5 # reduction candidate for 3,9 G4: 3,9 # 13 pairs G4: 5 # 9 pairs * PAIR H4: 3,9 COL H H2: 3,9,1,8 # reduction candidate for 3,9 H2: 3,9 => CTR * 97....21..5..7.8..83.4..76..2.8....779....14848.7.9.26318652479249387651567194382 H2: 1,8 # 9 pairs H7: 3,9,7 # reduction candidate for 3,9 H7: 3,9 # 11 pairs H9: 3,9,2,8 # reduction candidate for 3,9 H9: 3,9 => CTR * 97.5..2...5.97.....3.42.76..2.84..9779....14848.7.9.26318652.7.249387651567194832 H9: 2,8 # 9 pairs * PAIR A7: 3,6 BLK 7 B9: 3,6,4 # reduction candidate for 3,6 B9: 4 => CTR * 964...27..5.27641978.49..6..268....7.9...714.47...9...6189527342397..651547163... B9: 3,6 # 11 pairs * PAIR A7: 3,6 ROW 7 D7: 3,6,9 # reduction candidate for 3,6 D7: 9 => CTR * 964...27..5327641917249..6.3268...97795..3148481729...6189527342.9...6515.716.... D7: 3,6 # 15 pairs * PAIR A7: 3,6 COL A A2: 3,6,1,8 # reduction candidate for 3,6 A2: 3,6 # 12 pairs A4: 3,6,1 # reduction candidate for 3,6 A4: 3,6 # 11 pairs * PAIR B8: 3,4 BLK 7 B9: 3,4,6 # reduction candidate for 3,4 B9: 3,4 => CTR * 964...27.85327641917249..6.3268..597795..314.4.1..9...6189527342.9...6515.716.9.. B9: 6 # 11 pairs * PAIR B8: 3,4 ROW 8 E8: 3,4,8 # reduction candidate for 3,4 E8: 3,4 # 22 pairs F8: 3,4,7,8 # reduction candidate for 3,4 F8: 3,4 # 17 pairs * PAIR D8: 3,7 BLK 8 F8: 3,7,4,8 # reduction candidate for 3,7 F8: 4,8 # 18 pairs F8: 3,7 # 11 pairs * PAIR D8: 3,7 COL D D5: 3,7,2,5,6 # reduction candidate for 3,7 D5: 3,7 => CTR * 9.45.127..5297.41.7.142..6.12.8....789....14247.219..6.18.527.42.9...6515.719..2. D5: 2,5,6 # 8 pairs D6: 3,7,2,5,6 # reduction candidate for 3,7 D6: 3,7 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06912919-base-pr-000.dot * REASONING * DIS # H2: 3,9 => CTR => H2: 1,8 * DIS # H9: 3,9 => CTR => H9: 2,8 * DIS # B9: 4 => CTR => B9: 3,6 * DIS # D7: 9 => CTR => D7: 3,6 * DIS # B9: 3,4 => CTR => B9: 6 * DIS # D5: 3,7 => CTR => D5: 2,5,6 * CNT 6 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,B6,B8,D2,D8,E3,H4) * 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52...2.9...6515.71..... * PAIR A5: 7,8 COL A A3: 7,8,1,3 # reduction candidate for 7,8 A3: 1,3 # 15 pairs A3: 7,8 # 9 pairs * PAIR B6: 7,8 COL B B1: 7,8,3,6 # reduction candidate for 7,8 B1: 7,8 # 13 pairs B3: 7,8,3 # reduction candidate for 7,8 B3: 7,8 # 13 pairs * PAIR H4: 3,9 BLK 6 G4: 3,9,5 # reduction candidate for 3,9 G4: 3,9 # 13 pairs G4: 5 # 9 pairs * PAIR H4: 3,9 COL H H2: 3,9,1,8 # reduction candidate for 3,9 H2: 3,9 => CTR * 97....21..5..7.8..83.4..76..2.8....779....14848.7.9.26318652479249387651567194382 H7: 3,9,7 # reduction candidate for 3,9 H7: 3,9 # 11 pairs H9: 3,9,2,8 # reduction candidate for 3,9 H9: 3,9 => CTR * 97.5..2...5.97.....3.42.76..2.84..9779....14848.7.9.26318652.7.249387651567194832 * RESTART * PAIR H4: 3,9 COL H H7: 3,9,7 # reduction candidate for 3,9 H7: 7 => CTR * 97....2...5..7.....3.4..76..2.84..9779....14848.7.9.26318652.7.249387651567194382 * PAIR RESTART * PAIR H4: 3,9 BLK 6 G4: 3,9,5 # reduction candidate for 3,9 G4: 5 => CTR * 964...27..5327641917249..6.32.8..59779....14848.7.93266189527342.93.7651537164982 * PAIR A7: 3,6 BLK 7 B9: 3,6,4 # reduction candidate for 3,6 B9: 4 => CTR * 964...27..5297641...142..6..2.8....7.9....14.4....9....18.527.42.9...6515.71..... * PAIR A7: 3,6 COL A A2: 3,6,8 # reduction candidate for 3,6 A2: 8 => CTR * 9.4.1827.85..7.41.17249.86.625841..7793.2.148481739526318.527.42493876515.71.4.82 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A3,A5,B1,B6,C4,C5,D1,D8,F2,F4,F8,G6,G9,H6,H9,I2) * 9.4.6127.65297.41...142..6912.84.937.9..3.14.4.3.19..6318652794249.8.651567194... * PAIR B1: 3,8 BLK 1 B3: 3,8,7 # reduction candidate for 3,8 B3: 7 => CTR * 93456127865297841387142356912.84.93779.23.145483.19..6318652794249.8.651567194... * PAIR B1: 3,8 ROW 1 I1: 3,8,5 # reduction candidate for 3,8 I1: 3,8 => CTR * 9.456127.65297.41.7.142.56912.84.93789..3.1454732198.6318652794249.8.651567194... I1: 5 => SOLVED * 984361275652978413731425869125846937896537142473219586318652794249783651567194328 * DURATION: 0:00:22.498545 START: 07:04:45.316003 END: 07:05:07.814548 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06912919-base-pr-001.dot * REASONING * DIS # H2: 3,9 => CTR => H2: 1,8 * DIS H2: 1,8 # H9: 3,9 => CTR => H9: 2,8 * DIS H2: 1,8 + H9: 2,8 # H7: 7 => CTR => H7: 3,9 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 # G4: 5 => CTR => G4: 3,9 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 # B9: 4 => CTR => B9: 3,6 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 # A2: 8 => CTR => A2: 3,6 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 # B3: 7 => CTR => B3: 3,8 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 # I1: 3,8 => CTR => I1: 5 * PRF H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5 => SOL * STA H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5 * CNT 9 HDP CHAINS / 20 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6912919 umulig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 9.....2...5..7.......4...6..2.8....7.9....14.4....9....18.52...2.9...6515.71..... D2: 2,9 E3: 2,9 A5: 7,8 A3: 1,3,7,8 # reduction candidate for 7,8 B6: 7,8 B1: 3,6,7,8 # reduction candidate for 7,8 B3: 3,7,8 # reduction candidate for 7,8 H4: 3,9 G4: 3,5,9 # reduction candidate for 3,9 H2: 1,3,8,9 # reduction candidate for 3,9 H2: 3,9 => CTR * 97....21..5..7.8..83.4..76..2.8....779....14848.7.9.26318652479249387651567194382 H7: 3,7,9 # reduction candidate for 3,9 H7: 7 => CTR * 97.5..2...5.97.....3.42.76..2.84...779....14848.7.9.26318652.7.249387651567194..2 A7: 3,6 B9: 3,4,6 # reduction candidate for 3,6 B9: 4 => CTR * 964...27..5.27641978.49..6..268....7.9...714.47...9...6189527342397..651547163... A2: 3,6,8 # reduction candidate for 3,6 A2: 8 => CTR * 9.4.1827.85..7.41.17.4..86..25841..7793...1484817395263186527942493876515671.4.82 D8: 3,7 * ROUND 2: 9.4.6127.65297.41...142..6912.84.937.9..3.14.4.3.19..6318652794249.8.651567194... B1: 3,8 B3: 3,7,8 # reduction candidate for 3,8 B3: 7 => CTR * 93456127865297841387142356912.84.93779.23.145483.19..6318652794249.8.651567194... I1: 3,5,8 # reduction candidate for 3,8 I1: 3,8 => CTR * 9.456127.65297.41.7.142.56912.84.93789..3.1454732198.6318652794249.8.651567194... I1: 5 => SOLVED * 984361275652978413731425869125846937896537142473219586318652794249783651567194328 * SOLVED!
Solution
position: 984361275652978413731425869125846937896537142473219586318652794249783651567194328 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 # A3: 7,8 => UNS * INC # A3: 1,3 => UNS * INC # B1: 7,8 => UNS * INC # B3: 7,8 => UNS * INC # G4: 3,9 => UNS * INC # G4: 5 => UNS * DIS # H2: 3,9 => CTR => H2: 1,8 * INC # H2: 1,8 => UNS * INC # H7: 3,9 => UNS * DIS # H9: 3,9 => CTR => H9: 2,8 * INC # H9: 2,8 => UNS * INC # B9: 3,6 => UNS * DIS # B9: 4 => CTR => B9: 3,6 * INC # D7: 3,6 => UNS * DIS # D7: 9 => CTR => D7: 3,6 * INC # A2: 3,6 => UNS * INC # A4: 3,6 => UNS * DIS # B9: 3,4 => CTR => B9: 6 * INC # B9: 6 => UNS * INC # E8: 3,4 => UNS * INC # F8: 3,4 => UNS * INC # F8: 3,7 => UNS * INC # F8: 4,8 => UNS * DIS # D5: 3,7 => CTR => D5: 2,5,6 * INC # D5: 2,5,6 => UNS * INC # D6: 3,7 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 7,8 => UNS * INC # A3: 1,3 => UNS * INC # B1: 7,8 => UNS * INC # B3: 7,8 => UNS * INC # G4: 3,9 => UNS * INC # G4: 5 => UNS * DIS # H2: 3,9 => CTR => H2: 1,8 * INC H2: 1,8 # H7: 3,9 => UNS * DIS H2: 1,8 # H9: 3,9 => CTR => H9: 2,8 * INC H2: 1,8 + H9: 2,8 # H7: 3,9 => UNS * DIS H2: 1,8 + H9: 2,8 # H7: 7 => CTR => H7: 3,9 * INC H2: 1,8 + H9: 2,8 + H7: 3,9 # G4: 3,9 => UNS * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 # G4: 5 => CTR => G4: 3,9 * INC H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 # B9: 3,6 => UNS * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 # B9: 4 => CTR => B9: 3,6 * INC H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 # A2: 3,6 => UNS * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 # A2: 8 => CTR => A2: 3,6 * INC H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 # B3: 3,8 => UNS * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 # B3: 7 => CTR => B3: 3,8 * DIS H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 # I1: 3,8 => CTR => I1: 5 * PRF H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5 => SOL * STA H2: 1,8 + H9: 2,8 + H7: 3,9 + G4: 3,9 + B9: 3,6 + A2: 3,6 + B3: 3,8 + I1: 5 * CNT 21 HDP CHAINS / 20 HYP OPENED