Analysis of zz-menneske-no-06900773-base.sdk
Contents
Original Sudoku
level: medium
position: .6.4.3.........46...8.6...1..3....9259..7...66........1...4.97.............2.9.3. initial
Autosolve
position: .6.4.3.........46...8.6...1..3....9259..7...66........1...4.97.............2.9.3. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 3 => CTR => I2: 7,9 * DIS # C1: 7,9 => CTR => C1: 1,5 * DIS # G3: 2,5 => CTR => G3: 3,7 * DIS # G6: 3,7 => CTR => G6: 1,5,8 * DIS # B7: 5,8 => CTR => B7: 2,3 * CNT 5 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 # I2: 3 => CTR => I2: 7,9 * DIS I2: 7,9 # C1: 7,9 => CTR => C1: 1,5 * DIS I2: 7,9 + C1: 1,5 # A1: 2 => CTR => A1: 7,9 * PRF I2: 7,9 + C1: 1,5 + A1: 7,9 # C2: 1,5 => SOL * STA I2: 7,9 + C1: 1,5 + A1: 7,9 + C2: 1,5 * CNT 4 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.4.3.........46...8.6...1..3....9259..7...66........1...4.97.............2.9.3. | initial |
| .6.4.3.........46...8.6...1..3....9259..7...66........1...4.97.............2.9.3. | autosolve |
| 965413287371825469248967351813654792594372816627198543132546978489731625756289134 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) I1: 7,9 H3: 2,5 I6: 3,7 I7: 5,8 H8: 1,2 G9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,E1: 1.. / C1 = 1 => 7 pairs (_) / E1 = 1 => 24 pairs (_) E9,G9: 1.. / E9 = 1 => 8 pairs (_) / G9 = 1 => 22 pairs (_) B7,C7: 2.. / B7 = 2 => 0 pairs (X) / C7 = 2 => 9 pairs (_) G8,H8: 2.. / G8 = 2 => 7 pairs (_) / H8 = 2 => 22 pairs (_) C5,F5: 2.. / C5 = 2 => 0 pairs (X) / F5 = 2 => 8 pairs (_) B6,B7: 2.. / B6 = 2 => 9 pairs (_) / B7 = 2 => 0 pairs (X) I2,G3: 3.. / I2 = 3 => 0 pairs (X) / G3 = 3 => 10 pairs (_) D5,G5: 3.. / D5 = 3 => 10 pairs (_) / G5 = 3 => 0 pairs (X) B7,D7: 3.. / B7 = 3 => 9 pairs (_) / D7 = 3 => 0 pairs (X) E6,E8: 3.. / E6 = 3 => 0 pairs (X) / E8 = 3 => 9 pairs (_) I2,I6: 3.. / I2 = 3 => 0 pairs (X) / I6 = 3 => 10 pairs (_) A3,B3: 4.. / A3 = 4 => 0 pairs (X) / B3 = 4 => 6 pairs (_) H5,H6: 4.. / H5 = 4 => 7 pairs (_) / H6 = 4 => 9 pairs (_) I8,I9: 4.. / I8 = 4 => 7 pairs (_) / I9 = 4 => 8 pairs (_) D4,F4: 6.. / D4 = 6 => 6 pairs (_) / F4 = 6 => 12 pairs (_) G8,G9: 6.. / G8 = 6 => 22 pairs (_) / G9 = 6 => 8 pairs (_) C9,G9: 6.. / C9 = 6 => 22 pairs (_) / G9 = 6 => 8 pairs (_) D8,F8: 7.. / D8 = 7 => 7 pairs (_) / F8 = 7 => 9 pairs (_) G1,H1: 8.. / G1 = 8 => 11 pairs (_) / H1 = 8 => 7 pairs (_) I1,I2: 9.. / I1 = 9 => 7 pairs (_) / I2 = 9 => 9 pairs (_) D6,E6: 9.. / D6 = 9 => 0 pairs (X) / E6 = 9 => 9 pairs (_) A8,C8: 9.. / A8 = 9 => 10 pairs (_) / C8 = 9 => 6 pairs (_) A3,D3: 9.. / A3 = 9 => 0 pairs (X) / D3 = 9 => 9 pairs (_) * DURATION: 0:00:34.313158 START: 06:34:42.430565 END: 06:35:16.743723 2017-05-01 * CP COUNT: (23) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (G9,H3,H8,I1,I6,I7) * .6.4.3.........46...8.6...1..3....9259..7...66........1...4.97.............2.9.3. * PAIR I1: 7,9 BLK 3 I2: 7,9,3 # reduction candidate for 7,9 I2: 3 => CTR * .6.413..9.1..2.46334896...1..365419259..72..662..9...7132.4697.....3..1....28963. I2: 7,9 # 10 pairs * PAIR I1: 7,9 ROW 1 A1: 7,9,2 # reduction candidate for 7,9 A1: 7,9 # 9 pairs C1: 7,9,1,5 # reduction candidate for 7,9 C1: 7,9 => CTR * .6.413.........46...8.6..51..3....9259..7...66........1...4.97.......62...62.913. C1: 1,5 # 7 pairs * PAIR H3: 2,5 BLK 3 G1: 2,5,7,8 # reduction candidate for 2,5 G1: 2,5 # 9 pairs H1: 2,5,8 # reduction candidate for 2,5 H1: 2,5 # 11 pairs G3: 2,5,3,7 # reduction candidate for 2,5 G3: 2,5 => CTR * 26.453789..7128463348967251.13...59259..72..662..9...7132.4.978...73162...628913. G3: 3,7 # 7 pairs * PAIR H3: 2,5 ROW 3 F3: 2,5,7 # reduction candidate for 2,5 F3: 2,5 # 9 pairs F3: 7 # 7 pairs * PAIR I6: 3,7 BLK 6 G6: 3,7,1,5,8 # reduction candidate for 3,7 G6: 3,7 => CTR * .6.413....1..2.46...8.6...1..3654192591372846624.9..5.132.4697.....3..1....28963. G6: 1,5,8 # 6 pairs * PAIR I6: 3,7 COL I I2: 3,7,9 # reduction candidate for 3,7 I2: 9 # 9 pairs I2: 3,7 # 7 pairs * PAIR I7: 5,8 BLK 9 I8: 5,8,4 # reduction candidate for 5,8 I8: 5,8 # 8 pairs I9: 5,8,4 # reduction candidate for 5,8 I9: 5,8 # 7 pairs * PAIR I7: 5,8 ROW 7 B7: 5,8,2,3 # reduction candidate for 5,8 B7: 5,8 => CTR * .6.4.3..9....9.4639.8.6...1..36...9259..723.662..3...71.234697.............2.9.3. B7: 2,3 # 7 pairs D7: 5,8,3,6 # reduction candidate for 5,8 D7: 5,8 # 10 pairs F7: 5,8,6 # reduction candidate for 5,8 F7: 5,8 # 10 pairs * PAIR H8: 1,2 BLK 9 G8: 1,2,6 # reduction candidate for 1,2 G8: 6 # 22 pairs G8: 1,2 # 8 pairs * PAIR G9: 1,6 BLK 9 G8: 1,6,2 # reduction candidate for 1,6 G8: 1,6 # 22 pairs G8: 2 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06900773-base-pr-000.dot * REASONING * DIS # I2: 3 => CTR => I2: 7,9 * DIS # C1: 7,9 => CTR => C1: 1,5 * DIS # G3: 2,5 => CTR => G3: 3,7 * DIS # G6: 3,7 => CTR => G6: 1,5,8 * DIS # B7: 5,8 => CTR => B7: 2,3 * CNT 5 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (G9,H3,H8,I1,I6,I7) * .6.4.3.........46...8.6...1..3....9259..7...66........1...4.97.............2.9.3. * PAIR I1: 7,9 BLK 3 I2: 7,9,3 # reduction candidate for 7,9 I2: 3 => CTR * .6.413..9.1..2.46334896...1..365419259..72..662..9...7132.4697.....3..1....28963. * PAIR I1: 7,9 ROW 1 A1: 7,9,2 # reduction candidate for 7,9 A1: 7,9 # 19 pairs C1: 7,9,1,5 # reduction candidate for 7,9 C1: 7,9 => CTR * .6.413...3...2.46...8.6.3.1..3.5.79259.3728.6627.9.5.3132.4.978....3.62....28913. * RESTART * PAIR I1: 7,9 ROW 1 A1: 7,9,2 # reduction candidate for 7,9 A1: 2 => CTR * 26.4.3..73...2.469948.6.321..3....9259.372..662.9....3132.4.97...9.3.......2.9.3. * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A9,B8,B9,C1,C5,D7,E1,E4,F2,F7,G4,G6,H5,H6,I1,I2,I8,I9) * .6.4.328.3...2.46.248967351..3....9259.3728.662..9...3132.4.978...73162...628913. * PAIR A1: 7,9 BLK 1 C2: 7,9,1,5 # reduction candidate for 7,9 C2: 1,5 => SOLVED * 965413287371825469248967351813654792594372816627198543132546978489731625756289134 * DURATION: 0:00:10.565049 START: 06:35:37.848269 END: 06:35:48.413318 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06900773-base-pr-001.dot * REASONING * DIS # I2: 3 => CTR => I2: 7,9 * DIS I2: 7,9 # C1: 7,9 => CTR => C1: 1,5 * DIS I2: 7,9 + C1: 1,5 # A1: 2 => CTR => A1: 7,9 * PRF I2: 7,9 + C1: 1,5 + A1: 7,9 # C2: 1,5 => SOL * STA I2: 7,9 + C1: 1,5 + A1: 7,9 + C2: 1,5 * CNT 4 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6900773 umulig * PAIR REDUCTION .. * ROUND 1: .6.4.3.........46...8.6...1..3....9259..7...66........1...4.97.............2.9.3. I1: 7,9 I2: 3,7,9 # reduction candidate for 7,9 I2: 3 => CTR * .6.413..9.1..2.46334896...1..365419259..72..662..9...7132.4697.....3..1....28963. A1: 2,7,9 # reduction candidate for 7,9 A1: 2 => CTR * 2614.3..73...2.469948.6.321.13.5.792594372..662......3132.4.97.....3.21....21963. * ROUND 2: .6.4.328.3...2.46.248967351..3....9259.3728.662..9...3132.4.978...73162...628913. A1: 7,9 C2: 1,5,7,9 # reduction candidate for 7,9 C2: 1,5 => SOLVED * 965413287371825469248967351813654792594372816627198543132546978489731625756289134 * SOLVED! |:step:| 00 -------------------------------------------------- I2 != 3 G8 != 2 D6 != 8 => SOL H2 = 8 D4 = 6 F4 = 4 H6 != 5 B4 = 1 => SOL F6 = 8 => SOL |:step:| 01 --------------------------------------------------
Solution
position: 965413287371825469248967351813654792594372816627198543132546978489731625756289134 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 # I2: 7,9 => UNS * DIS # I2: 3 => CTR => I2: 7,9 * INC # A1: 7,9 => UNS * DIS # C1: 7,9 => CTR => C1: 1,5 * INC # C1: 1,5 => UNS * INC # G1: 2,5 => UNS * INC # H1: 2,5 => UNS * DIS # G3: 2,5 => CTR => G3: 3,7 * INC # G3: 3,7 => UNS * INC # F3: 2,5 => UNS * INC # F3: 7 => UNS * DIS # G6: 3,7 => CTR => G6: 1,5,8 * INC # G6: 1,5,8 => UNS * INC # I2: 3,7 => UNS * INC # I2: 9 => UNS * INC # I8: 5,8 => UNS * INC # I9: 5,8 => UNS * DIS # B7: 5,8 => CTR => B7: 2,3 * INC # B7: 2,3 => UNS * INC # D7: 5,8 => UNS * INC # F7: 5,8 => UNS * INC # G8: 1,2 => UNS * INC # G8: 6 => UNS * INC # G8: 1,6 => UNS * INC # G8: 2 => UNS * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I2: 7,9 => UNS * DIS # I2: 3 => CTR => I2: 7,9 * INC I2: 7,9 # A1: 7,9 => UNS * DIS I2: 7,9 # C1: 7,9 => CTR => C1: 1,5 * INC I2: 7,9 + C1: 1,5 # A1: 7,9 => UNS * DIS I2: 7,9 + C1: 1,5 # A1: 2 => CTR => A1: 7,9 * INC I2: 7,9 + C1: 1,5 + A1: 7,9 # C2: 7,9 => UNS * PRF I2: 7,9 + C1: 1,5 + A1: 7,9 # C2: 1,5 => SOL * STA I2: 7,9 + C1: 1,5 + A1: 7,9 + C2: 1,5 * CNT 8 HDP CHAINS / 8 HYP OPENED