Analysis of zz-menneske-no-06912341-base.sdk
Contents
Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6912341
level: medium
position: ...2.8........9.3..8.....45......5.4.76....2.2.9.........93.8...2.......3..7.4... initial
Autosolve
position: ...2.8........9.38.8.....45...6..5.4.76....2.2.9....8....93.8...2....4.33..7.4... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D5: 1,3 => CTR => D5: 4,5,8 * DIS # C4: 3 => CTR => C4: 1,8 * DIS # A8: 1,8 => CTR => A8: 5,6,7,9 * DIS # C4: 8 => CTR => C4: 1,3 * DIS # B1: 1,3 => CTR => B1: 4,5,6,9 * DIS # D5: 4,5 => CTR => D5: 1,3,8 * DIS # E5: 4,5 => CTR => E5: 1,8,9 * DIS # A2: 4,5 => CTR => A2: 1,6,7 * DIS # A7: 4,5 => CTR => A7: 1,6,7 * DIS # B1: 4,5 => CTR => B1: 1,3,6,9 * PRF # E4: 2,7 => SOL * DIS # E4: 9 => CTR => E4: 2,7 * PRF # E4: 7,9 => SOL * DIS # E4: 2 => CTR => E4: 7,9 * DIS # H1: 7,9 => CTR => H1: 1,6 * DIS # G5: 1,9 => CTR => G5: 3 * DIS # E5: 4,5,8 => CTR => E5: 1,9 * PRF # I9: 1,9 => SOL * CNT 18 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D5: 1,3 => CTR => D5: 4,5,8 * DIS D5: 4,5,8 # C4: 3 => CTR => C4: 1,8 * DIS D5: 4,5,8 + C4: 1,8 # A8: 1,8 => CTR => A8: 5,6,7,9 * DIS D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 # D5: 4,5 => CTR => D5: 8 * DIS D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 + D5: 8 # E5: 4,5 => CTR => E5: 1,9 * PRF D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 + D5: 8 + E5: 1,9 # E4: 2,7 => SOL * STA D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 + D5: 8 + E5: 1,9 + E4: 2,7 * CNT 6 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2.8........9.3..8.....45......5.4.76....2.2.9.........93.8...2.......3..7.4... | initial |
| ...2.8........9.38.8.....45...6..5.4.76....2.2.9....8....93.8...2....4.33..7.4... | autosolve |
| 593248167764159238182367945831672594476895321259413786645931872927586413318724659 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) D3: 1,3 A4: 1,8 B4: 1,3 A5: 4,5 B6: 4,5 F4: 2,7 H4: 7,9 I5: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 2.. / C2 = 2 => 0 pairs (X) / C3 = 2 => 8 pairs (_) G2,G3: 2.. / G2 = 2 => 8 pairs (_) / G3 = 2 => 0 pairs (X) E4,F4: 2.. / E4 = 2 => 0 pairs (X) / F4 = 2 => 0 pairs (_) F7,E9: 2.. / F7 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) I7,I9: 2.. / I7 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) C2,G2: 2.. / C2 = 2 => 0 pairs (X) / G2 = 2 => 8 pairs (_) C3,G3: 2.. / C3 = 2 => 8 pairs (_) / G3 = 2 => 0 pairs (X) F7,I7: 2.. / F7 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) E9,I9: 2.. / E9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) E4,E9: 2.. / E4 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) F4,F7: 2.. / F4 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) B1,C1: 3.. / B1 = 3 => 0 pairs (X) / C1 = 3 => 8 pairs (_) D3,F3: 3.. / D3 = 3 => 7 pairs (_) / F3 = 3 => 13 pairs (_) B4,C4: 3.. / B4 = 3 => 8 pairs (_) / C4 = 3 => 0 pairs (X) G5,G6: 3.. / G5 = 3 => 9 pairs (_) / G6 = 3 => 0 pairs (X) B1,B4: 3.. / B1 = 3 => 0 pairs (X) / B4 = 3 => 8 pairs (_) C1,C4: 3.. / C1 = 3 => 8 pairs (_) / C4 = 3 => 0 pairs (X) A5,B6: 4.. / A5 = 4 => 6 pairs (_) / B6 = 4 => 0 pairs (X) A5,B6: 5.. / A5 = 5 => 0 pairs (X) / B6 = 5 => 6 pairs (_) G6,I6: 6.. / G6 = 6 => 12 pairs (_) / I6 = 6 => 8 pairs (_) A4,C4: 8.. / A4 = 8 => 8 pairs (_) / C4 = 8 => 0 pairs (X) D5,E5: 8.. / D5 = 8 => 9 pairs (_) / E5 = 8 => 0 pairs (X) C9,E9: 8.. / C9 = 8 => 8 pairs (_) / E9 = 8 => 0 pairs (X) A4,A8: 8.. / A4 = 8 => 8 pairs (_) / A8 = 8 => 0 pairs (X) D5,D8: 8.. / D5 = 8 => 9 pairs (_) / D8 = 8 => 0 pairs (X) E4,E5: 9.. / E4 = 9 => 0 pairs (X) / E5 = 9 => 0 pairs (_) A8,B9: 9.. / A8 = 9 => 11 pairs (_) / B9 = 9 => 0 pairs (X) A3,G3: 9.. / A3 = 9 => 0 pairs (X) / G3 = 9 => 11 pairs (_) E4,H4: 9.. / E4 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) A8,H8: 9.. / A8 = 9 => 11 pairs (_) / H8 = 9 => 0 pairs (X) B1,B9: 9.. / B1 = 9 => 11 pairs (_) / B9 = 9 => 0 pairs (X) * DURATION: 0:00:45.272740 START: 06:58:35.553749 END: 06:59:20.826489 2017-05-01 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B4,B6,D3,F4,H4,I5) * ...2.8........9.38.8.....45...6..5.4.76....2.2.9....8....93.8...2....4.33..7.4... * PAIR D3: 1,3 BLK 2 F3: 1,3,6,7 # reduction candidate for 1,3 F3: 1,3 # 13 pairs F3: 6,7 # 8 pairs * PAIR D3: 1,3 COL D D5: 1,3,4,5,8 # reduction candidate for 1,3 D5: 1,3 => CTR * ...2.8........9.38.8.....458..692574476.85.2.259....8....93.8...2.8..4.33.87.4... D5: 4,5,8 # 8 pairs D6: 1,3,4,5 # reduction candidate for 1,3 D6: 1,3 # 11 pairs * PAIR A4: 1,8 BLK 4 C4: 1,8,3 # reduction candidate for 1,8 C4: 3 => CTR * .3.2.8........9.38.8.....45813692574.76....2.2.9....8....93.8...2....49339.7.4... C4: 1,8 # 8 pairs * PAIR A4: 1,8 COL A A8: 1,8,5,6,7,9 # reduction candidate for 1,8 A8: 1,8 => CTR * ...2.8........9.38.8.....45...692574.76....2.2.9....8....93.8...2....49339.7.4... A8: 5,6,7,9 # 8 pairs * PAIR B4: 1,3 BLK 4 C4: 1,3,8 # reduction candidate for 1,3 C4: 8 => CTR * ..32.8........9.38.8.....45.386..5.4.76....2.2.9....8....93.8..82....49339.784..2 C4: 1,3 # 8 pairs * PAIR B4: 1,3 COL B B1: 1,3,4,5,6,9 # reduction candidate for 1,3 B1: 1,3 => CTR * ...2.8........9.38.8.....45...692574.76....2.2.9....8....93.8...2....49339.7.4... B1: 4,5,6,9 # 8 pairs * PAIR A5: 4,5 ROW 5 D5: 4,5,1,3,8 # reduction candidate for 4,5 D5: 4,5 => CTR * ...2.8........9.38.8.....458..692574.76.8..2.2.9....8....93.8...2.8..4.33.87.4... D5: 1,3,8 # 8 pairs E5: 4,5,1,8,9 # reduction candidate for 4,5 E5: 4,5 => CTR * ...2.8........9.38.8.....45...692574.768...2.2.9....8....93.8...2....4.33..7.4... E5: 1,8,9 # 8 pairs * PAIR A5: 4,5 COL A A1: 4,5,1,6,7,9 # reduction candidate for 4,5 A1: 4,5 # 9 pairs A2: 4,5,1,6,7 # reduction candidate for 4,5 A2: 4,5 => CTR * ...2.8........9.38.8.....45...692574.76....2.2.9....8....93.8...2....49339.7.4... A2: 1,6,7 # 8 pairs A7: 4,5,1,6,7 # reduction candidate for 4,5 A7: 4,5 => CTR * ...2.8........9.38.8.....45...692574.76....2.2.9....8....93.8...2....49339.7.4... A7: 1,6,7 # 8 pairs * PAIR B6: 4,5 ROW 6 D6: 4,5,1,3 # reduction candidate for 4,5 D6: 4,5 # 10 pairs E6: 4,5,1,7 # reduction candidate for 4,5 E6: 4,5 # 12 pairs * PAIR B6: 4,5 COL B B1: 4,5,1,3,6,9 # reduction candidate for 4,5 B1: 4,5 => CTR * ..32.8........9.38.8.....45.3.692574.76....2.2.9....8....93.8...2....49339.7.4... B1: 1,3,6,9 # 8 pairs B2: 4,5,1,6 # reduction candidate for 4,5 B2: 4,5 # 10 pairs B7: 4,5,1,6 # reduction candidate for 4,5 B7: 4,5 # 10 pairs * PAIR F4: 2,7 BLK 5 E4: 2,7,9 # reduction candidate for 2,7 E4: 2,7 => SOLVED * 593248167764159238182367945831672594476895321259413786645931872927586413318724659 E4: 9 => CTR * ...2.8........9.38.8.....45...692574.76....2.2.9....8....93.8...2....4.33..7.4... * PAIR H4: 7,9 ROW 4 E4: 7,9,2 # reduction candidate for 7,9 E4: 7,9 => SOLVED * 593248167764159238182367945831672594476895321259413786645931872927586413318724659 E4: 2 => CTR * .932.8........9.38.8....945831627594.7689.3212.9....8....9328..92....4.33..7.4..2 * PAIR H4: 7,9 COL H H1: 7,9,1,6 # reduction candidate for 7,9 H1: 7,9 => CTR * .932.8.7......9.38.8.....45.3.627594.76.9..212.9...786...93.8...2....4.33..7.49.2 H1: 1,6 # 9 pairs H8: 7,9,1,5,6 # reduction candidate for 7,9 H8: 7,9 # 10 pairs * PAIR I5: 1,9 BLK 6 G5: 1,9,3 # reduction candidate for 1,9 G5: 1,9 => CTR * ...2.8........9.38.8.....45...6..574.76....2.2.9...386...93.8.7.2....4.33..7.4..2 G5: 3 # 9 pairs * PAIR I5: 1,9 ROW 5 E5: 1,9,4,5,8 # reduction candidate for 1,9 E5: 4,5,8 => CTR * ...2.8........9.38.8.....45...692574.76....2.2.9....8....93.8...2....4.33..7.4... E5: 1,9 # 9 pairs * PAIR I5: 1,9 COL I I1: 1,9,6,7 # reduction candidate for 1,9 I1: 1,9 # 11 pairs I9: 1,9,2,6 # reduction candidate for 1,9 I9: 1,9 => SOLVED * 593248167764159238182367945831672594476895321259413786645931872927586413318724659 I9: 2,6 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06912341-base-pr-000.dot * REASONING * DIS # D5: 1,3 => CTR => D5: 4,5,8 * DIS # C4: 3 => CTR => C4: 1,8 * DIS # A8: 1,8 => CTR => A8: 5,6,7,9 * DIS # C4: 8 => CTR => C4: 1,3 * DIS # B1: 1,3 => CTR => B1: 4,5,6,9 * DIS # D5: 4,5 => CTR => D5: 1,3,8 * DIS # E5: 4,5 => CTR => E5: 1,8,9 * DIS # A2: 4,5 => CTR => A2: 1,6,7 * DIS # A7: 4,5 => CTR => A7: 1,6,7 * DIS # B1: 4,5 => CTR => B1: 1,3,6,9 * PRF # E4: 2,7 => SOL * DIS # E4: 9 => CTR => E4: 2,7 * PRF # E4: 7,9 => SOL * DIS # E4: 2 => CTR => E4: 7,9 * DIS # H1: 7,9 => CTR => H1: 1,6 * DIS # G5: 1,9 => CTR => G5: 3 * DIS # E5: 4,5,8 => CTR => E5: 1,9 * PRF # I9: 1,9 => SOL * CNT 18 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B4,B6,D3,F4,H4,I5) * ...2.8........9.38.8.....45...6..5.4.76....2.2.9....8....93.8...2....4.33..7.4... * PAIR D3: 1,3 BLK 2 F3: 1,3,6,7 # reduction candidate for 1,3 F3: 1,3 # 13 pairs F3: 6,7 # 8 pairs * PAIR D3: 1,3 COL D D5: 1,3,4,5,8 # reduction candidate for 1,3 D5: 1,3 => CTR * ...2.8........9.38.8.....458..692574476.85.2.259....8....93.8...2.8..4.33.87.4... D6: 1,3,4,5 # reduction candidate for 1,3 D6: 1,3 # 11 pairs * RESTART * PAIR D3: 1,3 COL D D6: 1,3,4,5 # reduction candidate for 1,3 D6: 1,3 # 11 pairs D6: 4,5 # 9 pairs * PAIR RESTART * PAIR D3: 1,3 BLK 2 F3: 1,3,6,7 # reduction candidate for 1,3 F3: 1,3 # 13 pairs F3: 6,7 # 8 pairs * PAIR D3: 1,3 COL D D6: 1,3,4,5 # reduction candidate for 1,3 D6: 1,3 # 11 pairs D6: 4,5 # 9 pairs * PAIR A4: 1,8 BLK 4 C4: 1,8,3 # reduction candidate for 1,8 C4: 3 => CTR * .3.2.8........9.38.8.....45813692574.76....2.2.9....8....93.8...2....49339.7.4... * PAIR A4: 1,8 COL A A8: 1,8,5,6,7,9 # reduction candidate for 1,8 A8: 1,8 => CTR * ..32.8........9.38.8.....45.3.692574.76....2.2.9....8....93.8...2....49339.7.4... * PAIR RESTART * PAIR A5: 4,5 ROW 5 D5: 4,5,8 # reduction candidate for 4,5 D5: 4,5 => CTR * ..32.8........9.38.8.....45831692574.76.8..2.2.9....8....93.8...2.8..4.33.87.4... E5: 4,5,1,9 # reduction candidate for 4,5 E5: 4,5 => CTR * ..32.8........9.38.8.....45831692574.768...2.2.9....8....93.8...2....4.33..7.4... * PAIR RESTART * PAIR F4: 2,7 BLK 5 E4: 2,7,9 # reduction candidate for 2,7 E4: 2,7 => SOLVED * 593248167764159238182367945831672594476895321259413786645931872927586413318724659 * DURATION: 0:00:14.111283 START: 06:59:52.473015 END: 07:00:06.584298 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06912341-base-pr-001.dot * REASONING * DIS # D5: 1,3 => CTR => D5: 4,5,8 * DIS D5: 4,5,8 # C4: 3 => CTR => C4: 1,8 * DIS D5: 4,5,8 + C4: 1,8 # A8: 1,8 => CTR => A8: 5,6,7,9 * DIS D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 # D5: 4,5 => CTR => D5: 8 * DIS D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 + D5: 8 # E5: 4,5 => CTR => E5: 1,9 * PRF D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 + D5: 8 + E5: 1,9 # E4: 2,7 => SOL * STA D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 + D5: 8 + E5: 1,9 + E4: 2,7 * CNT 6 HDP CHAINS / 16 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6912341 umulig
Solution
position: 593248167764159238182367945831672594476895321259413786645931872927586413318724659 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 # F3: 1,3 => UNS * INC # F3: 6,7 => UNS * DIS # D5: 1,3 => CTR => D5: 4,5,8 * INC # D5: 4,5,8 => UNS * INC # D6: 1,3 => UNS * INC # C4: 1,8 => UNS * DIS # C4: 3 => CTR => C4: 1,8 * DIS # A8: 1,8 => CTR => A8: 5,6,7,9 * INC # A8: 5,6,7,9 => UNS * INC # C4: 1,3 => UNS * DIS # C4: 8 => CTR => C4: 1,3 * DIS # B1: 1,3 => CTR => B1: 4,5,6,9 * INC # B1: 4,5,6,9 => UNS * DIS # D5: 4,5 => CTR => D5: 1,3,8 * INC # D5: 1,3,8 => UNS * DIS # E5: 4,5 => CTR => E5: 1,8,9 * INC # E5: 1,8,9 => UNS * INC # A1: 4,5 => UNS * DIS # A2: 4,5 => CTR => A2: 1,6,7 * INC # A2: 1,6,7 => UNS * DIS # A7: 4,5 => CTR => A7: 1,6,7 * INC # A7: 1,6,7 => UNS * INC # D6: 4,5 => UNS * INC # E6: 4,5 => UNS * DIS # B1: 4,5 => CTR => B1: 1,3,6,9 * INC # B1: 1,3,6,9 => UNS * INC # B2: 4,5 => UNS * INC # B7: 4,5 => UNS * PRF # E4: 2,7 => SOL * DIS # E4: 9 => CTR => E4: 2,7 * PRF # E4: 7,9 => SOL * DIS # E4: 2 => CTR => E4: 7,9 * DIS # H1: 7,9 => CTR => H1: 1,6 * INC # H1: 1,6 => UNS * INC # H8: 7,9 => UNS * DIS # G5: 1,9 => CTR => G5: 3 * INC # G5: 3 => UNS * INC # E5: 1,9 => UNS * DIS # E5: 4,5,8 => CTR => E5: 1,9 * INC # I1: 1,9 => UNS * PRF # I9: 1,9 => SOL * INC # I9: 2,6 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F3: 1,3 => UNS * INC # F3: 6,7 => UNS * DIS # D5: 1,3 => CTR => D5: 4,5,8 * INC D5: 4,5,8 # D6: 1,3 => UNS * INC D5: 4,5,8 # D6: 1,3 => UNS * INC D5: 4,5,8 # D6: 4,5 => UNS * INC D5: 4,5,8 # F3: 1,3 => UNS * INC D5: 4,5,8 # F3: 6,7 => UNS * INC D5: 4,5,8 # D6: 1,3 => UNS * INC D5: 4,5,8 # D6: 4,5 => UNS * INC D5: 4,5,8 # C4: 1,8 => UNS * DIS D5: 4,5,8 # C4: 3 => CTR => C4: 1,8 * DIS D5: 4,5,8 + C4: 1,8 # A8: 1,8 => CTR => A8: 5,6,7,9 * DIS D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 # D5: 4,5 => CTR => D5: 8 * DIS D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 + D5: 8 # E5: 4,5 => CTR => E5: 1,9 * PRF D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 + D5: 8 + E5: 1,9 # E4: 2,7 => SOL * STA D5: 4,5,8 + C4: 1,8 + A8: 5,6,7,9 + D5: 8 + E5: 1,9 + E4: 2,7 * CNT 16 HDP CHAINS / 16 HYP OPENED