Analysis of zz-www.sudokuwiki.org-0080-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=80
level: medium
position: 1....7..5.3.6..7....7....4..52......6...8...2......43..6....1....5..3.2.9..1....8 initial
Autosolve
position: 1.6..7..5.3.6..7....7....4..52...8..6...8...2......43..6....1...15..3.2.9..1....8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G3: 2,3 => SOL * DIS # H2: 1 => CTR => H2: 8,9 * DIS # H2: 1,9 => CTR => H2: 8 * DIS # G3: 2 => CTR => G3: 3,6 * DIS # A7: 7,8 => CTR => A7: 2,3,4 * DIS # C7: 3,4 => CTR => C7: 8 * PRF # C5: 3,4 => SOL * DIS # C5: 1,9 => CTR => C5: 3,4 * CNT 8 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G3: 2,3 => SOL * STA G3: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1....7..5.3.6..7....7....4..52......6...8...2......43..6....1....5..3.2.9..1....8 | initial |
| 1.6..7..5.3.6..7....7....4..52...8..6...8...2......43..6....1...15..3.2.9..1....8 | autosolve |
| 186437295439625781527918346352741869674389512891256437268594173715863924943172658 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) G1: 2,3 H1: 8,9 I2: 1,9 I3: 3,6 A6: 7,8 G5: 5,9 C9: 3,4 G8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 1.. / E3 = 1 => 8 pairs (_) / F3 = 1 => 9 pairs (_) H2,I2: 1.. / H2 = 1 => 0 pairs (X) / I2 = 1 => 9 pairs (_) C5,C6: 1.. / C5 = 1 => 0 pairs (X) / C6 = 1 => 8 pairs (_) G1,G3: 2.. / G1 = 2 => 8 pairs (_) / G3 = 2 => 0 pairs (X) A7,B9: 2.. / A7 = 2 => 11 pairs (_) / B9 = 2 => 15 pairs (_) A4,C5: 3.. / A4 = 3 => 9 pairs (_) / C5 = 3 => 0 pairs (X) I7,G9: 3.. / I7 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) C5,D5: 3.. / C5 = 3 => 0 pairs (X) / D5 = 3 => 9 pairs (_) C9,G9: 3.. / C9 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) A4,A7: 3.. / A4 = 3 => 9 pairs (_) / A7 = 3 => 0 pairs (X) I3,I7: 3.. / I3 = 3 => 12 pairs (_) / I7 = 3 => 0 pairs (*) I7,I8: 4.. / I7 = 4 => 12 pairs (_) / I8 = 4 => 11 pairs (_) A2,A3: 5.. / A2 = 5 => 9 pairs (_) / A3 = 5 => 8 pairs (_) G5,H5: 5.. / G5 = 5 => 8 pairs (_) / H5 = 5 => 0 pairs (X) G5,G9: 5.. / G5 = 5 => 8 pairs (_) / G9 = 5 => 0 pairs (X) G3,I3: 6.. / G3 = 6 => 12 pairs (_) / I3 = 6 => 0 pairs (*) H4,H9: 6.. / H4 = 6 => 12 pairs (_) / H9 = 6 => 13 pairs (_) H1,H2: 8.. / H1 = 8 => 0 pairs (X) / H2 = 8 => 8 pairs (_) A8,D8: 8.. / A8 = 8 => 0 pairs (X) / D8 = 8 => 9 pairs (_) G5,G8: 9.. / G5 = 9 => 0 pairs (X) / G8 = 9 => 8 pairs (_) * DURATION: 0:00:27.887257 START: 04:52:19.862170 END: 04:52:47.749427 2017-05-01 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C9,G1,G5,G8,H1,I2,I3) * 1.6..7..5.3.6..7....7....4..52...8..6...8...2......43..6....1...15..3.2.9..1....8 * PAIR G1: 2,3 BLK 3 G3: 2,3,6 # reduction candidate for 2,3 G3: 2,3 => SOLVED * 186437295439625781527918346352741869674389512891256437268594173715863924943172658 G3: 6 # 12 pairs * PAIR G1: 2,3 ROW 1 D1: 2,3,4,8,9 # reduction candidate for 2,3 D1: 2,3 # 10 pairs E1: 2,3,4,9 # reduction candidate for 2,3 E1: 2,3 # 9 pairs * PAIR H1: 8,9 BLK 3 H2: 8,9,1 # reduction candidate for 8,9 H2: 1 => CTR * 1.6.372854386..719527...643352...89.64.38.572.8.5..43.263...15.815.6392.9741..368 H2: 8,9 # 9 pairs * PAIR H1: 8,9 ROW 1 B1: 8,9,2,4 # reduction candidate for 8,9 B1: 8,9 # 9 pairs D1: 8,9,2,3,4 # reduction candidate for 8,9 D1: 8,9 # 10 pairs * PAIR I2: 1,9 BLK 3 H2: 1,9,8 # reduction candidate for 1,9 H2: 1,9 => CTR * 1.6.372854386..7..527...643352...8..64.38.572.8.5..43.263...15.815.6392.9741..368 H2: 8 # 8 pairs * PAIR I2: 1,9 COL I I4: 1,9,6,7 # reduction candidate for 1,9 I4: 1,9 # 10 pairs I6: 1,9,6,7 # reduction candidate for 1,9 I6: 1,9 # 13 pairs * PAIR I3: 3,6 BLK 3 G3: 3,6,2 # reduction candidate for 3,6 G3: 2 => CTR * 1.6..73.5.396.87....7.31246352...86.674389512891...437.68...1.37158.39249.31..6.8 G3: 3,6 # 8 pairs * PAIR A6: 7,8 BLK 4 B6: 7,8,9 # reduction candidate for 7,8 B6: 9 # 12 pairs B6: 7,8 # 12 pairs * PAIR A6: 7,8 COL A A7: 7,8,2,3,4 # reduction candidate for 7,8 A7: 7,8 => CTR * 1.6..7..5.3.6..7....7....4.352...8..6..38...28.....43.768...1.34158.3.2.9231....8 A7: 2,3,4 # 8 pairs A8: 7,8,4 # reduction candidate for 7,8 A8: 7,8 # 11 pairs * PAIR G5: 5,9 BLK 6 H5: 5,9,1,7 # reduction candidate for 5,9 H5: 5,9 # 11 pairs H5: 1,7 # 9 pairs * PAIR C9: 3,4 BLK 7 A7: 3,4,2,7,8 # reduction candidate for 3,4 A7: 3,4 # 15 pairs C7: 3,4,8 # reduction candidate for 3,4 C7: 3,4 => CTR * 1.6.372.543.6..7..527...643352...8..64.38.5727..5..43.263...15.815.6392.9741..368 C7: 8 # 11 pairs * PAIR C9: 3,4 COL C C5: 3,4,1,9 # reduction candidate for 3,4 C5: 3,4 => SOLVED * 186437295439625781527918346352741869674389512891256437268594173715863924943172658 C5: 1,9 => CTR * 1.6.372.543.6..7..527...643352...8..64.38.572...5..43.263...15.815.6392.9741..368 * PAIR G8: 6,9 BLK 9 I8: 6,9,4,7 # reduction candidate for 6,9 I8: 6,9 # 15 pairs I8: 4,7 # 9 pairs * PAIR G8: 6,9 ROW 8 E8: 6,9,4,7 # reduction candidate for 6,9 E8: 4,7 # 14 pairs E8: 6,9 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0080-base-pr-000.dot * REASONING * PRF # G3: 2,3 => SOL * DIS # H2: 1 => CTR => H2: 8,9 * DIS # H2: 1,9 => CTR => H2: 8 * DIS # G3: 2 => CTR => G3: 3,6 * DIS # A7: 7,8 => CTR => A7: 2,3,4 * DIS # C7: 3,4 => CTR => C7: 8 * PRF # C5: 3,4 => SOL * DIS # C5: 1,9 => CTR => C5: 3,4 * CNT 8 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C9,G1,G5,G8,H1,I2,I3) * 1.6..7..5.3.6..7....7....4..52...8..6...8...2......43..6....1...15..3.2.9..1....8 * PAIR G1: 2,3 BLK 3 G3: 2,3,6 # reduction candidate for 2,3 G3: 2,3 => SOLVED * 186437295439625781527918346352741869674389512891256437268594173715863924943172658 * DURATION: 0:00:02.800826 START: 04:53:10.081967 END: 04:53:12.882793 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0080-base-pr-001.dot * REASONING * PRF # G3: 2,3 => SOL * STA G3: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=80
Solution
position: 186437295439625781527918346352741869674389512891256437268594173715863924943172658 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 # G3: 2,3 => SOL * INC # G3: 6 => UNS * INC # D1: 2,3 => UNS * INC # E1: 2,3 => UNS * INC # H2: 8,9 => UNS * DIS # H2: 1 => CTR => H2: 8,9 * INC # B1: 8,9 => UNS * INC # D1: 8,9 => UNS * DIS # H2: 1,9 => CTR => H2: 8 * INC # H2: 8 => UNS * INC # I4: 1,9 => UNS * INC # I6: 1,9 => UNS * INC # G3: 3,6 => UNS * DIS # G3: 2 => CTR => G3: 3,6 * INC # B6: 7,8 => UNS * INC # B6: 9 => UNS * DIS # A7: 7,8 => CTR => A7: 2,3,4 * INC # A7: 2,3,4 => UNS * INC # A8: 7,8 => UNS * INC # H5: 5,9 => UNS * INC # H5: 1,7 => UNS * INC # A7: 3,4 => UNS * DIS # C7: 3,4 => CTR => C7: 8 * INC # C7: 8 => UNS * PRF # C5: 3,4 => SOL * DIS # C5: 1,9 => CTR => C5: 3,4 * INC # I8: 6,9 => UNS * INC # I8: 4,7 => UNS * INC # E8: 6,9 => UNS * INC # E8: 4,7 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # G3: 2,3 => SOL * STA G3: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED