Analysis of zz-www.sudokuwiki.org-0082-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=82
level: medium
position: 9......5..6.4....98.5.6...3...1..3.2.........3.7..2...4...5.7.67....8.2..1......5 initial
Autosolve
position: 9.....65..6.4.5..98.5.6...35..1..3.2.........3.7..2...4...5.7.675...8.2..1......5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 1,2 => CTR => C2: 3 * DIS # A5: 6 => CTR => A5: 1,2 * CNT 2 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 1,2 => CTR => C2: 3 * DIS C2: 3 # C1: 4 => CTR => C1: 1,2 * DIS C2: 3 + C1: 1,2 # C9: 2,6 => CTR => C9: 8,9 * DIS C2: 3 + C1: 1,2 + C9: 8,9 # G8: 9 => CTR => G8: 1,4 * DIS C2: 3 + C1: 1,2 + C9: 8,9 + G8: 1,4 # I6: 1,4 => CTR => I6: 8 * PRF C2: 3 + C1: 1,2 + C9: 8,9 + G8: 1,4 + I6: 8 # E1: 1,2 => SOL * STA C2: 3 + C1: 1,2 + C9: 8,9 + G8: 1,4 + I6: 8 + E1: 1,2 * CNT 6 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9......5..6.4....98.5.6...3...1..3.2.........3.7..2...4...5.7.67....8.2..1......5 | initial |
| 9.....65..6.4.5..98.5.6...35..1..3.2.........3.7..2...4...5.7.675...8.2..1......5 | autosolve |
| 971823654263415879845769213586197342124386597397542168432951786759638421618274935 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) A2: 1,2 A9: 2,6 I8: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,C5: 1.. / A5 = 1 => 6 pairs (_) / C5 = 1 => 6 pairs (_) F7,E8: 1.. / F7 = 1 => 7 pairs (_) / E8 = 1 => 0 pairs (X) F7,H7: 1.. / F7 = 1 => 7 pairs (_) / H7 = 1 => 0 pairs (X) A2,A5: 1.. / A2 = 1 => 6 pairs (_) / A5 = 1 => 6 pairs (_) G2,G3: 2.. / G2 = 2 => 11 pairs (_) / G3 = 2 => 6 pairs (_) H7,H9: 3.. / H7 = 3 => 0 pairs (X) / H9 = 3 => 3 pairs (_) C2,E2: 3.. / C2 = 3 => 7 pairs (_) / E2 = 3 => 0 pairs (X) B1,B7: 3.. / B1 = 3 => 0 pairs (X) / B7 = 3 => 7 pairs (_) D5,D6: 5.. / D5 = 5 => 3 pairs (_) / D6 = 5 => 3 pairs (_) G5,G6: 5.. / G5 = 5 => 3 pairs (_) / G6 = 5 => 3 pairs (_) D5,G5: 5.. / D5 = 5 => 3 pairs (_) / G5 = 5 => 3 pairs (_) D6,G6: 5.. / D6 = 5 => 3 pairs (_) / G6 = 5 => 3 pairs (_) D6,H6: 6.. / D6 = 6 => 0 pairs (X) / H6 = 6 => 3 pairs (_) C8,D8: 6.. / C8 = 6 => 0 pairs (X) / D8 = 6 => 4 pairs (_) A5,A9: 6.. / A5 = 6 => 0 pairs (X) / A9 = 6 => 4 pairs (_) B1,B3: 7.. / B1 = 7 => 9 pairs (_) / B3 = 7 => 6 pairs (_) E2,H2: 7.. / E2 = 7 => 22 pairs (_) / H2 = 7 => 4 pairs (_) I1,I5: 7.. / I1 = 7 => 25 pairs (_) / I5 = 7 => 3 pairs (_) D3,F3: 9.. / D3 = 9 => 6 pairs (_) / F3 = 9 => 7 pairs (_) * DURATION: 0:00:22.129623 START: 04:54:19.699022 END: 04:54:41.828645 2017-05-01 * CP COUNT: (19) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,I8) * 9.....65..6.4.5..98.5.6...35..1..3.2.........3.7..2...4...5.7.675...8.2..1......5 * PAIR A2: 1,2 BLK 1 C1: 1,2,3,4 # reduction candidate for 1,2 C1: 1,2 # 13 pairs C2: 1,2,3 # reduction candidate for 1,2 C2: 1,2 => CTR * 9.....65..6.4358798.5.6.2.35..1..3.2........73.7..2..84...517.675...8.2..1......5 C2: 3 # 7 pairs * PAIR A2: 1,2 ROW 2 E2: 1,2,3,7,8 # reduction candidate for 1,2 E2: 1,2 # 20 pairs G2: 1,2,8 # reduction candidate for 1,2 G2: 1,2 # 10 pairs * PAIR A2: 1,2 COL A A5: 1,2,6 # reduction candidate for 1,2 A5: 6 => CTR * 972813654163425879845.6.2135841.6392621389547397542168439251786756..8421218..4935 A5: 1,2 # 4 pairs * PAIR A9: 2,6 BLK 7 C9: 2,6,3,8,9 # reduction candidate for 2,6 C9: 2,6 # 6 pairs C9: 3,8,9 # 3 pairs * PAIR A9: 2,6 ROW 9 D9: 2,6,3,7,9 # reduction candidate for 2,6 D9: 2,6 # 5 pairs D9: 3,7,9 # 3 pairs * PAIR A9: 2,6 COL A A5: 2,6,1 # reduction candidate for 2,6 A5: 2,6 # 6 pairs A5: 1 # 6 pairs * PAIR I8: 1,4 BLK 9 G8: 1,4,9 # reduction candidate for 1,4 G8: 1,4 # 10 pairs G8: 9 # 7 pairs * PAIR I8: 1,4 ROW 8 E8: 1,4,3,9 # reduction candidate for 1,4 E8: 3,9 # 10 pairs E8: 1,4 # 7 pairs * PAIR I8: 1,4 COL I I1: 1,4,7,8 # reduction candidate for 1,4 I1: 1,4 # 9 pairs I6: 1,4,8 # reduction candidate for 1,4 I6: 1,4 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0082-base-pr-000.dot * REASONING * DIS # C2: 1,2 => CTR => C2: 3 * DIS # A5: 6 => CTR => A5: 1,2 * CNT 2 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,I8) * 9.....65..6.4.5..98.5.6...35..1..3.2.........3.7..2...4...5.7.675...8.2..1......5 * PAIR A2: 1,2 BLK 1 C1: 1,2,3,4 # reduction candidate for 1,2 C1: 1,2 # 13 pairs C2: 1,2,3 # reduction candidate for 1,2 C2: 1,2 => CTR * 9.....65..6.4358798.5.6.2.35..1..3.2........73.7..2..84...517.675...8.2..1......5 * RESTART * PAIR A2: 1,2 BLK 1 C1: 1,2,4 # reduction candidate for 1,2 C1: 4 => CTR * 9.48136571634752898752694135.61.73.22.13.657.3.75.2.6.43..517.6759638.2.61.....35 * PAIR A2: 1,2 ROW 2 E2: 1,2,7,8 # reduction candidate for 1,2 E2: 1,2 # 20 pairs G2: 1,2,8 # reduction candidate for 1,2 G2: 1,2 # 16 pairs * PAIR A9: 2,6 BLK 7 C9: 2,6,8,9 # reduction candidate for 2,6 C9: 2,6 => CTR * 9.....65..634.51.98.5.6.2.35..1..3.212.......3.7..2.6143825179675963842..1....835 * PAIR A9: 2,6 ROW 9 D9: 2,6,7,9 # reduction candidate for 2,6 D9: 7,9 # 17 pairs D9: 2,6 # 17 pairs * PAIR I8: 1,4 BLK 9 G8: 1,4,9 # reduction candidate for 1,4 G8: 9 => CTR * 9.2.13654163425879845.6.2135841..3.2621.....73.7..21.843.25.7867563.8921218...435 * PAIR I8: 1,4 COL I I6: 1,4,8 # reduction candidate for 1,4 I6: 1,4 => CTR * 94....65..634.5..9875269..35..1..3.2.2.......3.7..2...432951786759638.2.618724935 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A5,A9,C1,C4,C7,C8,D1,D3,D5,D7,E2,E4,E5,E8,E9,F3,F5,H4,H5) * 97...3654.634.5879845.6.21358.1..3.2.2....5.739754216843..5178675...8421.18..4935 * PAIR C1: 1,2 ROW 1 E1: 1,2,8 # reduction candidate for 1,2 E1: 1,2 => SOLVED * 971823654263415879845769213586197342124386597397542168432951786759638421618274935 * DURATION: 0:00:15.371789 START: 04:54:54.393613 END: 04:55:09.765402 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0082-base-pr-001.dot * REASONING * DIS # C2: 1,2 => CTR => C2: 3 * DIS C2: 3 # C1: 4 => CTR => C1: 1,2 * DIS C2: 3 + C1: 1,2 # C9: 2,6 => CTR => C9: 8,9 * DIS C2: 3 + C1: 1,2 + C9: 8,9 # G8: 9 => CTR => G8: 1,4 * DIS C2: 3 + C1: 1,2 + C9: 8,9 + G8: 1,4 # I6: 1,4 => CTR => I6: 8 * PRF C2: 3 + C1: 1,2 + C9: 8,9 + G8: 1,4 + I6: 8 # E1: 1,2 => SOL * STA C2: 3 + C1: 1,2 + C9: 8,9 + G8: 1,4 + I6: 8 + E1: 1,2 * CNT 6 HDP CHAINS / 13 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=82
Solution
position: 971823654263415879845769213586197342124386597397542168432951786759638421618274935 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 # C1: 1,2 => UNS * DIS # C2: 1,2 => CTR => C2: 3 * INC # C2: 3 => UNS * INC # E2: 1,2 => UNS * INC # G2: 1,2 => UNS * INC # A5: 1,2 => UNS * DIS # A5: 6 => CTR => A5: 1,2 * INC # C9: 2,6 => UNS * INC # C9: 3,8,9 => UNS * INC # D9: 2,6 => UNS * INC # D9: 3,7,9 => UNS * INC # A5: 2,6 => UNS * INC # A5: 1 => UNS * INC # G8: 1,4 => UNS * INC # G8: 9 => UNS * INC # E8: 1,4 => UNS * INC # E8: 3,9 => UNS * INC # I1: 1,4 => UNS * INC # I6: 1,4 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 1,2 => UNS * DIS # C2: 1,2 => CTR => C2: 3 * INC C2: 3 # C1: 1,2 => UNS * DIS C2: 3 # C1: 4 => CTR => C1: 1,2 * INC C2: 3 + C1: 1,2 # E2: 1,2 => UNS * INC C2: 3 + C1: 1,2 # G2: 1,2 => UNS * DIS C2: 3 + C1: 1,2 # C9: 2,6 => CTR => C9: 8,9 * INC C2: 3 + C1: 1,2 + C9: 8,9 # D9: 2,6 => UNS * INC C2: 3 + C1: 1,2 + C9: 8,9 # D9: 7,9 => UNS * INC C2: 3 + C1: 1,2 + C9: 8,9 # G8: 1,4 => UNS * DIS C2: 3 + C1: 1,2 + C9: 8,9 # G8: 9 => CTR => G8: 1,4 * DIS C2: 3 + C1: 1,2 + C9: 8,9 + G8: 1,4 # I6: 1,4 => CTR => I6: 8 * PRF C2: 3 + C1: 1,2 + C9: 8,9 + G8: 1,4 + I6: 8 # E1: 1,2 => SOL * STA C2: 3 + C1: 1,2 + C9: 8,9 + G8: 1,4 + I6: 8 + E1: 1,2 * CNT 13 HDP CHAINS / 13 HYP OPENED