Analysis of zz-www.sudokuwiki.org-0152-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=152
level: medium
position: ..7...2...9..4..5.6..8........3....4..562.1..7....1...9....4..1.1..5..3...3...7.. initial
Autosolve
position: ..75..2...9..4..5.65.8........3.5..4..562.1..7..4.1..597.2345.1.1..5..3.5.3...7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E4: 8,9 => CTR => E4: 7 * DIS # G6: 8,9 => CTR => G6: 3,6 * DIS # C8: 6,8 => CTR => C8: 2,4 * DIS # H9: 6,8 => CTR => H9: 4,9 * DIS # I9: 6,8 => CTR => I9: 2,9 * DIS # G8: 6,8 => CTR => G8: 4,9 * DIS # H9: 6,8 => CTR => H9: 4,9 * DIS # I9: 6,8 => CTR => I9: 2,9 * DIS # H1: 6,8 => CTR => H1: 1,4,9 * CNT 9 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E4: 8,9 => CTR => E4: 7 * DIS E4: 7 # G6: 8,9 => CTR => G6: 3,6 * DIS E4: 7 + G6: 3,6 # C8: 6,8 => CTR => C8: 2,4 * DIS E4: 7 + G6: 3,6 + C8: 2,4 # H9: 6,8 => CTR => H9: 4,9 * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 # I9: 6,8 => CTR => I9: 2,9 * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # G8: 6,8 => CTR => G8: 4,9 * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 # H1: 6,8 => CTR => H1: 1,4,9 * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 # H6: 6,8 => CTR => H6: 2,9 * PRF E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 # H4: 2,9 => SOL * STA E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 + H4: 2,9 * CNT 9 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..7...2...9..4..5.6..8........3....4..562.1..7....1...9....4..1.1..5..3...3...7.. | initial |
| ..75..2...9..4..5.65.8........3.5..4..562.1..7..4.1..597.2345.1.1..5..3.5.3...7.. | autosolve |
| 847563219392147856651892473189375624435629187726481395978234561214756938563918742 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) D2: 1,7 E6: 8,9 C7: 6,8 D8: 7,9 D9: 1,9 F9: 6,8 H7: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H3: 1.. / H1 = 1 => 11 pairs (_) / H3 = 1 => 12 pairs (_) A4,C4: 1.. / A4 = 1 => 7 pairs (_) / C4 = 1 => 14 pairs (_) D9,E9: 1.. / D9 = 1 => 11 pairs (_) / E9 = 1 => 9 pairs (_) D2,D9: 1.. / D2 = 1 => 9 pairs (_) / D9 = 1 => 11 pairs (_) F2,F3: 2.. / F2 = 2 => 9 pairs (_) / F3 = 2 => 9 pairs (_) H4,H6: 2.. / H4 = 2 => 11 pairs (_) / H6 = 2 => 7 pairs (_) I8,I9: 2.. / I8 = 2 => 16 pairs (_) / I9 = 2 => 8 pairs (_) C3,F3: 2.. / C3 = 2 => 9 pairs (_) / F3 = 2 => 9 pairs (_) B9,I9: 2.. / B9 = 2 => 16 pairs (_) / I9 = 2 => 8 pairs (_) I5,G6: 3.. / I5 = 3 => 0 pairs (X) / G6 = 3 => 11 pairs (_) B6,G6: 3.. / B6 = 3 => 0 pairs (X) / G6 = 3 => 11 pairs (_) A5,B5: 4.. / A5 = 4 => 10 pairs (_) / B5 = 4 => 11 pairs (_) G8,H9: 4.. / G8 = 4 => 0 pairs (X) / H9 = 4 => 9 pairs (_) B9,H9: 4.. / B9 = 4 => 0 pairs (X) / H9 = 4 => 9 pairs (_) C3,C8: 4.. / C3 = 4 => 0 pairs (X) / C8 = 4 => 9 pairs (_) G3,G8: 4.. / G3 = 4 => 9 pairs (_) / G8 = 4 => 0 pairs (X) C7,H7: 6.. / C7 = 6 => 6 pairs (_) / H7 = 6 => 8 pairs (_) E1,E9: 6.. / E1 = 6 => 9 pairs (_) / E9 = 6 => 12 pairs (_) E4,F5: 7.. / E4 = 7 => 9 pairs (_) / F5 = 7 => 0 pairs (X) D8,F8: 7.. / D8 = 7 => 9 pairs (_) / F8 = 7 => 11 pairs (_) E4,H4: 7.. / E4 = 7 => 9 pairs (_) / H4 = 7 => 0 pairs (X) D2,D8: 7.. / D2 = 7 => 11 pairs (_) / D8 = 7 => 9 pairs (_) E3,E4: 7.. / E3 = 7 => 0 pairs (X) / E4 = 7 => 9 pairs (_) C7,H7: 8.. / C7 = 8 => 8 pairs (_) / H7 = 8 => 6 pairs (_) C4,C6: 9.. / C4 = 9 => 9 pairs (_) / C6 = 9 => 11 pairs (_) D8,D9: 9.. / D8 = 9 => 11 pairs (_) / D9 = 9 => 9 pairs (_) * DURATION: 0:00:33.795908 START: 06:17:56.304723 END: 06:18:30.100631 2017-05-01 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,D2,D8,D9,E6,F9,H7) * ..75..2...9..4..5.65.8........3.5..4..562.1..7..4.1..597.2345.1.1..5..3.5.3...7.. * PAIR D2: 1,7 BLK 2 E3: 1,7,9 # reduction candidate for 1,7 E3: 9 # 12 pairs E3: 1,7 # 9 pairs * PAIR E6: 8,9 BLK 5 E4: 8,9,7 # reduction candidate for 8,9 E4: 8,9 => CTR * ..756.2...9.14.65765.87.......3.5.74..56271..7..4.1.2597.2345.1.1.75..3.5.391.7.. E4: 7 # 9 pairs F5: 8,9,7 # reduction candidate for 8,9 F5: 8,9 # 9 pairs * PAIR E6: 8,9 ROW 6 C6: 8,9,2,6 # reduction candidate for 8,9 C6: 8,9 # 10 pairs G6: 8,9,3,6 # reduction candidate for 8,9 G6: 8,9 => CTR * 3475..2...9..423566528.34.7129375..4485629173736481925978234561214.5..3.5.3...74. G6: 3,6 # 8 pairs H6: 8,9,2,6 # reduction candidate for 8,9 H6: 8,9 # 17 pairs * PAIR C7: 6,8 BLK 7 C8: 6,8,2,4 # reduction candidate for 6,8 C8: 6,8 => CTR * .875..246.92.468576548729138213956744356271..76948132597.2345.121..5.43.543...7.2 C8: 2,4 # 8 pairs B9: 6,8,2,4 # reduction candidate for 6,8 B9: 6,8 # 13 pairs * PAIR C7: 6,8 COL C C4: 6,8,1,2,9 # reduction candidate for 6,8 C4: 6,8 # 14 pairs C6: 6,8,2,9 # reduction candidate for 6,8 C6: 6,8 # 12 pairs * PAIR F9: 6,8 BLK 8 F8: 6,8,7 # reduction candidate for 6,8 F8: 6,8 # 9 pairs E9: 6,8,1 # reduction candidate for 6,8 E9: 6,8 # 11 pairs * PAIR F9: 6,8 ROW 9 B9: 6,8,2,4 # reduction candidate for 6,8 B9: 6,8 # 13 pairs H9: 6,8,4,9 # reduction candidate for 6,8 H9: 6,8 => CTR * ..756.24..9.14..566548.2.17..1375..44.562.17.7.9481..597.2345.1.1.75.43954391.7.2 H9: 4,9 # 8 pairs I9: 6,8,2,9 # reduction candidate for 6,8 I9: 6,8 => CTR * ..756.2...9.14.65.65.8..4.....3.58.4.8562.1..7..4813.5976234581814756932523918746 I9: 2,9 # 8 pairs * PAIR H7: 6,8 BLK 9 G8: 6,8,4,9 # reduction candidate for 6,8 G8: 6,8 => CTR * ..75.62...9.742.566528.34.72.1375964..5629178769481325976234581814957632523168749 G8: 4,9 # 8 pairs I8: 6,8,2,9 # reduction candidate for 6,8 I8: 6,8 # 11 pairs H9: 6,8,4,9 # reduction candidate for 6,8 H9: 6,8 => CTR * ..756.24..9.14..566548.2.17..1375..44.562.17.7.9481..597.2345.1.1.75.43954391.7.2 H9: 4,9 # 8 pairs I9: 6,8,2,9 # reduction candidate for 6,8 I9: 6,8 => CTR * ..756.2...9.14.65.65.8..4.....3.58.4.8562.1..7..4813.5976234581814756932523918746 I9: 2,9 # 8 pairs * PAIR H7: 6,8 COL H H1: 6,8,1,4,9 # reduction candidate for 6,8 H1: 6,8 => CTR * 1.75..28..9..42.5.6528..41....3.5..4..562.1..7..4.1..5978234561214.56938563918742 H1: 1,4,9 # 7 pairs H4: 6,8,2,7,9 # reduction candidate for 6,8 H4: 6,8 # 12 pairs H6: 6,8,2,9 # reduction candidate for 6,8 H6: 6,8 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0152-base-pr-000.dot * REASONING * DIS # E4: 8,9 => CTR => E4: 7 * DIS # G6: 8,9 => CTR => G6: 3,6 * DIS # C8: 6,8 => CTR => C8: 2,4 * DIS # H9: 6,8 => CTR => H9: 4,9 * DIS # I9: 6,8 => CTR => I9: 2,9 * DIS # G8: 6,8 => CTR => G8: 4,9 * DIS # H9: 6,8 => CTR => H9: 4,9 * DIS # I9: 6,8 => CTR => I9: 2,9 * DIS # H1: 6,8 => CTR => H1: 1,4,9 * CNT 9 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,D2,D8,D9,E6,F9,H7) * ..75..2...9..4..5.65.8........3.5..4..562.1..7..4.1..597.2345.1.1..5..3.5.3...7.. * PAIR D2: 1,7 BLK 2 E3: 1,7,9 # reduction candidate for 1,7 E3: 9 # 12 pairs E3: 1,7 # 9 pairs * PAIR E6: 8,9 BLK 5 E4: 8,9,7 # reduction candidate for 8,9 E4: 8,9 => CTR * ..756.2...9.14.65765.87.......3.5.74..56271..7..4.1.2597.2345.1.1.75..3.5.391.7.. * RESTART * PAIR E6: 8,9 ROW 6 C6: 8,9,2,6 # reduction candidate for 8,9 C6: 8,9 # 12 pairs G6: 8,9,3,6 # reduction candidate for 8,9 G6: 8,9 => CTR * 3475.62.8.9..423566528.34.7129375..4485629173736481925978234561.14.5..3.5.3...74. H6: 8,9,2,6 # reduction candidate for 8,9 H6: 8,9 # 17 pairs * PAIR RESTART * PAIR E6: 8,9 ROW 6 C6: 8,9,2,6 # reduction candidate for 8,9 C6: 8,9 # 12 pairs H6: 8,9,2,6 # reduction candidate for 8,9 H6: 8,9 # 17 pairs * PAIR C7: 6,8 BLK 7 C8: 6,8,2,4 # reduction candidate for 6,8 C8: 6,8 => CTR * ..75..24..92.4..5.654892317..13759.44.56291737394.1..597.2345.121..5.43.543...7.2 B9: 6,8,2,4 # reduction candidate for 6,8 B9: 6,8 # 19 pairs * RESTART * PAIR C7: 6,8 BLK 7 B9: 6,8,2,4 # reduction candidate for 6,8 B9: 6,8 # 19 pairs B9: 2,4 # 14 pairs * PAIR C7: 6,8 COL C C4: 6,8,1,2,9 # reduction candidate for 6,8 C4: 6,8 # 15 pairs C6: 6,8,2,9 # reduction candidate for 6,8 C6: 6,8 # 16 pairs * PAIR F9: 6,8 BLK 8 F8: 6,8,7 # reduction candidate for 6,8 F8: 6,8 # 18 pairs E9: 6,8,1 # reduction candidate for 6,8 E9: 6,8 # 30 pairs * PAIR F9: 6,8 ROW 9 B9: 6,8,2,4 # reduction candidate for 6,8 B9: 6,8 # 19 pairs H9: 6,8,4,9 # reduction candidate for 6,8 H9: 6,8 => CTR * ..756.24.29.147.56654892......375..44.562.1..7..4.1..5976234581812.5.439543918762 I9: 6,8,2,9 # reduction candidate for 6,8 I9: 6,8 => CTR * ..756.2...9.14.65.65.89.4.....3758.4.856291737..4.1..5976234581814.5.932523918746 * RESTART * PAIR F9: 6,8 ROW 9 B9: 6,8,2,4 # reduction candidate for 6,8 B9: 2,4 # 30 pairs B9: 6,8 # 19 pairs * PAIR RESTART * PAIR F9: 6,8 BLK 8 F8: 6,8,7 # reduction candidate for 6,8 F8: 6,8 # 19 pairs E9: 6,8,1 # reduction candidate for 6,8 E9: 6,8 # 30 pairs * PAIR F9: 6,8 ROW 9 B9: 6,8,2,4 # reduction candidate for 6,8 B9: 2,4 # 30 pairs B9: 6,8 # 19 pairs * PAIR H7: 6,8 BLK 9 G8: 6,8,4,9 # reduction candidate for 6,8 G8: 6,8 => CTR * .875.62.33917428566528.34.7...3759.4..56291787.94813.5976234581814957632523168749 * RESTART * PAIR H7: 6,8 COL H H1: 6,8,1,4,9 # reduction candidate for 6,8 H1: 6,8 => CTR * 14756328939814265765.89.41....375..4..562917.7..481..597.2345.1.14.5.93.5.391.742 H4: 6,8,2,9 # reduction candidate for 6,8 H4: 6,8 # 17 pairs H6: 6,8,2,9 # reduction candidate for 6,8 H6: 6,8 => CTR * .8756.21.291.4..5.65.81....169375824..56281..728491365976234581812.57436543186792 * RESTART * PAIR H7: 6,8 COL H H4: 6,8,2,9 # reduction candidate for 6,8 H4: 2,9 => SOLVED * 847563219392147856651892473189375624435629187726481395978234561214756938563918742 * DURATION: 0:00:30.110523 START: 06:18:53.473895 END: 06:19:23.584418 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0152-base-pr-001.dot * REASONING * DIS # E4: 8,9 => CTR => E4: 7 * DIS E4: 7 # G6: 8,9 => CTR => G6: 3,6 * DIS E4: 7 + G6: 3,6 # C8: 6,8 => CTR => C8: 2,4 * DIS E4: 7 + G6: 3,6 + C8: 2,4 # H9: 6,8 => CTR => H9: 4,9 * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 # I9: 6,8 => CTR => I9: 2,9 * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # G8: 6,8 => CTR => G8: 4,9 * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 # H1: 6,8 => CTR => H1: 1,4,9 * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 # H6: 6,8 => CTR => H6: 2,9 * PRF E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 # H4: 2,9 => SOL * STA E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 + H4: 2,9 * CNT 9 HDP CHAINS / 31 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=152
Solution
position: 847563219392147856651892473189375624435629187726481395978234561214756938563918742 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 # E3: 1,7 => UNS * INC # E3: 9 => UNS * DIS # E4: 8,9 => CTR => E4: 7 * INC # E4: 7 => UNS * INC # F5: 8,9 => UNS * INC # C6: 8,9 => UNS * DIS # G6: 8,9 => CTR => G6: 3,6 * INC # G6: 3,6 => UNS * INC # H6: 8,9 => UNS * DIS # C8: 6,8 => CTR => C8: 2,4 * INC # C8: 2,4 => UNS * INC # B9: 6,8 => UNS * INC # C4: 6,8 => UNS * INC # C6: 6,8 => UNS * INC # F8: 6,8 => UNS * INC # E9: 6,8 => UNS * INC # B9: 6,8 => UNS * DIS # H9: 6,8 => CTR => H9: 4,9 * INC # H9: 4,9 => UNS * DIS # I9: 6,8 => CTR => I9: 2,9 * INC # I9: 2,9 => UNS * DIS # G8: 6,8 => CTR => G8: 4,9 * INC # G8: 4,9 => UNS * INC # I8: 6,8 => UNS * DIS # H9: 6,8 => CTR => H9: 4,9 * INC # H9: 4,9 => UNS * DIS # I9: 6,8 => CTR => I9: 2,9 * INC # I9: 2,9 => UNS * DIS # H1: 6,8 => CTR => H1: 1,4,9 * INC # H1: 1,4,9 => UNS * INC # H4: 6,8 => UNS * INC # H6: 6,8 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E3: 1,7 => UNS * INC # E3: 9 => UNS * DIS # E4: 8,9 => CTR => E4: 7 * INC E4: 7 # C6: 8,9 => UNS * DIS E4: 7 # G6: 8,9 => CTR => G6: 3,6 * INC E4: 7 + G6: 3,6 # H6: 8,9 => UNS * INC E4: 7 + G6: 3,6 # C6: 8,9 => UNS * INC E4: 7 + G6: 3,6 # H6: 8,9 => UNS * DIS E4: 7 + G6: 3,6 # C8: 6,8 => CTR => C8: 2,4 * INC E4: 7 + G6: 3,6 + C8: 2,4 # B9: 6,8 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 # B9: 6,8 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 # B9: 2,4 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 # C4: 6,8 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 # C6: 6,8 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 # F8: 6,8 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 # E9: 6,8 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 # B9: 6,8 => UNS * DIS E4: 7 + G6: 3,6 + C8: 2,4 # H9: 6,8 => CTR => H9: 4,9 * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 # I9: 6,8 => CTR => I9: 2,9 * INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # B9: 6,8 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # B9: 2,4 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # F8: 6,8 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # E9: 6,8 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # B9: 6,8 => UNS * INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # B9: 2,4 => UNS * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # G8: 6,8 => CTR => G8: 4,9 * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 # H1: 6,8 => CTR => H1: 1,4,9 * INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 # H4: 6,8 => UNS * DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 # H6: 6,8 => CTR => H6: 2,9 * INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 # H4: 6,8 => UNS * PRF E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 # H4: 2,9 => SOL * STA E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 + H4: 2,9 * CNT 31 HDP CHAINS / 31 HYP OPENED