Analysis of zz-www.sudokuwiki.org-0100-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=100
level: medium
position: .7.......5.....17...4..8..9...4..29....8.6....96..7...1..3..4...28.....5.......2. initial
Autosolve
position: .7.......5.....17...4..8..9...4..296...896....96..7...1..3..4...28.....5.......2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A5: 3,4 => CTR => A5: 2 * DIS # A9: 3,4 => CTR => A9: 6,7,9 * DIS # B9: 5,6 => CTR => B9: 3,4 * DIS # E7: 6,8 => CTR => E7: 2,5,7 * DIS # I9: 7,8 => CTR => I9: 1,3 * DIS # E7: 7,8 => CTR => E7: 2,5,6 * CNT 6 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A5: 3,4 => CTR => A5: 2 * DIS A5: 2 # B5: 5 => CTR => B5: 3,4 * PRF A5: 2 + B5: 3,4 # I6: 3,4 => SOL * STA A5: 2 + B5: 3,4 + I6: 3,4 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.......5.....17...4..8..9...4..29....8.6....96..7...1..3..4...28.....5.......2. | initial |
| .7.......5.....17...4..8..9...4..296...896....96..7...1..3..4...28.....5.......2. | autosolve |
| 972135648583964172614278539857413296231896754496527813169352487328741965745689321 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) A6: 3,4 B7: 5,6 H7: 6,8 I7: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,B3: 1.. / C1 = 1 => 0 pairs (X) / B3 = 1 => 4 pairs (_) H8,I9: 1.. / H8 = 1 => 5 pairs (_) / I9 = 1 => 5 pairs (_) I1,I2: 2.. / I1 = 2 => 4 pairs (_) / I2 = 2 => 12 pairs (_) A5,C5: 2.. / A5 = 2 => 19 pairs (_) / C5 = 2 => 0 pairs (X) D6,E6: 2.. / D6 = 2 => 5 pairs (_) / E6 = 2 => 17 pairs (_) E7,F7: 2.. / E7 = 2 => 0 pairs (X) / F7 = 2 => 19 pairs (_) B5,B9: 4.. / B5 = 4 => 0 pairs (X) / B9 = 4 => 4 pairs (_) D3,E3: 7.. / D3 = 7 => 4 pairs (_) / E3 = 7 => 4 pairs (_) A4,C4: 7.. / A4 = 7 => 0 pairs (X) / C4 = 7 => 6 pairs (_) G5,I5: 7.. / G5 = 7 => 4 pairs (_) / I5 = 7 => 0 pairs (X) A1,B2: 8.. / A1 = 8 => 0 pairs (X) / B2 = 8 => 5 pairs (_) A4,B4: 8.. / A4 = 8 => 5 pairs (_) / B4 = 8 => 0 pairs (X) E7,E9: 8.. / E7 = 8 => 0 pairs (X) / E9 = 8 => 4 pairs (_) B2,I2: 8.. / B2 = 8 => 5 pairs (_) / I2 = 8 => 0 pairs (X) A1,A4: 8.. / A1 = 8 => 0 pairs (X) / A4 = 8 => 5 pairs (_) B2,B4: 8.. / B2 = 8 => 5 pairs (_) / B4 = 8 => 0 pairs (X) G8,G9: 9.. / G8 = 9 => 5 pairs (_) / G9 = 9 => 4 pairs (_) C7,F7: 9.. / C7 = 9 => 19 pairs (_) / F7 = 9 => 0 pairs (X) * DURATION: 0:00:22.910617 START: 05:15:42.170714 END: 05:16:05.081331 2017-05-01 * CP COUNT: (18) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,H7,I7) * .7.......5.....17...4..8..9...4..296...896....96..7...1..3..4...28.....5.......2. * PAIR A6: 3,4 BLK 4 A5: 3,4,2 # reduction candidate for 3,4 A5: 3,4 => CTR * .719.....5.96..17.2.4178..9785413296.1289675..96257..1157329468928764315643581927 A5: 2 # 19 pairs B5: 3,4,1,5 # reduction candidate for 3,4 B5: 3,4 # 17 pairs * PAIR A6: 3,4 ROW 6 H6: 3,4,1,5,8 # reduction candidate for 3,4 H6: 3,4 # 8 pairs I6: 3,4,1,8 # reduction candidate for 3,4 I6: 3,4 # 7 pairs * PAIR A6: 3,4 COL A A8: 3,4,6,7,9 # reduction candidate for 3,4 A8: 3,4 # 20 pairs A9: 3,4,6,7,9 # reduction candidate for 3,4 A9: 3,4 => CTR * 97....86.58.96.17.614278..98.74..2962.1896743.96.27.1.169352487728.....5..5789621 A9: 6,7,9 # 4 pairs * PAIR B7: 5,6 BLK 7 B9: 5,6,3,4 # reduction candidate for 5,6 B9: 5,6 => CTR * 97.......582...17.634..85.9...4..29624.896...396..7...1.93.24...28.....5..3....2. B9: 3,4 # 5 pairs * PAIR B7: 5,6 ROW 7 E7: 5,6,2,7,8 # reduction candidate for 5,6 E7: 5,6 # 19 pairs E7: 2,7,8 # 4 pairs * PAIR H7: 6,8 BLK 9 G9: 6,8,3,7,9 # reduction candidate for 6,8 G9: 6,8 # 8 pairs G9: 3,7,9 # 4 pairs * PAIR H7: 6,8 ROW 7 E7: 6,8,2,5,7 # reduction candidate for 6,8 E7: 6,8 => CTR * 971.....2582...17...4..8..98.74..2962.58967...96..7...1593.24.7.28.....5..3....2. E7: 2,5,7 # 4 pairs * PAIR H7: 6,8 COL H H1: 6,8,3,4,5 # reduction candidate for 6,8 H1: 6,8 # 10 pairs H1: 3,4,5 # 4 pairs * PAIR I7: 7,8 BLK 9 G9: 7,8,3,6,9 # reduction candidate for 7,8 G9: 7,8 # 9 pairs I9: 7,8,1,3 # reduction candidate for 7,8 I9: 7,8 => CTR * 971.....2582...17...4..8..98.74..2962.58967...96..7...1593.246..28...315..3...92. I9: 1,3 # 5 pairs * PAIR I7: 7,8 ROW 7 E7: 7,8,2,5,6 # reduction candidate for 7,8 E7: 7,8 => CTR * 971.....2582...17...4..8..98.74..2962.5896....96..7...1593.246..28.....5..3....2. E7: 2,5,6 # 4 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0100-base-pr-000.dot * REASONING * DIS # A5: 3,4 => CTR => A5: 2 * DIS # A9: 3,4 => CTR => A9: 6,7,9 * DIS # B9: 5,6 => CTR => B9: 3,4 * DIS # E7: 6,8 => CTR => E7: 2,5,7 * DIS # I9: 7,8 => CTR => I9: 1,3 * DIS # E7: 7,8 => CTR => E7: 2,5,6 * CNT 6 HDP CHAINS / 23 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,H7,I7) * .7.......5.....17...4..8..9...4..296...896....96..7...1..3..4...28.....5.......2. * PAIR A6: 3,4 BLK 4 A5: 3,4,2 # reduction candidate for 3,4 A5: 3,4 => CTR * .719.....5.96..17.2.4178..9785413296.1289675..96257..1157329468928764315643581927 B5: 3,4,5 # reduction candidate for 3,4 B5: 3,4 # 17 pairs * RESTART * PAIR A6: 3,4 BLK 4 B5: 3,4,5 # reduction candidate for 3,4 B5: 5 => CTR * 97.541.6.58..63174614728..9837415296251896743496237...169352487.28.74..5745.89321 * PAIR A6: 3,4 ROW 6 I6: 3,4,1,8 # reduction candidate for 3,4 I6: 3,4 => SOLVED * 972135648583964172614278539857413296231896754496527813169352487328741965745689321 * DURATION: 0:00:07.761739 START: 05:16:20.919492 END: 05:16:28.681231 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0100-base-pr-001.dot * REASONING * DIS # A5: 3,4 => CTR => A5: 2 * DIS A5: 2 # B5: 5 => CTR => B5: 3,4 * PRF A5: 2 + B5: 3,4 # I6: 3,4 => SOL * STA A5: 2 + B5: 3,4 + I6: 3,4 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=100
Solution
position: 972135648583964172614278539857413296231896754496527813169352487328741965745689321 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:
* DIS # A5: 3,4 => CTR => A5: 2 * INC # A5: 2 => UNS * INC # B5: 3,4 => UNS * INC # H6: 3,4 => UNS * INC # I6: 3,4 => UNS * INC # A8: 3,4 => UNS * DIS # A9: 3,4 => CTR => A9: 6,7,9 * INC # A9: 6,7,9 => UNS * DIS # B9: 5,6 => CTR => B9: 3,4 * INC # B9: 3,4 => UNS * INC # E7: 5,6 => UNS * INC # E7: 2,7,8 => UNS * INC # G9: 6,8 => UNS * INC # G9: 3,7,9 => UNS * DIS # E7: 6,8 => CTR => E7: 2,5,7 * INC # E7: 2,5,7 => UNS * INC # H1: 6,8 => UNS * INC # H1: 3,4,5 => UNS * INC # G9: 7,8 => UNS * DIS # I9: 7,8 => CTR => I9: 1,3 * INC # I9: 1,3 => UNS * DIS # E7: 7,8 => CTR => E7: 2,5,6 * INC # E7: 2,5,6 => UNS * CNT 23 HDP CHAINS / 23 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A5: 3,4 => CTR => A5: 2 * INC A5: 2 # B5: 3,4 => UNS * INC A5: 2 # B5: 3,4 => UNS * DIS A5: 2 # B5: 5 => CTR => B5: 3,4 * PRF A5: 2 + B5: 3,4 # I6: 3,4 => SOL * STA A5: 2 + B5: 3,4 + I6: 3,4 * CNT 5 HDP CHAINS / 5 HYP OPENED