Analysis of zz-www.sudokuwiki.org-0044-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=44
level: medium
position: ....5..12.9.6...4....4....6.15......8...7...4..6...19.1....2....5...8.3.28..4.... initial
Autosolve
position: ....5..12.9.6...4....4....6.15......8...7...4..6...19.1....24...5...823.28..4.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C5: 2,3 => SOL * DIS # C5: 9 => CTR => C5: 2,3 * DIS # B6: 2,3 => CTR => B6: 4,7 * DIS # D5: 2,3 => CTR => D5: 1,5,9 * DIS # B3: 7 => CTR => B3: 2,3 * DIS # E4: 3,8 => CTR => E4: 6,9 * DIS # D6: 3,8 => CTR => D6: 2,5 * DIS # E2: 3,8 => CTR => E2: 1,2 * DIS # E3: 3,8 => CTR => E3: 1,2,9 * CNT 9 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:
* PRF # C5: 2,3 => SOL * STA C5: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....5..12.9.6...4....4....6.15......8...7...4..6...19.1....2....5...8.3.28..4.... | initial |
| ....5..12.9.6...4....4....6.15......8...7...4..6...19.1....24...5...823.28..4.... | autosolve |
| 467853912398621745521497386915364827832179654746285193179532468654718239283946571 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (2) B5: 2,3 E6: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 4 pairs (_) / C3 = 1 => 2 pairs (_) D5,F5: 1.. / D5 = 1 => 3 pairs (_) / F5 = 1 => 0 pairs (X) I8,I9: 1.. / I8 = 1 => 0 pairs (X) / I9 = 1 => 3 pairs (_) E2,E3: 2.. / E2 = 2 => 2 pairs (_) / E3 = 2 => 0 pairs (X) H4,H5: 2.. / H4 = 2 => 3 pairs (_) / H5 = 2 => 0 pairs (X) C2,E2: 2.. / C2 = 2 => 0 pairs (X) / E2 = 2 => 2 pairs (_) D4,H4: 2.. / D4 = 2 => 0 pairs (X) / H4 = 2 => 3 pairs (_) B6,D6: 2.. / B6 = 2 => 0 pairs (X) / D6 = 2 => 3 pairs (_) F4,F6: 4.. / F4 = 4 => 3 pairs (_) / F6 = 4 => 0 pairs (X) A8,C8: 4.. / A8 = 4 => 0 pairs (X) / C8 = 4 => 4 pairs (_) A4,F4: 4.. / A4 = 4 => 0 pairs (X) / F4 = 4 => 3 pairs (_) B1,B6: 4.. / B1 = 4 => 0 pairs (X) / B6 = 4 => 0 pairs (_) C1,C8: 4.. / C1 = 4 => 0 pairs (X) / C8 = 4 => 4 pairs (_) A2,A3: 5.. / A2 = 5 => 3 pairs (_) / A3 = 5 => 4 pairs (_) A1,B1: 6.. / A1 = 6 => 0 pairs (X) / B1 = 6 => 0 pairs (_) B7,A8: 6.. / B7 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) A8,E8: 6.. / A8 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) A1,A8: 6.. / A1 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) B1,B7: 6.. / B1 = 6 => 0 pairs (*) / B7 = 6 => 0 pairs (X) H7,I7: 8.. / H7 = 8 => 3 pairs (_) / I7 = 8 => 5 pairs (_) G1,G3: 9.. / G1 = 9 => 3 pairs (_) / G3 = 9 => 2 pairs (_) A4,C5: 9.. / A4 = 9 => 0 pairs (*) / C5 = 9 => 0 pairs (X) A4,A8: 9.. / A4 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) * DURATION: 0:00:29.785448 START: 04:17:57.266377 END: 04:18:27.051825 2017-05-01 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,E6) * ....5..12.9.6...4....4....6.15......8...7...4..6...19.1....24...5...823.28..4.... * PAIR B5: 2,3 BLK 4 C5: 2,3,9 # reduction candidate for 2,3 C5: 2,3 => SOLVED * 467853912398621745521497386915364827832179654746285193179532468654718239283946571 C5: 9 => CTR * 648.5..12.9.6...4....4....6.15......8.9.7...4..6.3.19.16..924..954.6823.28..4.... B6: 2,3,4,7 # reduction candidate for 2,3 B6: 2,3 => CTR * 648.5..12.9.6...4..7.4....6.15......8.9.7...4..6.3.19.16..924..954.6823.28..4.... B6: 4,7 # 4 pairs * PAIR B5: 2,3 ROW 5 D5: 2,3,1,5,9 # reduction candidate for 2,3 D5: 2,3 => CTR * 64..5..12.9.6...4..7.4....6415..6.2.839271..47265.419.16...24..954.6823.28..45... D5: 1,5,9 # 2 pairs * PAIR B5: 2,3 COL B B3: 2,3,7 # reduction candidate for 2,3 B3: 7 => CTR * 468.5..12.9.6...4..7.4....6915.64...8.3179..474623519813...24..654.1823.28..4...1 B3: 2,3 # 7 pairs * PAIR E6: 3,8 BLK 5 D4: 3,8,2,9 # reduction candidate for 3,8 D4: 3,8 # 7 pairs E4: 3,8,6,9 # reduction candidate for 3,8 E4: 3,8 => CTR * ...85..12.9.62..4..2.4....6915......832.7...4..62..19.1....24...5...823.28..4.... E4: 6,9 # 3 pairs D6: 3,8,2,5 # reduction candidate for 3,8 D6: 3,8 => CTR * 648.5..12.9.6...4..7.4....6.15......839.7...4.26.3.19.16..924..954.6823.28..4.... D6: 2,5 # 3 pairs * PAIR E6: 3,8 ROW 6 I6: 3,8,5,7 # reduction candidate for 3,8 I6: 3,8 # 6 pairs I6: 5,7 # 3 pairs * PAIR E6: 3,8 COL E E2: 3,8,1,2 # reduction candidate for 3,8 E2: 3,8 => CTR * .68.5..12.92681.4...142...6915.64...8.3179..4.4623519813...24..654.1823.28..4...1 E2: 1,2 # 3 pairs E3: 3,8,1,2,9 # reduction candidate for 3,8 E3: 3,8 => CTR * 46.95..12.9.62..455..48.976915..4...8..179..4.462.519.1...92468654718239289.46..1 E3: 1,2,9 # 2 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0044-base-pr-000.dot * REASONING * PRF # C5: 2,3 => SOL * DIS # C5: 9 => CTR => C5: 2,3 * DIS # B6: 2,3 => CTR => B6: 4,7 * DIS # D5: 2,3 => CTR => D5: 1,5,9 * DIS # B3: 7 => CTR => B3: 2,3 * DIS # E4: 3,8 => CTR => E4: 6,9 * DIS # D6: 3,8 => CTR => D6: 2,5 * DIS # E2: 3,8 => CTR => E2: 1,2 * DIS # E3: 3,8 => CTR => E3: 1,2,9 * CNT 9 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,E6) * ....5..12.9.6...4....4....6.15......8...7...4..6...19.1....24...5...823.28..4.... * PAIR B5: 2,3 BLK 4 C5: 2,3,9 # reduction candidate for 2,3 C5: 2,3 => SOLVED * 467853912398621745521497386915364827832179654746285193179532468654718239283946571 * DURATION: 0:00:02.620968 START: 04:18:40.033120 END: 04:18:42.654088 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0044-base-pr-001.dot * REASONING * PRF # C5: 2,3 => SOL * STA C5: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=44
Solution
position: 467853912398621745521497386915364827832179654746285193179532468654718239283946571 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 # C5: 2,3 => SOL * DIS # C5: 9 => CTR => C5: 2,3 * DIS # B6: 2,3 => CTR => B6: 4,7 * INC # B6: 4,7 => UNS * DIS # D5: 2,3 => CTR => D5: 1,5,9 * INC # D5: 1,5,9 => UNS * INC # B3: 2,3 => UNS * DIS # B3: 7 => CTR => B3: 2,3 * INC # D4: 3,8 => UNS * DIS # E4: 3,8 => CTR => E4: 6,9 * INC # E4: 6,9 => UNS * DIS # D6: 3,8 => CTR => D6: 2,5 * INC # D6: 2,5 => UNS * INC # I6: 3,8 => UNS * INC # I6: 5,7 => UNS * DIS # E2: 3,8 => CTR => E2: 1,2 * INC # E2: 1,2 => UNS * DIS # E3: 3,8 => CTR => E3: 1,2,9 * INC # E3: 1,2,9 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C5: 2,3 => SOL * STA C5: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED