Analysis of zz-www.sudokuwiki.org-0130-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=130
level: medium
position: .......2..182..7...2.746.....6..9....4.....5....3..8.....531.7...3...28..5....... initial
Autosolve
position: .......2..182..7...2.746..8..6..9....4.....5....3..8.....531.7.1.3...285.5....... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 5,9 => SOL * DIS # C1: 5,9 => CTR => C1: 4,7 * DIS # A2: 5,9 => CTR => A2: 3,4,6 * DIS # A3: 5,9 => CTR => A3: 3 * PRF # G3: 5,9 => SOL * DIS # E1: 5,9 => CTR => E1: 1,8 * DIS # A2: 5,9 => CTR => A2: 3,4,6 * DIS # F1: 8 => CTR => F1: 3,5 * DIS # A2: 3,5 => CTR => A2: 4,6,9 * DIS # A5: 7,9 => CTR => A5: 2,3,8 * DIS # B1: 7,9 => CTR => B1: 3,6 * DIS # F6: 2,5 => CTR => F6: 4,7 * CNT 12 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:
* PRF # A1: 5,9 => SOL * STA A1: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......2..182..7...2.746.....6..9....4.....5....3..8.....531.7...3...28..5....... | initial |
| .......2..182..7...2.746..8..6..9....4.....5....3..8.....531.7.1.3...285.5....... | autosolve |
| 967183524418295763325746918536879142849612357271354896682531479193467285754928631 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) C3: 5,9 E2: 5,9 F2: 3,5 B6: 7,9 F8: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,E1: 1.. / D1 = 1 => 8 pairs (_) / E1 = 1 => 6 pairs (_) G3,H3: 1.. / G3 = 1 => 8 pairs (_) / H3 = 1 => 6 pairs (_) C5,C6: 1.. / C5 = 1 => 6 pairs (_) / C6 = 1 => 7 pairs (_) A7,C7: 2.. / A7 = 2 => 11 pairs (_) / C7 = 2 => 5 pairs (_) E9,F9: 2.. / E9 = 2 => 6 pairs (_) / F9 = 2 => 6 pairs (_) F1,F2: 3.. / F1 = 3 => 20 pairs (_) / F2 = 3 => 5 pairs (_) B1,B4: 3.. / B1 = 3 => 0 pairs (X) / B4 = 3 => 17 pairs (_) D4,F6: 4.. / D4 = 4 => 0 pairs (X) / F6 = 4 => 17 pairs (_) D8,F8: 4.. / D8 = 4 => 17 pairs (_) / F8 = 4 => 0 pairs (X) D4,D8: 4.. / D4 = 4 => 0 pairs (X) / D8 = 4 => 17 pairs (_) F6,F8: 4.. / F6 = 4 => 17 pairs (_) / F8 = 4 => 0 pairs (X) G1,G3: 5.. / G1 = 5 => 6 pairs (_) / G3 = 5 => 0 pairs (X) A4,E4: 5.. / A4 = 5 => 11 pairs (_) / E4 = 5 => 8 pairs (_) A7,B7: 8.. / A7 = 8 => 0 pairs (X) / B7 = 8 => 6 pairs (_) B4,B7: 8.. / B4 = 8 => 0 pairs (X) / B7 = 8 => 6 pairs (_) * DURATION: 0:00:17.865607 START: 05:56:51.083403 END: 05:57:08.949010 2017-05-01 * CP COUNT: (15) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C3,E2,F2,F8) * .......2..182..7...2.746..8..6..9....4.....5....3..8.....531.7.1.3...285.5....... * PAIR C3: 5,9 BLK 1 A1: 5,9,3,4,6,7 # reduction candidate for 5,9 A1: 5,9 => SOLVED * 967183524418295763325746918536879142849612357271354896682531479193467285754928631 A1: 3,4,6,7 # 5 pairs C1: 5,9,4,7 # reduction candidate for 5,9 C1: 5,9 => CTR * .6.183.2.4182957..32.746..8.368.9...84.6.2.5.97.354862.82531.7.193467285.5.928..1 C1: 4,7 # 6 pairs A2: 5,9,3,4,6 # reduction candidate for 5,9 A2: 5,9 => CTR * .....5.2.5182937..329746518.3685914.84...2.5...5314896.82531.7.193467285.5.928.31 A2: 3,4,6 # 6 pairs A3: 5,9,3 # reduction candidate for 5,9 A3: 5,9 => CTR * .....352.3182957...2.746..8.36..9....4.....53...3.48...8.531.7.193467285.5.9....1 A3: 3 # 19 pairs * PAIR C3: 5,9 ROW 3 G3: 5,9,1,3 # reduction candidate for 5,9 G3: 5,9 => SOLVED * 967183524418295763325746918536879142849612357271354896682531479193467285754928631 G3: 1,3 # 7 pairs * PAIR C3: 5,9 COL C C6: 5,9,1,2,7 # reduction candidate for 5,9 C6: 5,9 # 9 pairs C6: 1,2,7 # 7 pairs * PAIR E2: 5,9 BLK 2 E1: 5,9,1,8 # reduction candidate for 5,9 E1: 5,9 => CTR * .3.198.2..182537..925746..85864.9...34.....5....3.58..8.2531.7.1.3..4285.5....... E1: 1,8 # 6 pairs * PAIR E2: 5,9 ROW 2 A2: 5,9,3,4,6 # reduction candidate for 5,9 A2: 5,9 => CTR * .....5.2.5182937..329746518.3685914.84...2.5...5314896.82531.7.193467285.5.928.31 A2: 3,4,6 # 6 pairs * PAIR F2: 3,5 BLK 2 F1: 3,5,8 # reduction candidate for 3,5 F1: 8 => CTR * .3...8.2..182537..925746..85864.9...34.....5....3.58..8.2531.7.1.3..4285.5....... F1: 3,5 # 8 pairs * PAIR F2: 3,5 ROW 2 A2: 3,5,4,6,9 # reduction candidate for 3,5 A2: 3,5 => CTR * .6.18..2..1829.764925746..8.368.9..2849612357.71354896.82531.79193467285.5.928.31 A2: 4,6,9 # 6 pairs * PAIR B6: 7,9 BLK 4 A5: 7,9,2,3,8 # reduction candidate for 7,9 A5: 7,9 => CTR * .......2..182..7...2.746..8..6..9....4.....5....3..8.....531.7.1.3...285.5....... A5: 2,3,8 # 5 pairs C5: 7,9,1,2 # reduction candidate for 7,9 C5: 7,9 # 13 pairs A6: 7,9,2,5 # reduction candidate for 7,9 A6: 7,9 # 11 pairs C6: 7,9,1,2,5 # reduction candidate for 7,9 C6: 7,9 # 14 pairs * PAIR B6: 7,9 ROW 6 I6: 7,9,1,2,4,6 # reduction candidate for 7,9 I6: 7,9 # 7 pairs I6: 1,2,4,6 # 5 pairs * PAIR B6: 7,9 COL B B1: 7,9,3,6 # reduction candidate for 7,9 B1: 7,9 => CTR * ...918.2..1825.7...2.746..8.368.9...84.....5....3.48...8.531.7.163497285.5.6....1 B1: 3,6 # 6 pairs B8: 7,9,6 # reduction candidate for 7,9 B8: 7,9 # 12 pairs * PAIR F8: 4,7 COL F F6: 4,7,2,5 # reduction candidate for 4,7 F6: 2,5 => CTR * .3.....2..182.37...2.746..8..64.9...34.....5....3..8.....531.7.1.3..4285.5....... F6: 4,7 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0130-base-pr-000.dot * REASONING * PRF # A1: 5,9 => SOL * DIS # C1: 5,9 => CTR => C1: 4,7 * DIS # A2: 5,9 => CTR => A2: 3,4,6 * DIS # A3: 5,9 => CTR => A3: 3 * PRF # G3: 5,9 => SOL * DIS # E1: 5,9 => CTR => E1: 1,8 * DIS # A2: 5,9 => CTR => A2: 3,4,6 * DIS # F1: 8 => CTR => F1: 3,5 * DIS # A2: 3,5 => CTR => A2: 4,6,9 * DIS # A5: 7,9 => CTR => A5: 2,3,8 * DIS # B1: 7,9 => CTR => B1: 3,6 * DIS # F6: 2,5 => CTR => F6: 4,7 * CNT 12 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C3,E2,F2,F8) * .......2..182..7...2.746..8..6..9....4.....5....3..8.....531.7.1.3...285.5....... * PAIR C3: 5,9 BLK 1 A1: 5,9,3,4,6,7 # reduction candidate for 5,9 A1: 5,9 => SOLVED * 967183524418295763325746918536879142849612357271354896682531479193467285754928631 * DURATION: 0:00:02.839150 START: 05:57:32.568632 END: 05:57:35.407782 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0130-base-pr-001.dot * REASONING * PRF # A1: 5,9 => SOL * STA A1: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=130
Solution
position: 967183524418295763325746918536879142849612357271354896682531479193467285754928631 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 # A1: 5,9 => SOL * INC # A1: 3,4,6,7 => UNS * DIS # C1: 5,9 => CTR => C1: 4,7 * INC # C1: 4,7 => UNS * DIS # A2: 5,9 => CTR => A2: 3,4,6 * INC # A2: 3,4,6 => UNS * DIS # A3: 5,9 => CTR => A3: 3 * INC # A3: 3 => UNS * PRF # G3: 5,9 => SOL * INC # G3: 1,3 => UNS * INC # C6: 5,9 => UNS * INC # C6: 1,2,7 => UNS * DIS # E1: 5,9 => CTR => E1: 1,8 * INC # E1: 1,8 => UNS * DIS # A2: 5,9 => CTR => A2: 3,4,6 * INC # A2: 3,4,6 => UNS * INC # F1: 3,5 => UNS * DIS # F1: 8 => CTR => F1: 3,5 * DIS # A2: 3,5 => CTR => A2: 4,6,9 * INC # A2: 4,6,9 => UNS * DIS # A5: 7,9 => CTR => A5: 2,3,8 * INC # A5: 2,3,8 => UNS * INC # C5: 7,9 => UNS * INC # A6: 7,9 => UNS * INC # C6: 7,9 => UNS * INC # I6: 7,9 => UNS * INC # I6: 1,2,4,6 => UNS * DIS # B1: 7,9 => CTR => B1: 3,6 * INC # B1: 3,6 => UNS * INC # B8: 7,9 => UNS * INC # F6: 4,7 => UNS * DIS # F6: 2,5 => CTR => F6: 4,7 * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 5,9 => SOL * STA A1: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED