Analysis of zz-www.sudokuwiki.org-0091-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=91
level: medium
position: ....38....4.2....52.....1....73...6..5..9..7..9...53....9.....64....6.2....91.... initial
Autosolve
position: ....38....4.2....52.....1....73..569.5..9..7..9...53....9.....64....692....91.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 6,7 => CTR => D1: 1,4,5 * DIS # E3: 6,7 => CTR => E3: 4,5 * DIS # A2: 6,7 => CTR => A2: 1,3,8,9 * DIS # C5: 1,2 => CTR => C5: 3,4,6,8 * DIS # I5: 1,2 => CTR => I5: 4,8 * CNT 5 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 6,7 => CTR => D1: 1,4,5 * DIS D1: 1,4,5 # E3: 6,7 => CTR => E3: 4,5 * DIS D1: 1,4,5 + E3: 4,5 # A2: 6,7 => CTR => A2: 1,3,8,9 * DIS D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # B4: 1,8 => CTR => B4: 2 * PRF D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 + B4: 2 # A5: 1,8 => SOL * STA D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 + B4: 2 + A5: 1,8 * CNT 5 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....38....4.2....52.....1....73...6..5..9..7..9...53....9.....64....6.2....91.... | initial |
| ....38....4.2....52.....1....73..569.5..9..7..9...53....9.....64....692....91.... | autosolve |
| 975138642341267895286459137127384569853691274694725381539842716418576923762913458 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) E2: 6,7 H1: 4,9 A4: 1,8 F5: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,F2: 1.. / D1 = 1 => 8 pairs (_) / F2 = 1 => 0 pairs (X) H7,I8: 1.. / H7 = 1 => 5 pairs (_) / I8 = 1 => 5 pairs (_) H6,H7: 1.. / H6 = 1 => 5 pairs (_) / H7 = 1 => 5 pairs (_) G1,I1: 2.. / G1 = 2 => 0 pairs (X) / I1 = 2 => 10 pairs (_) G1,G5: 2.. / G1 = 2 => 0 pairs (X) / G5 = 2 => 10 pairs (_) A5,C5: 3.. / A5 = 3 => 4 pairs (_) / C5 = 3 => 9 pairs (_) F7,F9: 3.. / F7 = 3 => 4 pairs (_) / F9 = 3 => 7 pairs (_) C5,C6: 4.. / C5 = 4 => 6 pairs (_) / C6 = 4 => 5 pairs (_) E4,F4: 4.. / E4 = 4 => 10 pairs (_) / F4 = 4 => 8 pairs (_) H7,H9: 5.. / H7 = 5 => 6 pairs (_) / H9 = 5 => 4 pairs (_) G1,G2: 6.. / G1 = 6 => 11 pairs (_) / G2 = 6 => 14 pairs (_) D6,E6: 7.. / D6 = 7 => 5 pairs (_) / E6 = 7 => 0 pairs (X) A1,A2: 9.. / A1 = 9 => 5 pairs (_) / A2 = 9 => 5 pairs (_) F2,F3: 9.. / F2 = 9 => 9 pairs (_) / F3 = 9 => 5 pairs (_) A1,H1: 9.. / A1 = 9 => 5 pairs (_) / H1 = 9 => 5 pairs (_) F3,H3: 9.. / F3 = 9 => 5 pairs (_) / H3 = 9 => 9 pairs (_) * DURATION: 0:00:18.487500 START: 05:06:41.974055 END: 05:07:00.461555 2017-05-01 * CP COUNT: (16) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,E2,F5,H1) * ....38....4.2....52.....1....73..569.5..9..7..9...53....9.....64....692....91.... * PAIR E2: 6,7 BLK 2 D1: 6,7,1,4,5 # reduction candidate for 6,7 D1: 6,7 => CTR * ..16382...4.2716.52.5.491..127384569.5..92.7..9.765312.1942...64..856921..291.... D1: 1,4,5 # 4 pairs D3: 6,7,4,5 # reduction candidate for 6,7 D3: 6,7 # 17 pairs E3: 6,7,4,5 # reduction candidate for 6,7 E3: 6,7 => CTR * 965138.4.741269..52..5.419...734.569.5.69..7.69.78531...942...6473856921...91.... E3: 4,5 # 5 pairs * PAIR E2: 6,7 ROW 2 A2: 6,7,1,3,8,9 # reduction candidate for 6,7 A2: 6,7 => CTR * 9..138642.412798352....4197..7342569.5..9127..927.53.4..942.7.647...692....91.... A2: 1,3,8,9 # 4 pairs G2: 6,7,8 # reduction candidate for 6,7 G2: 6,7 # 6 pairs * PAIR E2: 6,7 COL E E6: 6,7,2,8 # reduction candidate for 6,7 E6: 2,8 # 11 pairs E6: 6,7 # 7 pairs * PAIR H1: 4,9 BLK 3 H3: 4,9,3,8 # reduction candidate for 4,9 H3: 4,9 # 8 pairs H3: 3,8 # 6 pairs * PAIR A4: 1,8 BLK 4 B4: 1,8,2 # reduction candidate for 1,8 B4: 1,8 # 14 pairs A5: 1,8,3,6 # reduction candidate for 1,8 A5: 1,8 # 10 pairs C5: 1,8,2,3,4,6 # reduction candidate for 1,8 C5: 1,8 # 9 pairs A6: 1,8,6 # reduction candidate for 1,8 A6: 1,8 # 9 pairs C6: 1,8,2,4,6 # reduction candidate for 1,8 C6: 1,8 # 10 pairs * PAIR A4: 1,8 COL A A2: 1,8,3,6,7,9 # reduction candidate for 1,8 A2: 1,8 # 8 pairs A7: 1,8,3,5,7 # reduction candidate for 1,8 A7: 1,8 # 7 pairs * PAIR F5: 1,2 BLK 5 F4: 1,2,4 # reduction candidate for 1,2 F4: 1,2 # 10 pairs F4: 4 # 8 pairs * PAIR F5: 1,2 ROW 5 C5: 1,2,3,4,6,8 # reduction candidate for 1,2 C5: 1,2 => CTR * ...1382...4.2796.52..56419...734.56935.69..7.694785312..942...6473856921...91.... C5: 3,4,6,8 # 4 pairs I5: 1,2,4,8 # reduction candidate for 1,2 I5: 1,2 => CTR * 9.5138247.4.2796.527...419...734.569.5..9..7..9.7.53....94....64....692....91.... I5: 4,8 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0091-base-pr-000.dot * REASONING * DIS # D1: 6,7 => CTR => D1: 1,4,5 * DIS # E3: 6,7 => CTR => E3: 4,5 * DIS # A2: 6,7 => CTR => A2: 1,3,8,9 * DIS # C5: 1,2 => CTR => C5: 3,4,6,8 * DIS # I5: 1,2 => CTR => I5: 4,8 * CNT 5 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,E2,F5,H1) * ....38....4.2....52.....1....73..569.5..9..7..9...53....9.....64....692....91.... * PAIR E2: 6,7 BLK 2 D1: 6,7,1,4,5 # reduction candidate for 6,7 D1: 6,7 => CTR * ..16382...4.2716.52.5.491..127384569.5..92.7..9.765312.1942...64..856921..291.... D3: 6,7,4,5 # reduction candidate for 6,7 D3: 6,7 # 17 pairs E3: 6,7,4,5 # reduction candidate for 6,7 E3: 6,7 => CTR * 965138.4.741269..52..5.419...734.569.5.69..7.69.78531...942...6473856921...91.... * RESTART * PAIR E2: 6,7 BLK 2 D3: 6,7,4,5 # reduction candidate for 6,7 D3: 6,7 # 17 pairs D3: 4,5 # 13 pairs * PAIR E2: 6,7 ROW 2 A2: 6,7,1,3,8,9 # reduction candidate for 6,7 A2: 6,7 => CTR * 97..3864264.27.8.52..6..1.7..73..569.56.91274.947.53....9.....64....692....91.... G2: 6,7,8 # reduction candidate for 6,7 G2: 6,7 # 7 pairs * RESTART * PAIR E2: 6,7 ROW 2 G2: 6,7,8 # reduction candidate for 6,7 G2: 8 # 26 pairs G2: 6,7 # 7 pairs * PAIR E2: 6,7 COL E E6: 6,7,2,8 # reduction candidate for 6,7 E6: 2,8 # 16 pairs E6: 6,7 # 7 pairs * PAIR RESTART * PAIR E2: 6,7 BLK 2 D3: 6,7,4,5 # reduction candidate for 6,7 D3: 6,7 # 17 pairs D3: 4,5 # 13 pairs * PAIR E2: 6,7 ROW 2 G2: 6,7,8 # reduction candidate for 6,7 G2: 8 # 26 pairs G2: 6,7 # 7 pairs * PAIR E2: 6,7 COL E E6: 6,7,2,8 # reduction candidate for 6,7 E6: 2,8 # 16 pairs E6: 6,7 # 7 pairs * PAIR H1: 4,9 BLK 3 H3: 4,9,3,8 # reduction candidate for 4,9 H3: 4,9 # 9 pairs H3: 3,8 # 7 pairs * PAIR A4: 1,8 BLK 4 B4: 1,8,2 # reduction candidate for 1,8 B4: 1,8 => CTR * 975138642.4126..352.....197..73..569354691278692..5314..9.....64....6921...91...3 A5: 1,8,3,6 # reduction candidate for 1,8 A5: 1,8 => SOLVED * 975138642341267895286459137127384569853691274694725381539842716418576923762913458 * DURATION: 0:00:17.292781 START: 05:07:16.610382 END: 05:07:33.903163 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0091-base-pr-001.dot * REASONING * DIS # D1: 6,7 => CTR => D1: 1,4,5 * DIS D1: 1,4,5 # E3: 6,7 => CTR => E3: 4,5 * DIS D1: 1,4,5 + E3: 4,5 # A2: 6,7 => CTR => A2: 1,3,8,9 * DIS D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # B4: 1,8 => CTR => B4: 2 * PRF D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 + B4: 2 # A5: 1,8 => SOL * STA D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 + B4: 2 + A5: 1,8 * CNT 5 HDP CHAINS / 21 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=91
Solution
position: 975138642341267895286459137127384569853691274694725381539842716418576923762913458 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 # D1: 6,7 => CTR => D1: 1,4,5 * INC # D1: 1,4,5 => UNS * INC # D3: 6,7 => UNS * DIS # E3: 6,7 => CTR => E3: 4,5 * INC # E3: 4,5 => UNS * DIS # A2: 6,7 => CTR => A2: 1,3,8,9 * INC # A2: 1,3,8,9 => UNS * INC # G2: 6,7 => UNS * INC # E6: 6,7 => UNS * INC # E6: 2,8 => UNS * INC # H3: 4,9 => UNS * INC # H3: 3,8 => UNS * INC # B4: 1,8 => UNS * INC # A5: 1,8 => UNS * INC # C5: 1,8 => UNS * INC # A6: 1,8 => UNS * INC # C6: 1,8 => UNS * INC # A2: 1,8 => UNS * INC # A7: 1,8 => UNS * INC # F4: 1,2 => UNS * INC # F4: 4 => UNS * DIS # C5: 1,2 => CTR => C5: 3,4,6,8 * INC # C5: 3,4,6,8 => UNS * DIS # I5: 1,2 => CTR => I5: 4,8 * INC # I5: 4,8 => UNS * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 6,7 => CTR => D1: 1,4,5 * INC D1: 1,4,5 # D3: 6,7 => UNS * DIS D1: 1,4,5 # E3: 6,7 => CTR => E3: 4,5 * INC D1: 1,4,5 + E3: 4,5 # D3: 6,7 => UNS * INC D1: 1,4,5 + E3: 4,5 # D3: 4,5 => UNS * DIS D1: 1,4,5 + E3: 4,5 # A2: 6,7 => CTR => A2: 1,3,8,9 * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # G2: 6,7 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # G2: 6,7 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # G2: 8 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # E6: 6,7 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # E6: 2,8 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # D3: 6,7 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # D3: 4,5 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # G2: 6,7 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # G2: 8 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # E6: 6,7 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # E6: 2,8 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # H3: 4,9 => UNS * INC D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # H3: 3,8 => UNS * DIS D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 # B4: 1,8 => CTR => B4: 2 * PRF D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 + B4: 2 # A5: 1,8 => SOL * STA D1: 1,4,5 + E3: 4,5 + A2: 1,3,8,9 + B4: 2 + A5: 1,8 * CNT 21 HDP CHAINS / 21 HYP OPENED