Analysis of zz-www.sudokuwiki.org-0131-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=131
level: medium
position: ..9.3...5.2.........6..9.8.4..7.3.9.....4.....7.8.6..3...4..8.........3.5...2.7.4 initial
Autosolve
position: ..9.3...5.2.........6..9.8.4..7.3.9.....4.....7.8.6..3...4..8.........3.59.32.764 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D5: 1,5 => CTR => D5: 2,9 * DIS # F5: 1,5 => CTR => F5: 2 * PRF # E6: 1,5 => SOL * DIS # E6: 9 => CTR => E6: 1,5 * DIS # E2: 1,5 => CTR => E2: 6,7,8 * DIS # E3: 1,5 => CTR => E3: 7 * PRF # E3: 7 => SOL * DIS # E7: 1,5 => CTR => E7: 6,7,9 * DIS # E8: 1,5 => CTR => E8: 6,7,8,9 * DIS # C8: 1,8 => CTR => C8: 2,4,7 * DIS # C2: 1,8 => CTR => C2: 3,4,5,7 * DIS # C5: 1,8 => CTR => C5: 3,5 * CNT 12 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D5: 1,5 => CTR => D5: 2,9 * DIS D5: 2,9 # F5: 1,5 => CTR => F5: 2 * PRF D5: 2,9 + F5: 2 => SOL * STA D5: 2,9 + F5: 2 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..9.3...5.2.........6..9.8.4..7.3.9.....4.....7.8.6..3...4..8.........3.5...2.7.4 | initial |
| ..9.3...5.2.........6..9.8.4..7.3.9.....4.....7.8.6..3...4..8.........3.59.32.764 | autosolve |
| 789234615325168947146579382461753298853942176972816453637495821214687539598321764 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) E4: 1,5 C9: 1,8 F9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C9,F9: 1.. / C9 = 1 => 3 pairs (_) / F9 = 1 => 3 pairs (_) D5,F5: 2.. / D5 = 2 => 0 pairs (X) / F5 = 2 => 3 pairs (_) F1,F5: 2.. / F1 = 2 => 0 pairs (X) / F5 = 2 => 3 pairs (_) G2,G3: 3.. / G2 = 3 => 0 pairs (X) / G3 = 3 => 9 pairs (_) F1,F2: 4.. / F1 = 4 => 6 pairs (_) / F2 = 4 => 4 pairs (_) G6,H6: 4.. / G6 = 4 => 8 pairs (_) / H6 = 4 => 7 pairs (_) B8,C8: 4.. / B8 = 4 => 0 pairs (X) / C8 = 4 => 3 pairs (_) B3,G3: 4.. / B3 = 4 => 8 pairs (_) / G3 = 4 => 0 pairs (X) C2,C8: 4.. / C2 = 4 => 0 pairs (X) / C8 = 4 => 3 pairs (_) C2,B3: 5.. / C2 = 5 => 7 pairs (_) / B3 = 5 => 0 pairs (X) H7,G8: 5.. / H7 = 5 => 5 pairs (_) / G8 = 5 => 11 pairs (_) D1,G1: 6.. / D1 = 6 => 15 pairs (_) / G1 = 6 => 8 pairs (_) H5,I5: 7.. / H5 = 7 => 4 pairs (_) / I5 = 7 => 0 pairs (X) I4,I5: 8.. / I4 = 8 => 3 pairs (_) / I5 = 8 => 4 pairs (_) C9,F9: 8.. / C9 = 8 => 3 pairs (_) / F9 = 8 => 3 pairs (_) E2,E8: 8.. / E2 = 8 => 3 pairs (_) / E8 = 8 => 7 pairs (_) G2,I2: 9.. / G2 = 9 => 9 pairs (_) / I2 = 9 => 0 pairs (X) A5,A6: 9.. / A5 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) D5,E6: 9.. / D5 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) A5,D5: 9.. / A5 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) A6,E6: 9.. / A6 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) E7,I7: 9.. / E7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) D5,D8: 9.. / D5 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) G2,G8: 9.. / G2 = 9 => 9 pairs (_) / G8 = 9 => 0 pairs (X) * DURATION: 0:00:31.996625 START: 05:57:51.268151 END: 05:58:23.264776 2017-05-01 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,E4,F9) * ..9.3...5.2.........6..9.8.4..7.3.9.....4.....7.8.6..3...4..8.........3.59.32.764 * PAIR E4: 1,5 BLK 5 D5: 1,5,2,9 # reduction candidate for 1,5 D5: 1,5 => CTR * 819.3764532568491774615938245871329696354217817289645323746.8.968497..3.591328764 D5: 2,9 # 4 pairs F5: 1,5,2 # reduction candidate for 1,5 F5: 1,5 => CTR * ..9.32..5.2..849..1465793824..7.3.9.9..24....27.896..3..24..859..49..23159.32.764 F5: 2 # 3 pairs E6: 1,5,9 # reduction candidate for 1,5 E6: 1,5 => SOLVED * 789234615325168947146579382461753298853942176972816453637495821214687539598321764 E6: 9 => CTR * 819.3764532568491774615938245871329696354217817289645323746.8.968497..3.591328764 * PAIR E4: 1,5 ROW 4 B4: 1,5,6,8 # reduction candidate for 1,5 B4: 1,5 # 7 pairs C4: 1,5,2,8 # reduction candidate for 1,5 C4: 1,5 # 6 pairs G4: 1,5,2,6 # reduction candidate for 1,5 G4: 1,5 # 6 pairs * PAIR E4: 1,5 COL E E2: 1,5,6,7,8 # reduction candidate for 1,5 E2: 1,5 => CTR * ..9.3...5.2....9..1465793824..753.9.953.4.....7.896..3...46.8.96..98..3.598321764 E2: 6,7,8 # 3 pairs E3: 1,5,7 # reduction candidate for 1,5 E3: 1,5 => CTR * 819637425325.8.9..7462593814.8713.9.9.3542..8172896..323746.8.968497..32591328764 E3: 7 => SOLVED * 789234615325168947146579382461753298853942176972816453637495821214687539598321764 E7: 1,5,6,7,9 # reduction candidate for 1,5 E7: 1,5 => CTR * 819.3..75325.8.916.46..938.4.87.3.9...3.4...8.728.6..36374..829284.67531591328764 E7: 6,7,9 # 3 pairs E8: 1,5,6,7,8,9 # reduction candidate for 1,5 E8: 1,5 => CTR * 8.9.3..75.2..8.9..146.7938.4..7.3.9.9...4.....7.896..3...46.8.96..9...3.59.32.764 E8: 6,7,8,9 # 3 pairs * PAIR C9: 1,8 BLK 7 A8: 1,8,2,6,7 # reduction candidate for 1,8 A8: 1,8 # 9 pairs B8: 1,8,4,6 # reduction candidate for 1,8 B8: 1,8 # 5 pairs C8: 1,8,2,4,7 # reduction candidate for 1,8 C8: 1,8 => CTR * ..9.34625.24.8.31935621948.4..7.3.9...3942...97.8.6.4363749.85224....931591328764 C8: 2,4,7 # 3 pairs * PAIR C9: 1,8 COL C C2: 1,8,3,4,5,7 # reduction candidate for 1,8 C2: 1,8 => CTR * .49.3762572.5.43.9356..948.4..7.3.9...3942...97.8.6.43.3749.85...4..593.59.32.764 C2: 3,4,5,7 # 3 pairs C4: 1,8,2,5 # reduction candidate for 1,8 C4: 1,8 # 6 pairs C5: 1,8,3,5 # reduction candidate for 1,8 C5: 1,8 => CTR * ..913.62512....3793562794814..7.3.9..3.94251797.816243..349.85.......93.59.32.764 C5: 3,5 # 4 pairs * PAIR F9: 1,8 BLK 8 E8: 1,8,5,6,7,9 # reduction candidate for 1,8 E8: 1,8 # 9 pairs F8: 1,8,5,7 # reduction candidate for 1,8 F8: 1,8 # 7 pairs * PAIR F9: 1,8 COL F F1: 1,8,2,4,7 # reduction candidate for 1,8 F1: 1,8 # 7 pairs F2: 1,8,4,5,7 # reduction candidate for 1,8 F2: 1,8 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0131-base-pr-000.dot * REASONING * DIS # D5: 1,5 => CTR => D5: 2,9 * DIS # F5: 1,5 => CTR => F5: 2 * PRF # E6: 1,5 => SOL * DIS # E6: 9 => CTR => E6: 1,5 * DIS # E2: 1,5 => CTR => E2: 6,7,8 * DIS # E3: 1,5 => CTR => E3: 7 * PRF # E3: 7 => SOL * DIS # E7: 1,5 => CTR => E7: 6,7,9 * DIS # E8: 1,5 => CTR => E8: 6,7,8,9 * DIS # C8: 1,8 => CTR => C8: 2,4,7 * DIS # C2: 1,8 => CTR => C2: 3,4,5,7 * DIS # C5: 1,8 => CTR => C5: 3,5 * CNT 12 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,E4,F9) * ..9.3...5.2.........6..9.8.4..7.3.9.....4.....7.8.6..3...4..8.........3.59.32.764 * PAIR E4: 1,5 BLK 5 D5: 1,5,2,9 # reduction candidate for 1,5 D5: 1,5 => CTR * 819.3764532568491774615938245871329696354217817289645323746.8.968497..3.591328764 F5: 1,5,2 # reduction candidate for 1,5 F5: 1,5 => CTR * ..9.32..5.2..849..1465793824..7.3.9.9..24....27.896..3..24..859..49..23159.32.764 F5: 2 => SOLVED * 789234615325168947146579382461753298853942176972816453637495821214687539598321764 * DURATION: 0:00:03.304509 START: 05:58:45.561300 END: 05:58:48.865809 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0131-base-pr-001.dot * REASONING * DIS # D5: 1,5 => CTR => D5: 2,9 * DIS D5: 2,9 # F5: 1,5 => CTR => F5: 2 * PRF D5: 2,9 + F5: 2 => SOL * STA D5: 2,9 + F5: 2 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=131
Solution
position: 789234615325168947146579382461753298853942176972816453637495821214687539598321764 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 # D5: 1,5 => CTR => D5: 2,9 * INC # D5: 2,9 => UNS * DIS # F5: 1,5 => CTR => F5: 2 * INC # F5: 2 => UNS * PRF # E6: 1,5 => SOL * DIS # E6: 9 => CTR => E6: 1,5 * INC # B4: 1,5 => UNS * INC # C4: 1,5 => UNS * INC # G4: 1,5 => UNS * DIS # E2: 1,5 => CTR => E2: 6,7,8 * INC # E2: 6,7,8 => UNS * DIS # E3: 1,5 => CTR => E3: 7 * PRF # E3: 7 => SOL * DIS # E7: 1,5 => CTR => E7: 6,7,9 * INC # E7: 6,7,9 => UNS * DIS # E8: 1,5 => CTR => E8: 6,7,8,9 * INC # E8: 6,7,8,9 => UNS * INC # A8: 1,8 => UNS * INC # B8: 1,8 => UNS * DIS # C8: 1,8 => CTR => C8: 2,4,7 * INC # C8: 2,4,7 => UNS * DIS # C2: 1,8 => CTR => C2: 3,4,5,7 * INC # C2: 3,4,5,7 => UNS * INC # C4: 1,8 => UNS * DIS # C5: 1,8 => CTR => C5: 3,5 * INC # C5: 3,5 => UNS * INC # E8: 1,8 => UNS * INC # F8: 1,8 => UNS * INC # F1: 1,8 => UNS * INC # F2: 1,8 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D5: 1,5 => CTR => D5: 2,9 * DIS D5: 2,9 # F5: 1,5 => CTR => F5: 2 * PRF D5: 2,9 + F5: 2 => SOL * STA D5: 2,9 + F5: 2 * CNT 3 HDP CHAINS / 2 HYP OPENED