Analysis of zz-www.sudokuwiki.org-0114-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=114
level: medium
position: ..1.3.....4.1.6.9.8.....3..2....5.......9..1...73....2..3.....4.6.7.1.5.....5.8.. initial
Autosolve
position: ..1.3....34.1.6.9.8.....3.12....5.3..3..9..1...73....2..3...1.4.6.7.1.53....538.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 2,5 => CTR => C3: 6,9 * DIS # E6: 4,8 => CTR => E6: 1,6 * DIS # H6: 6 => CTR => H6: 4,8 * PRF # C8: 4,9 => SOL * DIS # A9: 4,9 => CTR => A9: 1,7 * DIS # C8: 2,9 => CTR => C8: 4,8 * CNT 6 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 # C3: 2,5 => CTR => C3: 6,9 * DIS C3: 6,9 # E6: 4,8 => CTR => E6: 1,6 * DIS C3: 6,9 + E6: 1,6 # H6: 6 => CTR => H6: 4,8 * DIS C3: 6,9 + E6: 1,6 + H6: 4,8 # E4: 4,8 => CTR => E4: 1,6,7 * DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 # D5: 4,8 => CTR => D5: 2,6 * DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 # F5: 4,8 => CTR => F5: 2,7 * PRF C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 # C8: 4,9 => SOL * STA C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 + C8: 4,9 * CNT 7 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..1.3.....4.1.6.9.8.....3..2....5.......9..1...73....2..3.....4.6.7.1.5.....5.8.. | initial |
| ..1.3....34.1.6.9.8.....3.12....5.3..3..9..1...73....2..3...1.4.6.7.1.53....538.. | autosolve |
| 721938645345126798896547321219875436438692517657314982583269174964781253172453869 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) C2: 2,5 F6: 4,8 A8: 4,9 G8: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,E6: 1.. / E4 = 1 => 6 pairs (_) / E6 = 1 => 4 pairs (_) A9,B9: 1.. / A9 = 1 => 4 pairs (_) / B9 = 1 => 7 pairs (_) B4,E4: 1.. / B4 = 1 => 4 pairs (_) / E4 = 1 => 6 pairs (_) A6,A9: 1.. / A6 = 1 => 7 pairs (_) / A9 = 1 => 4 pairs (_) D5,F5: 2.. / D5 = 2 => 4 pairs (_) / F5 = 2 => 9 pairs (_) E8,D9: 4.. / E8 = 4 => 0 pairs (X) / D9 = 4 => 9 pairs (_) D1,D3: 5.. / D1 = 5 => 10 pairs (_) / D3 = 5 => 4 pairs (_) A7,B7: 5.. / A7 = 5 => 5 pairs (_) / B7 = 5 => 7 pairs (_) A1,C3: 6.. / A1 = 6 => 0 pairs (X) / C3 = 6 => 4 pairs (_) C3,H3: 6.. / C3 = 6 => 4 pairs (_) / H3 = 6 => 0 pairs (X) E4,F5: 7.. / E4 = 7 => 8 pairs (_) / F5 = 7 => 4 pairs (_) B7,C8: 8.. / B7 = 8 => 18 pairs (_) / C8 = 8 => 5 pairs (_) E2,I2: 8.. / E2 = 8 => 8 pairs (_) / I2 = 8 => 6 pairs (_) C8,E8: 8.. / C8 = 8 => 5 pairs (_) / E8 = 8 => 18 pairs (_) H1,H6: 8.. / H1 = 8 => 10 pairs (_) / H6 = 8 => 5 pairs (_) G8,I9: 9.. / G8 = 9 => 11 pairs (_) / I9 = 9 => 12 pairs (_) I4,I9: 9.. / I4 = 9 => 11 pairs (_) / I9 = 9 => 12 pairs (_) * DURATION: 0:00:19.195270 START: 05:32:51.094453 END: 05:33:10.289723 2017-05-01 * CP COUNT: (17) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C2,F6,G8) * ..1.3....34.1.6.9.8.....3.12....5.3..3..9..1...73....2..3...1.4.6.7.1.53....538.. * PAIR C2: 2,5 BLK 1 B1: 2,5,7,9 # reduction candidate for 2,5 B1: 2,5 # 7 pairs B3: 2,5,7,9 # reduction candidate for 2,5 B3: 2,5 # 7 pairs C3: 2,5,6,9 # reduction candidate for 2,5 C3: 2,5 => CTR * 6.1.3....34.176298872...3612....5.3953..9..1.9.736.5.2753689124468721953129453876 C3: 6,9 # 5 pairs * PAIR C2: 2,5 ROW 2 G2: 2,5,7 # reduction candidate for 2,5 G2: 7 # 7 pairs G2: 2,5 # 7 pairs * PAIR F6: 4,8 BLK 5 D4: 4,8,6 # reduction candidate for 4,8 D4: 4,8 # 8 pairs E4: 4,8,1,6,7 # reduction candidate for 4,8 E4: 4,8 # 8 pairs D5: 4,8,2,6 # reduction candidate for 4,8 D5: 4,8 # 12 pairs F5: 4,8,2,7 # reduction candidate for 4,8 F5: 4,8 # 14 pairs E6: 4,8,1,6 # reduction candidate for 4,8 E6: 4,8 => CTR * ..1.3468.34.1862978.6.7234128.61573963.297418..7348562..38691.4468721953...4538.6 E6: 1,6 # 5 pairs * PAIR F6: 4,8 ROW 6 H6: 4,8,6 # reduction candidate for 4,8 H6: 6 => CTR * ..1.3.68.34.1862978.6...3412....5.3963..9..18..73...62..3...1.4.68721953....538.6 H6: 4,8 # 6 pairs * PAIR F6: 4,8 COL F F1: 4,8,2,7,9 # reduction candidate for 4,8 F1: 4,8 # 7 pairs F1: 2,7,9 # 4 pairs * PAIR A8: 4,9 BLK 7 C8: 4,9,2,8 # reduction candidate for 4,9 C8: 4,9 => SOLVED * 721938645345126798896547321219875436438692517657314982583269174964781253172453869 C8: 2,8 # 5 pairs A9: 4,9,1,7 # reduction candidate for 4,9 A9: 4,9 => CTR * ..193..853451862978..57.3.1284615739.36297418197348562..38.9124.68721953912453876 A9: 1,7 # 5 pairs C9: 4,9,2 # reduction candidate for 4,9 C9: 4,9 # 8 pairs * PAIR A8: 4,9 COL A A6: 4,9,1,5,6 # reduction candidate for 4,9 A6: 4,9 # 7 pairs A6: 1,5,6 # 4 pairs * PAIR G8: 2,9 ROW 8 C8: 2,9,4,8 # reduction candidate for 2,9 C8: 2,9 => CTR * .21.3..4.3451267988.654.3212...75.3663..9..17.573.4.82583...174469781253..2453869 C8: 4,8 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0114-base-pr-000.dot * REASONING * DIS # C3: 2,5 => CTR => C3: 6,9 * DIS # E6: 4,8 => CTR => E6: 1,6 * DIS # H6: 6 => CTR => H6: 4,8 * PRF # C8: 4,9 => SOL * DIS # A9: 4,9 => CTR => A9: 1,7 * DIS # C8: 2,9 => CTR => C8: 4,8 * CNT 6 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C2,F6,G8) * ..1.3....34.1.6.9.8.....3.12....5.3..3..9..1...73....2..3...1.4.6.7.1.53....538.. * PAIR C2: 2,5 BLK 1 B1: 2,5,7,9 # reduction candidate for 2,5 B1: 2,5 # 7 pairs B3: 2,5,7,9 # reduction candidate for 2,5 B3: 2,5 # 7 pairs C3: 2,5,6,9 # reduction candidate for 2,5 C3: 2,5 => CTR * 6.1.3....34.176298872...3612....5.3953..9..1.9.736.5.2753689124468721953129453876 * PAIR C2: 2,5 ROW 2 G2: 2,5,7 # reduction candidate for 2,5 G2: 7 # 8 pairs G2: 2,5 # 8 pairs * PAIR RESTART * PAIR C2: 2,5 BLK 1 B1: 2,5,7,9 # reduction candidate for 2,5 B1: 2,5 # 7 pairs B3: 2,5,7,9 # reduction candidate for 2,5 B3: 2,5 # 7 pairs * PAIR C2: 2,5 ROW 2 G2: 2,5,7 # reduction candidate for 2,5 G2: 7 # 8 pairs G2: 2,5 # 8 pairs * PAIR F6: 4,8 BLK 5 D4: 4,8,6 # reduction candidate for 4,8 D4: 4,8 # 9 pairs E4: 4,8,1,6,7 # reduction candidate for 4,8 E4: 4,8 # 9 pairs D5: 4,8,2,6 # reduction candidate for 4,8 D5: 4,8 # 13 pairs F5: 4,8,2,7 # reduction candidate for 4,8 F5: 4,8 # 15 pairs E6: 4,8,1,6 # reduction candidate for 4,8 E6: 4,8 => CTR * ..1.3468.34.1862978.6.7234128.61573963.297418..7348562..38691.4468721953...4538.6 * PAIR F6: 4,8 ROW 6 H6: 4,8,6 # reduction candidate for 4,8 H6: 6 => CTR * ..1.3.68.34.1862978.6...3412....5.3963..9..18..731..62..3...1.4.687219531...538.6 * PAIR F6: 4,8 COL F F1: 4,8,2,7,9 # reduction candidate for 4,8 F1: 4,8 # 10 pairs F1: 2,7,9 # 7 pairs * PAIR RESTART * PAIR F6: 4,8 BLK 5 D4: 4,8,6 # reduction candidate for 4,8 D4: 4,8 # 10 pairs E4: 4,8,1,6,7 # reduction candidate for 4,8 E4: 4,8 => CTR * ..1.3....34.1.6.988.....3.121..45.3..3.297.1...7318..2.83.6.1.4.6.781.531..4538.. D5: 4,8,2,6 # reduction candidate for 4,8 D5: 4,8 => CTR * ..1.3....34.126.988...473.1218675439.3.892.1...7314.82583269174.6.781953179453826 F5: 4,8,2,7 # reduction candidate for 4,8 F5: 4,8 => CTR * 7.183....34.126.988.6547321218675439.3.298.17..7314.82583962174.6.781.5317.4538.. * RESTART * PAIR F6: 4,8 COL F F1: 4,8,2,7,9 # reduction candidate for 4,8 F1: 4,8 # 12 pairs F1: 2,7,9 # 10 pairs * PAIR A8: 4,9 BLK 7 C8: 4,9,2,8 # reduction candidate for 4,9 C8: 4,9 => SOLVED * 721938645345126798896547321219875436438692517657314982583269174964781253172453869 * DURATION: 0:00:18.847842 START: 05:33:26.956401 END: 05:33:45.804243 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0114-base-pr-001.dot * REASONING * DIS # C3: 2,5 => CTR => C3: 6,9 * DIS C3: 6,9 # E6: 4,8 => CTR => E6: 1,6 * DIS C3: 6,9 + E6: 1,6 # H6: 6 => CTR => H6: 4,8 * DIS C3: 6,9 + E6: 1,6 + H6: 4,8 # E4: 4,8 => CTR => E4: 1,6,7 * DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 # D5: 4,8 => CTR => D5: 2,6 * DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 # F5: 4,8 => CTR => F5: 2,7 * PRF C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 # C8: 4,9 => SOL * STA C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 + C8: 4,9 * CNT 7 HDP CHAINS / 25 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=114
Solution
position: 721938645345126798896547321219875436438692517657314982583269174964781253172453869 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:
* INC # B1: 2,5 => UNS * INC # B3: 2,5 => UNS * DIS # C3: 2,5 => CTR => C3: 6,9 * INC # C3: 6,9 => UNS * INC # G2: 2,5 => UNS * INC # G2: 7 => UNS * INC # D4: 4,8 => UNS * INC # E4: 4,8 => UNS * INC # D5: 4,8 => UNS * INC # F5: 4,8 => UNS * DIS # E6: 4,8 => CTR => E6: 1,6 * INC # E6: 1,6 => UNS * INC # H6: 4,8 => UNS * DIS # H6: 6 => CTR => H6: 4,8 * INC # F1: 4,8 => UNS * INC # F1: 2,7,9 => UNS * PRF # C8: 4,9 => SOL * INC # C8: 2,8 => UNS * DIS # A9: 4,9 => CTR => A9: 1,7 * INC # A9: 1,7 => UNS * INC # C9: 4,9 => UNS * INC # A6: 4,9 => UNS * INC # A6: 1,5,6 => UNS * DIS # C8: 2,9 => CTR => C8: 4,8 * INC # C8: 4,8 => UNS * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 2,5 => UNS * INC # B3: 2,5 => UNS * DIS # C3: 2,5 => CTR => C3: 6,9 * INC C3: 6,9 # G2: 2,5 => UNS * INC C3: 6,9 # G2: 7 => UNS * INC C3: 6,9 # B1: 2,5 => UNS * INC C3: 6,9 # B3: 2,5 => UNS * INC C3: 6,9 # G2: 2,5 => UNS * INC C3: 6,9 # G2: 7 => UNS * INC C3: 6,9 # D4: 4,8 => UNS * INC C3: 6,9 # E4: 4,8 => UNS * INC C3: 6,9 # D5: 4,8 => UNS * INC C3: 6,9 # F5: 4,8 => UNS * DIS C3: 6,9 # E6: 4,8 => CTR => E6: 1,6 * INC C3: 6,9 + E6: 1,6 # H6: 4,8 => UNS * DIS C3: 6,9 + E6: 1,6 # H6: 6 => CTR => H6: 4,8 * INC C3: 6,9 + E6: 1,6 + H6: 4,8 # F1: 4,8 => UNS * INC C3: 6,9 + E6: 1,6 + H6: 4,8 # F1: 2,7,9 => UNS * INC C3: 6,9 + E6: 1,6 + H6: 4,8 # D4: 4,8 => UNS * DIS C3: 6,9 + E6: 1,6 + H6: 4,8 # E4: 4,8 => CTR => E4: 1,6,7 * DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 # D5: 4,8 => CTR => D5: 2,6 * DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 # F5: 4,8 => CTR => F5: 2,7 * INC C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 # F1: 4,8 => UNS * INC C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 # F1: 2,7,9 => UNS * PRF C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 # C8: 4,9 => SOL * STA C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 + C8: 4,9 * CNT 25 HDP CHAINS / 25 HYP OPENED