Analysis of zz-www.sudokuwiki.org-0125-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=125
level: medium
position: 6..7.4....3..9..8...96....11.........4.3...9.........27....14......3..5....4.7..6 initial
Autosolve
position: 6..7.4....3..9.68...96.3..11.........4.3...9.........27....14......3..5....4.7.16 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 2,5 => CTR => E1: 1,8 * PRF # D2: 2,5 => SOL * DIS # D2: 1 => CTR => D2: 2,5 * DIS # E3: 2,5 => CTR => E3: 8 * DIS # A2: 2,5 => CTR => A2: 4 * PRF # A2: 4 => SOL * DIS # C2: 2,5 => CTR => C2: 1,4,7 * DIS # I2: 5 => CTR => I2: 4,7 * DIS # D7: 2,5 => CTR => D7: 8,9 * PRF # E7: 2,5 => SOL * DIS # E7: 6 => CTR => E7: 2,5 * DIS # A9: 2,5 => CTR => A9: 3,8,9 * DIS # E1: 2,5 => CTR => E1: 1,8 * DIS # E3: 2,5 => CTR => E3: 8 * DIS # E4: 2,5 => CTR => E4: 4,6,7 * DIS # E5: 2,5 => CTR => E5: 1,6,7 * DIS # G9: 2,3 => CTR => G9: 8,9 * CNT 17 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 2,5 => CTR => E1: 1,8 * PRF E1: 1,8 # D2: 2,5 => SOL * STA E1: 1,8 + D2: 2,5 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..7.4....3..9..8...96....11.........4.3...9.........27....14......3..5....4.7..6 | initial |
| 6..7.4....3..9.68...96.3..11.........4.3...9.........27....14......3..5....4.7.16 | autosolve |
| 682714539431295687579683241123579864847362195965148372796851423214936758358427916 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) F2: 2,5 H1: 2,3 H3: 4,7 E9: 2,5 H7: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,D2: 1.. / E1 = 1 => 0 pairs (*) / D2 = 1 => 0 pairs (X) G5,G6: 1.. / G5 = 1 => 5 pairs (_) / G6 = 1 => 0 pairs (X) B8,C8: 1.. / B8 = 1 => 5 pairs (_) / C8 = 1 => 0 pairs (X) C2,D2: 1.. / C2 = 1 => 0 pairs (*) / D2 = 1 => 0 pairs (X) E5,G5: 1.. / E5 = 1 => 0 pairs (X) / G5 = 1 => 5 pairs (_) B1,B8: 1.. / B1 = 1 => 0 pairs (X) / B8 = 1 => 5 pairs (_) D2,D6: 1.. / D2 = 1 => 0 pairs (X) / D6 = 1 => 0 pairs (_) H1,H7: 2.. / H1 = 2 => 7 pairs (_) / H7 = 2 => 5 pairs (_) A6,A9: 3.. / A6 = 3 => 5 pairs (_) / A9 = 3 => 5 pairs (_) H1,H7: 3.. / H1 = 3 => 5 pairs (_) / H7 = 3 => 7 pairs (_) I2,H3: 4.. / I2 = 4 => 0 pairs (X) / H3 = 4 => 8 pairs (_) E4,E6: 4.. / E4 = 4 => 0 pairs (X) / E6 = 4 => 6 pairs (_) A8,C8: 4.. / A8 = 4 => 0 pairs (X) / C8 = 4 => 0 pairs (_) A3,H3: 4.. / A3 = 4 => 0 pairs (X) / H3 = 4 => 8 pairs (_) E6,H6: 4.. / E6 = 4 => 6 pairs (_) / H6 = 4 => 0 pairs (X) C2,C8: 4.. / C2 = 4 => 0 pairs (X) / C8 = 4 => 0 pairs (_) I2,I4: 4.. / I2 = 4 => 0 pairs (X) / I4 = 4 => 8 pairs (_) H4,H6: 6.. / H4 = 6 => 6 pairs (_) / H6 = 6 => 6 pairs (_) E7,F8: 6.. / E7 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) C2,B3: 7.. / C2 = 7 => 0 pairs (X) / B3 = 7 => 9 pairs (_) G8,I8: 7.. / G8 = 7 => 8 pairs (_) / I8 = 7 => 0 pairs (X) C2,I2: 7.. / C2 = 7 => 0 pairs (X) / I2 = 7 => 9 pairs (_) E1,E3: 8.. / E1 = 8 => 0 pairs (X) / E3 = 8 => 5 pairs (_) G1,I1: 9.. / G1 = 9 => 8 pairs (_) / I1 = 9 => 7 pairs (_) * DURATION: 0:00:35.068806 START: 05:48:54.442171 END: 05:49:29.510977 2017-05-01 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E9,F2,H1,H3,H7) * 6..7.4....3..9.68...96.3..11.........4.3...9.........27....14......3..5....4.7.16 * PAIR F2: 2,5 BLK 2 E1: 2,5,1,8 # reduction candidate for 2,5 E1: 2,5 => CTR * 6..7.4....3419.687.79683.411.......484.3...95....4.1.27...614..4...3.75....4.7.16 E1: 1,8 # 6 pairs D2: 2,5,1 # reduction candidate for 2,5 D2: 2,5 => SOLVED * 682714539431295687579683241123579864847362195965148372796851423214936758358427916 D2: 1 => CTR * 6..7.4...5341926878796532411..27.364247316.9.....4.1727..5614234...3.75....427.16 E3: 2,5,8 # reduction candidate for 2,5 E3: 2,5 => CTR * 6..784...5341926878796532411..27.364247316.9.....4.1727..5614234...3.75....427.16 E3: 8 # 5 pairs * PAIR F2: 2,5 ROW 2 A2: 2,5,4 # reduction candidate for 2,5 A2: 2,5 => CTR * 6..7.4...5341926878796532411..27.364247316.9.....4.1727..5614234...3.75....427.16 A2: 4 => SOLVED * 682714539431295687579683241123579864847362195965148372796851423214936758358427916 C2: 2,5,1,4,7 # reduction candidate for 2,5 C2: 2,5 => CTR * 6.17.4...43.19.687.796.3.411.....3.4.4.31..9.....4.1.27....14...14.3675....4.7.16 C2: 1,4,7 # 5 pairs * PAIR F2: 2,5 COL F F4: 2,5,6,8,9 # reduction candidate for 2,5 F4: 2,5 # 7 pairs F5: 2,5,6,8 # reduction candidate for 2,5 F5: 2,5 # 6 pairs * PAIR H1: 2,3 BLK 3 G1: 2,3,5,9 # reduction candidate for 2,3 G1: 2,3 # 9 pairs G1: 5,9 # 6 pairs * PAIR H3: 4,7 BLK 3 I2: 4,7,5 # reduction candidate for 4,7 I2: 5 => CTR * 6.17.4...437192685..96.37411.....3.4.4.31.59.....4.1.27....14....4.3..5....4.7.16 I2: 4,7 # 7 pairs * PAIR H3: 4,7 COL H H4: 4,7,6 # reduction candidate for 4,7 H4: 4,7 # 6 pairs H6: 4,7,6 # reduction candidate for 4,7 H6: 4,7 # 6 pairs * PAIR E9: 2,5 BLK 8 D7: 2,5,8,9 # reduction candidate for 2,5 D7: 2,5 => CTR * 6..7.4....3719.68...96.3..11.........4.3...9.........27....14....4.3.257...4.7.16 D7: 8,9 # 10 pairs E7: 2,5,6 # reduction candidate for 2,5 E7: 2,5 => SOLVED * 682714539431295687579683241123579864847362195965148372796851423214936758358427916 E7: 6 => CTR * 6..7.4...5341926878796532411..27.364247316.9.....4.1727..5614234...3.75....427.16 * PAIR E9: 2,5 ROW 9 A9: 2,5,3,8,9 # reduction candidate for 2,5 A9: 2,5 => CTR * 6..7.4.29.3719.68...96.3..11..2......4.3...9.3..5....27..9.1438914836257.834.7916 A9: 3,8,9 # 5 pairs B9: 2,5,8,9 # reduction candidate for 2,5 B9: 2,5 # 7 pairs C9: 2,5,3,8 # reduction candidate for 2,5 C9: 2,5 # 7 pairs * PAIR E9: 2,5 COL E E1: 2,5,1,8 # reduction candidate for 2,5 E1: 2,5 => CTR * 6..7.4....3419.687.79683.411.......484.3...95....4.1.27...614..4...3.75....4.7.16 E1: 1,8 # 6 pairs E3: 2,5,8 # reduction candidate for 2,5 E3: 2,5 => CTR * 6..784...5341926878796532411..27.364247316.9.....4.1727..5614234...3.75....427.16 E3: 8 # 5 pairs E4: 2,5,4,6,7 # reduction candidate for 2,5 E4: 2,5 => CTR * 6..714....31.9.687.79683.411.......4.4.37.19....14...27...614...1..3..5....4.7.16 E4: 4,6,7 # 5 pairs E5: 2,5,1,6,7 # reduction candidate for 2,5 E5: 2,5 => CTR * 6..714....31.9.687.79683.411.......4.473.619....14...27...614...1..3..5....4.7.16 E5: 1,6,7 # 5 pairs * PAIR H7: 2,3 BLK 9 G9: 2,3,8,9 # reduction candidate for 2,3 G9: 2,3 => CTR * 6..7.4923.3..9.6875796.3.411.......4.4.3...95....4...27....143.....3.75....4.7216 G9: 8,9 # 6 pairs * PAIR H7: 2,3 ROW 7 C7: 2,3,5,6,8 # reduction candidate for 2,3 C7: 2,3 # 8 pairs C7: 5,6,8 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0125-base-pr-000.dot * REASONING * DIS # E1: 2,5 => CTR => E1: 1,8 * PRF # D2: 2,5 => SOL * DIS # D2: 1 => CTR => D2: 2,5 * DIS # E3: 2,5 => CTR => E3: 8 * DIS # A2: 2,5 => CTR => A2: 4 * PRF # A2: 4 => SOL * DIS # C2: 2,5 => CTR => C2: 1,4,7 * DIS # I2: 5 => CTR => I2: 4,7 * DIS # D7: 2,5 => CTR => D7: 8,9 * PRF # E7: 2,5 => SOL * DIS # E7: 6 => CTR => E7: 2,5 * DIS # A9: 2,5 => CTR => A9: 3,8,9 * DIS # E1: 2,5 => CTR => E1: 1,8 * DIS # E3: 2,5 => CTR => E3: 8 * DIS # E4: 2,5 => CTR => E4: 4,6,7 * DIS # E5: 2,5 => CTR => E5: 1,6,7 * DIS # G9: 2,3 => CTR => G9: 8,9 * CNT 17 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E9,F2,H1,H3,H7) * 6..7.4....3..9.68...96.3..11.........4.3...9.........27....14......3..5....4.7.16 * PAIR F2: 2,5 BLK 2 E1: 2,5,1,8 # reduction candidate for 2,5 E1: 2,5 => CTR * 6..7.4....3419.687.79683.411.......484.3...95....4.1.27...614..4...3.75....4.7.16 D2: 2,5,1 # reduction candidate for 2,5 D2: 2,5 => SOLVED * 682714539431295687579683241123579864847362195965148372796851423214936758358427916 * DURATION: 0:00:03.562530 START: 05:49:57.663908 END: 05:50:01.226438 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0125-base-pr-001.dot * REASONING * DIS # E1: 2,5 => CTR => E1: 1,8 * PRF E1: 1,8 # D2: 2,5 => SOL * STA E1: 1,8 + D2: 2,5 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=125
Solution
position: 682714539431295687579683241123579864847362195965148372796851423214936758358427916 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 # E1: 2,5 => CTR => E1: 1,8 * INC # E1: 1,8 => UNS * PRF # D2: 2,5 => SOL * DIS # D2: 1 => CTR => D2: 2,5 * DIS # E3: 2,5 => CTR => E3: 8 * INC # E3: 8 => UNS * DIS # A2: 2,5 => CTR => A2: 4 * PRF # A2: 4 => SOL * DIS # C2: 2,5 => CTR => C2: 1,4,7 * INC # C2: 1,4,7 => UNS * INC # F4: 2,5 => UNS * INC # F5: 2,5 => UNS * INC # G1: 2,3 => UNS * INC # G1: 5,9 => UNS * INC # I2: 4,7 => UNS * DIS # I2: 5 => CTR => I2: 4,7 * INC # H4: 4,7 => UNS * INC # H6: 4,7 => UNS * DIS # D7: 2,5 => CTR => D7: 8,9 * INC # D7: 8,9 => UNS * PRF # E7: 2,5 => SOL * DIS # E7: 6 => CTR => E7: 2,5 * DIS # A9: 2,5 => CTR => A9: 3,8,9 * INC # A9: 3,8,9 => UNS * INC # B9: 2,5 => UNS * INC # C9: 2,5 => UNS * DIS # E1: 2,5 => CTR => E1: 1,8 * INC # E1: 1,8 => UNS * DIS # E3: 2,5 => CTR => E3: 8 * INC # E3: 8 => UNS * DIS # E4: 2,5 => CTR => E4: 4,6,7 * INC # E4: 4,6,7 => UNS * DIS # E5: 2,5 => CTR => E5: 1,6,7 * INC # E5: 1,6,7 => UNS * DIS # G9: 2,3 => CTR => G9: 8,9 * INC # G9: 8,9 => UNS * INC # C7: 2,3 => UNS * INC # C7: 5,6,8 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 2,5 => CTR => E1: 1,8 * PRF E1: 1,8 # D2: 2,5 => SOL * STA E1: 1,8 + D2: 2,5 * CNT 2 HDP CHAINS / 2 HYP OPENED