Analysis of zz-www.sudokuwiki.org-0005-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=5
level: medium
position: 4....9.3....6...29..1.........7..2...6.583.7.....1..........8..93...6....5.2....6 initial
Autosolve
position: 4....9.3....6...29.91.........7642...6.583.7....912.........8..93...6....5.2....6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 7,8 => CTR => B1: 2 * DIS # G5: 1,4 => CTR => G5: 9 * DIS # I8: 1,4 => CTR => I8: 2,5,7 * CNT 3 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 7,8 => CTR => B1: 2 * DIS B1: 2 # G5: 1,4 => CTR => G5: 9 * DIS B1: 2 + G5: 9 # I8: 1,4 => CTR => I8: 2,5,7 * DIS B1: 2 + G5: 9 + I8: 2,5,7 # C2: 7,8 => CTR => C2: 3,5 * DIS B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 # A3: 7,8 => CTR => A3: 3,5,6 * DIS B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 + A3: 3,5,6 # F2: 7,8 => CTR => F2: 1,5 * PRF B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 + A3: 3,5,6 + F2: 1,5 # B6: 4 => SOL * STA B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 + A3: 3,5,6 + F2: 1,5 + B6: 4 * CNT 7 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4....9.3....6...29..1.........7..2...6.583.7.....1..........8..93...6....5.2....6 | initial |
| 4....9.3....6...29.91.........7642...6.583.7....912.........8..93...6....5.2....6 | autosolve |
| 425879631873641529691325487389764215162583974547912368216497853938156742754238196 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) B2: 7,8 D1: 1,8 B4: 1,8 A5: 1,2 I5: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,F2: 1.. / D1 = 1 => 10 pairs (_) / F2 = 1 => 11 pairs (_) F2,G2: 1.. / F2 = 1 => 11 pairs (_) / G2 = 1 => 10 pairs (_) B4,B7: 1.. / B4 = 1 => 7 pairs (_) / B7 = 1 => 14 pairs (_) E1,E3: 2.. / E1 = 2 => 0 pairs (X) / E3 = 2 => 8 pairs (_) A5,C5: 2.. / A5 = 2 => 8 pairs (_) / C5 = 2 => 17 pairs (_) I7,I8: 2.. / I7 = 2 => 0 pairs (X) / I8 = 2 => 5 pairs (_) A3,E3: 2.. / A3 = 2 => 0 pairs (X) / E3 = 2 => 8 pairs (_) C8,I8: 2.. / C8 = 2 => 0 pairs (X) / I8 = 2 => 5 pairs (_) B1,B7: 2.. / B1 = 2 => 8 pairs (_) / B7 = 2 => 0 pairs (X) I7,G9: 3.. / I7 = 3 => 7 pairs (_) / G9 = 3 => 6 pairs (_) E9,G9: 3.. / E9 = 3 => 7 pairs (_) / G9 = 3 => 6 pairs (_) D3,D7: 3.. / D3 = 3 => 9 pairs (_) / D7 = 3 => 14 pairs (_) G6,G9: 3.. / G6 = 3 => 7 pairs (_) / G9 = 3 => 6 pairs (_) E2,G2: 4.. / E2 = 4 => 7 pairs (_) / G2 = 4 => 14 pairs (_) B6,B7: 4.. / B6 = 4 => 6 pairs (_) / B7 = 4 => 11 pairs (_) C1,A3: 6.. / C1 = 6 => 5 pairs (_) / A3 = 6 => 10 pairs (_) G6,H6: 6.. / G6 = 6 => 16 pairs (_) / H6 = 6 => 5 pairs (_) A7,C7: 6.. / A7 = 6 => 5 pairs (_) / C7 = 6 => 10 pairs (_) C1,G1: 6.. / C1 = 6 => 5 pairs (_) / G1 = 6 => 10 pairs (_) A3,A7: 6.. / A3 = 6 => 10 pairs (_) / A7 = 6 => 5 pairs (_) C1,C7: 6.. / C1 = 6 => 5 pairs (_) / C7 = 6 => 10 pairs (_) H3,H6: 6.. / H3 = 6 => 16 pairs (_) / H6 = 6 => 5 pairs (_) D8,F9: 8.. / D8 = 8 => 12 pairs (_) / F9 = 8 => 10 pairs (_) C8,D8: 8.. / C8 = 8 => 10 pairs (_) / D8 = 8 => 12 pairs (_) C4,C5: 9.. / C4 = 9 => 6 pairs (_) / C5 = 9 => 0 pairs (X) H4,G5: 9.. / H4 = 9 => 0 pairs (X) / G5 = 9 => 6 pairs (_) E7,E9: 9.. / E7 = 9 => 5 pairs (_) / E9 = 9 => 7 pairs (_) C4,H4: 9.. / C4 = 9 => 6 pairs (_) / H4 = 9 => 0 pairs (X) C5,G5: 9.. / C5 = 9 => 0 pairs (X) / G5 = 9 => 6 pairs (_) E7,H7: 9.. / E7 = 9 => 5 pairs (_) / H7 = 9 => 7 pairs (_) G5,G9: 9.. / G5 = 9 => 6 pairs (_) / G9 = 9 => 0 pairs (X) * DURATION: 0:00:35.939768 START: 03:26:14.238004 END: 03:26:50.177772 2017-05-01 * CP COUNT: (31) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B2,B4,D1,I5) * 4....9.3....6...29.91.........7642...6.583.7....912.........8..93...6....5.2....6 * PAIR B2: 7,8 BLK 1 B1: 7,8,2 # reduction candidate for 7,8 B1: 7,8 => CTR * 4.2.79635.7.64.12969132548..1.76429.269583.7..4.91236..26.9.8.393..567.2.5.23.9.6 B1: 2 # 8 pairs C1: 7,8,2,5,6 # reduction candidate for 7,8 C1: 7,8 # 14 pairs A2: 7,8,3,5 # reduction candidate for 7,8 A2: 7,8 # 12 pairs C2: 7,8,3,5 # reduction candidate for 7,8 C2: 7,8 # 12 pairs A3: 7,8,2,3,5,6 # reduction candidate for 7,8 A3: 7,8 # 14 pairs * PAIR B2: 7,8 ROW 2 F2: 7,8,1,5 # reduction candidate for 7,8 F2: 7,8 # 13 pairs F2: 1,5 # 7 pairs * PAIR B2: 7,8 COL B B6: 7,8,4 # reduction candidate for 7,8 B6: 7,8 # 11 pairs B6: 4 # 6 pairs * PAIR D1: 1,8 BLK 2 F2: 1,8,5,7 # reduction candidate for 1,8 F2: 5,7 # 12 pairs F2: 1,8 # 8 pairs * PAIR D1: 1,8 ROW 1 I1: 1,8,5,7 # reduction candidate for 1,8 I1: 5,7 # 10 pairs I1: 1,8 # 7 pairs * PAIR D1: 1,8 COL D D8: 1,8,4 # reduction candidate for 1,8 D8: 4 # 19 pairs D8: 1,8 # 8 pairs * PAIR B4: 1,8 BLK 4 A4: 1,8,3,5 # reduction candidate for 1,8 A4: 1,8 # 15 pairs A4: 3,5 # 6 pairs * PAIR B4: 1,8 ROW 4 H4: 1,8,5,9 # reduction candidate for 1,8 H4: 1,8 # 9 pairs I4: 1,8,3,5 # reduction candidate for 1,8 I4: 1,8 # 11 pairs * PAIR A5: 1,2 COL A A7: 1,2,6,7 # reduction candidate for 1,2 A7: 1,2 # 17 pairs A7: 6,7 # 6 pairs * PAIR I5: 1,4 BLK 6 G5: 1,4,9 # reduction candidate for 1,4 G5: 1,4 => CTR * 4.2.7963....64..29691325487...76429.269583174...91236...6.9.85393..567.2.5.23.9.6 G5: 9 # 6 pairs * PAIR I5: 1,4 COL I I7: 1,4,2,3,5,7 # reduction candidate for 1,4 I7: 1,4 # 12 pairs I8: 1,4,2,5,7 # reduction candidate for 1,4 I8: 1,4 => CTR * 42.1.9.3....64.129.9132......97642..264583971...912....4....8.29328.6714.5.2..396 I8: 2,5,7 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0005-base-pr-000.dot * REASONING * DIS # B1: 7,8 => CTR => B1: 2 * DIS # G5: 1,4 => CTR => G5: 9 * DIS # I8: 1,4 => CTR => I8: 2,5,7 * CNT 3 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B2,B4,D1,I5) * 4....9.3....6...29.91.........7642...6.583.7....912.........8..93...6....5.2....6 * PAIR B2: 7,8 BLK 1 B1: 7,8,2 # reduction candidate for 7,8 B1: 7,8 => CTR * 4.2.79635.7.64.12969132548..1.76429.269583.7..4.91236..26.9.8.393..567.2.5.23.9.6 C1: 7,8,5,6 # reduction candidate for 7,8 C1: 7,8 # 14 pairs A2: 7,8,3,5 # reduction candidate for 7,8 A2: 7,8 # 12 pairs C2: 7,8,3,5 # reduction candidate for 7,8 C2: 7,8 # 12 pairs A3: 7,8,3,5,6 # reduction candidate for 7,8 A3: 7,8 # 14 pairs * PAIR B2: 7,8 ROW 2 F2: 7,8,1,5 # reduction candidate for 7,8 F2: 7,8 # 17 pairs F2: 1,5 # 9 pairs * PAIR B2: 7,8 COL B B6: 7,8,4 # reduction candidate for 7,8 B6: 7,8 # 11 pairs B6: 4 # 10 pairs * PAIR D1: 1,8 BLK 2 F2: 1,8,5,7 # reduction candidate for 1,8 F2: 5,7 # 16 pairs F2: 1,8 # 10 pairs * PAIR D1: 1,8 ROW 1 I1: 1,8,5,7 # reduction candidate for 1,8 I1: 5,7 # 14 pairs I1: 1,8 # 9 pairs * PAIR D1: 1,8 COL D D8: 1,8,4 # reduction candidate for 1,8 D8: 4 # 19 pairs D8: 1,8 # 10 pairs * PAIR B4: 1,8 BLK 4 A4: 1,8,3,5 # reduction candidate for 1,8 A4: 1,8 # 15 pairs A4: 3,5 # 9 pairs * PAIR B4: 1,8 ROW 4 H4: 1,8,5,9 # reduction candidate for 1,8 H4: 1,8 # 12 pairs I4: 1,8,3,5 # reduction candidate for 1,8 I4: 1,8 # 14 pairs * PAIR A5: 1,2 COL A A7: 1,2,6,7 # reduction candidate for 1,2 A7: 1,2 # 18 pairs A7: 6,7 # 9 pairs * PAIR I5: 1,4 BLK 6 G5: 1,4,9 # reduction candidate for 1,4 G5: 1,4 => CTR * 426879.3....64152959132..8....76429.269583.7....91236...2.9.8.393...67.2.5.23.9.6 * PAIR I5: 1,4 COL I I7: 1,4,2,3,5,7 # reduction candidate for 1,4 I7: 1,4 # 17 pairs I8: 1,4,2,5,7 # reduction candidate for 1,4 I8: 1,4 => CTR * 42.1.9.3....6..129.91.2......97642..264583971...912....4.3..8.29328.6714.5.24.3.6 * RESTART * PAIR I5: 1,4 COL I I7: 1,4,2,3,5,7 # reduction candidate for 1,4 I7: 1,4 # 17 pairs I7: 2,3,5,7 # 9 pairs * PAIR RESTART * PAIR I5: 1,4 COL I I7: 1,4,2,3,5,7 # reduction candidate for 1,4 I7: 1,4 # 17 pairs I7: 2,3,5,7 # 9 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,B2,B4,C5,D1,D3,E1,E2,I5) * 42...9.3....6...29.91.2......97642...6.58397....912.........8..93...6....5.2....6 * PAIR B2: 7,8 BLK 1 C1: 7,8,5,6 # reduction candidate for 7,8 C1: 7,8 # 16 pairs A2: 7,8,3,5 # reduction candidate for 7,8 A2: 7,8 # 13 pairs C2: 7,8,3,5 # reduction candidate for 7,8 C2: 7,8 => CTR * 425.7963.3..64..2969132...7..97642.3.62583974.439125682.643.89593..567.2.5.29.3.6 A3: 7,8,3,5,6 # reduction candidate for 7,8 A3: 7,8 => CTR * 4268.913....641729791325....197642..264583971.7.912...6421.78..938456.121572.8..6 * PAIR B2: 7,8 ROW 2 F2: 7,8,1,5 # reduction candidate for 7,8 F2: 7,8 => CTR * 42.1.963..7.64812969132....389764251162583974.4.9123682164..89393.8.651285.2.1..6 * PAIR B2: 7,8 COL B B6: 7,8,4 # reduction candidate for 7,8 B6: 4 => SOLVED * 425879631873641529691325487389764215162583974547912368216497853938156742754238196 * DURATION: 0:00:29.536803 START: 03:27:07.540270 END: 03:27:37.077073 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0005-base-pr-001.dot * REASONING * DIS # B1: 7,8 => CTR => B1: 2 * DIS B1: 2 # G5: 1,4 => CTR => G5: 9 * DIS B1: 2 + G5: 9 # I8: 1,4 => CTR => I8: 2,5,7 * DIS B1: 2 + G5: 9 + I8: 2,5,7 # C2: 7,8 => CTR => C2: 3,5 * DIS B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 # A3: 7,8 => CTR => A3: 3,5,6 * DIS B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 + A3: 3,5,6 # F2: 7,8 => CTR => F2: 1,5 * PRF B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 + A3: 3,5,6 + F2: 1,5 # B6: 4 => SOL * STA B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 + A3: 3,5,6 + F2: 1,5 + B6: 4 * CNT 7 HDP CHAINS / 35 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=5
Solution
position: 425879631873641529691325487389764215162583974547912368216497853938156742754238196 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 # B1: 7,8 => CTR => B1: 2 * INC # B1: 2 => UNS * INC # C1: 7,8 => UNS * INC # A2: 7,8 => UNS * INC # C2: 7,8 => UNS * INC # A3: 7,8 => UNS * INC # F2: 7,8 => UNS * INC # F2: 1,5 => UNS * INC # B6: 7,8 => UNS * INC # B6: 4 => UNS * INC # F2: 1,8 => UNS * INC # F2: 5,7 => UNS * INC # I1: 1,8 => UNS * INC # I1: 5,7 => UNS * INC # D8: 1,8 => UNS * INC # D8: 4 => UNS * INC # A4: 1,8 => UNS * INC # A4: 3,5 => UNS * INC # H4: 1,8 => UNS * INC # I4: 1,8 => UNS * INC # A7: 1,2 => UNS * INC # A7: 6,7 => UNS * DIS # G5: 1,4 => CTR => G5: 9 * INC # G5: 9 => UNS * INC # I7: 1,4 => UNS * DIS # I8: 1,4 => CTR => I8: 2,5,7 * INC # I8: 2,5,7 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 7,8 => CTR => B1: 2 * INC B1: 2 # C1: 7,8 => UNS * INC B1: 2 # A2: 7,8 => UNS * INC B1: 2 # C2: 7,8 => UNS * INC B1: 2 # A3: 7,8 => UNS * INC B1: 2 # F2: 7,8 => UNS * INC B1: 2 # F2: 1,5 => UNS * INC B1: 2 # B6: 7,8 => UNS * INC B1: 2 # B6: 4 => UNS * INC B1: 2 # F2: 1,8 => UNS * INC B1: 2 # F2: 5,7 => UNS * INC B1: 2 # I1: 1,8 => UNS * INC B1: 2 # I1: 5,7 => UNS * INC B1: 2 # D8: 1,8 => UNS * INC B1: 2 # D8: 4 => UNS * INC B1: 2 # A4: 1,8 => UNS * INC B1: 2 # A4: 3,5 => UNS * INC B1: 2 # H4: 1,8 => UNS * INC B1: 2 # I4: 1,8 => UNS * INC B1: 2 # A7: 1,2 => UNS * INC B1: 2 # A7: 6,7 => UNS * DIS B1: 2 # G5: 1,4 => CTR => G5: 9 * INC B1: 2 + G5: 9 # I7: 1,4 => UNS * DIS B1: 2 + G5: 9 # I8: 1,4 => CTR => I8: 2,5,7 * INC B1: 2 + G5: 9 + I8: 2,5,7 # I7: 1,4 => UNS * INC B1: 2 + G5: 9 + I8: 2,5,7 # I7: 2,3,5,7 => UNS * INC B1: 2 + G5: 9 + I8: 2,5,7 # I7: 1,4 => UNS * INC B1: 2 + G5: 9 + I8: 2,5,7 # I7: 2,3,5,7 => UNS * INC B1: 2 + G5: 9 + I8: 2,5,7 # C1: 7,8 => UNS * INC B1: 2 + G5: 9 + I8: 2,5,7 # A2: 7,8 => UNS * DIS B1: 2 + G5: 9 + I8: 2,5,7 # C2: 7,8 => CTR => C2: 3,5 * DIS B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 # A3: 7,8 => CTR => A3: 3,5,6 * DIS B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 + A3: 3,5,6 # F2: 7,8 => CTR => F2: 1,5 * INC B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 + A3: 3,5,6 + F2: 1,5 # B6: 7,8 => UNS * PRF B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 + A3: 3,5,6 + F2: 1,5 # B6: 4 => SOL * STA B1: 2 + G5: 9 + I8: 2,5,7 + C2: 3,5 + A3: 3,5,6 + F2: 1,5 + B6: 4 * CNT 35 HDP CHAINS / 35 HYP OPENED