Analysis of zz-www.sudokuwiki.org-0011-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=11
level: medium
position: 2....51.........64..4.6......9.8.3.....5.4.....5.1.2......7.5..53.....1...69....8 initial
Autosolve
position: 26...51...5.....64..4.6......9.8.3.....5.4.....5.1.2......7.5..53.....1...695...8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 7,8 => CTR => C2: 1,3 * PRF # D1: 7,8 => SOL * DIS # D1: 4 => CTR => D1: 7,8 * DIS # H1: 7,8 => CTR => H1: 3,9 * DIS # C5: 7,8 => CTR => C5: 1,2,3 * PRF # D8: 2,4 => SOL * DIS # I7: 2,3 => CTR => I7: 6 * DIS # D7: 2,3 => CTR => D7: 1,4,6,8 * DIS # G8: 4,7 => CTR => G8: 6,9 * PRF # G8: 6,9 => SOL * PRF # B9: 4,7 => SOL * CNT 11 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 7,8 => CTR => C2: 1,3 * PRF C2: 1,3 # D1: 7,8 => SOL * STA C2: 1,3 + D1: 7,8 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2....51.........64..4.6......9.8.3.....5.4.....5.1.2......7.5..53.....1...69....8 | initial |
| 26...51...5.....64..4.6......9.8.3.....5.4.....5.1.2......7.5..53.....1...695...8 | autosolve |
| 267845193851239764394761852419682375723594681685317249942178536538426917176953428 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) C1: 7,8 E1: 4,9 H3: 2,5 I3: 2,5 E8: 2,4 H7: 2,3 G9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I4,I5: 1.. / I4 = 1 => 0 pairs (X) / I5 = 1 => 7 pairs (_) H3,I3: 2.. / H3 = 2 => 0 pairs (X) / I3 = 2 => 7 pairs (_) H1,I1: 3.. / H1 = 3 => 0 pairs (X) / I1 = 3 => 8 pairs (_) F9,H9: 3.. / F9 = 3 => 11 pairs (_) / H9 = 3 => 10 pairs (_) C2,C5: 3.. / C2 = 3 => 12 pairs (_) / C5 = 3 => 14 pairs (_) E2,E5: 3.. / E2 = 3 => 14 pairs (_) / E5 = 3 => 12 pairs (_) I1,I7: 3.. / I1 = 3 => 8 pairs (_) / I7 = 3 => 0 pairs (X) D1,E1: 4.. / D1 = 4 => 0 pairs (X) / E1 = 4 => 0 pairs (_) H4,H6: 4.. / H4 = 4 => 6 pairs (_) / H6 = 4 => 0 pairs (*) G8,G9: 4.. / G8 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) E1,E8: 4.. / E1 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) H3,I3: 5.. / H3 = 5 => 7 pairs (_) / I3 = 5 => 0 pairs (X) H4,I4: 5.. / H4 = 5 => 0 pairs (X) / I4 = 5 => 7 pairs (_) H3,H4: 5.. / H3 = 5 => 7 pairs (_) / H4 = 5 => 0 pairs (X) I3,I4: 5.. / I3 = 5 => 0 pairs (X) / I4 = 5 => 7 pairs (_) G5,G8: 6.. / G5 = 6 => 8 pairs (_) / G8 = 6 => 0 pairs (X) E5,F6: 9.. / E5 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) A7,B7: 9.. / A7 = 9 => 8 pairs (_) / B7 = 9 => 7 pairs (_) G8,I8: 9.. / G8 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) B3,B7: 9.. / B3 = 9 => 8 pairs (_) / B7 = 9 => 7 pairs (_) * DURATION: 0:00:31.856766 START: 03:34:20.752357 END: 03:34:52.609123 2017-05-01 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,E1,E8,G9,H3,H7,I3) * 26...51...5.....64..4.6......9.8.3.....5.4.....5.1.2......7.5..53.....1...695...8 * PAIR C1: 7,8 BLK 1 A2: 7,8,1,3,9 # reduction candidate for 7,8 A2: 7,8 # 11 pairs C2: 7,8,1,3 # reduction candidate for 7,8 C2: 7,8 => CTR * 26...51...5.....64..4.6......9.8.3....35.4.....5.1.2....1.7.5..532.4..1...69514.8 C2: 1,3 # 8 pairs A3: 7,8,1,3,9 # reduction candidate for 7,8 A3: 7,8 # 15 pairs B3: 7,8,1,9 # reduction candidate for 7,8 B3: 7,8 # 9 pairs * PAIR C1: 7,8 ROW 1 D1: 7,8,4 # reduction candidate for 7,8 D1: 7,8 => SOLVED * 267845193851239764394761852419682375723594681685317249942178536538426917176953428 D1: 4 => CTR * 267495183.5.....64..4.6......9.8.3.....5.489...5.192......7.5..53..4..19..695.4.8 H1: 7,8,3,9 # reduction candidate for 7,8 H1: 7,8 => CTR * 267495183.5.....64..4.6......9.8.3.....5.489...5.1924.....7.5..53..4..19..695.4.8 H1: 3,9 # 8 pairs * PAIR C1: 7,8 COL C C5: 7,8,1,2,3 # reduction candidate for 7,8 C5: 7,8 => CTR * 26...51...53....64..4.6......9.8.3.....534...3.5.192....1.7.5..532.4..1...69514.8 C5: 1,2,3 # 7 pairs C8: 7,8,2 # reduction candidate for 7,8 C8: 7,8 # 10 pairs * PAIR E8: 2,4 BLK 8 D7: 2,4,1,3,6,8 # reduction candidate for 2,4 D7: 2,4 # 15 pairs D8: 2,4,6,8 # reduction candidate for 2,4 D8: 2,4 => SOLVED * 267845193851239764394761852419682375723594681685317249942178536538426917176953428 D8: 6,8 # 8 pairs * PAIR H7: 2,3 BLK 9 I7: 2,3,6 # reduction candidate for 2,3 I7: 2,3 => CTR * 26...51...5.....64..4.6......9.8.3.....5.4.....5.1.2......7.5..53.....1...695...8 I7: 6 # 9 pairs H9: 2,3,7 # reduction candidate for 2,3 H9: 2,3 # 10 pairs * PAIR H7: 2,3 ROW 7 D7: 2,3,1,4,6,8 # reduction candidate for 2,3 D7: 2,3 => CTR * 267845193.53.9..64..4.6...2..9.8.3.5..25.46.1..5.1.2.9...378526538426917726951438 D7: 1,4,6,8 # 7 pairs F7: 2,3,1,6,8 # reduction candidate for 2,3 F7: 2,3 # 11 pairs * PAIR G9: 4,7 BLK 9 G8: 4,7,6,9 # reduction candidate for 4,7 G8: 4,7 => CTR * 268495173.5.....64..4.6..52..9.8.345...5.4691.45.192874...7.5.653..4.719..695.4.8 G8: 6,9 => SOLVED * 267845193851239764394761852419682375723594681685317249942178536538426917176953428 * PAIR G9: 4,7 ROW 9 A9: 4,7,1 # reduction candidate for 4,7 A9: 4,7 # 12 pairs B9: 4,7,1,2 # reduction candidate for 4,7 B9: 4,7 => SOLVED * 267845193851239764394761852419682375723594681685317249942178536538426917176953428 B9: 1,2 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0011-base-pr-000.dot * REASONING * DIS # C2: 7,8 => CTR => C2: 1,3 * PRF # D1: 7,8 => SOL * DIS # D1: 4 => CTR => D1: 7,8 * DIS # H1: 7,8 => CTR => H1: 3,9 * DIS # C5: 7,8 => CTR => C5: 1,2,3 * PRF # D8: 2,4 => SOL * DIS # I7: 2,3 => CTR => I7: 6 * DIS # D7: 2,3 => CTR => D7: 1,4,6,8 * DIS # G8: 4,7 => CTR => G8: 6,9 * PRF # G8: 6,9 => SOL * PRF # B9: 4,7 => SOL * CNT 11 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,E1,E8,G9,H3,H7,I3) * 26...51...5.....64..4.6......9.8.3.....5.4.....5.1.2......7.5..53.....1...695...8 * PAIR C1: 7,8 BLK 1 A2: 7,8,1,3,9 # reduction candidate for 7,8 A2: 7,8 # 11 pairs C2: 7,8,1,3 # reduction candidate for 7,8 C2: 7,8 => CTR * 26...51...5.....64..4.6......9.8.3....35.4.....5.1.2....1.7.5..532.4..1...69514.8 A3: 7,8,1,3,9 # reduction candidate for 7,8 A3: 7,8 # 15 pairs B3: 7,8,1,9 # reduction candidate for 7,8 B3: 7,8 # 9 pairs * PAIR C1: 7,8 ROW 1 D1: 7,8,4 # reduction candidate for 7,8 D1: 7,8 => SOLVED * 267845193851239764394761852419682375723594681685317249942178536538426917176953428 * DURATION: 0:00:05.808494 START: 03:35:16.107568 END: 03:35:21.916062 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0011-base-pr-001.dot * REASONING * DIS # C2: 7,8 => CTR => C2: 1,3 * PRF C2: 1,3 # D1: 7,8 => SOL * STA C2: 1,3 + D1: 7,8 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=11
Solution
position: 267845193851239764394761852419682375723594681685317249942178536538426917176953428 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 # A2: 7,8 => UNS * DIS # C2: 7,8 => CTR => C2: 1,3 * INC # C2: 1,3 => UNS * INC # A3: 7,8 => UNS * INC # B3: 7,8 => UNS * PRF # D1: 7,8 => SOL * DIS # D1: 4 => CTR => D1: 7,8 * DIS # H1: 7,8 => CTR => H1: 3,9 * INC # H1: 3,9 => UNS * DIS # C5: 7,8 => CTR => C5: 1,2,3 * INC # C5: 1,2,3 => UNS * INC # C8: 7,8 => UNS * INC # D7: 2,4 => UNS * PRF # D8: 2,4 => SOL * INC # D8: 6,8 => UNS * DIS # I7: 2,3 => CTR => I7: 6 * INC # I7: 6 => UNS * INC # H9: 2,3 => UNS * DIS # D7: 2,3 => CTR => D7: 1,4,6,8 * INC # D7: 1,4,6,8 => UNS * INC # F7: 2,3 => UNS * DIS # G8: 4,7 => CTR => G8: 6,9 * PRF # G8: 6,9 => SOL * INC # A9: 4,7 => UNS * PRF # B9: 4,7 => SOL * INC # B9: 1,2 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 7,8 => UNS * DIS # C2: 7,8 => CTR => C2: 1,3 * INC C2: 1,3 # A3: 7,8 => UNS * INC C2: 1,3 # B3: 7,8 => UNS * PRF C2: 1,3 # D1: 7,8 => SOL * STA C2: 1,3 + D1: 7,8 * CNT 5 HDP CHAINS / 5 HYP OPENED