Analysis of zz-www.sudokuwiki.org-0263-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=263
level: medium
position: ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6... initial
Autosolve
position: ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I4: 1 => SOL * DIS # H2: 9 => CTR => H2: 4,7 * CNT 2 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I4: 1 => SOL * STA I4: 1 * CNT 1 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6... | initial |
| ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6... | autosolve |
| 527394816498261573613875924965723481284619357731458269146982735859137642372546198 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) I1: 6,8 G3: 3,9 H4: 5,8 G5: 1,3 H5: 5,8 G6: 2,3 C9: 2,3 H8: 4,7 H9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,E5: 1.. / E4 = 1 => 11 pairs (_) / E5 = 1 => 0 pairs (*) I4,G5: 1.. / I4 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) A7,A9: 1.. / A7 = 1 => 10 pairs (_) / A9 = 1 => 10 pairs (_) E4,I4: 1.. / E4 = 1 => 11 pairs (_) / I4 = 1 => 0 pairs (*) E5,G5: 1.. / E5 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) I4,G6: 2.. / I4 = 2 => 16 pairs (_) / G6 = 2 => 10 pairs (_) C5,A6: 4.. / C5 = 4 => 9 pairs (_) / A6 = 4 => 18 pairs (_) D5,D6: 4.. / D5 = 4 => 18 pairs (_) / D6 = 4 => 9 pairs (_) E8,E9: 4.. / E8 = 4 => 14 pairs (_) / E9 = 4 => 11 pairs (_) C5,D5: 4.. / C5 = 4 => 9 pairs (_) / D5 = 4 => 18 pairs (_) A6,D6: 4.. / A6 = 4 => 18 pairs (_) / D6 = 4 => 9 pairs (_) C3,C5: 4.. / C3 = 4 => 18 pairs (_) / C5 = 4 => 9 pairs (_) E1,F3: 5.. / E1 = 5 => 15 pairs (_) / F3 = 5 => 11 pairs (_) H4,H5: 5.. / H4 = 5 => 9 pairs (_) / H5 = 5 => 10 pairs (_) I7,I8: 5.. / I7 = 5 => 11 pairs (_) / I8 = 5 => 13 pairs (_) D5,E5: 6.. / D5 = 6 => 11 pairs (_) / E5 = 6 => 12 pairs (_) A7,C7: 6.. / A7 = 6 => 11 pairs (_) / C7 = 6 => 10 pairs (_) G1,H2: 7.. / G1 = 7 => 13 pairs (_) / H2 = 7 => 17 pairs (_) C4,A6: 7.. / C4 = 7 => 10 pairs (_) / A6 = 7 => 0 pairs (*) G7,H8: 7.. / G7 = 7 => 17 pairs (_) / H8 = 7 => 13 pairs (_) A2,H2: 7.. / A2 = 7 => 13 pairs (_) / H2 = 7 => 17 pairs (_) F8,H8: 7.. / F8 = 7 => 17 pairs (_) / H8 = 7 => 13 pairs (_) C1,C4: 7.. / C1 = 7 => 0 pairs (*) / C4 = 7 => 0 pairs (X) G1,G7: 7.. / G1 = 7 => 13 pairs (_) / G7 = 7 => 17 pairs (_) H2,H8: 7.. / H2 = 7 => 17 pairs (_) / H8 = 7 => 13 pairs (_) D3,F3: 8.. / D3 = 8 => 11 pairs (_) / F3 = 8 => 16 pairs (_) G1,I1: 8.. / G1 = 8 => 21 pairs (_) / I1 = 8 => 10 pairs (_) H4,H5: 8.. / H4 = 8 => 10 pairs (_) / H5 = 8 => 9 pairs (_) G1,G9: 8.. / G1 = 8 => 21 pairs (_) / G9 = 8 => 10 pairs (_) B1,B2: 9.. / B1 = 9 => 11 pairs (_) / B2 = 9 => 15 pairs (_) H2,H9: 9.. / H2 = 9 => 0 pairs (X) / H9 = 9 => 9 pairs (_) * DURATION: 0:00:28.897832 START: 13:51:47.775413 END: 13:52:16.673245 2019-04-28 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,G3,G5,G6,H4,H5,H8,H9,I1) * ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6... * PAIR H4: 5,8 ROW 4 F4: 5,8,2,3,7 # reduction candidate for 5,8 F4: 5,8 # 12 pairs F4: 2,3,7 # 9 pairs * PAIR G5: 1,3 BLK 6 I4: 1,3,2 # reduction candidate for 1,3 I4: 2 # 16 pairs I4: 1,3 # 10 pairs * PAIR G5: 1,3 ROW 5 E5: 1,3,5,6,9 # reduction candidate for 1,3 E5: 1,3 # 15 pairs E5: 5,6,9 # 11 pairs * PAIR H5: 5,8 ROW 5 B5: 5,8,3 # reduction candidate for 5,8 B5: 5,8 # 12 pairs F5: 5,8,3,9 # reduction candidate for 5,8 F5: 5,8 # 21 pairs * PAIR G6: 2,3 BLK 6 I4: 2,3,1 # reduction candidate for 2,3 I4: 1 => SOLVED * 527394816498261573613875924965723481284619357731458269146982735859137642372546198 I4: 2,3 # 11 pairs * PAIR G6: 2,3 ROW 6 E6: 2,3,5 # reduction candidate for 2,3 E6: 2,3 # 11 pairs F6: 2,3,5,7,8 # reduction candidate for 2,3 F6: 2,3 # 15 pairs * PAIR C9: 2,3 BLK 7 B8: 2,3,5,8 # reduction candidate for 2,3 B8: 5,8 # 16 pairs B8: 2,3 # 14 pairs * PAIR C9: 2,3 ROW 9 E9: 2,3,4,9 # reduction candidate for 2,3 E9: 2,3 # 22 pairs E9: 4,9 # 11 pairs * PAIR H8: 4,7 COL H H2: 4,7,9 # reduction candidate for 4,7 H2: 9 => CTR * .923.4718738.21594.1..7.326967.1.4.32...3.1.73.1457269.46782931829143675.73596842 H2: 4,7 # 9 pairs * PAIR H9: 4,9 ROW 9 E9: 4,9,2,3 # reduction candidate for 4,9 E9: 2,3 # 22 pairs E9: 4,9 # 11 pairs * PAIR H9: 4,9 COL H H2: 4,9,7 # reduction candidate for 4,9 H2: 7 # 17 pairs H2: 4,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0263-base-pr-000.dot * REASONING * PRF # I4: 1 => SOL * DIS # H2: 9 => CTR => H2: 4,7 * CNT 2 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,G3,G5,G6,H4,H5,H8,H9,I1) * ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6... * PAIR H4: 5,8 ROW 4 F4: 5,8,2,3,7 # reduction candidate for 5,8 F4: 5,8 # 12 pairs F4: 2,3,7 # 9 pairs * PAIR G5: 1,3 BLK 6 I4: 1,3,2 # reduction candidate for 1,3 I4: 2 # 16 pairs I4: 1,3 # 10 pairs * PAIR G5: 1,3 ROW 5 E5: 1,3,5,6,9 # reduction candidate for 1,3 E5: 1,3 # 15 pairs E5: 5,6,9 # 11 pairs * PAIR H5: 5,8 ROW 5 B5: 5,8,3 # reduction candidate for 5,8 B5: 5,8 # 12 pairs F5: 5,8,3,9 # reduction candidate for 5,8 F5: 5,8 # 21 pairs * PAIR G6: 2,3 BLK 6 I4: 2,3,1 # reduction candidate for 2,3 I4: 1 => SOLVED * 527394816498261573613875924965723481284619357731458269146982735859137642372546198 * DURATION: 0:00:05.827161 START: 13:52:28.197527 END: 13:52:34.024688 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0263-base-pr-001.dot * REASONING * PRF # I4: 1 => SOL * STA I4: 1 * CNT 1 HDP CHAINS / 10 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=263
Solution
position: 527394816498261573613875924965723481284619357731458269146982735859137642372546198 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 # F4: 5,8 => UNS * INC # F4: 2,3,7 => UNS * INC # I4: 1,3 => UNS * INC # I4: 2 => UNS * INC # E5: 1,3 => UNS * INC # E5: 5,6,9 => UNS * INC # B5: 5,8 => UNS * INC # F5: 5,8 => UNS * INC # I4: 2,3 => UNS * PRF # I4: 1 => SOL * INC # E6: 2,3 => UNS * INC # F6: 2,3 => UNS * INC # B8: 2,3 => UNS * INC # B8: 5,8 => UNS * INC # E9: 2,3 => UNS * INC # E9: 4,9 => UNS * INC # H2: 4,7 => UNS * DIS # H2: 9 => CTR => H2: 4,7 * INC # E9: 4,9 => UNS * INC # E9: 2,3 => UNS * INC # H2: 4,9 => UNS * INC # H2: 7 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F4: 5,8 => UNS * INC # F4: 2,3,7 => UNS * INC # I4: 1,3 => UNS * INC # I4: 2 => UNS * INC # E5: 1,3 => UNS * INC # E5: 5,6,9 => UNS * INC # B5: 5,8 => UNS * INC # F5: 5,8 => UNS * INC # I4: 2,3 => UNS * PRF # I4: 1 => SOL * STA I4: 1 * CNT 10 HDP CHAINS / 10 HYP OPENED