Analysis of zz-www.sudokuwiki.org-0004-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=4
level: medium
position: ...3..4.....8.2..9.4...7.2..2......7...1.5...89.....5...376.........1..86.4...1.. initial
Autosolve
position: ...3..4.....842..9.4...7.2..2......7...1.5...89.....5...376.........1..86.4...1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B5: 6,7 => CTR => B5: 3 * DIS # B9: 5,7 => CTR => B9: 8 * DIS # B2: 5,7 => CTR => B2: 1,3,6 * DIS # D8: 2,9 => CTR => D8: 4,5 * DIS # F7: 4,9 => CTR => F7: 8 * CNT 5 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B5: 6,7 => CTR => B5: 3 * DIS B5: 3 # B9: 5,7 => CTR => B9: 8 * DIS B5: 3 + B9: 8 # A8: 2,9 => CTR => A8: 5,7 * DIS B5: 3 + B9: 8 + A8: 5,7 # C1: 8 => CTR => C1: 2,9 * PRF B5: 3 + B9: 8 + A8: 5,7 + C1: 2,9 # G8: 2,9 => SOL * STA B5: 3 + B9: 8 + A8: 5,7 + C1: 2,9 + G8: 2,9 * CNT 5 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...3..4.....8.2..9.4...7.2..2......7...1.5...89.....5...376.........1..86.4...1.. | initial |
| ...3..4.....842..9.4...7.2..2......7...1.5...89.....5...376.........1..86.4...1.. | autosolve |
| 279316485165842739348597621526984317437125896891673254913768542752431968684259173 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) C3: 8,9 F1: 6,9 C5: 6,7 B8: 5,7 C8: 2,9 H7: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,E3: 1.. / E1 = 1 => 8 pairs (_) / E3 = 1 => 7 pairs (_) H4,I6: 1.. / H4 = 1 => 7 pairs (_) / I6 = 1 => 18 pairs (_) A7,B7: 1.. / A7 = 1 => 18 pairs (_) / B7 = 1 => 12 pairs (_) C6,I6: 1.. / C6 = 1 => 7 pairs (_) / I6 = 1 => 18 pairs (_) A1,C1: 2.. / A1 = 2 => 7 pairs (_) / C1 = 2 => 6 pairs (_) C1,C8: 2.. / C1 = 2 => 6 pairs (_) / C8 = 2 => 7 pairs (_) B2,B5: 3.. / B2 = 3 => 0 pairs (X) / B5 = 3 => 7 pairs (_) A4,A5: 4.. / A4 = 4 => 10 pairs (_) / A5 = 4 => 8 pairs (_) F7,D8: 4.. / F7 = 4 => 0 pairs (X) / D8 = 4 => 9 pairs (_) D8,H8: 4.. / D8 = 4 => 9 pairs (_) / H8 = 4 => 0 pairs (X) A4,C4: 5.. / A4 = 5 => 11 pairs (_) / C4 = 5 => 6 pairs (_) C2,C4: 5.. / C2 = 5 => 11 pairs (_) / C4 = 5 => 6 pairs (_) F1,D3: 6.. / F1 = 6 => 10 pairs (_) / D3 = 6 => 12 pairs (_) G8,H8: 6.. / G8 = 6 => 9 pairs (_) / H8 = 6 => 9 pairs (_) E5,E6: 7.. / E5 = 7 => 0 pairs (X) / E6 = 7 => 7 pairs (_) C6,E6: 7.. / C6 = 7 => 0 pairs (X) / E6 = 7 => 7 pairs (_) B9,H9: 7.. / B9 = 7 => 0 pairs (X) / H9 = 7 => 10 pairs (_) G2,G8: 7.. / G2 = 7 => 8 pairs (_) / G8 = 7 => 0 pairs (X) C1,C3: 8.. / C1 = 8 => 7 pairs (_) / C3 = 8 => 8 pairs (_) H1,G3: 8.. / H1 = 8 => 8 pairs (_) / G3 = 8 => 7 pairs (_) B7,B9: 8.. / B7 = 8 => 0 pairs (X) / B9 = 8 => 12 pairs (_) C1,H1: 8.. / C1 = 8 => 7 pairs (_) / H1 = 8 => 8 pairs (_) C3,G3: 8.. / C3 = 8 => 8 pairs (_) / G3 = 8 => 7 pairs (_) B7,F7: 8.. / B7 = 8 => 0 pairs (X) / F7 = 8 => 12 pairs (_) * DURATION: 0:00:31.938540 START: 03:24:43.019109 END: 03:25:14.957649 2017-05-01 * CP COUNT: (24) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C3,C5,C8,F1,H7) * ...3..4.....842..9.4...7.2..2......7...1.5...89.....5...376.........1..86.4...1.. * PAIR C3: 8,9 BLK 1 C1: 8,9,2 # reduction candidate for 8,9 C1: 8,9 # 7 pairs C1: 2 # 6 pairs * PAIR F1: 6,9 BLK 2 D3: 6,9,5 # reduction candidate for 6,9 D3: 5 # 13 pairs D3: 6,9 # 9 pairs * PAIR F1: 6,9 COL F F4: 6,9,3,4,8 # reduction candidate for 6,9 F4: 6,9 # 10 pairs F4: 3,4,8 # 6 pairs * PAIR C5: 6,7 BLK 4 B5: 6,7,3 # reduction candidate for 6,7 B5: 6,7 => CTR * ...3..4..13.8425.9.4...7.2..25....17...1.5...891.7..5..13768......4.17686.4...1.. B5: 3 # 7 pairs C6: 6,7,1 # reduction candidate for 6,7 C6: 6,7 # 18 pairs * PAIR C5: 6,7 COL C C2: 6,7,1,5 # reduction candidate for 6,7 C2: 1,5 # 11 pairs C2: 6,7 # 8 pairs * PAIR B8: 5,7 BLK 7 A8: 5,7,2,9 # reduction candidate for 5,7 A8: 5,7 # 16 pairs B9: 5,7,8 # reduction candidate for 5,7 B9: 5,7 => CTR * 2.8396475...842..9349517826.2.98.637.3612598489167.25.183769542952431768674258193 B9: 8 # 12 pairs * PAIR B8: 5,7 ROW 8 G8: 5,7,2,3,6,9 # reduction candidate for 5,7 G8: 5,7 # 33 pairs G8: 2,3,6,9 # 8 pairs * PAIR B8: 5,7 COL B B1: 5,7,1,6 # reduction candidate for 5,7 B1: 5,7 # 15 pairs B2: 5,7,1,3,6 # reduction candidate for 5,7 B2: 5,7 => CTR * 7623.948..51842769.486.7.2.1259....743.1.5.9689627435121376894....4.1..86845.3172 B2: 1,3,6 # 6 pairs * PAIR C8: 2,9 BLK 7 A7: 2,9,1,5 # reduction candidate for 2,9 A7: 2,9 # 16 pairs A8: 2,9,5,7 # reduction candidate for 2,9 A8: 2,9 # 17 pairs * PAIR C8: 2,9 ROW 8 D8: 2,9,4,5 # reduction candidate for 2,9 D8: 2,9 => CTR * ...3..4.....8427.9.4...7.2..2......7...1.5...89.....5.183764.9.....31648654...173 D8: 4,5 # 7 pairs E8: 2,9,3,5 # reduction candidate for 2,9 E8: 2,9 # 18 pairs G8: 2,9,3,5,6,7 # reduction candidate for 2,9 G8: 2,9 # 21 pairs * PAIR C8: 2,9 COL C C1: 2,9,8 # reduction candidate for 2,9 C1: 2,9 # 8 pairs C1: 8 # 7 pairs * PAIR H7: 4,9 BLK 9 H8: 4,9,3,6,7 # reduction candidate for 4,9 H8: 4,9 # 22 pairs H8: 3,6,7 # 9 pairs * PAIR H7: 4,9 ROW 7 F7: 4,9,8 # reduction candidate for 4,9 F7: 4,9 => CTR * 2.8396475...842..9349517826.2.98.637.3612598489167.25.183769542952431768674258193 F7: 8 # 12 pairs * PAIR H7: 4,9 COL H H4: 4,9,1,3,6,8 # reduction candidate for 4,9 H4: 4,9 # 18 pairs H5: 4,9,3,6,8 # reduction candidate for 4,9 H5: 4,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0004-base-pr-000.dot * REASONING * DIS # B5: 6,7 => CTR => B5: 3 * DIS # B9: 5,7 => CTR => B9: 8 * DIS # B2: 5,7 => CTR => B2: 1,3,6 * DIS # D8: 2,9 => CTR => D8: 4,5 * DIS # F7: 4,9 => CTR => F7: 8 * CNT 5 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C3,C5,C8,F1,H7) * ...3..4.....842..9.4...7.2..2......7...1.5...89.....5...376.........1..86.4...1.. * PAIR C3: 8,9 BLK 1 C1: 8,9,2 # reduction candidate for 8,9 C1: 8,9 # 7 pairs C1: 2 # 6 pairs * PAIR F1: 6,9 BLK 2 D3: 6,9,5 # reduction candidate for 6,9 D3: 5 # 13 pairs D3: 6,9 # 9 pairs * PAIR F1: 6,9 COL F F4: 6,9,3,4,8 # reduction candidate for 6,9 F4: 6,9 # 10 pairs F4: 3,4,8 # 6 pairs * PAIR C5: 6,7 BLK 4 B5: 6,7,3 # reduction candidate for 6,7 B5: 6,7 => CTR * ...3..4..13.8425.9.4...7.2..25....17...1.5...891.7..5..13768......4.17686.4...1.. C6: 6,7,1 # reduction candidate for 6,7 C6: 6,7 # 18 pairs * RESTART * PAIR C5: 6,7 BLK 4 C6: 6,7,1 # reduction candidate for 6,7 C6: 6,7 # 18 pairs C6: 1 # 10 pairs * PAIR B8: 5,7 BLK 7 A8: 5,7,2,9 # reduction candidate for 5,7 A8: 5,7 # 20 pairs B9: 5,7,8 # reduction candidate for 5,7 B9: 5,7 => CTR * 2.8396475.6.842319349517826.2198...7.3.12598.89.67.25.183769542952431768674258193 * RESTART * PAIR B8: 5,7 BLK 7 A8: 5,7,2,9 # reduction candidate for 5,7 A8: 2,9 => CTR * 7.23..48.3..8427.9948.17.23.2......743.1.5...89.....5...3768...279451638684...175 * PAIR C8: 2,9 ROW 8 G8: 2,9,6 # reduction candidate for 2,9 G8: 2,9 # 25 pairs G8: 6 # 23 pairs * PAIR C8: 2,9 COL C C1: 2,9,8 # reduction candidate for 2,9 C1: 8 => CTR * 27839641..6.8427.9.49..782..2..8...743.1.5.8.89.....5.913768542752431.98684..9173 * PAIR RESTART * PAIR C8: 2,9 ROW 8 G8: 2,9,6 # reduction candidate for 2,9 G8: 2,9 => SOLVED * 279316485165842739348597621526984317437125896891673254913768542752431968684259173 * DURATION: 0:00:18.265082 START: 03:25:40.272514 END: 03:25:58.537596 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0004-base-pr-001.dot * REASONING * DIS # B5: 6,7 => CTR => B5: 3 * DIS B5: 3 # B9: 5,7 => CTR => B9: 8 * DIS B5: 3 + B9: 8 # A8: 2,9 => CTR => A8: 5,7 * DIS B5: 3 + B9: 8 + A8: 5,7 # C1: 8 => CTR => C1: 2,9 * PRF B5: 3 + B9: 8 + A8: 5,7 + C1: 2,9 # G8: 2,9 => SOL * STA B5: 3 + B9: 8 + A8: 5,7 + C1: 2,9 + G8: 2,9 * CNT 5 HDP CHAINS / 19 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=4
Solution
position: 279316485165842739348597621526984317437125896891673254913768542752431968684259173 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 # C1: 8,9 => UNS * INC # C1: 2 => UNS * INC # D3: 6,9 => UNS * INC # D3: 5 => UNS * INC # F4: 6,9 => UNS * INC # F4: 3,4,8 => UNS * DIS # B5: 6,7 => CTR => B5: 3 * INC # B5: 3 => UNS * INC # C6: 6,7 => UNS * INC # C2: 6,7 => UNS * INC # C2: 1,5 => UNS * INC # A8: 5,7 => UNS * DIS # B9: 5,7 => CTR => B9: 8 * INC # B9: 8 => UNS * INC # G8: 5,7 => UNS * INC # G8: 2,3,6,9 => UNS * INC # B1: 5,7 => UNS * DIS # B2: 5,7 => CTR => B2: 1,3,6 * INC # B2: 1,3,6 => UNS * INC # A7: 2,9 => UNS * INC # A8: 2,9 => UNS * DIS # D8: 2,9 => CTR => D8: 4,5 * INC # D8: 4,5 => UNS * INC # E8: 2,9 => UNS * INC # G8: 2,9 => UNS * INC # C1: 2,9 => UNS * INC # C1: 8 => UNS * INC # H8: 4,9 => UNS * INC # H8: 3,6,7 => UNS * DIS # F7: 4,9 => CTR => F7: 8 * INC # F7: 8 => UNS * INC # H4: 4,9 => UNS * INC # H5: 4,9 => UNS * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 8,9 => UNS * INC # C1: 2 => UNS * INC # D3: 6,9 => UNS * INC # D3: 5 => UNS * INC # F4: 6,9 => UNS * INC # F4: 3,4,8 => UNS * DIS # B5: 6,7 => CTR => B5: 3 * INC B5: 3 # C6: 6,7 => UNS * INC B5: 3 # C6: 6,7 => UNS * INC B5: 3 # C6: 1 => UNS * INC B5: 3 # A8: 5,7 => UNS * DIS B5: 3 # B9: 5,7 => CTR => B9: 8 * INC B5: 3 + B9: 8 # A8: 5,7 => UNS * DIS B5: 3 + B9: 8 # A8: 2,9 => CTR => A8: 5,7 * INC B5: 3 + B9: 8 + A8: 5,7 # G8: 2,9 => UNS * INC B5: 3 + B9: 8 + A8: 5,7 # G8: 6 => UNS * INC B5: 3 + B9: 8 + A8: 5,7 # C1: 2,9 => UNS * DIS B5: 3 + B9: 8 + A8: 5,7 # C1: 8 => CTR => C1: 2,9 * PRF B5: 3 + B9: 8 + A8: 5,7 + C1: 2,9 # G8: 2,9 => SOL * STA B5: 3 + B9: 8 + A8: 5,7 + C1: 2,9 + G8: 2,9 * CNT 19 HDP CHAINS / 19 HYP OPENED