Analysis of zz-www.sudokuwiki.org-0024-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=24
level: medium
position: 85...2.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3...97 initial
Autosolve
position: 85..62.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3.6.97 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H3: 8 => CTR => H3: 5,7 * CNT 1 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H3: 8 => CTR => H3: 5,7 * DIS H3: 5,7 # H8: 1,2 => CTR => H8: 6,8 * DIS H3: 5,7 + H8: 6,8 # H2: 8 => CTR => H2: 1,2 * DIS H3: 5,7 + H8: 6,8 + H2: 1,2 # I8: 1,2 => CTR => I8: 6,8 * PRF H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 # F3: 3,5 => SOL * STA H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 + F3: 3,5 * CNT 5 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 85...2.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3...97 | initial |
| 85..62.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3.6.97 | autosolve |
| 851462739364975821279183654145837962687219543923654178436798215792541386518326497 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) D1: 4,9 G1: 7,9 G5: 5,7 H6: 5,7 A9: 4,5 C9: 2,8 E9: 2,5 G7: 2,4 H7: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,A2: 1.. / C1 = 1 => 9 pairs (_) / A2 = 1 => 11 pairs (_) E7,F8: 1.. / E7 = 1 => 0 pairs (X) / F8 = 1 => 9 pairs (_) C1,I1: 1.. / C1 = 1 => 9 pairs (_) / I1 = 1 => 11 pairs (_) A4,E4: 1.. / A4 = 1 => 9 pairs (_) / E4 = 1 => 9 pairs (_) E7,H7: 1.. / E7 = 1 => 0 pairs (X) / H7 = 1 => 9 pairs (_) C1,C5: 1.. / C1 = 1 => 9 pairs (_) / C5 = 1 => 11 pairs (_) F5,F8: 1.. / F5 = 1 => 0 pairs (X) / F8 = 1 => 9 pairs (_) A7,B7: 3.. / A7 = 3 => 9 pairs (_) / B7 = 3 => 11 pairs (_) D1,F3: 4.. / D1 = 4 => 9 pairs (_) / F3 = 4 => 0 pairs (X) I1,I3: 4.. / I1 = 4 => 0 pairs (X) / I3 = 4 => 9 pairs (_) D4,F6: 4.. / D4 = 4 => 0 pairs (X) / F6 = 4 => 9 pairs (_) G7,G9: 4.. / G7 = 4 => 8 pairs (_) / G9 = 4 => 12 pairs (_) D1,I1: 4.. / D1 = 4 => 9 pairs (_) / I1 = 4 => 0 pairs (X) F3,I3: 4.. / F3 = 4 => 0 pairs (X) / I3 = 4 => 9 pairs (_) A9,G9: 4.. / A9 = 4 => 8 pairs (_) / G9 = 4 => 12 pairs (_) D1,D4: 4.. / D1 = 4 => 9 pairs (_) / D4 = 4 => 0 pairs (X) F3,F6: 4.. / F3 = 4 => 0 pairs (X) / F6 = 4 => 9 pairs (_) G5,H6: 5.. / G5 = 5 => 9 pairs (_) / H6 = 5 => 0 pairs (X) A8,A9: 5.. / A8 = 5 => 8 pairs (_) / A9 = 5 => 12 pairs (_) A9,E9: 5.. / A9 = 5 => 12 pairs (_) / E9 = 5 => 8 pairs (_) G2,G5: 5.. / G2 = 5 => 0 pairs (X) / G5 = 5 => 9 pairs (_) A2,B2: 6.. / A2 = 6 => 11 pairs (_) / B2 = 6 => 9 pairs (_) H8,I8: 6.. / H8 = 6 => 10 pairs (_) / I8 = 6 => 9 pairs (_) A5,I5: 6.. / A5 = 6 => 9 pairs (_) / I5 = 6 => 10 pairs (_) B2,B4: 6.. / B2 = 6 => 9 pairs (_) / B4 = 6 => 11 pairs (_) H4,H8: 6.. / H4 = 6 => 9 pairs (_) / H8 = 6 => 10 pairs (_) G1,H3: 7.. / G1 = 7 => 9 pairs (_) / H3 = 7 => 0 pairs (X) G5,H6: 7.. / G5 = 7 => 0 pairs (X) / H6 = 7 => 9 pairs (_) D7,D8: 7.. / D7 = 7 => 9 pairs (_) / D8 = 7 => 11 pairs (_) C1,G1: 7.. / C1 = 7 => 0 pairs (X) / G1 = 7 => 9 pairs (_) G1,G5: 7.. / G1 = 7 => 9 pairs (_) / G5 = 7 => 0 pairs (X) H3,H6: 7.. / H3 = 7 => 0 pairs (X) / H6 = 7 => 9 pairs (_) D2,E3: 8.. / D2 = 8 => 9 pairs (_) / E3 = 8 => 13 pairs (_) C8,C9: 8.. / C8 = 8 => 10 pairs (_) / C9 = 8 => 12 pairs (_) E6,I6: 8.. / E6 = 8 => 9 pairs (_) / I6 = 8 => 12 pairs (_) C9,G9: 8.. / C9 = 8 => 12 pairs (_) / G9 = 8 => 10 pairs (_) D2,D4: 8.. / D2 = 8 => 9 pairs (_) / D4 = 8 => 13 pairs (_) * DURATION: 0:00:44.667159 START: 03:51:59.801736 END: 03:52:44.468895 2017-05-01 * CP COUNT: (37) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C9,D1,E9,G1,G5,G7,H6,H7) * 85..62.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3.6.97 * PAIR D1: 4,9 BLK 2 F3: 4,9,3,5 # reduction candidate for 4,9 F3: 4,9 # 12 pairs F3: 3,5 # 10 pairs * PAIR D1: 4,9 ROW 1 I1: 4,9,1 # reduction candidate for 4,9 I1: 1 # 11 pairs I1: 4,9 # 9 pairs * PAIR D1: 4,9 COL D D4: 4,9,2,8 # reduction candidate for 4,9 D4: 4,9 # 14 pairs D4: 2,8 # 10 pairs * PAIR G1: 7,9 ROW 1 C1: 7,9,1 # reduction candidate for 7,9 C1: 7,9 # 11 pairs C1: 1 # 9 pairs * PAIR H6: 5,7 COL H H3: 5,7,8 # reduction candidate for 5,7 H3: 8 => CTR * 85..6273...487.9522..15468...5..78...8....54....68517...67.8215...541368518326497 H3: 5,7 # 10 pairs * PAIR C9: 2,8 BLK 7 C8: 2,8,7,9 # reduction candidate for 2,8 C8: 7,9 # 13 pairs C8: 2,8 # 11 pairs * PAIR C9: 2,8 ROW 9 G9: 2,8,4 # reduction candidate for 2,8 G9: 4 # 12 pairs G9: 2,8 # 8 pairs * PAIR E9: 2,5 BLK 8 D8: 2,5,7,9 # reduction candidate for 2,5 D8: 2,5 # 12 pairs D8: 7,9 # 10 pairs * PAIR E9: 2,5 COL E E5: 2,5,1,3,9 # reduction candidate for 2,5 E5: 2,5 # 11 pairs E6: 2,5,3,8,9 # reduction candidate for 2,5 E6: 2,5 # 14 pairs * PAIR G7: 2,4 BLK 9 G9: 2,4,8 # reduction candidate for 2,4 G9: 2,4 # 12 pairs G9: 8 # 10 pairs * PAIR G7: 2,4 ROW 7 B7: 2,4,3,7,9 # reduction candidate for 2,4 B7: 2,4 # 10 pairs B7: 3,7,9 # 9 pairs * PAIR H7: 1,2 BLK 9 H8: 1,2,6,8 # reduction candidate for 1,2 H8: 1,2 # 13 pairs I8: 1,2,6,8 # reduction candidate for 1,2 I8: 1,2 # 14 pairs * PAIR H7: 1,2 ROW 7 E7: 1,2,9 # reduction candidate for 1,2 E7: 1,2 # 10 pairs E7: 9 # 9 pairs * PAIR H7: 1,2 COL H H2: 1,2,5,8 # reduction candidate for 1,2 H2: 1,2 # 13 pairs H2: 5,8 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0024-base-pr-000.dot * REASONING * DIS # H3: 8 => CTR => H3: 5,7 * CNT 1 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C9,D1,E9,G1,G5,G7,H6,H7) * 85..62.3...4.7....2..1..6....5..7....8.....4....6..1....6..8..5....4.3...1.3.6.97 * PAIR D1: 4,9 BLK 2 F3: 4,9,3,5 # reduction candidate for 4,9 F3: 4,9 # 12 pairs F3: 3,5 # 10 pairs * PAIR D1: 4,9 ROW 1 I1: 4,9,1 # reduction candidate for 4,9 I1: 1 # 11 pairs I1: 4,9 # 9 pairs * PAIR D1: 4,9 COL D D4: 4,9,2,8 # reduction candidate for 4,9 D4: 4,9 # 14 pairs D4: 2,8 # 10 pairs * PAIR G1: 7,9 ROW 1 C1: 7,9,1 # reduction candidate for 7,9 C1: 7,9 # 11 pairs C1: 1 # 9 pairs * PAIR H6: 5,7 COL H H3: 5,7,8 # reduction candidate for 5,7 H3: 8 => CTR * 85..6273...487.9522..15468...5..78...8....54....68517...67.8215...541368518326497 * PAIR RESTART * PAIR C9: 2,8 BLK 7 C8: 2,8,7,9 # reduction candidate for 2,8 C8: 7,9 # 15 pairs C8: 2,8 # 12 pairs * PAIR C9: 2,8 ROW 9 G9: 2,8,4 # reduction candidate for 2,8 G9: 4 # 14 pairs G9: 2,8 # 9 pairs * PAIR E9: 2,5 BLK 8 D8: 2,5,7,9 # reduction candidate for 2,5 D8: 2,5 # 13 pairs D8: 7,9 # 11 pairs * PAIR E9: 2,5 COL E E5: 2,5,1,3,9 # reduction candidate for 2,5 E5: 2,5 # 12 pairs E6: 2,5,3,8,9 # reduction candidate for 2,5 E6: 2,5 # 15 pairs * PAIR G7: 2,4 BLK 9 G9: 2,4,8 # reduction candidate for 2,4 G9: 2,4 # 14 pairs G9: 8 # 11 pairs * PAIR G7: 2,4 ROW 7 B7: 2,4,3,7,9 # reduction candidate for 2,4 B7: 2,4 # 12 pairs B7: 3,7,9 # 10 pairs * PAIR H7: 1,2 BLK 9 H8: 1,2,6,8 # reduction candidate for 1,2 H8: 1,2 => CTR * 8574629311649735822..185674.4581726.6815297437296341589.6..84.55.8.4.3.6412356897 I8: 1,2,6,8 # reduction candidate for 1,2 I8: 1,2 # 15 pairs * RESTART * PAIR H7: 1,2 BLK 9 I8: 1,2,6,8 # reduction candidate for 1,2 I8: 1,2 # 15 pairs I8: 6,8 # 14 pairs * PAIR H7: 1,2 ROW 7 E7: 1,2,9 # reduction candidate for 1,2 E7: 9 # 12 pairs E7: 1,2 # 12 pairs * PAIR H7: 1,2 COL H H2: 1,2,8 # reduction candidate for 1,2 H2: 8 => CTR * 85.462.3...4.7.28.2..18.654..58.792..8....54..2.6.4178..6..84155.8.41362412356897 * PAIR RESTART * PAIR H7: 1,2 BLK 9 I8: 1,2,6,8 # reduction candidate for 1,2 I8: 1,2 => CTR * 85..62.3...487....2..1..6.8..5..7.8..8.5..74....68.15...6..84.55.8.4.36.412356897 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A9,D1,E7,E9,G1,G4,G5,G7,G9,H3,H4,H6,H8,I8) * 85..62.3...4.7..2.2..1..6....5..7....8.....4....6..1....6..8.15....413...183.6.97 * PAIR D1: 4,9 BLK 2 F3: 4,9,3,5 # reduction candidate for 4,9 F3: 3,5 => SOLVED * 851462739364975821279183654145837962687219543923654178436798215792541386518326497 * DURATION: 0:00:24.013222 START: 03:53:01.674221 END: 03:53:25.687443 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0024-base-pr-001.dot * REASONING * DIS # H3: 8 => CTR => H3: 5,7 * DIS H3: 5,7 # H8: 1,2 => CTR => H8: 6,8 * DIS H3: 5,7 + H8: 6,8 # H2: 8 => CTR => H2: 1,2 * DIS H3: 5,7 + H8: 6,8 + H2: 1,2 # I8: 1,2 => CTR => I8: 6,8 * PRF H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 # F3: 3,5 => SOL * STA H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 + F3: 3,5 * CNT 5 HDP CHAINS / 33 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=24
Solution
position: 851462739364975821279183654145837962687219543923654178436798215792541386518326497 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 # F3: 4,9 => UNS * INC # F3: 3,5 => UNS * INC # I1: 4,9 => UNS * INC # I1: 1 => UNS * INC # D4: 4,9 => UNS * INC # D4: 2,8 => UNS * INC # C1: 7,9 => UNS * INC # C1: 1 => UNS * INC # H3: 5,7 => UNS * DIS # H3: 8 => CTR => H3: 5,7 * INC # C8: 2,8 => UNS * INC # C8: 7,9 => UNS * INC # G9: 2,8 => UNS * INC # G9: 4 => UNS * INC # D8: 2,5 => UNS * INC # D8: 7,9 => UNS * INC # E5: 2,5 => UNS * INC # E6: 2,5 => UNS * INC # G9: 2,4 => UNS * INC # G9: 8 => UNS * INC # B7: 2,4 => UNS * INC # B7: 3,7,9 => UNS * INC # H8: 1,2 => UNS * INC # I8: 1,2 => UNS * INC # E7: 1,2 => UNS * INC # E7: 9 => UNS * INC # H2: 1,2 => UNS * INC # H2: 5,8 => UNS * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F3: 4,9 => UNS * INC # F3: 3,5 => UNS * INC # I1: 4,9 => UNS * INC # I1: 1 => UNS * INC # D4: 4,9 => UNS * INC # D4: 2,8 => UNS * INC # C1: 7,9 => UNS * INC # C1: 1 => UNS * INC # H3: 5,7 => UNS * DIS # H3: 8 => CTR => H3: 5,7 * INC H3: 5,7 # C8: 2,8 => UNS * INC H3: 5,7 # C8: 7,9 => UNS * INC H3: 5,7 # G9: 2,8 => UNS * INC H3: 5,7 # G9: 4 => UNS * INC H3: 5,7 # D8: 2,5 => UNS * INC H3: 5,7 # D8: 7,9 => UNS * INC H3: 5,7 # E5: 2,5 => UNS * INC H3: 5,7 # E6: 2,5 => UNS * INC H3: 5,7 # G9: 2,4 => UNS * INC H3: 5,7 # G9: 8 => UNS * INC H3: 5,7 # B7: 2,4 => UNS * INC H3: 5,7 # B7: 3,7,9 => UNS * DIS H3: 5,7 # H8: 1,2 => CTR => H8: 6,8 * INC H3: 5,7 + H8: 6,8 # I8: 1,2 => UNS * INC H3: 5,7 + H8: 6,8 # I8: 1,2 => UNS * INC H3: 5,7 + H8: 6,8 # I8: 6,8 => UNS * INC H3: 5,7 + H8: 6,8 # E7: 1,2 => UNS * INC H3: 5,7 + H8: 6,8 # E7: 9 => UNS * INC H3: 5,7 + H8: 6,8 # H2: 1,2 => UNS * DIS H3: 5,7 + H8: 6,8 # H2: 8 => CTR => H2: 1,2 * DIS H3: 5,7 + H8: 6,8 + H2: 1,2 # I8: 1,2 => CTR => I8: 6,8 * INC H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 # F3: 4,9 => UNS * PRF H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 # F3: 3,5 => SOL * STA H3: 5,7 + H8: 6,8 + H2: 1,2 + I8: 6,8 + F3: 3,5 * CNT 33 HDP CHAINS / 33 HYP OPENED