Analysis of zz-www.sudokuwiki.org-0151-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=151
level: medium
position: ....4..3...28.....98......5.....8..3..1...7..5..6.....3...6..49..7..42...4..1.... initial
Autosolve
position: ....4..3...28.....98......5.....85.38.1...7..5..6.....3...6..49.9738425..4..1.3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C6: 9 => CTR => C6: 3,4 * DIS # D4: 4,9 => CTR => D4: 1,2,7 * CNT 2 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C6: 9 => CTR => C6: 3,4 * DIS C6: 3,4 # A4: 2,6 => CTR => A4: 4,7 * PRF C6: 3,4 + A4: 4,7 # D4: 2,7 => SOL * STA C6: 3,4 + A4: 4,7 + D4: 2,7 * CNT 3 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....4..3...28.....98......5.....8..3..1...7..5..6.....3...6..49..7..42...4..1.... | initial |
| ....4..3...28.....98......5.....85.38.1...7..5..6.....3...6..49.9738425..4..1.3.. | autosolve |
| 756942138132856974984173625469728513821435796573691482315267849697384251248519367 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C1: 5,6 C3: 3,4 C4: 4,9 C7: 5,8 A8: 1,6 A9: 2,6 G7: 1,8 I8: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,F6: 1.. / D4 = 1 => 13 pairs (_) / F6 = 1 => 11 pairs (_) B7,A8: 1.. / B7 = 1 => 19 pairs (_) / A8 = 1 => 11 pairs (_) G7,I8: 1.. / G7 = 1 => 11 pairs (_) / I8 = 1 => 19 pairs (_) D4,H4: 1.. / D4 = 1 => 13 pairs (_) / H4 = 1 => 11 pairs (_) B7,G7: 1.. / B7 = 1 => 19 pairs (_) / G7 = 1 => 11 pairs (_) A8,I8: 1.. / A8 = 1 => 11 pairs (_) / I8 = 1 => 19 pairs (_) I1,H3: 2.. / I1 = 2 => 0 pairs (X) / H3 = 2 => 11 pairs (_) B7,A9: 2.. / B7 = 2 => 19 pairs (_) / A9 = 2 => 13 pairs (_) A4,A9: 2.. / A4 = 2 => 19 pairs (_) / A9 = 2 => 13 pairs (_) B2,C3: 3.. / B2 = 3 => 19 pairs (_) / C3 = 3 => 10 pairs (_) C3,C6: 3.. / C3 = 3 => 10 pairs (_) / C6 = 3 => 19 pairs (_) A2,C3: 4.. / A2 = 4 => 10 pairs (_) / C3 = 4 => 19 pairs (_) D4,D5: 4.. / D4 = 4 => 0 pairs (X) / D5 = 4 => 10 pairs (_) C3,G3: 4.. / C3 = 4 => 19 pairs (_) / G3 = 4 => 10 pairs (_) D5,I5: 4.. / D5 = 4 => 10 pairs (_) / I5 = 4 => 0 pairs (X) A2,A4: 4.. / A2 = 4 => 10 pairs (_) / A4 = 4 => 19 pairs (_) E2,E5: 5.. / E2 = 5 => 8 pairs (_) / E5 = 5 => 8 pairs (_) F3,G3: 6.. / F3 = 6 => 9 pairs (_) / G3 = 6 => 19 pairs (_) A8,I8: 6.. / A8 = 6 => 19 pairs (_) / I8 = 6 => 11 pairs (_) C1,C9: 6.. / C1 = 6 => 10 pairs (_) / C9 = 6 => 11 pairs (_) D7,F7: 7.. / D7 = 7 => 10 pairs (_) / F7 = 7 => 9 pairs (_) H9,I9: 7.. / H9 = 7 => 12 pairs (_) / I9 = 7 => 10 pairs (_) G1,I1: 8.. / G1 = 8 => 12 pairs (_) / I1 = 8 => 12 pairs (_) C7,C9: 8.. / C7 = 8 => 11 pairs (_) / C9 = 8 => 19 pairs (_) C7,G7: 8.. / C7 = 8 => 11 pairs (_) / G7 = 8 => 19 pairs (_) H6,H9: 8.. / H6 = 8 => 9 pairs (_) / H9 = 8 => 10 pairs (_) C4,C6: 9.. / C4 = 9 => 9 pairs (_) / C6 = 9 => 0 pairs (X) D9,F9: 9.. / D9 = 9 => 9 pairs (_) / F9 = 9 => 9 pairs (_) * DURATION: 0:00:36.289688 START: 06:16:31.191443 END: 06:17:07.481131 2017-05-01 * CP COUNT: (28) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,C1,C3,C4,C7,G7,I8) * ....4..3...28.....98......5.....85.38.1...7..5..6.....3...6..49.9738425..4..1.3.. * PAIR C1: 5,6 BLK 1 B1: 5,6,1,7 # reduction candidate for 5,6 B1: 5,6 # 10 pairs B2: 5,6,1,3,7 # reduction candidate for 5,6 B2: 5,6 # 14 pairs * PAIR C1: 5,6 ROW 1 F1: 5,6,1,2,7,9 # reduction candidate for 5,6 F1: 5,6 # 15 pairs F1: 1,2,7,9 # 8 pairs * PAIR C1: 5,6 COL C C9: 5,6,8 # reduction candidate for 5,6 C9: 8 # 19 pairs C9: 5,6 # 11 pairs * PAIR C3: 3,4 COL C C6: 3,4,9 # reduction candidate for 3,4 C6: 9 => CTR * ....4..384.28.....983176425..4..85138.14..79.5.96....43...6..49.9738425..4..1.3.. C6: 3,4 # 9 pairs * PAIR C4: 4,9 BLK 4 C6: 4,9,3 # reduction candidate for 4,9 C6: 3 # 19 pairs C6: 4,9 # 10 pairs * PAIR C4: 4,9 ROW 4 D4: 4,9,1,2,7 # reduction candidate for 4,9 D4: 4,9 => CTR * ....4..3.4.28.....983.2.475....785138.1...7..57.631...3...6..49.9738425..4..1.3.7 D4: 1,2,7 # 10 pairs * PAIR C7: 5,8 BLK 7 C9: 5,8,6 # reduction candidate for 5,8 C9: 6 # 11 pairs C9: 5,8 # 10 pairs * PAIR A8: 1,6 COL A A1: 1,6,7 # reduction candidate for 1,6 A1: 1,6 # 16 pairs A2: 1,6,4,7 # reduction candidate for 1,6 A2: 1,6 # 21 pairs * PAIR A9: 2,6 COL A A4: 2,6,4,7 # reduction candidate for 2,6 A4: 4,7 # 14 pairs A4: 2,6 # 14 pairs * PAIR G7: 1,8 COL G G1: 1,8,6,9 # reduction candidate for 1,8 G1: 1,8 # 11 pairs G6: 1,8,4,9 # reduction candidate for 1,8 G6: 1,8 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0151-base-pr-000.dot * REASONING * DIS # C6: 9 => CTR => C6: 3,4 * DIS # D4: 4,9 => CTR => D4: 1,2,7 * CNT 2 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,C1,C3,C4,C7,G7,I8) * ....4..3...28.....98......5.....85.38.1...7..5..6.....3...6..49.9738425..4..1.3.. * PAIR C1: 5,6 BLK 1 B1: 5,6,1,7 # reduction candidate for 5,6 B1: 5,6 # 10 pairs B2: 5,6,1,3,7 # reduction candidate for 5,6 B2: 5,6 # 14 pairs * PAIR C1: 5,6 ROW 1 F1: 5,6,1,2,7,9 # reduction candidate for 5,6 F1: 5,6 # 15 pairs F1: 1,2,7,9 # 8 pairs * PAIR C1: 5,6 COL C C9: 5,6,8 # reduction candidate for 5,6 C9: 8 # 19 pairs C9: 5,6 # 11 pairs * PAIR C3: 3,4 COL C C6: 3,4,9 # reduction candidate for 3,4 C6: 9 => CTR * ....4..384.28.....983176425..4..85138.14..79.5.96....43...6..49.9738425..4..1.3.. * PAIR RESTART * PAIR C7: 5,8 BLK 7 C9: 5,8,6 # reduction candidate for 5,8 C9: 6 # 12 pairs C9: 5,8 # 11 pairs * PAIR A8: 1,6 COL A A1: 1,6,7 # reduction candidate for 1,6 A1: 1,6 # 17 pairs A2: 1,6,4,7 # reduction candidate for 1,6 A2: 1,6 # 21 pairs * PAIR A9: 2,6 COL A A4: 2,6,4,7 # reduction candidate for 2,6 A4: 2,6 => CTR * 7...4..3.4.28.7.91983126475..94785138.1..37645.46.1...3..76..49197384256.4..1.3.. * PAIR RESTART * PAIR G7: 1,8 COL G G1: 1,8,6,9 # reduction candidate for 1,8 G1: 1,8 # 18 pairs G6: 1,8,4,9 # reduction candidate for 1,8 G6: 1,8 # 32 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,A8,B7,C1,C3,C6,C7,C9,D7,D9,E4,F7,F9,G7,I8) * ....4..3...28.....98......5..9..85.38.1...7..5..6.....3...6..49.9738425.24..1.3.. * PAIR C1: 5,6 ROW 1 F1: 5,6,1,2,7,9 # reduction candidate for 5,6 F1: 5,6 # 23 pairs F1: 1,2,7,9 # 15 pairs * PAIR A4: 4,7 ROW 4 D4: 4,7,1,2 # reduction candidate for 4,7 D4: 1,2 # 20 pairs D4: 4,7 # 19 pairs * PAIR A4: 4,7 COL A A2: 4,7,1,6 # reduction candidate for 4,7 A2: 1,6 # 21 pairs A2: 4,7 # 17 pairs * PAIR E4: 2,7 BLK 5 D4: 2,7,1,4 # reduction candidate for 2,7 D4: 2,7 => SOLVED * 756942138132856974984173625469728513821435796573691482315267849697384251248519367 * DURATION: 0:00:19.300806 START: 06:17:22.094042 END: 06:17:41.394848 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0151-base-pr-001.dot * REASONING * DIS # C6: 9 => CTR => C6: 3,4 * DIS C6: 3,4 # A4: 2,6 => CTR => A4: 4,7 * PRF C6: 3,4 + A4: 4,7 # D4: 2,7 => SOL * STA C6: 3,4 + A4: 4,7 + D4: 2,7 * CNT 3 HDP CHAINS / 22 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=151
Solution
position: 756942138132856974984173625469728513821435796573691482315267849697384251248519367 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 # B1: 5,6 => UNS * INC # B2: 5,6 => UNS * INC # F1: 5,6 => UNS * INC # F1: 1,2,7,9 => UNS * INC # C9: 5,6 => UNS * INC # C9: 8 => UNS * INC # C6: 3,4 => UNS * DIS # C6: 9 => CTR => C6: 3,4 * INC # C6: 4,9 => UNS * INC # C6: 3 => UNS * DIS # D4: 4,9 => CTR => D4: 1,2,7 * INC # D4: 1,2,7 => UNS * INC # C9: 5,8 => UNS * INC # C9: 6 => UNS * INC # A1: 1,6 => UNS * INC # A2: 1,6 => UNS * INC # A4: 2,6 => UNS * INC # A4: 4,7 => UNS * INC # G1: 1,8 => UNS * INC # G6: 1,8 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 5,6 => UNS * INC # B2: 5,6 => UNS * INC # F1: 5,6 => UNS * INC # F1: 1,2,7,9 => UNS * INC # C9: 5,6 => UNS * INC # C9: 8 => UNS * INC # C6: 3,4 => UNS * DIS # C6: 9 => CTR => C6: 3,4 * INC C6: 3,4 # C9: 5,8 => UNS * INC C6: 3,4 # C9: 6 => UNS * INC C6: 3,4 # A1: 1,6 => UNS * INC C6: 3,4 # A2: 1,6 => UNS * DIS C6: 3,4 # A4: 2,6 => CTR => A4: 4,7 * INC C6: 3,4 + A4: 4,7 # G1: 1,8 => UNS * INC C6: 3,4 + A4: 4,7 # G6: 1,8 => UNS * INC C6: 3,4 + A4: 4,7 # F1: 5,6 => UNS * INC C6: 3,4 + A4: 4,7 # F1: 1,2,7,9 => UNS * INC C6: 3,4 + A4: 4,7 # D4: 4,7 => UNS * INC C6: 3,4 + A4: 4,7 # D4: 1,2 => UNS * INC C6: 3,4 + A4: 4,7 # A2: 4,7 => UNS * INC C6: 3,4 + A4: 4,7 # A2: 1,6 => UNS * PRF C6: 3,4 + A4: 4,7 # D4: 2,7 => SOL * STA C6: 3,4 + A4: 4,7 + D4: 2,7 * CNT 22 HDP CHAINS / 22 HYP OPENED