Analysis of zz-www.sudokuwiki.org-interesting-anchor-base.sdk
Contents
Original Sudoku
level: medium
position: 1..6..2...3.....7...8.....56..3....4....47..9....8.32.5....34...4...9.3...281.... initial
Autosolve
position: 1..6..2.3.3.....7...8.3...56..3....4..3.47..9....8632.5....34...4...9.3.3.2814... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 1,2 => CTR => D2: 4,5,9 * DIS # D3: 1,2 => CTR => D3: 4,7,9 * DIS # I8: 1,7 => CTR => I8: 2,6,8 * DIS # I8: 7,8 => CTR => I8: 1,2,6 * CNT 4 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 1,2 => CTR => D2: 4,5,9 * DIS D2: 4,5,9 # D3: 1,2 => CTR => D3: 4,7,9 * DIS D2: 4,5,9 + D3: 4,7,9 # I8: 1,7 => CTR => I8: 2,6,8 * DIS D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # D5: 2,5 => CTR => D5: 1 * PRF D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 + D5: 1 # E4: 9 => SOL * STA D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 + D5: 1 + E4: 9 * CNT 5 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1..6..2...3.....7...8.....56..3....4....47..9....8.32.5....34...4...9.3...281.... | initial |
| 1..6..2.3.3.....7...8.3...56..3....4..3.47..9....8632.5....34...4...9.3.3.2814... | autosolve |
| 154678293936425178278931645615392784823147569497586321589763412741259836362814957 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) F1: 5,8 F3: 1,2 A5: 2,8 I6: 1,7 A8: 7,8 D7: 2,7 I9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I7,I8: 2.. / I7 = 2 => 10 pairs (_) / I8 = 2 => 8 pairs (_) D2,D3: 4.. / D2 = 4 => 8 pairs (_) / D3 = 4 => 22 pairs (_) H1,H3: 4.. / H1 = 4 => 6 pairs (_) / H3 = 4 => 11 pairs (_) A6,C6: 4.. / A6 = 4 => 9 pairs (_) / C6 = 4 => 7 pairs (_) C1,H1: 4.. / C1 = 4 => 11 pairs (_) / H1 = 4 => 6 pairs (_) D8,E8: 5.. / D8 = 5 => 12 pairs (_) / E8 = 5 => 12 pairs (_) G9,H9: 5.. / G9 = 5 => 9 pairs (_) / H9 = 5 => 8 pairs (_) C2,B3: 6.. / C2 = 6 => 14 pairs (_) / B3 = 6 => 0 pairs (X) G5,H5: 6.. / G5 = 6 => 8 pairs (_) / H5 = 6 => 8 pairs (_) E7,E8: 6.. / E7 = 6 => 7 pairs (_) / E8 = 6 => 14 pairs (_) E1,D3: 7.. / E1 = 7 => 9 pairs (_) / D3 = 7 => 20 pairs (_) G4,I6: 7.. / G4 = 7 => 9 pairs (_) / I6 = 7 => 9 pairs (_) F1,F2: 8.. / F1 = 8 => 7 pairs (_) / F2 = 8 => 0 pairs (X) B7,A8: 8.. / B7 = 8 => 9 pairs (_) / A8 = 8 => 18 pairs (_) F1,H1: 8.. / F1 = 8 => 7 pairs (_) / H1 = 8 => 0 pairs (X) A5,A8: 8.. / A5 = 8 => 9 pairs (_) / A8 = 8 => 18 pairs (_) E4,D6: 9.. / E4 = 9 => 14 pairs (_) / D6 = 9 => 10 pairs (_) * DURATION: 0:00:13.968069 START: 23:24:45.936241 END: 23:24:59.904310 2019-04-28 * CP COUNT: (17) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,D7,F1,F3,I6,I9) * 1..6..2.3.3.....7...8.3...56..3....4..3.47..9....8632.5....34...4...9.3.3.2814... * PAIR F1: 5,8 BLK 2 F2: 5,8,1,2 # reduction candidate for 5,8 F2: 1,2 # 15 pairs F2: 5,8 # 11 pairs * PAIR F3: 1,2 BLK 2 D2: 1,2,4,5,9 # reduction candidate for 1,2 D2: 1,2 => CTR * 1..67.243.3..9..7.978432..56..3....4..3.47..9...98632.5....34...4...9.3.3.2814957 D2: 4,5,9 # 7 pairs F2: 1,2,5,8 # reduction candidate for 1,2 F2: 1,2 # 15 pairs D3: 1,2,4,7,9 # reduction candidate for 1,2 D3: 1,2 => CTR * 15467.2.323.49..7.978.3..456..3....48.3.47..94..98632.58...34..74...9.3.362814957 D3: 4,7,9 # 7 pairs * PAIR F3: 1,2 COL F F4: 1,2,5 # reduction candidate for 1,2 F4: 5 # 15 pairs F4: 1,2 # 11 pairs * PAIR A5: 2,8 BLK 4 B4: 2,8,1,5,7,9 # reduction candidate for 2,8 B4: 2,8 # 9 pairs B5: 2,8,1,5 # reduction candidate for 2,8 B5: 2,8 # 9 pairs * PAIR I6: 1,7 BLK 6 G4: 1,7,5,8 # reduction candidate for 1,7 G4: 5,8 # 10 pairs G4: 1,7 # 9 pairs * PAIR I6: 1,7 ROW 6 B6: 1,7,5,9 # reduction candidate for 1,7 B6: 1,7 # 10 pairs C6: 1,7,4,5,9 # reduction candidate for 1,7 C6: 1,7 # 12 pairs * PAIR I6: 1,7 COL I I7: 1,7,2,6,8 # reduction candidate for 1,7 I7: 1,7 # 10 pairs I8: 1,7,2,6,8 # reduction candidate for 1,7 I8: 1,7 => CTR * 1..6782.323....678768.3...56..3....4..3.47.69....8632.5..7634.2846..9.3.372814..6 I8: 2,6,8 # 7 pairs * PAIR A8: 7,8 BLK 7 B7: 7,8,1,6,9 # reduction candidate for 7,8 B7: 1,6,9 # 18 pairs B7: 7,8 # 10 pairs * PAIR A8: 7,8 ROW 8 G8: 7,8,1,6 # reduction candidate for 7,8 G8: 7,8 # 10 pairs I8: 7,8,1,2,6 # reduction candidate for 7,8 I8: 7,8 => CTR * 1..67.2.3.36....71..8.3...56..3....48.3.47..9....8632.589763412741..9638362814..7 I8: 1,2,6 # 7 pairs * PAIR D7: 2,7 BLK 8 E7: 2,7,6 # reduction candidate for 2,7 E7: 2,7 # 14 pairs D8: 2,7,5 # reduction candidate for 2,7 D8: 2,7 # 12 pairs E8: 2,7,5,6 # reduction candidate for 2,7 E8: 2,7 # 13 pairs * PAIR D7: 2,7 ROW 7 I7: 2,7,1,6,8 # reduction candidate for 2,7 I7: 2,7 # 9 pairs I7: 1,6,8 # 8 pairs * PAIR D7: 2,7 COL D D3: 2,7,1,4,9 # reduction candidate for 2,7 D3: 2,7 # 18 pairs D3: 1,4,9 # 9 pairs * PAIR I9: 6,7 BLK 9 I7: 6,7,1,2,8 # reduction candidate for 6,7 I7: 6,7 # 16 pairs G8: 6,7,1,8 # reduction candidate for 6,7 G8: 6,7 # 12 pairs I8: 6,7,1,2,8 # reduction candidate for 6,7 I8: 6,7 # 17 pairs G9: 6,7,5,9 # reduction candidate for 6,7 G9: 6,7 # 12 pairs * PAIR I9: 6,7 ROW 9 B9: 6,7,9 # reduction candidate for 6,7 B9: 9 # 11 pairs B9: 6,7 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-interesting-anchor-base-pr-000.dot * REASONING * DIS # D2: 1,2 => CTR => D2: 4,5,9 * DIS # D3: 1,2 => CTR => D3: 4,7,9 * DIS # I8: 1,7 => CTR => I8: 2,6,8 * DIS # I8: 7,8 => CTR => I8: 1,2,6 * CNT 4 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,D7,F1,F3,I6,I9) * 1..6..2.3.3.....7...8.3...56..3....4..3.47..9....8632.5....34...4...9.3.3.2814... * PAIR F1: 5,8 BLK 2 F2: 5,8,1,2 # reduction candidate for 5,8 F2: 1,2 # 15 pairs F2: 5,8 # 11 pairs * PAIR F3: 1,2 BLK 2 D2: 1,2,4,5,9 # reduction candidate for 1,2 D2: 1,2 => CTR * 1..67.243.3..9..7.978432..56..3....4..3.47..9...98632.5....34...4...9.3.3.2814957 F2: 1,2,5,8 # reduction candidate for 1,2 F2: 1,2 # 15 pairs D3: 1,2,4,7,9 # reduction candidate for 1,2 D3: 1,2 => CTR * 15467.2.323.49..7.978.3..456..3....48.3.47..94..98632.58...34..74...9.3.362814957 * RESTART * PAIR F3: 1,2 BLK 2 F2: 1,2,5,8 # reduction candidate for 1,2 F2: 5,8 # 15 pairs F2: 1,2 # 15 pairs * PAIR A5: 2,8 BLK 4 B4: 2,8,1,5,7,9 # reduction candidate for 2,8 B4: 2,8 # 10 pairs B5: 2,8,1,5 # reduction candidate for 2,8 B5: 2,8 # 11 pairs * PAIR I6: 1,7 BLK 6 G4: 1,7,5,8 # reduction candidate for 1,7 G4: 5,8 # 11 pairs G4: 1,7 # 10 pairs * PAIR I6: 1,7 ROW 6 B6: 1,7,5,9 # reduction candidate for 1,7 B6: 1,7 # 12 pairs C6: 1,7,4,5,9 # reduction candidate for 1,7 C6: 1,7 # 14 pairs * PAIR I6: 1,7 COL I I7: 1,7,2,6,8 # reduction candidate for 1,7 I7: 1,7 # 11 pairs I8: 1,7,2,6,8 # reduction candidate for 1,7 I8: 1,7 => CTR * 1..6782.323....678768.32..56..3.5..4..3.47569....8632.5..7634.2846..9.3.372814956 * RESTART * PAIR I6: 1,7 COL I I7: 1,7,2,6,8 # reduction candidate for 1,7 I7: 1,7 # 11 pairs I7: 2,6,8 # 8 pairs * PAIR RESTART * PAIR I6: 1,7 BLK 6 G4: 1,7,5,8 # reduction candidate for 1,7 G4: 5,8 # 12 pairs G4: 1,7 # 10 pairs * PAIR I6: 1,7 ROW 6 B6: 1,7,5,9 # reduction candidate for 1,7 B6: 1,7 # 12 pairs C6: 1,7,4,5,9 # reduction candidate for 1,7 C6: 1,7 # 14 pairs * PAIR I6: 1,7 COL I I7: 1,7,2,6,8 # reduction candidate for 1,7 I7: 1,7 # 11 pairs I7: 2,6,8 # 8 pairs * PAIR A8: 7,8 BLK 7 B7: 7,8,1,6,9 # reduction candidate for 7,8 B7: 1,6,9 # 20 pairs B7: 7,8 # 11 pairs * PAIR A8: 7,8 ROW 8 G8: 7,8,1,6 # reduction candidate for 7,8 G8: 7,8 # 12 pairs G8: 1,6 # 9 pairs * PAIR D7: 2,7 BLK 8 E7: 2,7,6 # reduction candidate for 2,7 E7: 2,7 # 16 pairs D8: 2,7,5 # reduction candidate for 2,7 D8: 2,7 # 14 pairs E8: 2,7,5,6 # reduction candidate for 2,7 E8: 2,7 # 15 pairs * PAIR D7: 2,7 ROW 7 I7: 2,7,1,6,8 # reduction candidate for 2,7 I7: 2,7 # 10 pairs I7: 1,6,8 # 9 pairs * PAIR I9: 6,7 BLK 9 I7: 6,7,1,2,8 # reduction candidate for 6,7 I7: 6,7 # 17 pairs G8: 6,7,1,8 # reduction candidate for 6,7 G8: 6,7 # 14 pairs G9: 6,7,5,9 # reduction candidate for 6,7 G9: 6,7 # 14 pairs * PAIR I9: 6,7 ROW 9 B9: 6,7,9 # reduction candidate for 6,7 B9: 9 # 13 pairs B9: 6,7 # 11 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,A8,D7,F1,F3,F4,I6,I9) * 1..6..2.3.3.....7...8.3...56..3....4..3.47..9....8632.5....34...4...9.3.3.2814... * PAIR F1: 5,8 BLK 2 F2: 5,8,1,2 # reduction candidate for 5,8 F2: 5,8 # 15 pairs F2: 1,2 # 15 pairs * PAIR F3: 1,2 BLK 2 F2: 1,2,5,8 # reduction candidate for 1,2 F2: 5,8 # 15 pairs F2: 1,2 # 15 pairs * PAIR A5: 2,8 BLK 4 B4: 2,8,1,5,7,9 # reduction candidate for 2,8 B4: 2,8 # 10 pairs B5: 2,8,1,5 # reduction candidate for 2,8 B5: 2,8 # 11 pairs * PAIR F4: 2,5 BLK 5 E4: 2,5,9 # reduction candidate for 2,5 E4: 2,5 # 18 pairs D5: 2,5,1 # reduction candidate for 2,5 D5: 2,5 => CTR * 1..67.2.3.3.....7.7.8.3...56.739...42.3547..9...1863275..7.34..84...9732372814..6 * RESTART * PAIR F4: 2,5 BLK 5 E4: 2,5,9 # reduction candidate for 2,5 E4: 9 => SOLVED * 154678293936425178278931645615392784823147569497586321589763412741259836362814957 * DURATION: 0:00:24.232205 START: 23:25:16.283256 END: 23:25:40.515461 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-interesting-anchor-base-pr-001.dot * REASONING * DIS # D2: 1,2 => CTR => D2: 4,5,9 * DIS D2: 4,5,9 # D3: 1,2 => CTR => D3: 4,7,9 * DIS D2: 4,5,9 + D3: 4,7,9 # I8: 1,7 => CTR => I8: 2,6,8 * DIS D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # D5: 2,5 => CTR => D5: 1 * PRF D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 + D5: 1 # E4: 9 => SOL * STA D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 + D5: 1 + E4: 9 * CNT 5 HDP CHAINS / 47 HYP OPENED
Header Info
http://www.sudokuwiki.org/Interesting_Sudokus 25 Clues, minimal "Anchor“ Discovered by Klaus Brenner
Solution
position: 154678293936425178278931645615392784823147569497586321589763412741259836362814957 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 # F2: 5,8 => UNS * INC # F2: 1,2 => UNS * DIS # D2: 1,2 => CTR => D2: 4,5,9 * INC # D2: 4,5,9 => UNS * INC # F2: 1,2 => UNS * DIS # D3: 1,2 => CTR => D3: 4,7,9 * INC # D3: 4,7,9 => UNS * INC # F4: 1,2 => UNS * INC # F4: 5 => UNS * INC # B4: 2,8 => UNS * INC # B5: 2,8 => UNS * INC # G4: 1,7 => UNS * INC # G4: 5,8 => UNS * INC # B6: 1,7 => UNS * INC # C6: 1,7 => UNS * INC # I7: 1,7 => UNS * DIS # I8: 1,7 => CTR => I8: 2,6,8 * INC # I8: 2,6,8 => UNS * INC # B7: 7,8 => UNS * INC # B7: 1,6,9 => UNS * INC # G8: 7,8 => UNS * DIS # I8: 7,8 => CTR => I8: 1,2,6 * INC # I8: 1,2,6 => UNS * INC # E7: 2,7 => UNS * INC # D8: 2,7 => UNS * INC # E8: 2,7 => UNS * INC # I7: 2,7 => UNS * INC # I7: 1,6,8 => UNS * INC # D3: 2,7 => UNS * INC # D3: 1,4,9 => UNS * INC # I7: 6,7 => UNS * INC # G8: 6,7 => UNS * INC # I8: 6,7 => UNS * INC # G9: 6,7 => UNS * INC # B9: 6,7 => UNS * INC # B9: 9 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F2: 5,8 => UNS * INC # F2: 1,2 => UNS * DIS # D2: 1,2 => CTR => D2: 4,5,9 * INC D2: 4,5,9 # F2: 1,2 => UNS * DIS D2: 4,5,9 # D3: 1,2 => CTR => D3: 4,7,9 * INC D2: 4,5,9 + D3: 4,7,9 # F2: 1,2 => UNS * INC D2: 4,5,9 + D3: 4,7,9 # F2: 5,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 # B4: 2,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 # B5: 2,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 # G4: 1,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 # G4: 5,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 # B6: 1,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 # C6: 1,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 # I7: 1,7 => UNS * DIS D2: 4,5,9 + D3: 4,7,9 # I8: 1,7 => CTR => I8: 2,6,8 * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # I7: 1,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # I7: 2,6,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # G4: 1,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # G4: 5,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # B6: 1,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # C6: 1,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # I7: 1,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # I7: 2,6,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # B7: 7,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # B7: 1,6,9 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # G8: 7,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # G8: 1,6 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # E7: 2,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # D8: 2,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # E8: 2,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # I7: 2,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # I7: 1,6,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # I7: 6,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # G8: 6,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # G9: 6,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # B9: 6,7 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # B9: 9 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # F2: 5,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # F2: 1,2 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # F2: 1,2 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # F2: 5,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # B4: 2,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # B5: 2,8 => UNS * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # E4: 2,5 => UNS * DIS D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 # D5: 2,5 => CTR => D5: 1 * INC D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 + D5: 1 # E4: 2,5 => UNS * PRF D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 + D5: 1 # E4: 9 => SOL * STA D2: 4,5,9 + D3: 4,7,9 + I8: 2,6,8 + D5: 1 + E4: 9 * CNT 47 HDP CHAINS / 47 HYP OPENED