Analysis of xx-top95-055-base.sdk
Contents
Original Sudoku
level: medium
position: ...52.....9...3..4......7...1.....4..8..453..6...1...87.2........8....32.4..8..1. initial
Autosolve
position: ...52.....9...3..4......7...1.....4..8..453.16.4.1...87.2......1.8....32.4..8..17 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E4: 6,7 => CTR => E4: 3,9 * DIS # E8: 6,7 => CTR => E8: 5,9 * PRF # E4: 6,9 => SOL * DIS # E7: 6,9 => CTR => E7: 3,5 * DIS # E8: 6,9 => CTR => E8: 5,7 * DIS # D5: 2,9 => CTR => D5: 6,7 * DIS # C9: 5,6 => CTR => C9: 3,9 * DIS # G8: 5,6 => CTR => G8: 4,9 * DIS # B3: 5,6 => CTR => B3: 2,3 * DIS # D9: 3 => CTR => D9: 2,6 * DIS # G8: 5,6 => CTR => G8: 4,9 * DIS # C9: 5,6 => CTR => C9: 3,9 * CNT 12 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E4: 6,7 => CTR => E4: 3,9 * DIS E4: 3,9 # E8: 6,7 => CTR => E8: 5,9 * DIS E4: 3,9 + E8: 5,9 # E7: 6,9 => CTR => E7: 3,5 * DIS E4: 3,9 + E8: 5,9 + E7: 3,5 # D5: 2,9 => CTR => D5: 6,7 * PRF E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # B7: 5,6 => SOL * STA E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 + B7: 5,6 * CNT 5 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...52.....9...3..4......7...1.....4..8..453..6...1...87.2........8....32.4..8..1. | initial |
| ...52.....9...3..4......7...1.....4..8..453.16.4.1...87.2......1.8....32.4..8..17 | autosolve |
| 476529183895173624321864795517398246289645371634712958752431869168957432943286517 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) E2: 6,7 E3: 6,9 A5: 2,9 C5: 7,9 B8: 5,6 F9: 2,6 G9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,G2: 1.. / G1 = 1 => 7 pairs (_) / G2 = 1 => 7 pairs (_) D7,F7: 1.. / D7 = 1 => 7 pairs (_) / F7 = 1 => 7 pairs (_) D9,F9: 2.. / D9 = 2 => 13 pairs (_) / F9 = 2 => 8 pairs (_) B3,B6: 2.. / B3 = 2 => 8 pairs (_) / B6 = 2 => 0 pairs (X) I1,I3: 3.. / I1 = 3 => 9 pairs (_) / I3 = 3 => 8 pairs (_) B6,D6: 3.. / B6 = 3 => 13 pairs (_) / D6 = 3 => 0 pairs (X) E4,E7: 3.. / E4 = 3 => 0 pairs (X) / E7 = 3 => 0 pairs (_) A1,A3: 4.. / A1 = 4 => 7 pairs (_) / A3 = 4 => 8 pairs (_) G7,G8: 4.. / G7 = 4 => 10 pairs (_) / G8 = 4 => 9 pairs (_) A1,F1: 4.. / A1 = 4 => 7 pairs (_) / F1 = 4 => 8 pairs (_) E7,E8: 5.. / E7 = 5 => 0 pairs (X) / E8 = 5 => 9 pairs (_) D5,H5: 6.. / D5 = 6 => 8 pairs (_) / H5 = 6 => 10 pairs (_) H5,H6: 7.. / H5 = 7 => 8 pairs (_) / H6 = 7 => 8 pairs (_) B1,B6: 7.. / B1 = 7 => 7 pairs (_) / B6 = 7 => 0 pairs (X) D4,F4: 8.. / D4 = 8 => 7 pairs (_) / F4 = 8 => 7 pairs (_) G7,H7: 8.. / G7 = 8 => 9 pairs (_) / H7 = 8 => 10 pairs (_) A9,C9: 9.. / A9 = 9 => 8 pairs (_) / C9 = 9 => 9 pairs (_) * DURATION: 0:00:19.465129 START: 00:00:53.112446 END: 00:01:12.577575 2017-05-04 * CP COUNT: (17) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B8,C5,E2,E3,F9,G9) * ...52.....9...3..4......7...1.....4..8..453.16.4.1...87.2......1.8....32.4..8..17 * PAIR E2: 6,7 BLK 2 F1: 6,7,1,4,8,9 # reduction candidate for 6,7 F1: 6,7 # 8 pairs D2: 6,7,1,8 # reduction candidate for 6,7 D2: 6,7 # 8 pairs * PAIR E2: 6,7 ROW 2 C2: 6,7,1,5 # reduction candidate for 6,7 C2: 6,7 # 9 pairs C2: 1,5 # 8 pairs * PAIR E2: 6,7 COL E E4: 6,7,3,9 # reduction candidate for 6,7 E4: 6,7 => CTR * .7.52...3.9..63..4....9.7.5.17....4..896453716.4.1..58752.3....168.5..32943286517 E4: 3,9 # 8 pairs E8: 6,7,5,9 # reduction candidate for 6,7 E8: 6,7 => CTR * .7652.193.91763824.2319.765.1.83..46.8.645371634.17.58762351489158479632.4.286517 E8: 5,9 # 8 pairs * PAIR E3: 6,9 BLK 2 F1: 6,9,1,4,7,8 # reduction candidate for 6,9 F1: 6,9 # 8 pairs D3: 6,9,1,4,8 # reduction candidate for 6,9 D3: 6,9 # 9 pairs F3: 6,9,1,4,8 # reduction candidate for 6,9 F3: 6,9 # 9 pairs * PAIR E3: 6,9 ROW 3 H3: 6,9,2,5,8 # reduction candidate for 6,9 H3: 6,9 # 10 pairs I3: 6,9,3,5 # reduction candidate for 6,9 I3: 6,9 # 10 pairs * PAIR E3: 6,9 COL E E4: 6,9,3,7 # reduction candidate for 6,9 E4: 6,9 => SOLVED * 476529183895173624321864795517398246289645371634712958752431869168957432943286517 E4: 3,7 # 8 pairs E7: 6,9,3,5 # reduction candidate for 6,9 E7: 6,9 => CTR * 47.529863.96.73124.2..6.795.1..3.649.8.645371634917258752391486168754932.4.286517 E7: 3,5 # 8 pairs E8: 6,9,5,7 # reduction candidate for 6,9 E8: 6,9 => CTR * .7.529.63.96.73.24.2..6.795.1..3..46.8.645371634.1..58762351489158.9.632.4.286517 E8: 5,7 # 8 pairs * PAIR A5: 2,9 BLK 4 A4: 2,9,3,5 # reduction candidate for 2,9 A4: 2,9 # 12 pairs A4: 3,5 # 8 pairs * PAIR A5: 2,9 ROW 5 D5: 2,9,6,7 # reduction candidate for 2,9 D5: 2,9 => CTR * .7.52.....9...3..4.3..9.7...1.....4..87.45361624319578752.3....168.5..32.4..82617 D5: 6,7 # 8 pairs H5: 2,9,6,7 # reduction candidate for 2,9 H5: 2,9 # 9 pairs * PAIR C5: 7,9 BLK 4 C4: 7,9,3,5 # reduction candidate for 7,9 C4: 7,9 # 11 pairs C4: 3,5 # 9 pairs * PAIR C5: 7,9 ROW 5 D5: 7,9,2,6 # reduction candidate for 7,9 D5: 7,9 # 12 pairs H5: 7,9,2,6 # reduction candidate for 7,9 H5: 7,9 # 9 pairs * PAIR B8: 5,6 BLK 7 B7: 5,6,3 # reduction candidate for 5,6 B7: 5,6 # 13 pairs C9: 5,6,3,9 # reduction candidate for 5,6 C9: 5,6 => CTR * ...52.....9...3..4......7...1..3..4.28..453.1634.1...87.2......1.8....3294.382.17 C9: 3,9 # 9 pairs * PAIR B8: 5,6 ROW 8 E8: 5,6,7,9 # reduction candidate for 5,6 E8: 5,6 # 9 pairs G8: 5,6,4,9 # reduction candidate for 5,6 G8: 5,6 => CTR * 476528193895.63.2432..9.765517.3..46289645371634.1..58762351489158.7.632943286517 G8: 4,9 # 8 pairs * PAIR B8: 5,6 COL B B3: 5,6,2,3 # reduction candidate for 5,6 B3: 5,6 => CTR * ...52.....9...3..4......7...1.....4..8..453.162431...87.2.3....1.8.5..32.4..8..17 B3: 2,3 # 8 pairs * PAIR F9: 2,6 BLK 8 D9: 2,6,3 # reduction candidate for 2,6 D9: 3 => CTR * ...52.....9...3..4......7...1..3..4..8..453.1634.1...87.2......1.8....32.4.382.17 D9: 2,6 # 13 pairs * PAIR F9: 2,6 COL F F4: 2,6,7,8,9 # reduction candidate for 2,6 F4: 2,6 # 9 pairs F4: 7,8,9 # 7 pairs * PAIR G9: 5,6 BLK 9 G7: 5,6,4,8,9 # reduction candidate for 5,6 G7: 5,6 # 19 pairs H7: 5,6,8,9 # reduction candidate for 5,6 H7: 5,6 # 12 pairs I7: 5,6,9 # reduction candidate for 5,6 I7: 5,6 # 10 pairs G8: 5,6,4,9 # reduction candidate for 5,6 G8: 5,6 => CTR * 476528193895.63.2432..9.765517.3..46289645371634.1..58762351489158.7.632943286517 G8: 4,9 # 8 pairs * PAIR G9: 5,6 ROW 9 C9: 5,6,3,9 # reduction candidate for 5,6 C9: 5,6 => CTR * ...52.....9...3..4......7...1..3..4.28..453.1634.1...87.2......1.8....3294.382.17 C9: 3,9 # 9 pairs * PAIR G9: 5,6 COL G G2: 5,6,1,2,8 # reduction candidate for 5,6 G2: 5,6 # 15 pairs G4: 5,6,2,9 # reduction candidate for 5,6 G4: 5,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-055-base-pr-000.dot * REASONING * DIS # E4: 6,7 => CTR => E4: 3,9 * DIS # E8: 6,7 => CTR => E8: 5,9 * PRF # E4: 6,9 => SOL * DIS # E7: 6,9 => CTR => E7: 3,5 * DIS # E8: 6,9 => CTR => E8: 5,7 * DIS # D5: 2,9 => CTR => D5: 6,7 * DIS # C9: 5,6 => CTR => C9: 3,9 * DIS # G8: 5,6 => CTR => G8: 4,9 * DIS # B3: 5,6 => CTR => B3: 2,3 * DIS # D9: 3 => CTR => D9: 2,6 * DIS # G8: 5,6 => CTR => G8: 4,9 * DIS # C9: 5,6 => CTR => C9: 3,9 * CNT 12 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B8,C5,E2,E3,F9,G9) * ...52.....9...3..4......7...1.....4..8..453.16.4.1...87.2......1.8....32.4..8..17 * PAIR E2: 6,7 BLK 2 F1: 6,7,1,4,8,9 # reduction candidate for 6,7 F1: 6,7 # 8 pairs D2: 6,7,1,8 # reduction candidate for 6,7 D2: 6,7 # 8 pairs * PAIR E2: 6,7 ROW 2 C2: 6,7,1,5 # reduction candidate for 6,7 C2: 6,7 # 9 pairs C2: 1,5 # 8 pairs * PAIR E2: 6,7 COL E E4: 6,7,3,9 # reduction candidate for 6,7 E4: 6,7 => CTR * .7.52...3.9..63..4....9.7.5.17....4..896453716.4.1..58752.3....168.5..32943286517 E8: 6,7,5,9 # reduction candidate for 6,7 E8: 6,7 => CTR * .7652.193.91763824.2319.765.1.83..46.8.645371634.17.58762351489158479632.4.286517 * PAIR RESTART * PAIR E3: 6,9 BLK 2 F1: 6,9,1,4,8 # reduction candidate for 6,9 F1: 6,9 # 10 pairs D3: 6,9,1,4,8 # reduction candidate for 6,9 D3: 6,9 # 11 pairs F3: 6,9,1,4,8 # reduction candidate for 6,9 F3: 6,9 # 11 pairs * PAIR E3: 6,9 ROW 3 H3: 6,9,2,5,8 # reduction candidate for 6,9 H3: 6,9 # 11 pairs I3: 6,9,3,5 # reduction candidate for 6,9 I3: 6,9 # 11 pairs * PAIR E3: 6,9 COL E E7: 6,9,3,5 # reduction candidate for 6,9 E7: 6,9 => CTR * 47.529863.96.73124.2..6.795.1..3.649.8.645371634917258752391486168754932.4.286517 * PAIR RESTART * PAIR A5: 2,9 BLK 4 A4: 2,9,3,5 # reduction candidate for 2,9 A4: 2,9 # 19 pairs A4: 3,5 # 10 pairs * PAIR A5: 2,9 ROW 5 D5: 2,9,6,7 # reduction candidate for 2,9 D5: 2,9 => CTR * .7.52.....9..73..4....6.7...1.....4..87.453616.4.1..787.2......1.8....32.4..8..17 H5: 2,9,6,7 # reduction candidate for 2,9 H5: 2,9 # 16 pairs * RESTART * PAIR A5: 2,9 ROW 5 H5: 2,9,6,7 # reduction candidate for 2,9 H5: 2,9 # 16 pairs H5: 6,7 # 11 pairs * PAIR RESTART * PAIR A5: 2,9 BLK 4 A4: 2,9,3,5 # reduction candidate for 2,9 A4: 2,9 # 19 pairs A4: 3,5 # 11 pairs * PAIR A5: 2,9 ROW 5 H5: 2,9,6,7 # reduction candidate for 2,9 H5: 2,9 # 16 pairs H5: 6,7 # 11 pairs * PAIR C5: 7,9 BLK 4 C4: 7,9,3,5 # reduction candidate for 7,9 C4: 3,5 # 16 pairs C4: 7,9 # 14 pairs * PAIR C5: 7,9 ROW 5 H5: 7,9,2,6 # reduction candidate for 7,9 H5: 2,6 # 15 pairs H5: 7,9 # 11 pairs * PAIR B8: 5,6 BLK 7 B7: 5,6,3 # reduction candidate for 5,6 B7: 5,6 => SOLVED * 476529183895173624321864795517398246289645371634712958752431869168957432943286517 * DURATION: 0:00:21.276824 START: 00:01:43.839183 END: 00:02:05.116007 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-055-base-pr-001.dot * REASONING * DIS # E4: 6,7 => CTR => E4: 3,9 * DIS E4: 3,9 # E8: 6,7 => CTR => E8: 5,9 * DIS E4: 3,9 + E8: 5,9 # E7: 6,9 => CTR => E7: 3,5 * DIS E4: 3,9 + E8: 5,9 + E7: 3,5 # D5: 2,9 => CTR => D5: 6,7 * PRF E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # B7: 5,6 => SOL * STA E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 + B7: 5,6 * CNT 5 HDP CHAINS / 27 HYP OPENED
Header Info
Top 95 Sudokus 055 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 476529183895173624321864795517398246289645371634712958752431869168957432943286517 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 # F1: 6,7 => UNS * INC # D2: 6,7 => UNS * INC # C2: 6,7 => UNS * INC # C2: 1,5 => UNS * DIS # E4: 6,7 => CTR => E4: 3,9 * INC # E4: 3,9 => UNS * DIS # E8: 6,7 => CTR => E8: 5,9 * INC # E8: 5,9 => UNS * INC # F1: 6,9 => UNS * INC # D3: 6,9 => UNS * INC # F3: 6,9 => UNS * INC # H3: 6,9 => UNS * INC # I3: 6,9 => UNS * PRF # E4: 6,9 => SOL * INC # E4: 3,7 => UNS * DIS # E7: 6,9 => CTR => E7: 3,5 * INC # E7: 3,5 => UNS * DIS # E8: 6,9 => CTR => E8: 5,7 * INC # E8: 5,7 => UNS * INC # A4: 2,9 => UNS * INC # A4: 3,5 => UNS * DIS # D5: 2,9 => CTR => D5: 6,7 * INC # D5: 6,7 => UNS * INC # H5: 2,9 => UNS * INC # C4: 7,9 => UNS * INC # C4: 3,5 => UNS * INC # D5: 7,9 => UNS * INC # H5: 7,9 => UNS * INC # B7: 5,6 => UNS * DIS # C9: 5,6 => CTR => C9: 3,9 * INC # C9: 3,9 => UNS * INC # E8: 5,6 => UNS * DIS # G8: 5,6 => CTR => G8: 4,9 * INC # G8: 4,9 => UNS * DIS # B3: 5,6 => CTR => B3: 2,3 * INC # B3: 2,3 => UNS * INC # D9: 2,6 => UNS * DIS # D9: 3 => CTR => D9: 2,6 * INC # F4: 2,6 => UNS * INC # F4: 7,8,9 => UNS * INC # G7: 5,6 => UNS * INC # H7: 5,6 => UNS * INC # I7: 5,6 => UNS * DIS # G8: 5,6 => CTR => G8: 4,9 * INC # G8: 4,9 => UNS * DIS # C9: 5,6 => CTR => C9: 3,9 * INC # C9: 3,9 => UNS * INC # G2: 5,6 => UNS * INC # G4: 5,6 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 6,7 => UNS * INC # D2: 6,7 => UNS * INC # C2: 6,7 => UNS * INC # C2: 1,5 => UNS * DIS # E4: 6,7 => CTR => E4: 3,9 * DIS E4: 3,9 # E8: 6,7 => CTR => E8: 5,9 * INC E4: 3,9 + E8: 5,9 # F1: 6,9 => UNS * INC E4: 3,9 + E8: 5,9 # D3: 6,9 => UNS * INC E4: 3,9 + E8: 5,9 # F3: 6,9 => UNS * INC E4: 3,9 + E8: 5,9 # H3: 6,9 => UNS * INC E4: 3,9 + E8: 5,9 # I3: 6,9 => UNS * DIS E4: 3,9 + E8: 5,9 # E7: 6,9 => CTR => E7: 3,5 * INC E4: 3,9 + E8: 5,9 + E7: 3,5 # A4: 2,9 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 # A4: 3,5 => UNS * DIS E4: 3,9 + E8: 5,9 + E7: 3,5 # D5: 2,9 => CTR => D5: 6,7 * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # H5: 2,9 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # H5: 2,9 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # H5: 6,7 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # A4: 2,9 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # A4: 3,5 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # H5: 2,9 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # H5: 6,7 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # C4: 7,9 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # C4: 3,5 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # H5: 7,9 => UNS * INC E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # H5: 2,6 => UNS * PRF E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 # B7: 5,6 => SOL * STA E4: 3,9 + E8: 5,9 + E7: 3,5 + D5: 6,7 + B7: 5,6 * CNT 27 HDP CHAINS / 27 HYP OPENED