Analysis of xx-top95-016-base.sdk
Contents
Original Sudoku
level: medium
position: 6..3.2....4.....1..........7.26............543.........8.15........4.2........7.. initial
Autosolve
position: 6..3.2....4.....12.2.4.....7526.4..........543.4....2728.15........4.2..4.....7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 8,9 => CTR => G1: 4,5 * PRF # G2: 8,9 => SOL * DIS # I3: 8,9 => CTR => I3: 3,6 * DIS # C1: 8,9 => CTR => C1: 1,5,7 * DIS # I4: 3 => CTR => I4: 8,9 * DIS # G4: 3,9 => CTR => G4: 1,8 * DIS # I4: 3,9 => CTR => I4: 8 * DIS # E4: 1,8 => CTR => E4: 3,9 * PRF # H3: 3,9 => SOL * DIS # H7: 3,9 => CTR => H7: 4,6 * DIS # C8: 1,5 => CTR => C8: 6,7,9 * DIS # C9: 6,9 => CTR => C9: 1,5 * CNT 12 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G1: 8,9 => CTR => G1: 4,5 * PRF G1: 4,5 # G2: 8,9 => SOL * STA G1: 4,5 + G2: 8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..3.2....4.....1..........7.26............543.........8.15........4.2........7.. | initial |
| 6..3.2....4.....12.2.4.....7526.4..........543.4....2728.15........4.2..4.....7.. | autosolve |
| 615382479943765812827491536752634198168279354394518627286157943579843261431926785 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) I1: 8,9 H4: 3,9 I8: 1,5 I9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I8,I9: 1.. / I8 = 1 => 3 pairs (_) / I9 = 1 => 0 pairs (X) E4,G4: 1.. / E4 = 1 => 0 pairs (X) / G4 = 1 => 4 pairs (_) D5,E5: 2.. / D5 = 2 => 5 pairs (_) / E5 = 2 => 5 pairs (_) D9,E9: 2.. / D9 = 2 => 5 pairs (_) / E9 = 2 => 5 pairs (_) D5,D9: 2.. / D5 = 2 => 5 pairs (_) / D9 = 2 => 5 pairs (_) E5,E9: 2.. / E5 = 2 => 5 pairs (_) / E9 = 2 => 5 pairs (_) C2,C3: 3.. / C2 = 3 => 0 pairs (*) / C3 = 3 => 0 pairs (X) B8,B9: 3.. / B8 = 3 => 0 pairs (X) / B9 = 3 => 5 pairs (_) C2,G2: 3.. / C2 = 3 => 0 pairs (*) / G2 = 3 => 0 pairs (X) G1,H1: 4.. / G1 = 4 => 5 pairs (_) / H1 = 4 => 0 pairs (X) G7,H7: 4.. / G7 = 4 => 0 pairs (X) / H7 = 4 => 5 pairs (_) G1,G7: 4.. / G1 = 4 => 5 pairs (_) / G7 = 4 => 0 pairs (X) H1,H7: 4.. / H1 = 4 => 0 pairs (X) / H7 = 4 => 5 pairs (_) D6,F6: 5.. / D6 = 5 => 4 pairs (_) / F6 = 5 => 6 pairs (_) I8,I9: 5.. / I8 = 5 => 0 pairs (X) / I9 = 5 => 3 pairs (_) C1,G1: 5.. / C1 = 5 => 3 pairs (_) / G1 = 5 => 0 pairs (X) C9,I9: 5.. / C9 = 5 => 0 pairs (X) / I9 = 5 => 3 pairs (_) D2,D6: 5.. / D2 = 5 => 6 pairs (_) / D6 = 5 => 4 pairs (_) E2,F2: 6.. / E2 = 6 => 4 pairs (_) / F2 = 6 => 0 pairs (X) H3,I3: 6.. / H3 = 6 => 0 pairs (X) / I3 = 6 => 5 pairs (_) G5,G6: 6.. / G5 = 6 => 0 pairs (X) / G6 = 6 => 5 pairs (_) B6,G6: 6.. / B6 = 6 => 0 pairs (X) / G6 = 6 => 5 pairs (_) E2,E9: 6.. / E2 = 6 => 4 pairs (_) / E9 = 6 => 0 pairs (X) I3,I7: 6.. / I3 = 6 => 5 pairs (_) / I7 = 6 => 0 pairs (X) H1,H3: 7.. / H1 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) C7,F7: 7.. / C7 = 7 => 0 pairs (X) / F7 = 7 => 8 pairs (_) B1,B8: 7.. / B1 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) A5,C5: 8.. / A5 = 8 => 5 pairs (_) / C5 = 8 => 5 pairs (_) H8,H9: 8.. / H8 = 8 => 5 pairs (_) / H9 = 8 => 5 pairs (_) * DURATION: 0:00:44.709608 START: 23:11:01.336946 END: 23:11:46.046554 2017-05-03 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (H4,I1,I8,I9) * 6..3.2....4.....12.2.4.....7526.4..........543.4....2728.15........4.2..4.....7.. * PAIR I1: 8,9 BLK 3 G1: 8,9,4,5 # reduction candidate for 8,9 G1: 8,9 => CTR * 615372.4..47.6.312.234..5767526.4...1.8....543.4....2728.1574..57..4.2.1431.2.7.5 G1: 4,5 # 5 pairs G2: 8,9,3,5 # reduction candidate for 8,9 G2: 8,9 => SOLVED * 615382479943765812827491536752634198168279354394518627286157943579843261431926785 G2: 3,5 # 5 pairs G3: 8,9,3,5 # reduction candidate for 8,9 G3: 8,9 # 9 pairs I3: 8,9,3,6 # reduction candidate for 8,9 I3: 8,9 => CTR * 6..3.247..4.....12.2.4...6.7526.4.93....3..543.4....27289157346.7..4328.43....7.. I3: 3,6 # 5 pairs * PAIR I1: 8,9 ROW 1 C1: 8,9,1,5,7 # reduction candidate for 8,9 C1: 8,9 => CTR * 61.37254..47.6.312.234...767526.4..........543.4....2728.1574...7..4.2..43..2.7.. C1: 1,5,7 # 4 pairs E1: 8,9,1,7 # reduction candidate for 8,9 E1: 8,9 # 8 pairs * PAIR I1: 8,9 COL I I4: 8,9,3 # reduction candidate for 8,9 I4: 3 => CTR * 6..3.2....47.6.312.234.....7526.4.93.......543.4....27286157.39.7..432..4.....7.. I4: 8,9 # 7 pairs * PAIR H4: 3,9 BLK 6 G4: 3,9,1,8 # reduction candidate for 3,9 G4: 3,9 => CTR * 6..3.2..9.47.6.312.234.1..6752614938.......543.4....2728.1574.3.7..432..4.....7.. G4: 1,8 # 5 pairs I4: 3,9,8 # reduction candidate for 3,9 I4: 3,9 => CTR * 6..3.2....47.6.312.234.....7526.4..........543.4....2728.157....7..4.2..43..2.7.. I4: 8 # 7 pairs G5: 3,9,1,6 # reduction candidate for 3,9 G5: 3,9 # 10 pairs * PAIR H4: 3,9 ROW 4 E4: 3,9,1,8 # reduction candidate for 3,9 E4: 1,8 => CTR * 6..3.2....47.6.312.234.....7526.4..........543.4....2728.157....7..4.2..43..2.7.. E4: 3,9 # 9 pairs * PAIR H4: 3,9 COL H H3: 3,9,6,7 # reduction candidate for 3,9 H3: 3,9 => SOLVED * 615382479943765812827491536752634198168279354394518627286157943579843261431926785 H3: 6,7 # 5 pairs H7: 3,9,4,6 # reduction candidate for 3,9 H7: 3,9 => CTR * 6..372.4..47.6.312.234...767526.4..........543.4....272861574...7..432..4.....7.. H7: 4,6 # 5 pairs H8: 3,9,6,8 # reduction candidate for 3,9 H8: 3,9 # 10 pairs H9: 3,9,6,8 # reduction candidate for 3,9 H9: 3,9 # 10 pairs * PAIR I8: 1,5 ROW 8 A8: 1,5,9 # reduction candidate for 1,5 A8: 1,5 # 5 pairs C8: 1,5,6,7,9 # reduction candidate for 1,5 C8: 1,5 => CTR * 6..37254..47.6.312.234...767526.4..........543.4....272861574..97.84.2..43..2.78. C8: 6,7,9 # 4 pairs * PAIR I9: 1,5 ROW 9 C9: 1,5,6,9 # reduction candidate for 1,5 C9: 6,9 => CTR * 67.3.2....4.....12.2.4...767526.4..........543.4....2728.15.....3..4.2.141....7.5 C9: 1,5 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-016-base-pr-000.dot * REASONING * DIS # G1: 8,9 => CTR => G1: 4,5 * PRF # G2: 8,9 => SOL * DIS # I3: 8,9 => CTR => I3: 3,6 * DIS # C1: 8,9 => CTR => C1: 1,5,7 * DIS # I4: 3 => CTR => I4: 8,9 * DIS # G4: 3,9 => CTR => G4: 1,8 * DIS # I4: 3,9 => CTR => I4: 8 * DIS # E4: 1,8 => CTR => E4: 3,9 * PRF # H3: 3,9 => SOL * DIS # H7: 3,9 => CTR => H7: 4,6 * DIS # C8: 1,5 => CTR => C8: 6,7,9 * DIS # C9: 6,9 => CTR => C9: 1,5 * CNT 12 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (H4,I1,I8,I9) * 6..3.2....4.....12.2.4.....7526.4..........543.4....2728.15........4.2..4.....7.. * PAIR I1: 8,9 BLK 3 G1: 8,9,4,5 # reduction candidate for 8,9 G1: 8,9 => CTR * 615372.4..47.6.312.234..5767526.4...1.8....543.4....2728.1574..57..4.2.1431.2.7.5 G2: 8,9,3,5 # reduction candidate for 8,9 G2: 8,9 => SOLVED * 615382479943765812827491536752634198168279354394518627286157943579843261431926785 * DURATION: 0:00:03.866436 START: 23:12:11.866373 END: 23:12:15.732809 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-016-base-pr-001.dot * REASONING * DIS # G1: 8,9 => CTR => G1: 4,5 * PRF G1: 4,5 # G2: 8,9 => SOL * STA G1: 4,5 + G2: 8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 95 Sudokus 016 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 615382479943765812827491536752634198168279354394518627286157943579843261431926785 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:
* DIS # G1: 8,9 => CTR => G1: 4,5 * INC # G1: 4,5 => UNS * PRF # G2: 8,9 => SOL * INC # G2: 3,5 => UNS * INC # G3: 8,9 => UNS * DIS # I3: 8,9 => CTR => I3: 3,6 * INC # I3: 3,6 => UNS * DIS # C1: 8,9 => CTR => C1: 1,5,7 * INC # C1: 1,5,7 => UNS * INC # E1: 8,9 => UNS * INC # I4: 8,9 => UNS * DIS # I4: 3 => CTR => I4: 8,9 * DIS # G4: 3,9 => CTR => G4: 1,8 * INC # G4: 1,8 => UNS * DIS # I4: 3,9 => CTR => I4: 8 * INC # I4: 8 => UNS * INC # G5: 3,9 => UNS * INC # E4: 3,9 => UNS * DIS # E4: 1,8 => CTR => E4: 3,9 * PRF # H3: 3,9 => SOL * INC # H3: 6,7 => UNS * DIS # H7: 3,9 => CTR => H7: 4,6 * INC # H7: 4,6 => UNS * INC # H8: 3,9 => UNS * INC # H9: 3,9 => UNS * INC # A8: 1,5 => UNS * DIS # C8: 1,5 => CTR => C8: 6,7,9 * INC # C8: 6,7,9 => UNS * INC # C9: 1,5 => UNS * DIS # C9: 6,9 => CTR => C9: 1,5 * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G1: 8,9 => CTR => G1: 4,5 * PRF G1: 4,5 # G2: 8,9 => SOL * STA G1: 4,5 + G2: 8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED