Analysis of xx-top95-007-base.sdk
Contents
Original Sudoku
level: medium
position: 6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6..... initial
Autosolve
position: 6.2.5.........3.42.....2...43..28....1....2........7..5..27...........81...68..27 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 1,8 => CTR => G1: 3,9 * DIS # I7: 6 => CTR => I7: 3,9 * DIS # B7: 4,9 => CTR => B7: 6,8 * DIS # C7: 4,9 => CTR => C7: 1,3,6,8 * DIS # B8: 4,9 => CTR => B8: 2,6,7 * PRF # C8: 4,9 => SOL * DIS # C9: 4,9 => CTR => C9: 1,3 * DIS # G9: 4,9 => CTR => G9: 3,5 * DIS # G7: 6,9 => CTR => G7: 3,4 * DIS # I7: 6,9 => CTR => I7: 3 * DIS # C7: 6,9 => CTR => C7: 1,3,4,8 * PRF # H3: 6,9 => SOL * CNT 12 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G1: 1,8 => CTR => G1: 3,9 * DIS G1: 3,9 # I7: 6 => CTR => I7: 3,9 * DIS G1: 3,9 + I7: 3,9 # B7: 4,9 => CTR => B7: 6,8 * DIS G1: 3,9 + I7: 3,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8 * DIS G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 # B8: 4,9 => CTR => B8: 2,6,7 * PRF G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 # C8: 4,9 => SOL * STA G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 + C8: 4,9 * CNT 6 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6..... | initial |
| 6.2.5.........3.42.....2...43..28....1....2........7..5..27...........81...68..27 | autosolve |
| 682154379951763842374892165437528916816937254295416738568271493729345681143689527 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) I1: 3,9 I5: 4,8 I6: 4,8 B9: 4,9 H7: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F7,F9: 1.. / F7 = 1 => 5 pairs (_) / F9 = 1 => 0 pairs (X) C7,F7: 1.. / C7 = 1 => 0 pairs (X) / F7 = 1 => 5 pairs (_) A6,B6: 2.. / A6 = 2 => 6 pairs (_) / B6 = 2 => 6 pairs (_) A8,B8: 2.. / A8 = 2 => 6 pairs (_) / B8 = 2 => 6 pairs (_) A6,A8: 2.. / A6 = 2 => 6 pairs (_) / A8 = 2 => 6 pairs (_) B6,B8: 2.. / B6 = 2 => 6 pairs (_) / B8 = 2 => 6 pairs (_) A3,C3: 3.. / A3 = 3 => 6 pairs (_) / C3 = 3 => 8 pairs (_) G1,I1: 3.. / G1 = 3 => 8 pairs (_) / I1 = 3 => 0 pairs (X) H5,H6: 3.. / H5 = 3 => 6 pairs (_) / H6 = 3 => 5 pairs (_) D8,E8: 3.. / D8 = 3 => 6 pairs (_) / E8 = 3 => 6 pairs (_) A3,A9: 3.. / A3 = 3 => 6 pairs (_) / A9 = 3 => 8 pairs (_) I1,I7: 3.. / I1 = 3 => 0 pairs (X) / I7 = 3 => 8 pairs (_) I5,I6: 4.. / I5 = 4 => 5 pairs (_) / I6 = 4 => 4 pairs (_) B2,C2: 5.. / B2 = 5 => 5 pairs (_) / C2 = 5 => 0 pairs (X) H3,I3: 5.. / H3 = 5 => 0 pairs (X) / I3 = 5 => 6 pairs (_) G8,G9: 5.. / G8 = 5 => 0 pairs (X) / G9 = 5 => 5 pairs (_) F9,G9: 5.. / F9 = 5 => 0 pairs (X) / G9 = 5 => 5 pairs (_) B2,B6: 5.. / B2 = 5 => 5 pairs (_) / B6 = 5 => 0 pairs (X) I3,I4: 5.. / I3 = 5 => 6 pairs (_) / I4 = 5 => 0 pairs (X) E2,E3: 6.. / E2 = 6 => 5 pairs (_) / E3 = 6 => 0 pairs (X) F5,F6: 6.. / F5 = 6 => 0 pairs (X) / F6 = 6 => 5 pairs (_) E2,G2: 6.. / E2 = 6 => 5 pairs (_) / G2 = 6 => 0 pairs (X) H1,H3: 7.. / H1 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) C4,D4: 7.. / C4 = 7 => 8 pairs (_) / D4 = 7 => 0 pairs (X) F1,F5: 7.. / F1 = 7 => 0 pairs (X) / F5 = 7 => 0 pairs (_) I5,I6: 8.. / I5 = 8 => 4 pairs (_) / I6 = 8 => 5 pairs (_) B7,C7: 8.. / B7 = 8 => 0 pairs (X) / C7 = 8 => 7 pairs (_) * DURATION: 0:00:38.517004 START: 22:56:40.026984 END: 22:57:18.543988 2017-05-03 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,H7,I1,I5,I6) * 6.2.5.........3.42.....2...43..28....1....2........7..5..27...........81...68..27 * PAIR I1: 3,9 BLK 3 G1: 3,9,1,8 # reduction candidate for 3,9 G1: 1,8 => CTR * 6.2.5...3.5.7.3.42.....2...437.28....1...72.......67..5..27....7......81...68..27 G1: 3,9 # 9 pairs * PAIR I1: 3,9 COL I I7: 3,9,6 # reduction candidate for 3,9 I7: 6 => CTR * 6.2.5...3.5.7.3.42.....2...437.28....1...72.......67..5..27..967......81...68..27 I7: 3,9 # 8 pairs * PAIR B9: 4,9 BLK 7 B7: 4,9,6,8 # reduction candidate for 4,9 B7: 4,9 => CTR * 6.2.5....9517638423.4..2...437.28...81...72.426....7.85.8271...726....811.368..27 B7: 6,8 # 6 pairs C7: 4,9,1,3,6,8 # reduction candidate for 4,9 C7: 4,9 => CTR * 6.2.5.....5.7.3.42.....2...437.28....1...72.......67..58.271...7......81...68..27 C7: 1,3,6,8 # 5 pairs B8: 4,9,2,6,7 # reduction candidate for 4,9 B8: 4,9 => CTR * 6.2.5.3.9.5..63.42.....2...43.72891.71....2.882....7.45682714932.7...681...68.527 B8: 2,6,7 # 5 pairs C8: 4,9,6,7 # reduction candidate for 4,9 C8: 4,9 => SOLVED * 682154379951763842374892165437528916816937254295416738568271493729345681143689527 C8: 6,7 # 6 pairs C9: 4,9,1,3 # reduction candidate for 4,9 C9: 4,9 => CTR * 6.2.5.....5.7.3.42.....2...437.28....1...72.......67..58.27....7......81...68..27 C9: 1,3 # 6 pairs * PAIR B9: 4,9 ROW 9 F9: 4,9,1,5 # reduction candidate for 4,9 F9: 4,9 # 8 pairs G9: 4,9,3,5 # reduction candidate for 4,9 G9: 4,9 => CTR * 6.2.5.....5.7.3.42.....2...437.28....1...72.......67..5..271...7.....581...685.27 G9: 3,5 # 6 pairs * PAIR B9: 4,9 COL B B1: 4,9,7,8 # reduction candidate for 4,9 B1: 4,9 # 8 pairs B3: 4,9,7,8 # reduction candidate for 4,9 B3: 4,9 # 8 pairs * PAIR H7: 6,9 BLK 9 G7: 6,9,3,4 # reduction candidate for 6,9 G7: 6,9 => CTR * 6.2.5.3.9.5.7.3.42.....2...437.28....1...72.......67..5..27...37......81...68..27 G7: 3,4 # 6 pairs I7: 6,9,3 # reduction candidate for 6,9 I7: 6,9 => CTR * 6.2.5...3.5.7.3.42.....2...437.28....1...72.......67..5..27....7......81...68..27 I7: 3 # 8 pairs G8: 6,9,4,5 # reduction candidate for 6,9 G8: 6,9 # 10 pairs * PAIR H7: 6,9 ROW 7 B7: 6,9,4,8 # reduction candidate for 6,9 B7: 6,9 # 12 pairs C7: 6,9,1,3,4,8 # reduction candidate for 6,9 C7: 6,9 => CTR * 672854319...7.3.42.94162875437.281.6.1...72......167..5892714637......81.4.68..27 C7: 1,3,4,8 # 5 pairs * PAIR H7: 6,9 COL H H3: 6,9,1,5,7 # reduction candidate for 6,9 H3: 6,9 => SOLVED * 682154379951763842374892165437528916816937254295416738568271493729345681143689527 H3: 1,5,7 # 5 pairs H4: 6,9,1,5 # reduction candidate for 6,9 H4: 6,9 # 9 pairs H5: 6,9,3,5 # reduction candidate for 6,9 H5: 6,9 # 9 pairs H6: 6,9,1,3,5 # reduction candidate for 6,9 H6: 6,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-007-base-pr-000.dot * REASONING * DIS # G1: 1,8 => CTR => G1: 3,9 * DIS # I7: 6 => CTR => I7: 3,9 * DIS # B7: 4,9 => CTR => B7: 6,8 * DIS # C7: 4,9 => CTR => C7: 1,3,6,8 * DIS # B8: 4,9 => CTR => B8: 2,6,7 * PRF # C8: 4,9 => SOL * DIS # C9: 4,9 => CTR => C9: 1,3 * DIS # G9: 4,9 => CTR => G9: 3,5 * DIS # G7: 6,9 => CTR => G7: 3,4 * DIS # I7: 6,9 => CTR => I7: 3 * DIS # C7: 6,9 => CTR => C7: 1,3,4,8 * PRF # H3: 6,9 => SOL * CNT 12 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,H7,I1,I5,I6) * 6.2.5.........3.42.....2...43..28....1....2........7..5..27...........81...68..27 * PAIR I1: 3,9 BLK 3 G1: 3,9,1,8 # reduction candidate for 3,9 G1: 1,8 => CTR * 6.2.5...3.5.7.3.42.....2...437.28....1...72.......67..5..27....7......81...68..27 * PAIR I1: 3,9 COL I I7: 3,9,6 # reduction candidate for 3,9 I7: 6 => CTR * 6.2.5.9.3.5.7.3.42.....2..5437.28..9.1...72.......67..5..27..967......81...68..27 * PAIR RESTART * PAIR B9: 4,9 BLK 7 B7: 4,9,6,8 # reduction candidate for 4,9 B7: 4,9 => CTR * 6.2.5....9517638423.4..2...437.28...81...72.426....7.85.8271...726....811.368..27 C7: 4,9,1,3,6,8 # reduction candidate for 4,9 C7: 4,9 => CTR * 672854.1..5.7.3.42.....2.75437.281.6.1...72.......67..58.271.6.7......81...68..27 B8: 4,9,2,6,7 # reduction candidate for 4,9 B8: 4,9 => CTR * 6.2.5.3.9.5..63.42.....2...43.72891.71....2.882....7.45682714932.7...681...68.527 C8: 4,9,6,7 # reduction candidate for 4,9 C8: 4,9 => SOLVED * 682154379951763842374892165437528916816937254295416738568271493729345681143689527 * DURATION: 0:00:09.722970 START: 22:57:44.909648 END: 22:57:54.632618 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-007-base-pr-001.dot * REASONING * DIS # G1: 1,8 => CTR => G1: 3,9 * DIS G1: 3,9 # I7: 6 => CTR => I7: 3,9 * DIS G1: 3,9 + I7: 3,9 # B7: 4,9 => CTR => B7: 6,8 * DIS G1: 3,9 + I7: 3,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8 * DIS G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 # B8: 4,9 => CTR => B8: 2,6,7 * PRF G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 # C8: 4,9 => SOL * STA G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 + C8: 4,9 * CNT 6 HDP CHAINS / 8 HYP OPENED
Header Info
Top 95 Sudokus 007 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 682154379951763842374892165437528916816937254295416738568271493729345681143689527 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 # G1: 3,9 => UNS * DIS # G1: 1,8 => CTR => G1: 3,9 * INC # I7: 3,9 => UNS * DIS # I7: 6 => CTR => I7: 3,9 * DIS # B7: 4,9 => CTR => B7: 6,8 * INC # B7: 6,8 => UNS * DIS # C7: 4,9 => CTR => C7: 1,3,6,8 * INC # C7: 1,3,6,8 => UNS * DIS # B8: 4,9 => CTR => B8: 2,6,7 * INC # B8: 2,6,7 => UNS * PRF # C8: 4,9 => SOL * INC # C8: 6,7 => UNS * DIS # C9: 4,9 => CTR => C9: 1,3 * INC # C9: 1,3 => UNS * INC # F9: 4,9 => UNS * DIS # G9: 4,9 => CTR => G9: 3,5 * INC # G9: 3,5 => UNS * INC # B1: 4,9 => UNS * INC # B3: 4,9 => UNS * DIS # G7: 6,9 => CTR => G7: 3,4 * INC # G7: 3,4 => UNS * DIS # I7: 6,9 => CTR => I7: 3 * INC # I7: 3 => UNS * INC # G8: 6,9 => UNS * INC # B7: 6,9 => UNS * DIS # C7: 6,9 => CTR => C7: 1,3,4,8 * INC # C7: 1,3,4,8 => UNS * PRF # H3: 6,9 => SOL * INC # H3: 1,5,7 => UNS * INC # H4: 6,9 => UNS * INC # H5: 6,9 => UNS * INC # H6: 6,9 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 3,9 => UNS * DIS # G1: 1,8 => CTR => G1: 3,9 * INC G1: 3,9 # I7: 3,9 => UNS * DIS G1: 3,9 # I7: 6 => CTR => I7: 3,9 * DIS G1: 3,9 + I7: 3,9 # B7: 4,9 => CTR => B7: 6,8 * DIS G1: 3,9 + I7: 3,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8 * DIS G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 # B8: 4,9 => CTR => B8: 2,6,7 * PRF G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 # C8: 4,9 => SOL * STA G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 + C8: 4,9 * CNT 8 HDP CHAINS / 8 HYP OPENED