Analysis of xx-top95-009-base.sdk
Contents
Original Sudoku
level: medium
position: 6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6..... initial
Autosolve
position: 6.2.5.........4.32.....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 # I3: 4,9 => CTR => I3: 5,6 * DIS # I7: 6 => CTR => I7: 4,9 * DIS # B7: 4,9 => CTR => B7: 6,8 * DIS # C7: 4,9 => CTR => C7: 1,3,6,8 * DIS # G9: 4,9 => CTR => G9: 3,5 * DIS # G7: 6,9 => CTR => G7: 3,4 * DIS # I7: 6,9 => CTR => I7: 4 * DIS # C7: 6,9 => CTR => C7: 1,3,4,8 * PRF # H3: 6,9 => SOL * CNT 9 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 # I3: 4,9 => CTR => I3: 5,6 * DIS I3: 5,6 # I7: 6 => CTR => I7: 4,9 * DIS I3: 5,6 + I7: 4,9 # B7: 4,9 => CTR => B7: 6,8 * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8 * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # G7: 6,9 => CTR => G7: 3,4 * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 # G8: 3,5 => CTR => G8: 6,9 * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # D1: 3,7 => CTR => D1: 1,8 * PRF I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8 => SOL * STA I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8 * CNT 8 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6..... | initial |
| 6.2.5.........4.32.....2...43..28....1....2........7..5..27...........81...68..27 | autosolve |
| 682153479951764832374892165437528916816947253295316748568271394729435681143689527 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) I1: 4,9 I5: 3,8 I6: 3,8 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 => 5 pairs (_) / B6 = 2 => 6 pairs (_) A8,B8: 2.. / A8 = 2 => 6 pairs (_) / B8 = 2 => 5 pairs (_) A6,A8: 2.. / A6 = 2 => 5 pairs (_) / A8 = 2 => 6 pairs (_) B6,B8: 2.. / B6 = 2 => 6 pairs (_) / B8 = 2 => 5 pairs (_) A3,C3: 3.. / A3 = 3 => 6 pairs (_) / C3 = 3 => 8 pairs (_) D1,F1: 3.. / D1 = 3 => 6 pairs (_) / F1 = 3 => 0 pairs (*) I5,I6: 3.. / I5 = 3 => 5 pairs (_) / I6 = 3 => 4 pairs (_) H5,H6: 4.. / H5 = 4 => 6 pairs (_) / H6 = 4 => 5 pairs (_) D8,E8: 4.. / D8 = 4 => 6 pairs (_) / E8 = 4 => 6 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 => 6 pairs (_) / E3 = 6 => 0 pairs (X) F5,F6: 6.. / F5 = 6 => 0 pairs (X) / F6 = 6 => 5 pairs (_) E2,G2: 6.. / E2 = 6 => 6 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 => 5 pairs (_) * DURATION: 0:00:36.269949 START: 23:00:22.564669 END: 23:00:58.834618 2017-05-03 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,H7,I1,I5,I6) * 6.2.5.........4.32.....2...43..28....1....2........7..5..27...........81...68..27 * PAIR I1: 4,9 BLK 3 G1: 4,9,1,8 # reduction candidate for 4,9 G1: 4,9 # 10 pairs G3: 4,9,1,6,8 # reduction candidate for 4,9 G3: 4,9 # 9 pairs I3: 4,9,5,6 # reduction candidate for 4,9 I3: 4,9 => CTR * 6.2.5..7......4.32.....2.5.437.28965.165.724..25..671.5..27..96.6.....81...68..27 I3: 5,6 # 6 pairs * PAIR I1: 4,9 ROW 1 B1: 4,9,7,8 # reduction candidate for 4,9 B1: 4,9 # 11 pairs B1: 7,8 # 6 pairs * PAIR I1: 4,9 COL I I7: 4,9,6 # reduction candidate for 4,9 I7: 6 => CTR * 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..5..27..967......81...68..27 I7: 4,9 # 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....9517648323.4..2...437.28...81...72.326....7.85.82713..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.....5.7.4.32.....2...437.28....1...72.......67..58.2713..7......81...68..27 C7: 1,3,6,8 # 5 pairs C9: 4,9,1,3 # reduction candidate for 4,9 C9: 4,9 # 9 pairs * PAIR B9: 4,9 ROW 9 G9: 4,9,3,5 # reduction candidate for 4,9 G9: 4,9 => CTR * 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..5..2713..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 # 11 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...9.5.7.4.32.....2...437.28....1...72.......67..58.27...47......81...68..27 G7: 3,4 # 6 pairs I7: 6,9,4 # reduction candidate for 6,9 I7: 6,9 => CTR * 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..5..27....7......81...68..27 I7: 4 # 8 pairs G8: 6,9,3,5 # 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 # 10 pairs C7: 6,9,1,3,4,8 # reduction candidate for 6,9 C7: 6,9 => CTR * 6.2.5...9.5.7.4.32.....2...437.28....1...72.......67..58.2713.47......81...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 * 682153479951764832374892165437528916816947253295316748568271394729435681143689527 H3: 1,5,7 # 5 pairs H4: 6,9,1,5 # reduction candidate for 6,9 H4: 6,9 # 9 pairs H5: 6,9,4,5 # reduction candidate for 6,9 H5: 6,9 # 9 pairs H6: 6,9,1,4,5 # reduction candidate for 6,9 H6: 6,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-009-base-pr-000.dot * REASONING * DIS # I3: 4,9 => CTR => I3: 5,6 * DIS # I7: 6 => CTR => I7: 4,9 * DIS # B7: 4,9 => CTR => B7: 6,8 * DIS # C7: 4,9 => CTR => C7: 1,3,6,8 * DIS # G9: 4,9 => CTR => G9: 3,5 * DIS # G7: 6,9 => CTR => G7: 3,4 * DIS # I7: 6,9 => CTR => I7: 4 * DIS # C7: 6,9 => CTR => C7: 1,3,4,8 * PRF # H3: 6,9 => SOL * CNT 9 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,H7,I1,I5,I6) * 6.2.5.........4.32.....2...43..28....1....2........7..5..27...........81...68..27 * PAIR I1: 4,9 BLK 3 G1: 4,9,1,8 # reduction candidate for 4,9 G1: 4,9 # 10 pairs G3: 4,9,1,6,8 # reduction candidate for 4,9 G3: 4,9 # 9 pairs I3: 4,9,5,6 # reduction candidate for 4,9 I3: 4,9 => CTR * 6.2.5..7......4.32.....2.5.437.28965.165.724..25..671.5..27..96.6.....81...68..27 * PAIR I1: 4,9 ROW 1 B1: 4,9,7,8 # reduction candidate for 4,9 B1: 4,9 # 12 pairs B1: 7,8 # 7 pairs * PAIR I1: 4,9 COL I I7: 4,9,6 # reduction candidate for 4,9 I7: 6 => CTR * 6.2.5...4.5.7.4.32.....2..5437.28..9.1...72.......67..5..27..967......81...68..27 * PAIR RESTART * PAIR I1: 4,9 BLK 3 G1: 4,9,1,8 # reduction candidate for 4,9 G1: 4,9 # 12 pairs G3: 4,9,1,6,8 # reduction candidate for 4,9 G3: 4,9 # 11 pairs * PAIR I1: 4,9 ROW 1 B1: 4,9,7,8 # reduction candidate for 4,9 B1: 4,9 # 14 pairs B1: 7,8 # 9 pairs * PAIR B9: 4,9 BLK 7 B7: 4,9,6,8 # reduction candidate for 4,9 B7: 4,9 => CTR * 6.2.5....9517648323.4..2...437.28...81...72.326....7.85.827136.726....811.368..27 C7: 4,9,1,3,6,8 # reduction candidate for 4,9 C7: 4,9 => CTR * 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..58.27136.7......81...68..27 C9: 4,9,1,3 # reduction candidate for 4,9 C9: 4,9 # 12 pairs * RESTART * PAIR B9: 4,9 BLK 7 C9: 4,9,1,3 # reduction candidate for 4,9 C9: 4,9 # 12 pairs C9: 1,3 # 11 pairs * PAIR B9: 4,9 COL B B1: 4,9,7,8 # reduction candidate for 4,9 B1: 4,9 # 14 pairs B3: 4,9,7,8 # reduction candidate for 4,9 B3: 4,9 # 11 pairs * PAIR H7: 6,9 BLK 9 G7: 6,9,3,4 # reduction candidate for 6,9 G7: 6,9 => CTR * 6.2.5...9.5.7.4.32.....2...437.28....1...72.......67..58.27...47......81...68..27 G8: 6,9,3,5 # reduction candidate for 6,9 G8: 6,9 # 11 pairs * RESTART * PAIR H7: 6,9 BLK 9 G8: 6,9,3,5 # reduction candidate for 6,9 G8: 3,5 => CTR * 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..58.27..697......81...68..27 * PAIR H7: 6,9 COL H H4: 6,9,1,5 # reduction candidate for 6,9 H4: 6,9 # 14 pairs H5: 6,9,4,5 # reduction candidate for 6,9 H5: 6,9 # 14 pairs H6: 6,9,1,4,5 # reduction candidate for 6,9 H6: 6,9 # 17 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B7,B9,F1,F7,G8,H1,H7,I3,I4,I5,I6) * 6.2.5...9.....4.32.....2...43..28....1....2........7..5..27.3.4.......81...68.527 * PAIR F1: 3,7 BLK 2 D1: 3,7,1,8 # reduction candidate for 3,7 D1: 3,7 => CTR * 642.5.819.....4632.9...2.7543..281.6.1....2........7..581279364......981...681527 D1: 1,8 => SOLVED * 682153479951764832374892165437528916816947253295316748568271394729435681143689527 * DURATION: 0:00:24.072576 START: 23:01:22.106162 END: 23:01:46.178738 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-009-base-pr-001.dot * REASONING * DIS # I3: 4,9 => CTR => I3: 5,6 * DIS I3: 5,6 # I7: 6 => CTR => I7: 4,9 * DIS I3: 5,6 + I7: 4,9 # B7: 4,9 => CTR => B7: 6,8 * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8 * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # G7: 6,9 => CTR => G7: 3,4 * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 # G8: 3,5 => CTR => G8: 6,9 * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # D1: 3,7 => CTR => D1: 1,8 * PRF I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8 => SOL * STA I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8 * CNT 8 HDP CHAINS / 26 HYP OPENED
Header Info
Top 95 Sudokus 009 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 682153479951764832374892165437528916816947253295316748568271394729435681143689527 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: 4,9 => UNS * INC # G3: 4,9 => UNS * DIS # I3: 4,9 => CTR => I3: 5,6 * INC # I3: 5,6 => UNS * INC # B1: 4,9 => UNS * INC # B1: 7,8 => UNS * INC # I7: 4,9 => UNS * DIS # I7: 6 => CTR => I7: 4,9 * 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 * INC # C9: 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: 4 * INC # I7: 4 => 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 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 4,9 => UNS * INC # G3: 4,9 => UNS * DIS # I3: 4,9 => CTR => I3: 5,6 * INC I3: 5,6 # B1: 4,9 => UNS * INC I3: 5,6 # B1: 7,8 => UNS * INC I3: 5,6 # I7: 4,9 => UNS * DIS I3: 5,6 # I7: 6 => CTR => I7: 4,9 * INC I3: 5,6 + I7: 4,9 # G1: 4,9 => UNS * INC I3: 5,6 + I7: 4,9 # G3: 4,9 => UNS * INC I3: 5,6 + I7: 4,9 # B1: 4,9 => UNS * INC I3: 5,6 + I7: 4,9 # B1: 7,8 => UNS * DIS I3: 5,6 + I7: 4,9 # B7: 4,9 => CTR => B7: 6,8 * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8 * INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # C9: 4,9 => UNS * INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # C9: 4,9 => UNS * INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # C9: 1,3 => UNS * INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # B1: 4,9 => UNS * INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # B3: 4,9 => UNS * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # G7: 6,9 => CTR => G7: 3,4 * INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 # G8: 6,9 => UNS * INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 # G8: 6,9 => UNS * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 # G8: 3,5 => CTR => G8: 6,9 * INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # H4: 6,9 => UNS * INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # H5: 6,9 => UNS * INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # H6: 6,9 => UNS * DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # D1: 3,7 => CTR => D1: 1,8 * PRF I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8 => SOL * STA I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8 * CNT 27 HDP CHAINS / 26 HYP OPENED