Analysis of xx-top95-048-base.sdk
Contents
Original Sudoku
level: hard
position: .26.39......6....19.....7.......4..9.5....2....85.....3..2..9..4....762.........4 initial
Autosolve
position: .26.39......6..3919..4..762.....4..9.5....2....85.....3..24.9..4....762...2.....4 autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:29.210471
The following important HDP chains were detected:
* DIS # A5: 1,7 # F2: 5,8 => CTR => F2: 2 * DIS # A5: 1,7 + F2: 2 # E2: 7 => CTR => E2: 5,8 * DIS # A5: 1,7 + F2: 2 + E2: 5,8 # H1: 5,8 => CTR => H1: 4 * DIS # A5: 1,7 + F2: 2 + E2: 5,8 + H1: 4 => CTR => A5: 6 * PRF A5: 6 # F2: 5,8 => SOL * STA A5: 6 + F2: 5,8 * CNT 5 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .26.39......6....19.....7.......4..9.5....2....85.....3..2..9..4....762.........4 | initial |
| .26.39......6..3919..4..762.....4..9.5....2....85.....3..24.9..4....762...2.....4 | autosolve |
| 126739845847625391935481762213864579654973218798512436361248957489157623572396184 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A1: 1,7 A2: 5,8 D1: 1,7 I1: 5,8 A4: 2,6 C5: 4,9 B6: 4,9 E4: 2,6 G6: 1,4 A9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,D1: 1.. / A1 = 1 => 17 pairs (_) / D1 = 1 => 0 pairs (X) E2,F2: 2.. / E2 = 2 => 21 pairs (_) / F2 = 2 => 10 pairs (_) A4,A6: 2.. / A4 = 2 => 8 pairs (_) / A6 = 2 => 9 pairs (_) A4,E4: 2.. / A4 = 2 => 8 pairs (_) / E4 = 2 => 9 pairs (_) F2,F6: 2.. / F2 = 2 => 10 pairs (_) / F6 = 2 => 21 pairs (_) B3,C3: 3.. / B3 = 3 => 13 pairs (_) / C3 = 3 => 13 pairs (_) B4,C4: 3.. / B4 = 3 => 13 pairs (_) / C4 = 3 => 13 pairs (_) I8,H9: 3.. / I8 = 3 => 11 pairs (_) / H9 = 3 => 16 pairs (_) D8,I8: 3.. / D8 = 3 => 16 pairs (_) / I8 = 3 => 11 pairs (_) B3,B4: 3.. / B3 = 3 => 13 pairs (_) / B4 = 3 => 13 pairs (_) C3,C4: 3.. / C3 = 3 => 13 pairs (_) / C4 = 3 => 13 pairs (_) B2,C2: 4.. / B2 = 4 => 10 pairs (_) / C2 = 4 => 14 pairs (_) G1,H1: 4.. / G1 = 4 => 12 pairs (_) / H1 = 4 => 10 pairs (_) C5,B6: 4.. / C5 = 4 => 10 pairs (_) / B6 = 4 => 14 pairs (_) C5,H5: 4.. / C5 = 4 => 10 pairs (_) / H5 = 4 => 14 pairs (_) B2,B6: 4.. / B2 = 4 => 10 pairs (_) / B6 = 4 => 14 pairs (_) C2,C5: 4.. / C2 = 4 => 14 pairs (_) / C5 = 4 => 10 pairs (_) G1,G6: 4.. / G1 = 4 => 12 pairs (_) / G6 = 4 => 10 pairs (_) G4,H4: 5.. / G4 = 5 => 12 pairs (_) / H4 = 5 => 12 pairs (_) A2,A9: 5.. / A2 = 5 => 13 pairs (_) / A9 = 5 => 14 pairs (_) I5,I6: 6.. / I5 = 6 => 13 pairs (_) / I6 = 6 => 10 pairs (_) B7,B9: 6.. / B7 = 6 => 10 pairs (_) / B9 = 6 => 16 pairs (_) A4,E4: 6.. / A4 = 6 => 9 pairs (_) / E4 = 6 => 8 pairs (_) B7,F7: 6.. / B7 = 6 => 10 pairs (_) / F7 = 6 => 16 pairs (_) D1,E2: 7.. / D1 = 7 => 17 pairs (_) / E2 = 7 => 0 pairs (X) A1,D1: 7.. / A1 = 7 => 0 pairs (X) / D1 = 7 => 17 pairs (_) B9,H9: 7.. / B9 = 7 => 13 pairs (_) / H9 = 7 => 13 pairs (_) A2,A9: 8.. / A2 = 8 => 14 pairs (_) / A9 = 8 => 13 pairs (_) C5,B6: 9.. / C5 = 9 => 14 pairs (_) / B6 = 9 => 10 pairs (_) B6,E6: 9.. / B6 = 9 => 10 pairs (_) / E6 = 9 => 14 pairs (_) C5,C8: 9.. / C5 = 9 => 14 pairs (_) / C8 = 9 => 10 pairs (_) * DURATION: 0:00:46.078892 START: 23:49:44.773382 END: 23:50:30.852274 2017-05-03 * CP COUNT: (31) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:28.930403 START: 23:51:05.074986 END: 23:51:34.005389 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-048-base-pr-002.dot * REASONING * DIS # A5: 1,7 # F2: 5,8 => CTR => F2: 2 * DIS # A5: 1,7 + F2: 2 # E2: 7 => CTR => E2: 5,8 * DIS # A5: 1,7 + F2: 2 + E2: 5,8 # H1: 5,8 => CTR => H1: 4 * DIS # A5: 1,7 + F2: 2 + E2: 5,8 + H1: 4 => CTR => A5: 6 * PRF A5: 6 # F2: 5,8 => SOL * STA A5: 6 + F2: 5,8 * CNT 5 HDP CHAINS / 28 HYP OPENED
Header Info
Top 95 Sudokus 048 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 126739845847625391935481762213864579654973218798512436361248957489157623572396184 solved
See section Deep 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 # A5: 1,7 => UNS * INC # A6: 1,7 => UNS * INC # E2: 5,8 => UNS * INC # F2: 5,8 => UNS * INC # D4: 1,7 => UNS * INC # D5: 1,7 => UNS * INC # G1: 5,8 => UNS * INC # H1: 5,8 => UNS * INC # I7: 5,8 => UNS * INC # I8: 5,8 => UNS * INC # A6: 2,6 => UNS * INC # A6: 1,7 => UNS * INC # E6: 2,6 => UNS * INC # F6: 2,6 => UNS * INC # H5: 1,4 => UNS * INC # H6: 1,4 => UNS * INC # E9: 5,8 => UNS * INC # F9: 5,8 => UNS * INC # G9: 5,8 => UNS * INC # H9: 5,8 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A5: 1,7 => UNS * INC # A6: 1,7 => UNS * INC # E2: 5,8 => UNS * INC # F2: 5,8 => UNS * INC # D4: 1,7 => UNS * INC # D5: 1,7 => UNS * INC # G1: 5,8 => UNS * INC # H1: 5,8 => UNS * INC # I7: 5,8 => UNS * INC # I8: 5,8 => UNS * INC # A6: 2,6 => UNS * INC # A6: 1,7 => UNS * INC # E6: 2,6 => UNS * INC # F6: 2,6 => UNS * INC # H5: 1,4 => UNS * INC # H6: 1,4 => UNS * INC # E9: 5,8 => UNS * INC # F9: 5,8 => UNS * INC # G9: 5,8 => UNS * INC # H9: 5,8 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # A5: 1,7 => UNS * INC # A6: 1,7 => UNS * INC # E2: 5,8 => UNS * INC # F2: 5,8 => UNS * INC # D4: 1,7 => UNS * INC # D5: 1,7 => UNS * INC # G1: 5,8 => UNS * INC # H1: 5,8 => UNS * INC # I7: 5,8 => UNS * INC # I8: 5,8 => UNS * INC # A6: 2,6 => UNS * INC # A6: 1,7 => UNS * INC # E6: 2,6 => UNS * INC # F6: 2,6 => UNS * INC # H5: 1,4 => UNS * INC # H6: 1,4 => UNS * INC # E9: 5,8 => UNS * INC # F9: 5,8 => UNS * INC # G9: 5,8 => UNS * INC # H9: 5,8 => UNS * INC # A5: 1,7 # E2: 5,8 => UNS * DIS # A5: 1,7 # F2: 5,8 => CTR => F2: 2 * INC # A5: 1,7 + F2: 2 # E2: 5,8 => UNS * DIS # A5: 1,7 + F2: 2 # E2: 7 => CTR => E2: 5,8 * DIS # A5: 1,7 + F2: 2 + E2: 5,8 # H1: 5,8 => CTR => H1: 4 * DIS # A5: 1,7 + F2: 2 + E2: 5,8 + H1: 4 => CTR => A5: 6 * INC A5: 6 # E2: 5,8 => UNS * PRF A5: 6 # F2: 5,8 => SOL * STA A5: 6 + F2: 5,8 * CNT 28 HDP CHAINS / 28 HYP OPENED