Analysis of xx-top95-028-base.sdk
Contents
Original Sudoku
level: medium
position: 6..3.2....4.....8..........7.26............543.........8.15........8.2........7.. initial
Autosolve
position: 6.83.25...4.....82.2.......7.26.....8......543.4....2728.15........8.2.5......7.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G2: 1,9 => SOL * DIS # G2: 3 => CTR => G2: 1,9 * DIS # G3: 1,9 => CTR => G3: 3,4 * DIS # I3: 1,9 => CTR => I3: 3,6 * PRF # B1: 1,9 => SOL * DIS # B1: 7 => CTR => B1: 1,9 * DIS # E1: 1,9 => CTR => E1: 4,7 * DIS # I4: 3 => CTR => I4: 1,9 * DIS # E4: 1,9 => CTR => E4: 3,4 * DIS # F4: 1,9 => CTR => F4: 3,4,5,8 * DIS # E5: 1,9 => CTR => E5: 2,3,7 * PRF # F5: 1,9 => SOL * DIS # F6: 1,9 => CTR => F6: 5,8 * DIS # G6: 1,9 => CTR => G6: 6,8 * DIS # E1: 1,9 => CTR => E1: 4,7 * DIS # E2: 1,9 => CTR => E2: 6,7 * DIS # G4: 3,9 => CTR => G4: 1,8 * DIS # I4: 3,9 => CTR => I4: 1 * DIS # F4: 3,9 => CTR => F4: 1,4,5,8 * PRF # H3: 3,9 => SOL * CNT 20 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G2: 1,9 => SOL * STA G2: 1,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..3.2....4.....8..........7.26............543.........8.15........8.2........7.. | initial |
| 6.83.25...4.....82.2.......7.26.....8......543.4....2728.15........8.2.5......7.8 | autosolve |
| 618342579943765182527891436752634891861279354394518627286157943179483265435926718 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) I1: 1,9 E6: 1,9 H4: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H8,H9: 1.. / H8 = 1 => 4 pairs (_) / H9 = 1 => 3 pairs (_) D5,E5: 2.. / D5 = 2 => 4 pairs (_) / E5 = 2 => 5 pairs (_) D9,E9: 2.. / D9 = 2 => 5 pairs (_) / E9 = 2 => 4 pairs (_) D5,D9: 2.. / D5 = 2 => 4 pairs (_) / D9 = 2 => 5 pairs (_) E5,E9: 2.. / E5 = 2 => 5 pairs (_) / E9 = 2 => 4 pairs (_) C2,C3: 3.. / C2 = 3 => 0 pairs (*) / C3 = 3 => 0 pairs (X) B8,B9: 3.. / B8 = 3 => 0 pairs (X) / B9 = 3 => 3 pairs (_) C2,G2: 3.. / C2 = 3 => 0 pairs (*) / G2 = 3 => 0 pairs (X) E4,F4: 4.. / E4 = 4 => 0 pairs (X) / F4 = 4 => 5 pairs (_) A8,A9: 4.. / A8 = 4 => 4 pairs (_) / A9 = 4 => 5 pairs (_) E1,H1: 4.. / E1 = 4 => 6 pairs (_) / H1 = 4 => 0 pairs (X) G3,G7: 4.. / G3 = 4 => 7 pairs (_) / G7 = 4 => 0 pairs (X) B4,B6: 5.. / B4 = 5 => 3 pairs (_) / B6 = 5 => 0 pairs (X) A9,C9: 5.. / A9 = 5 => 0 pairs (X) / C9 = 5 => 3 pairs (_) B4,F4: 5.. / B4 = 5 => 3 pairs (_) / F4 = 5 => 0 pairs (X) E2,F2: 6.. / E2 = 6 => 3 pairs (_) / F2 = 6 => 0 pairs (X) H3,I3: 6.. / H3 = 6 => 0 pairs (X) / I3 = 6 => 4 pairs (_) G5,G6: 6.. / G5 = 6 => 0 pairs (X) / G6 = 6 => 3 pairs (_) B6,G6: 6.. / B6 = 6 => 0 pairs (X) / G6 = 6 => 3 pairs (_) E2,E9: 6.. / E2 = 6 => 3 pairs (_) / E9 = 6 => 0 pairs (X) I3,I7: 6.. / I3 = 6 => 4 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 => 7 pairs (_) B1,B8: 7.. / B1 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) D3,F3: 8.. / D3 = 8 => 4 pairs (_) / F3 = 8 => 3 pairs (_) G4,G6: 8.. / G4 = 8 => 3 pairs (_) / G6 = 8 => 0 pairs (X) F4,G4: 8.. / F4 = 8 => 0 pairs (X) / G4 = 8 => 3 pairs (_) D3,D6: 8.. / D3 = 8 => 4 pairs (_) / D6 = 8 => 3 pairs (_) * DURATION: 0:00:38.166270 START: 23:23:58.839641 END: 23:24:37.005911 2017-05-03 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E6,H4,I1) * 6.83.25...4.....82.2.......7.26.....8......543.4....2728.15........8.2.5......7.8 * PAIR I1: 1,9 BLK 3 G2: 1,9,3 # reduction candidate for 1,9 G2: 1,9 => SOLVED * 618342579943765182527891436752634891861279354394518627286157943179483265435926718 G2: 3 => CTR * 6.83.25...47.6.382.23......7.26.....8......543.4....2728.157....7..8.2.5.35.2.7.8 G3: 1,9,3,4 # reduction candidate for 1,9 G3: 1,9 => CTR * 6.83.25...47.6.382.23.....67.26.....8......543.4....2728.1574...7..8.2.5.35.2.7.8 G3: 3,4 # 4 pairs I3: 1,9,3,6 # reduction candidate for 1,9 I3: 1,9 => CTR * 6.834257..4....382.23...46.7.26.48938...3..543.4....2728915...6.7..8.2.5.3....7.8 I3: 3,6 # 4 pairs * PAIR I1: 1,9 ROW 1 B1: 1,9,7 # reduction candidate for 1,9 B1: 1,9 => SOLVED * 618342579943765182527891436752634891861279354394518627286157943179483265435926718 B1: 7 => CTR * 6783.25...4.....82.2.....767.26.....8......543.4....2728.15........8.2.5......7.8 E1: 1,9,4,7 # reduction candidate for 1,9 E1: 1,9 => CTR * 6783.254..4.....82.2.....767.26.....8......543.4....2728.15.4......8.2.5......7.8 E1: 4,7 # 4 pairs * PAIR I1: 1,9 COL I I4: 1,9,3 # reduction candidate for 1,9 I4: 3 => CTR * 6.83.25...47.6.382.23......7.26...938......543.4....27286157.39.7..832.5......7.8 I4: 1,9 # 6 pairs * PAIR E6: 1,9 BLK 5 E4: 1,9,3,4 # reduction candidate for 1,9 E4: 1,9 => CTR * 6.83.25...47.6.382.23......7526.48..8......543.4....2728.157....7.48.2.54352..7.8 E4: 3,4 # 4 pairs F4: 1,9,3,4,5,8 # reduction candidate for 1,9 F4: 1,9 => CTR * 6.837254..47.6.382.23....7675264.8..8......543.4....2728.1574...7..8.2.5.35.2.7.8 F4: 3,4,5,8 # 3 pairs E5: 1,9,2,3,7 # reduction candidate for 1,9 E5: 1,9 => CTR * 6.83.25...4.....82.2.......7.26.....8..2.73543.4...62728715.......78.2.5....2.7.8 E5: 2,3,7 # 3 pairs F5: 1,9,3,7 # reduction candidate for 1,9 F5: 1,9 => SOLVED * 618342579943765182527891436752634891861279354394518627286157943179483265435926718 F5: 3,7 # 4 pairs F6: 1,9,5,8 # reduction candidate for 1,9 F6: 1,9 => CTR * 6.837254..47.6.382.23....767.264....8......543.4....2728.1574...7..8.2.5.35.2.7.8 F6: 5,8 # 4 pairs * PAIR E6: 1,9 ROW 6 B6: 1,9,5,6 # reduction candidate for 1,9 B6: 1,9 # 6 pairs G6: 1,9,6,8 # reduction candidate for 1,9 G6: 1,9 => CTR * 6.83.25...47.6.382.23......7526..8..8.....654364....2728.157....7..8.2.5.35.2.7.8 G6: 6,8 # 4 pairs * PAIR E6: 1,9 COL E E1: 1,9,4,7 # reduction candidate for 1,9 E1: 1,9 => CTR * 6783.254..4.....82.2.....767.26.....8......543.4....2728.15.4......8.2.5......7.8 E1: 4,7 # 4 pairs E2: 1,9,6,7 # reduction candidate for 1,9 E2: 1,9 => CTR * 6.83.25.9.437.6182.2....4..7526348918..927354394.1.62728715.946...48.2.54.52697.8 E2: 6,7 # 4 pairs E3: 1,9,4,7 # reduction candidate for 1,9 E3: 1,9 # 7 pairs * PAIR H4: 3,9 BLK 6 G4: 3,9,1,8 # reduction candidate for 3,9 G4: 3,9 => CTR * 618372549947561382523894176752648931891...65436491582728.1574.3.7.4832.5......7.8 G4: 1,8 # 4 pairs I4: 3,9,1 # reduction candidate for 3,9 I4: 3,9 => CTR * 6.83.25...47.6.382.23......7.26.....8......543.4....2728.157....7..8.2.5.35.2.7.8 I4: 1 # 8 pairs G5: 3,9,1,6 # reduction candidate for 3,9 G5: 3,9 # 9 pairs * PAIR H4: 3,9 ROW 4 E4: 3,9,1,4 # reduction candidate for 3,9 E4: 3,9 # 11 pairs F4: 3,9,1,4,5,8 # reduction candidate for 3,9 F4: 3,9 => CTR * 618372549.47...382.23.9.1767526498318.1....543.4.1..2728.1574.3.7..832.5......7.8 F4: 1,4,5,8 # 3 pairs * PAIR H4: 3,9 COL H H3: 3,9,4,6,7 # reduction candidate for 3,9 H3: 3,9 => SOLVED * 618342579943765182527891436752634891861279354394518627286157943179483265435926718 H3: 4,6,7 # 3 pairs H7: 3,9,4,6 # reduction candidate for 3,9 H7: 3,9 # 6 pairs H8: 3,9,1,4,6 # reduction candidate for 3,9 H8: 3,9 # 7 pairs H9: 3,9,1,4,6 # reduction candidate for 3,9 H9: 3,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-028-base-pr-000.dot * REASONING * PRF # G2: 1,9 => SOL * DIS # G2: 3 => CTR => G2: 1,9 * DIS # G3: 1,9 => CTR => G3: 3,4 * DIS # I3: 1,9 => CTR => I3: 3,6 * PRF # B1: 1,9 => SOL * DIS # B1: 7 => CTR => B1: 1,9 * DIS # E1: 1,9 => CTR => E1: 4,7 * DIS # I4: 3 => CTR => I4: 1,9 * DIS # E4: 1,9 => CTR => E4: 3,4 * DIS # F4: 1,9 => CTR => F4: 3,4,5,8 * DIS # E5: 1,9 => CTR => E5: 2,3,7 * PRF # F5: 1,9 => SOL * DIS # F6: 1,9 => CTR => F6: 5,8 * DIS # G6: 1,9 => CTR => G6: 6,8 * DIS # E1: 1,9 => CTR => E1: 4,7 * DIS # E2: 1,9 => CTR => E2: 6,7 * DIS # G4: 3,9 => CTR => G4: 1,8 * DIS # I4: 3,9 => CTR => I4: 1 * DIS # F4: 3,9 => CTR => F4: 1,4,5,8 * PRF # H3: 3,9 => SOL * CNT 20 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E6,H4,I1) * 6.83.25...4.....82.2.......7.26.....8......543.4....2728.15........8.2.5......7.8 * PAIR I1: 1,9 BLK 3 G2: 1,9,3 # reduction candidate for 1,9 G2: 1,9 => SOLVED * 618342579943765182527891436752634891861279354394518627286157943179483265435926718 * DURATION: 0:00:02.571853 START: 23:25:10.083465 END: 23:25:12.655318 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-028-base-pr-001.dot * REASONING * PRF # G2: 1,9 => SOL * STA G2: 1,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 95 Sudokus 028 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 618342579943765182527891436752634891861279354394518627286157943179483265435926718 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:
* PRF # G2: 1,9 => SOL * DIS # G2: 3 => CTR => G2: 1,9 * DIS # G3: 1,9 => CTR => G3: 3,4 * INC # G3: 3,4 => UNS * DIS # I3: 1,9 => CTR => I3: 3,6 * INC # I3: 3,6 => UNS * PRF # B1: 1,9 => SOL * DIS # B1: 7 => CTR => B1: 1,9 * DIS # E1: 1,9 => CTR => E1: 4,7 * INC # E1: 4,7 => UNS * INC # I4: 1,9 => UNS * DIS # I4: 3 => CTR => I4: 1,9 * DIS # E4: 1,9 => CTR => E4: 3,4 * INC # E4: 3,4 => UNS * DIS # F4: 1,9 => CTR => F4: 3,4,5,8 * INC # F4: 3,4,5,8 => UNS * DIS # E5: 1,9 => CTR => E5: 2,3,7 * INC # E5: 2,3,7 => UNS * PRF # F5: 1,9 => SOL * INC # F5: 3,7 => UNS * DIS # F6: 1,9 => CTR => F6: 5,8 * INC # F6: 5,8 => UNS * INC # B6: 1,9 => UNS * DIS # G6: 1,9 => CTR => G6: 6,8 * INC # G6: 6,8 => UNS * DIS # E1: 1,9 => CTR => E1: 4,7 * INC # E1: 4,7 => UNS * DIS # E2: 1,9 => CTR => E2: 6,7 * INC # E2: 6,7 => UNS * INC # E3: 1,9 => UNS * DIS # G4: 3,9 => CTR => G4: 1,8 * INC # G4: 1,8 => UNS * DIS # I4: 3,9 => CTR => I4: 1 * INC # I4: 1 => UNS * INC # G5: 3,9 => UNS * INC # E4: 3,9 => UNS * DIS # F4: 3,9 => CTR => F4: 1,4,5,8 * INC # F4: 1,4,5,8 => UNS * PRF # H3: 3,9 => SOL * INC # H3: 4,6,7 => UNS * INC # H7: 3,9 => UNS * INC # H8: 3,9 => UNS * INC # H9: 3,9 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # G2: 1,9 => SOL * STA G2: 1,9 * CNT 1 HDP CHAINS / 1 HYP OPENED