Analysis of xx-top95-031-base.sdk
Contents
Original Sudoku
level: medium
position: 38.6.......9.......2..3.51......5....3..1..6....4......17.5..8.......9.......7.32 initial
Autosolve
position: 3856.1...1.95......2..3.51......5....3..1..6....4......17.5..8...31..9.......7132 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C4: 4,6 => CTR => C4: 1,2,8 * DIS # C9: 4,6 => CTR => C9: 8 * DIS # F7: 2,9 => CTR => F7: 3 * DIS # A8: 4,6 => CTR => A8: 2,8 * DIS # B9: 4,6 => CTR => B9: 5,9 * DIS # C9: 4,6 => CTR => C9: 8 * DIS # E9: 8,9 => CTR => E9: 4,6 * DIS # A9: 8,9 => CTR => A9: 4,5,6 * DIS # D4: 8,9 => CTR => D4: 2,3,7 * PRF # D5: 8,9 => SOL * CNT 10 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C4: 4,6 => CTR => C4: 1,2,8 * DIS C4: 1,2,8 # C9: 4,6 => CTR => C9: 8 * PRF C4: 1,2,8 + C9: 8 # A3: 4,6 => SOL * STA C4: 1,2,8 + C9: 8 + A3: 4,6 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 38.6.......9.......2..3.51......5....3..1..6....4......17.5..8.......9.......7.32 | initial |
| 3856.1...1.95......2..3.51......5....3..1..6....4......17.5..8...31..9.......7132 | autosolve |
| 385621497179584326426739518762395841534812769891476253917253684243168975658947132 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C3: 4,6 I3: 6,8 A7: 2,9 B8: 4,6 D9: 8,9 G7: 4,6 I7: 4,6 H8: 5,7 I8: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C4,C6: 1.. / C4 = 1 => 9 pairs (_) / C6 = 1 => 9 pairs (_) I4,I6: 1.. / I4 = 1 => 9 pairs (_) / I6 = 1 => 9 pairs (_) C4,I4: 1.. / C4 = 1 => 9 pairs (_) / I4 = 1 => 9 pairs (_) C6,I6: 1.. / C6 = 1 => 9 pairs (_) / I6 = 1 => 9 pairs (_) A7,A8: 2.. / A7 = 2 => 0 pairs (X) / A8 = 2 => 14 pairs (_) G2,I2: 3.. / G2 = 3 => 11 pairs (_) / I2 = 3 => 10 pairs (_) D4,F6: 3.. / D4 = 3 => 10 pairs (_) / F6 = 3 => 0 pairs (X) D7,F7: 3.. / D7 = 3 => 0 pairs (X) / F7 = 3 => 10 pairs (_) D4,D7: 3.. / D4 = 3 => 10 pairs (_) / D7 = 3 => 0 pairs (X) F6,F7: 3.. / F6 = 3 => 0 pairs (X) / F7 = 3 => 10 pairs (_) G7,I7: 4.. / G7 = 4 => 10 pairs (_) / I7 = 4 => 9 pairs (_) A9,B9: 5.. / A9 = 5 => 8 pairs (_) / B9 = 5 => 9 pairs (_) H8,I8: 5.. / H8 = 5 => 8 pairs (_) / I8 = 5 => 9 pairs (_) A5,I5: 5.. / A5 = 5 => 9 pairs (_) / I5 = 5 => 8 pairs (_) B6,B9: 5.. / B6 = 5 => 8 pairs (_) / B9 = 5 => 9 pairs (_) H6,H8: 5.. / H6 = 5 => 9 pairs (_) / H8 = 5 => 8 pairs (_) G7,I7: 6.. / G7 = 6 => 9 pairs (_) / I7 = 6 => 10 pairs (_) F6,F8: 6.. / F6 = 6 => 10 pairs (_) / F8 = 6 => 0 pairs (X) G2,G7: 6.. / G2 = 6 => 10 pairs (_) / G7 = 6 => 9 pairs (_) B2,A3: 7.. / B2 = 7 => 15 pairs (_) / A3 = 7 => 15 pairs (_) H8,I8: 7.. / H8 = 7 => 9 pairs (_) / I8 = 7 => 8 pairs (_) A3,D3: 7.. / A3 = 7 => 15 pairs (_) / D3 = 7 => 15 pairs (_) D3,F3: 9.. / D3 = 9 => 0 pairs (X) / F3 = 9 => 13 pairs (_) H1,I1: 9.. / H1 = 9 => 10 pairs (_) / I1 = 9 => 9 pairs (_) * DURATION: 0:00:34.910856 START: 23:26:56.712947 END: 23:27:31.623803 2017-05-03 * CP COUNT: (24) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,C3,D9,G7,H8,I3,I7,I8) * 3856.1...1.95......2..3.51......5....3..1..6....4......17.5..8...31..9.......7132 * PAIR C3: 4,6 BLK 1 B2: 4,6,7 # reduction candidate for 4,6 B2: 4,6 # 15 pairs A3: 4,6,7 # reduction candidate for 4,6 A3: 4,6 # 15 pairs * PAIR C3: 4,6 COL C C4: 4,6,1,2,8 # reduction candidate for 4,6 C4: 4,6 => CTR * 3856.1...1.95......2.839516..6..5..1.32718469..14.....917.5.6842.318.9..658947132 C4: 1,2,8 # 9 pairs C9: 4,6,8 # reduction candidate for 4,6 C9: 4,6 => CTR * 3856.1.491695.4...724.3.5164...65...93.71.46565.49....217359684843126957596847132 C9: 8 # 16 pairs * PAIR I3: 6,8 BLK 3 G2: 6,8,3 # reduction candidate for 6,8 G2: 6,8 # 10 pairs I2: 6,8,3 # reduction candidate for 6,8 I2: 6,8 # 11 pairs * PAIR A7: 2,9 ROW 7 D7: 2,9,3 # reduction candidate for 2,9 D7: 2,9 # 10 pairs F7: 2,9,3 # reduction candidate for 2,9 F7: 2,9 => CTR * 3856.1...1695.4...724839516.....5....32718469...4.3...9173526842431869...5.947132 F7: 3 # 10 pairs * PAIR B8: 4,6 BLK 7 A8: 4,6,2,8 # reduction candidate for 4,6 A8: 4,6 => CTR * 3856.1...1.95......2..3.51......5....3..1..6....4.....217.5..8...31..9.......7132 A8: 2,8 # 10 pairs A9: 4,6,5,8,9 # reduction candidate for 4,6 A9: 4,6 # 16 pairs B9: 4,6,5,9 # reduction candidate for 4,6 B9: 4,6 => CTR * 3856.1...1795......2.739518.9...5....3..1..65.5.49....917.5..8.2.31..9575.89.7132 B9: 5,9 # 10 pairs C9: 4,6,8 # reduction candidate for 4,6 C9: 4,6 => CTR * 3856.1.491695.4...724.3.5164...65...93.71.46565.49....217359684843126957596847132 C9: 8 # 16 pairs * PAIR B8: 4,6 ROW 8 E8: 4,6,2,8 # reduction candidate for 4,6 E8: 4,6 # 24 pairs F8: 4,6,2,8 # reduction candidate for 4,6 F8: 4,6 # 16 pairs * PAIR B8: 4,6 COL B B2: 4,6,7 # reduction candidate for 4,6 B2: 4,6 # 15 pairs B4: 4,6,7,9 # reduction candidate for 4,6 B4: 4,6 # 18 pairs * PAIR D9: 8,9 BLK 8 E9: 8,9,4,6 # reduction candidate for 8,9 E9: 8,9 => CTR * 3856.1...1.95......2..3.51......5....3..1..6....4......17.5..8...31..9.......7132 E9: 4,6 # 13 pairs * PAIR D9: 8,9 ROW 9 A9: 8,9,4,5,6 # reduction candidate for 8,9 A9: 8,9 => CTR * 3856412971.95...4..2..3.51......5...53.71.469...4......17.5.684..31.4975.54.67132 A9: 4,5,6 # 9 pairs * PAIR D9: 8,9 COL D D3: 8,9,7 # reduction candidate for 8,9 D3: 8,9 # 15 pairs D4: 8,9,2,3,7 # reduction candidate for 8,9 D4: 8,9 => CTR * 3856.1...1.95......2.739518.....5....3.218.6....4.3...917352.8..431.69......47132 D4: 2,3,7 # 9 pairs D5: 8,9,2,7 # reduction candidate for 8,9 D5: 8,9 => SOLVED * 385621497179584326426739518762395841534812769891476253917253684243168975658947132 D5: 2,7 # 10 pairs * PAIR H8: 5,7 COL H H6: 5,7,2,9 # reduction candidate for 5,7 H6: 5,7 # 12 pairs H6: 2,9 # 9 pairs * PAIR I8: 5,7 COL I I5: 5,7,4,8,9 # reduction candidate for 5,7 I5: 5,7 # 11 pairs I6: 5,7,1,3,8,9 # reduction candidate for 5,7 I6: 5,7 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-031-base-pr-000.dot * REASONING * DIS # C4: 4,6 => CTR => C4: 1,2,8 * DIS # C9: 4,6 => CTR => C9: 8 * DIS # F7: 2,9 => CTR => F7: 3 * DIS # A8: 4,6 => CTR => A8: 2,8 * DIS # B9: 4,6 => CTR => B9: 5,9 * DIS # C9: 4,6 => CTR => C9: 8 * DIS # E9: 8,9 => CTR => E9: 4,6 * DIS # A9: 8,9 => CTR => A9: 4,5,6 * DIS # D4: 8,9 => CTR => D4: 2,3,7 * PRF # D5: 8,9 => SOL * CNT 10 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,C3,D9,G7,H8,I3,I7,I8) * 3856.1...1.95......2..3.51......5....3..1..6....4......17.5..8...31..9.......7132 * PAIR C3: 4,6 BLK 1 B2: 4,6,7 # reduction candidate for 4,6 B2: 4,6 # 15 pairs A3: 4,6,7 # reduction candidate for 4,6 A3: 4,6 # 15 pairs * PAIR C3: 4,6 COL C C4: 4,6,1,2,8 # reduction candidate for 4,6 C4: 4,6 => CTR * 3856.1...1.95......2.839516..6..5..1.32718469..14.....917.5.6842.318.9..658947132 C9: 4,6,8 # reduction candidate for 4,6 C9: 4,6 => CTR * 3856.1.491695.4...724.3.5164...65...93.71.46565.49....217359684843126957596847132 * RESTART * PAIR RESTART * PAIR C3: 4,6 BLK 1 A3: 4,6,7 # reduction candidate for 4,6 A3: 4,6 => SOLVED * 385621497179584326426739518762395841534812769891476253917253684243168975658947132 * DURATION: 0:00:06.479515 START: 23:28:01.259666 END: 23:28:07.739181 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-031-base-pr-001.dot * REASONING * DIS # C4: 4,6 => CTR => C4: 1,2,8 * DIS C4: 1,2,8 # C9: 4,6 => CTR => C9: 8 * PRF C4: 1,2,8 + C9: 8 # A3: 4,6 => SOL * STA C4: 1,2,8 + C9: 8 + A3: 4,6 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 95 Sudokus 031 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 385621497179584326426739518762395841534812769891476253917253684243168975658947132 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 # B2: 4,6 => UNS * INC # A3: 4,6 => UNS * DIS # C4: 4,6 => CTR => C4: 1,2,8 * INC # C4: 1,2,8 => UNS * DIS # C9: 4,6 => CTR => C9: 8 * INC # C9: 8 => UNS * INC # G2: 6,8 => UNS * INC # I2: 6,8 => UNS * INC # D7: 2,9 => UNS * DIS # F7: 2,9 => CTR => F7: 3 * INC # F7: 3 => UNS * DIS # A8: 4,6 => CTR => A8: 2,8 * INC # A8: 2,8 => UNS * INC # A9: 4,6 => UNS * DIS # B9: 4,6 => CTR => B9: 5,9 * INC # B9: 5,9 => UNS * DIS # C9: 4,6 => CTR => C9: 8 * INC # C9: 8 => UNS * INC # E8: 4,6 => UNS * INC # F8: 4,6 => UNS * INC # B2: 4,6 => UNS * INC # B4: 4,6 => UNS * DIS # E9: 8,9 => CTR => E9: 4,6 * INC # E9: 4,6 => UNS * DIS # A9: 8,9 => CTR => A9: 4,5,6 * INC # A9: 4,5,6 => UNS * INC # D3: 8,9 => UNS * DIS # D4: 8,9 => CTR => D4: 2,3,7 * INC # D4: 2,3,7 => UNS * PRF # D5: 8,9 => SOL * INC # D5: 2,7 => UNS * INC # H6: 5,7 => UNS * INC # H6: 2,9 => UNS * INC # I5: 5,7 => UNS * INC # I6: 5,7 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 4,6 => UNS * INC # A3: 4,6 => UNS * DIS # C4: 4,6 => CTR => C4: 1,2,8 * DIS C4: 1,2,8 # C9: 4,6 => CTR => C9: 8 * PRF C4: 1,2,8 + C9: 8 # A3: 4,6 => SOL * STA C4: 1,2,8 + C9: 8 + A3: 4,6 * CNT 5 HDP CHAINS / 5 HYP OPENED