Analysis of xx-top95-081-base.sdk
Contents
Original Sudoku
level: medium
position: 15.3......7..4.2....4.72.....8.........9..1.8.1..8.79......38...........6....7423 initial
Autosolve
position: 1523.8....7..4.2....4.72.....87........9..1.8.1..8.79......38...........6....7423 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 6,9 => CTR => F2: 1,5 * PRF # F2: 1,5 => SOL * DIS # I2: 6,9 => CTR => I2: 1,5 * DIS # A8: 8,9 => CTR => A8: 2,3,4,5,7 * DIS # B8: 8,9 => CTR => B8: 2,3,4 * DIS # B3: 8,9 => CTR => B3: 3,6 * CNT 6 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 6,9 => CTR => F2: 1,5 * PRF F2: 1,5 => SOL * STA F2: 1,5 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 15.3......7..4.2....4.72.....8.........9..1.8.1..8.79......38...........6....7423 | initial |
| 1523.8....7..4.2....4.72.....87........9..1.8.1..8.79......38...........6....7423 | autosolve |
| 152398647973641285864572931598714362247936158316285794725463819431829576689157423 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) E1: 6,9 G1: 6,9 H1: 4,7 I1: 4,7 B9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,F4: 1.. / E4 = 1 => 9 pairs (_) / F4 = 1 => 6 pairs (_) I4,I6: 2.. / I4 = 2 => 5 pairs (_) / I6 = 2 => 0 pairs (X) A6,C6: 3.. / A6 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) E4,E5: 3.. / E4 = 3 => 8 pairs (_) / E5 = 3 => 5 pairs (_) E5,H5: 3.. / E5 = 3 => 5 pairs (_) / H5 = 3 => 8 pairs (_) B3,B8: 3.. / B3 = 3 => 0 pairs (X) / B8 = 3 => 5 pairs (_) G3,G4: 3.. / G3 = 3 => 7 pairs (_) / G4 = 3 => 7 pairs (_) H1,I1: 4.. / H1 = 4 => 5 pairs (_) / I1 = 4 => 3 pairs (_) C2,B3: 6.. / C2 = 6 => 0 pairs (X) / B3 = 6 => 0 pairs (_) E1,G1: 6.. / E1 = 6 => 0 pairs (X) / G1 = 6 => 0 pairs (_) H1,I1: 7.. / H1 = 7 => 3 pairs (_) / I1 = 7 => 5 pairs (_) A5,C5: 7.. / A5 = 7 => 6 pairs (_) / C5 = 7 => 5 pairs (_) H2,H3: 8.. / H2 = 8 => 7 pairs (_) / H3 = 8 => 6 pairs (_) D8,D9: 8.. / D8 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) A2,H2: 8.. / A2 = 8 => 6 pairs (_) / H2 = 8 => 7 pairs (_) B9,D9: 8.. / B9 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) E1,F2: 9.. / E1 = 9 => 0 pairs (*) / F2 = 9 => 0 pairs (X) A4,B4: 9.. / A4 = 9 => 0 pairs (X) / B4 = 9 => 0 pairs (_) E1,G1: 9.. / E1 = 9 => 0 pairs (*) / G1 = 9 => 0 pairs (X) F2,F8: 9.. / F2 = 9 => 0 pairs (X) / F8 = 9 => 0 pairs (_) * DURATION: 0:00:27.948327 START: 00:49:16.836695 END: 00:49:44.785022 2017-05-04 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,E1,G1,H1,I1) * 1523.8....7..4.2....4.72.....87........9..1.8.1..8.79......38...........6....7423 * PAIR E1: 6,9 BLK 2 F2: 6,9,1,5 # reduction candidate for 6,9 F2: 6,9 => CTR * 1523.8....79.462...64.72...9.87........9..1.8.1..8.79......38...........69.8.7423 F2: 1,5 => SOLVED * 152398647973641285864572931598714362247936158316285794725463819431829576689157423 * PAIR E1: 6,9 COL E E7: 6,9,1,2,5 # reduction candidate for 6,9 E7: 6,9 # 8 pairs E8: 6,9,1,2,5 # reduction candidate for 6,9 E8: 6,9 # 9 pairs * PAIR G1: 6,9 BLK 3 I2: 6,9,1,5 # reduction candidate for 6,9 I2: 6,9 => CTR * 1523986...7..4.2.9..4.72.....87........9..1.8.1..8.79...9..38.....8.95..68...7423 I2: 1,5 # 6 pairs G3: 6,9,3,5 # reduction candidate for 6,9 G3: 6,9 # 11 pairs I3: 6,9,1,5 # reduction candidate for 6,9 I3: 6,9 # 8 pairs * PAIR G1: 6,9 COL G G8: 6,9,5 # reduction candidate for 6,9 G8: 6,9 # 8 pairs G8: 5 # 6 pairs * PAIR B9: 8,9 BLK 7 A8: 8,9,2,3,4,5,7 # reduction candidate for 8,9 A8: 8,9 => CTR * 1523.8....79.4.2...64.72.....87........9..1.8.1..8.79......38...3...9...6....7423 A8: 2,3,4,5,7 # 5 pairs B8: 8,9,2,3,4 # reduction candidate for 8,9 B8: 8,9 => CTR * 1523.8...876.4.23.934.72.8..987..3...6.93.1.8.1..8.79......38...........6....7423 B8: 2,3,4 # 5 pairs * PAIR B9: 8,9 COL B B3: 8,9,3,6 # reduction candidate for 8,9 B3: 8,9 => CTR * 1523986...76.4.2.9.94672...9.87........9..1.8.13.8.79...9..38...3.8.95..68...7423 B3: 3,6 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-081-base-pr-000.dot * REASONING * DIS # F2: 6,9 => CTR => F2: 1,5 * PRF # F2: 1,5 => SOL * DIS # I2: 6,9 => CTR => I2: 1,5 * DIS # A8: 8,9 => CTR => A8: 2,3,4,5,7 * DIS # B8: 8,9 => CTR => B8: 2,3,4 * DIS # B3: 8,9 => CTR => B3: 3,6 * CNT 6 HDP CHAINS / 16 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,E1,G1,H1,I1) * 1523.8....7..4.2....4.72.....87........9..1.8.1..8.79......38...........6....7423 * PAIR E1: 6,9 BLK 2 F2: 6,9,1,5 # reduction candidate for 6,9 F2: 6,9 => CTR * 1523.8....79.462...64.72...9.87........9..1.8.1..8.79......38...........69.8.7423 F2: 1,5 => SOLVED * 152398647973641285864572931598714362247936158316285794725463819431829576689157423 * DURATION: 0:00:03.261960 START: 00:49:56.330509 END: 00:49:59.592469 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-081-base-pr-001.dot * REASONING * DIS # F2: 6,9 => CTR => F2: 1,5 * PRF F2: 1,5 => SOL * STA F2: 1,5 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 95 Sudokus 081 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 152398647973641285864572931598714362247936158316285794725463819431829576689157423 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:
* DIS # F2: 6,9 => CTR => F2: 1,5 * PRF # F2: 1,5 => SOL * INC # E7: 6,9 => UNS * INC # E8: 6,9 => UNS * DIS # I2: 6,9 => CTR => I2: 1,5 * INC # I2: 1,5 => UNS * INC # G3: 6,9 => UNS * INC # I3: 6,9 => UNS * INC # G8: 6,9 => UNS * INC # G8: 5 => UNS * DIS # A8: 8,9 => CTR => A8: 2,3,4,5,7 * INC # A8: 2,3,4,5,7 => UNS * DIS # B8: 8,9 => CTR => B8: 2,3,4 * INC # B8: 2,3,4 => UNS * DIS # B3: 8,9 => CTR => B3: 3,6 * INC # B3: 3,6 => UNS * CNT 16 HDP CHAINS / 16 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F2: 6,9 => CTR => F2: 1,5 * PRF F2: 1,5 => SOL * STA F2: 1,5 * CNT 2 HDP CHAINS / 1 HYP OPENED