Analysis of xx-top500-444-base.sdk
Contents
Original Sudoku
level: medium
position: 5.1.........6...8....2........4..62.3...8....9.........4..7.....2....4.......3..9 initial
Autosolve
position: 5.1..4.622.76...844.62...9....4..6233.2.8.94.9.432.....4..72..6.2..6.4..6...432.9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 3,9 => CTR => B1: 8 * DIS # B1: 9 => CTR => B1: 3,8 * DIS # B1: 3,9 => CTR => B1: 8 * DIS # D7: 1,8 => CTR => D7: 5,9 * DIS # D7: 1,8 => CTR => D7: 5,9 * DIS # D8: 1,8 => CTR => D8: 5,9 * CNT 6 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 # B1: 3,9 => CTR => B1: 8 * DIS B1: 8 # D7: 1,8 => CTR => D7: 5,9 * PRF B1: 8 + D7: 5,9 # G7: 5 => SOL * STA B1: 8 + D7: 5,9 + G7: 5 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5.1.........6...8....2........4..62.3...8....9.........4..7.....2....4.......3..9 | initial |
| 5.1..4.622.76...844.62...9....4..6233.2.8.94.9.432.....4..72..6.2..6.4..6...432.9 | autosolve |
| 581794362297635184436218795178459623352186947964327851843972516729561438615843279 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B2: 3,9 B3: 3,8 D1: 7,8 E1: 3,9 F3: 7,8 G1: 3,7 C4: 5,8 A7: 1,8 C7: 3,9 C8: 3,9 C9: 5,8 D9: 1,8 H9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C7,C8: 3.. / C7 = 3 => 12 pairs (_) / C8 = 3 => 11 pairs (_) H7,H8: 3.. / H7 = 3 => 11 pairs (_) / H8 = 3 => 12 pairs (_) C7,H7: 3.. / C7 = 3 => 12 pairs (_) / H7 = 3 => 11 pairs (_) C8,H8: 3.. / C8 = 3 => 11 pairs (_) / H8 = 3 => 12 pairs (_) B9,C9: 5.. / B9 = 5 => 16 pairs (_) / C9 = 5 => 14 pairs (_) C4,C9: 5.. / C4 = 5 => 16 pairs (_) / C9 = 5 => 14 pairs (_) B5,B6: 6.. / B5 = 6 => 13 pairs (_) / B6 = 6 => 13 pairs (_) F5,F6: 6.. / F5 = 6 => 13 pairs (_) / F6 = 6 => 13 pairs (_) B5,F5: 6.. / B5 = 6 => 13 pairs (_) / F5 = 6 => 13 pairs (_) B6,F6: 6.. / B6 = 6 => 13 pairs (_) / F6 = 6 => 13 pairs (_) D1,F3: 7.. / D1 = 7 => 15 pairs (_) / F3 = 7 => 0 pairs (X) A8,B9: 7.. / A8 = 7 => 15 pairs (_) / B9 = 7 => 16 pairs (_) D1,G1: 7.. / D1 = 7 => 15 pairs (_) / G1 = 7 => 0 pairs (X) B9,H9: 7.. / B9 = 7 => 16 pairs (_) / H9 = 7 => 15 pairs (_) A4,A8: 7.. / A4 = 7 => 16 pairs (_) / A8 = 7 => 15 pairs (_) D1,D5: 7.. / D1 = 7 => 15 pairs (_) / D5 = 7 => 0 pairs (X) B1,B3: 8.. / B1 = 8 => 15 pairs (_) / B3 = 8 => 0 pairs (X) D1,F3: 8.. / D1 = 8 => 0 pairs (X) / F3 = 8 => 15 pairs (_) A4,C4: 8.. / A4 = 8 => 16 pairs (_) / C4 = 8 => 14 pairs (_) G6,I6: 8.. / G6 = 8 => 19 pairs (_) / I6 = 8 => 17 pairs (_) G7,I8: 8.. / G7 = 8 => 17 pairs (_) / I8 = 8 => 19 pairs (_) B1,D1: 8.. / B1 = 8 => 15 pairs (_) / D1 = 8 => 0 pairs (X) B3,F3: 8.. / B3 = 8 => 0 pairs (X) / F3 = 8 => 15 pairs (_) C9,D9: 8.. / C9 = 8 => 16 pairs (_) / D9 = 8 => 14 pairs (_) C4,C9: 8.. / C4 = 8 => 14 pairs (_) / C9 = 8 => 16 pairs (_) F3,F8: 8.. / F3 = 8 => 15 pairs (_) / F8 = 8 => 0 pairs (X) G6,G7: 8.. / G6 = 8 => 19 pairs (_) / G7 = 8 => 17 pairs (_) I6,I8: 8.. / I6 = 8 => 17 pairs (_) / I8 = 8 => 19 pairs (_) B1,B2: 9.. / B1 = 9 => 0 pairs (X) / B2 = 9 => 14 pairs (_) E4,F4: 9.. / E4 = 9 => 0 pairs (X) / F4 = 9 => 15 pairs (_) C7,C8: 9.. / C7 = 9 => 11 pairs (_) / C8 = 9 => 12 pairs (_) D7,D8: 9.. / D7 = 9 => 12 pairs (_) / D8 = 9 => 11 pairs (_) B1,E1: 9.. / B1 = 9 => 0 pairs (X) / E1 = 9 => 14 pairs (_) C7,D7: 9.. / C7 = 9 => 11 pairs (_) / D7 = 9 => 12 pairs (_) C8,D8: 9.. / C8 = 9 => 12 pairs (_) / D8 = 9 => 11 pairs (_) F2,F4: 9.. / F2 = 9 => 0 pairs (X) / F4 = 9 => 15 pairs (_) * DURATION: 0:01:08.423454 START: 17:55:05.197314 END: 17:56:13.620768 2017-05-04 * CP COUNT: (36) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B2,B3,C4,C7,C8,C9,D1,D9,E1,F3,G1,H9) * 5.1..4.622.76...844.62...9....4..6233.2.8.94.9.432.....4..72..6.2..6.4..6...432.9 * PAIR B2: 3,9 BLK 1 B1: 3,9,8 # reduction candidate for 3,9 B1: 3,9 => CTR * 5.18.47622.76...844862.7.9....4..6233.278.94.9.432.....4..72..6.2..684..6.8143279 B1: 8 # 15 pairs * PAIR B2: 3,9 ROW 2 E2: 3,9,1,5 # reduction candidate for 3,9 E2: 3,9 # 18 pairs E2: 1,5 # 14 pairs * PAIR B3: 3,8 BLK 1 B1: 3,8,9 # reduction candidate for 3,8 B1: 9 => CTR * 5918347622376...844862.739....4..6233.278.94.9.432.....4..72..6.2..684..6.8143279 B1: 3,8 # 14 pairs * PAIR E1: 3,9 BLK 2 E2: 3,9,1,5 # reduction candidate for 3,9 E2: 3,9 # 18 pairs E2: 1,5 # 14 pairs * PAIR E1: 3,9 ROW 1 B1: 3,9,8 # reduction candidate for 3,9 B1: 3,9 => CTR * 5.18.47622.76...844862.7.9....4..6233.278.94.9.432.....4..72..6.2..684..6.8143279 B1: 8 # 15 pairs * PAIR G1: 3,7 BLK 3 G3: 3,7,1,5 # reduction candidate for 3,7 G3: 3,7 # 17 pairs G3: 1,5 # 14 pairs * PAIR A7: 1,8 BLK 7 A8: 1,8,7 # reduction candidate for 1,8 A8: 1,8 # 16 pairs A8: 7 # 15 pairs * PAIR A7: 1,8 ROW 7 D7: 1,8,5,9 # reduction candidate for 1,8 D7: 1,8 => CTR * 5817943622976...844.62.8.9....4..6233.258.94.9.432..5..49.72536.239654.86...432.9 D7: 5,9 # 14 pairs G7: 1,8,5 # reduction candidate for 1,8 G7: 1,8 # 16 pairs * PAIR A7: 1,8 COL A A4: 1,8,7 # reduction candidate for 1,8 A4: 7 # 16 pairs A4: 1,8 # 15 pairs * PAIR D9: 1,8 BLK 8 D7: 1,8,5,9 # reduction candidate for 1,8 D7: 1,8 => CTR * 5817943622976...844.62.8.9....4..6233.258.94.9.432..5..49.72536.239654.86...432.9 D7: 5,9 # 14 pairs D8: 1,8,5,9 # reduction candidate for 1,8 D8: 1,8 => CTR * 581794362297631584436258.9...84196233.258.94.9.432.815843972156.29.654386..843279 D8: 5,9 # 14 pairs F8: 1,8,5 # reduction candidate for 1,8 F8: 1,8 # 17 pairs * PAIR H9: 1,7 BLK 9 H8: 1,7,3,5 # reduction candidate for 1,7 H8: 1,7 # 15 pairs I8: 1,7,5,8 # reduction candidate for 1,7 I8: 1,7 # 20 pairs * PAIR H9: 1,7 ROW 9 B9: 1,7,5 # reduction candidate for 1,7 B9: 5 # 16 pairs B9: 1,7 # 14 pairs * PAIR H9: 1,7 COL H H6: 1,7,5 # reduction candidate for 1,7 H6: 1,7 # 18 pairs H6: 5 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-444-base-pr-000.dot * REASONING * DIS # B1: 3,9 => CTR => B1: 8 * DIS # B1: 9 => CTR => B1: 3,8 * DIS # B1: 3,9 => CTR => B1: 8 * DIS # D7: 1,8 => CTR => D7: 5,9 * DIS # D7: 1,8 => CTR => D7: 5,9 * DIS # D8: 1,8 => CTR => D8: 5,9 * CNT 6 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B2,B3,C4,C7,C8,C9,D1,D9,E1,F3,G1,H9) * 5.1..4.622.76...844.62...9....4..6233.2.8.94.9.432.....4..72..6.2..6.4..6...432.9 * PAIR B2: 3,9 BLK 1 B1: 3,9,8 # reduction candidate for 3,9 B1: 3,9 => CTR * 5.18.47622.76...844862.7.9....4..6233.278.94.9.432.....4..72..6.2..684..6.8143279 * PAIR A7: 1,8 BLK 7 A8: 1,8,7 # reduction candidate for 1,8 A8: 7 # 17 pairs A8: 1,8 # 16 pairs * PAIR A7: 1,8 ROW 7 D7: 1,8,5,9 # reduction candidate for 1,8 D7: 1,8 => CTR * 581794362297631584436258.9....4196233.258.94.9.432..5..49.72.36.239654..6...432.9 G7: 1,8,5 # reduction candidate for 1,8 G7: 1,8 # 18 pairs * RESTART * PAIR A7: 1,8 ROW 7 G7: 1,8,5 # reduction candidate for 1,8 G7: 5 => SOLVED * 581794362297635184436218795178459623352186947964327851843972516729561438615843279 * DURATION: 0:00:11.111522 START: 17:56:43.874639 END: 17:56:54.986161 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-444-base-pr-001.dot * REASONING * DIS # B1: 3,9 => CTR => B1: 8 * DIS B1: 8 # D7: 1,8 => CTR => D7: 5,9 * PRF B1: 8 + D7: 5,9 # G7: 5 => SOL * STA B1: 8 + D7: 5,9 + G7: 5 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 444 solution: 581794362297635184436218795178459623352186947964327851843972516729561438615843279 info: 95317 FNBTHYK S8.f 46871 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 581794362297635184436218795178459623352186947964327851843972516729561438615843279 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 # B1: 3,9 => CTR => B1: 8 * INC # B1: 8 => UNS * INC # E2: 3,9 => UNS * INC # E2: 1,5 => UNS * INC # B1: 3,8 => UNS * DIS # B1: 9 => CTR => B1: 3,8 * INC # E2: 3,9 => UNS * INC # E2: 1,5 => UNS * DIS # B1: 3,9 => CTR => B1: 8 * INC # B1: 8 => UNS * INC # G3: 3,7 => UNS * INC # G3: 1,5 => UNS * INC # A8: 1,8 => UNS * INC # A8: 7 => UNS * DIS # D7: 1,8 => CTR => D7: 5,9 * INC # D7: 5,9 => UNS * INC # G7: 1,8 => UNS * INC # A4: 1,8 => UNS * INC # A4: 7 => UNS * DIS # D7: 1,8 => CTR => D7: 5,9 * INC # D7: 5,9 => UNS * DIS # D8: 1,8 => CTR => D8: 5,9 * INC # D8: 5,9 => UNS * INC # F8: 1,8 => UNS * INC # H8: 1,7 => UNS * INC # I8: 1,7 => UNS * INC # B9: 1,7 => UNS * INC # B9: 5 => UNS * INC # H6: 1,7 => UNS * INC # H6: 5 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 3,9 => CTR => B1: 8 * INC B1: 8 # A8: 1,8 => UNS * INC B1: 8 # A8: 7 => UNS * DIS B1: 8 # D7: 1,8 => CTR => D7: 5,9 * INC B1: 8 + D7: 5,9 # G7: 1,8 => UNS * INC B1: 8 + D7: 5,9 # G7: 1,8 => UNS * PRF B1: 8 + D7: 5,9 # G7: 5 => SOL * STA B1: 8 + D7: 5,9 + G7: 5 * CNT 7 HDP CHAINS / 7 HYP OPENED