Analysis of xx-top500-469-base.sdk
Contents
Original Sudoku
level: medium
position: 3...6..........1.4......9...41..9..8....3..2...........5.8.1...2......6....4..... initial
Autosolve
position: 3...6.....6..8.1.4......9.66412.93.8....3..2...........568.1..32......6....4.6... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 5,7,8 => CTR => A3: 1,4 * DIS # D5: 5,7 => CTR => D5: 1,6 * DIS # F5: 5,7 => CTR => F5: 4,8 * PRF # D6: 5,7 => SOL * DIS # F6: 5,7 => CTR => F6: 4,8 * DIS # E8: 5,7 => CTR => E8: 9 * DIS # H6: 9 => CTR => H6: 1,4 * PRF # G5: 5,7 => SOL * DIS # I5: 5,7 => CTR => I5: 1,9 * DIS # G6: 5,7 => CTR => G6: 4,6 * DIS # I6: 5,7 => CTR => I6: 1,9 * DIS # H1: 5,7 => CTR => H1: 8 * DIS # A7: 7 => CTR => A7: 4,9 * DIS # H6: 1 => CTR => H6: 4,9 * DIS # I8: 1,9 => CTR => I8: 5,7 * DIS # I9: 1,9 => CTR => I9: 2,5,7 * DIS # B9: 1,9 => CTR => B9: 3,7,8 * DIS # H6: 1,9 => CTR => H6: 4 * CNT 18 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 5,7,8 => CTR => A3: 1,4 * DIS A3: 1,4 # D5: 5,7 => CTR => D5: 1,6 * DIS A3: 1,4 + D5: 1,6 # F5: 5,7 => CTR => F5: 4,8 * PRF A3: 1,4 + D5: 1,6 + F5: 4,8 # D6: 5,7 => SOL * STA A3: 1,4 + D5: 1,6 + F5: 4,8 + D6: 5,7 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3...6..........1.4......9...41..9..8....3..2...........5.8.1...2......6....4..... | initial |
| 3...6.....6..8.1.4......9.66412.93.8....3..2...........568.1..32......6....4.6... | autosolve |
| 394165782765982134182347956641259378879634521523718649456871293218593467937426815 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) E3: 1,4 B6: 2,3 C6: 2,3 E4: 5,7 E6: 1,4 H4: 5,7 H7: 4,9 H9: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,D1: 1.. / B1 = 1 => 0 pairs (X) / D1 = 1 => 16 pairs (_) D5,I5: 1.. / D5 = 1 => 0 pairs (X) / I5 = 1 => 16 pairs (_) B8,I8: 1.. / B8 = 1 => 16 pairs (_) / I8 = 1 => 0 pairs (X) A3,A9: 1.. / A3 = 1 => 16 pairs (_) / A9 = 1 => 0 pairs (X) E3,E6: 1.. / E3 = 1 => 0 pairs (X) / E6 = 1 => 16 pairs (_) H6,H9: 1.. / H6 = 1 => 0 pairs (X) / H9 = 1 => 16 pairs (_) F2,F3: 2.. / F2 = 2 => 8 pairs (_) / F3 = 2 => 6 pairs (_) G1,I1: 2.. / G1 = 2 => 10 pairs (_) / I1 = 2 => 9 pairs (_) B6,C6: 2.. / B6 = 2 => 6 pairs (_) / C6 = 2 => 6 pairs (_) E7,E9: 2.. / E7 = 2 => 9 pairs (_) / E9 = 2 => 10 pairs (_) C2,F2: 2.. / C2 = 2 => 6 pairs (_) / F2 = 2 => 8 pairs (_) E7,G7: 2.. / E7 = 2 => 9 pairs (_) / G7 = 2 => 10 pairs (_) B3,B6: 2.. / B3 = 2 => 6 pairs (_) / B6 = 2 => 6 pairs (_) I1,I9: 2.. / I1 = 2 => 9 pairs (_) / I9 = 2 => 10 pairs (_) H2,H3: 3.. / H2 = 3 => 8 pairs (_) / H3 = 3 => 9 pairs (_) B6,C6: 3.. / B6 = 3 => 6 pairs (_) / C6 = 3 => 6 pairs (_) B9,C9: 3.. / B9 = 3 => 6 pairs (_) / C9 = 3 => 6 pairs (_) D8,F8: 3.. / D8 = 3 => 11 pairs (_) / F8 = 3 => 9 pairs (_) B6,B9: 3.. / B6 = 3 => 6 pairs (_) / B9 = 3 => 6 pairs (_) C6,C9: 3.. / C6 = 3 => 6 pairs (_) / C9 = 3 => 6 pairs (_) A7,C8: 4.. / A7 = 4 => 16 pairs (_) / C8 = 4 => 0 pairs (X) C1,F1: 4.. / C1 = 4 => 16 pairs (_) / F1 = 4 => 0 pairs (X) F5,G5: 4.. / F5 = 4 => 16 pairs (_) / G5 = 4 => 0 pairs (X) C8,G8: 4.. / C8 = 4 => 0 pairs (X) / G8 = 4 => 16 pairs (_) A3,A7: 4.. / A3 = 4 => 0 pairs (X) / A7 = 4 => 16 pairs (_) E3,E6: 4.. / E3 = 4 => 16 pairs (_) / E6 = 4 => 0 pairs (X) H6,H7: 4.. / H6 = 4 => 16 pairs (_) / H7 = 4 => 0 pairs (X) E4,H4: 5.. / E4 = 5 => 14 pairs (_) / H4 = 5 => 15 pairs (_) D5,D6: 6.. / D5 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) G5,G6: 6.. / G5 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) D5,G5: 6.. / D5 = 6 => 0 pairs (*) / G5 = 6 => 0 pairs (X) D6,G6: 6.. / D6 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) E4,H4: 7.. / E4 = 7 => 15 pairs (_) / H4 = 7 => 14 pairs (_) H1,H3: 8.. / H1 = 8 => 8 pairs (_) / H3 = 8 => 0 pairs (X) F5,F6: 8.. / F5 = 8 => 0 pairs (X) / F6 = 8 => 8 pairs (_) G8,G9: 8.. / G8 = 8 => 0 pairs (X) / G9 = 8 => 16 pairs (_) A6,F6: 8.. / A6 = 8 => 0 pairs (X) / F6 = 8 => 8 pairs (_) D1,D2: 9.. / D1 = 9 => 0 pairs (X) / D2 = 9 => 9 pairs (_) * DURATION: 0:01:14.776143 START: 18:43:13.630116 END: 18:44:28.406259 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C6,E3,E4,E6,H4,H7,H9) * 3...6.....6..8.1.4......9.66412.93.8....3..2...........568.1..32......6....4.6... * PAIR E3: 1,4 ROW 3 A3: 1,4,5,7,8 # reduction candidate for 1,4 A3: 5,7,8 => CTR * 3...6.....6..8.1.4......9.66412.93.8....3..2..........4568.1.932.....46.1..4.6... A3: 1,4 # 9 pairs * PAIR E4: 5,7 BLK 5 D5: 5,7,1,6 # reduction candidate for 5,7 D5: 5,7 => CTR * 39416..8..6.98.1.418..4.9.66412.93.8879534621523618749456871.93218.9.46.9..4.681. D5: 1,6 # 9 pairs F5: 5,7,4,8 # reduction candidate for 5,7 F5: 5,7 => CTR * 3...64....6..8.1.44...1.9.66412.93.8...63.421...14869..568.1.43214...86....4.6.1. F5: 4,8 # 9 pairs D6: 5,7,1,6 # reduction candidate for 5,7 D6: 5,7 => SOLVED * 394165782765982134182347956641259378879634521523718649456871293218593467937426815 D6: 1,6 # 9 pairs F6: 5,7,4,8 # reduction candidate for 5,7 F6: 5,7 => CTR * 3...64....6..8.1.44...1.9.66412.93.8...6384218..14.69..568.1.43214...86....4.6.1. F6: 4,8 # 9 pairs * PAIR E4: 5,7 COL E E8: 5,7,9 # reduction candidate for 5,7 E8: 5,7 => CTR * 31..64....6..8.1.44...1.9.66412.93.8...63.421....4.6...568.1.432.4...86.1..4.6.9. E8: 9 # 9 pairs E9: 5,7,2,9 # reduction candidate for 5,7 E9: 5,7 # 10 pairs * PAIR E6: 1,4 ROW 6 H6: 1,4,9 # reduction candidate for 1,4 H6: 9 => CTR * 3...6.....6..8.1.4......9.66412.93.8....3..2........9..568.1.432.4....6....4.6.1. H6: 1,4 # 9 pairs * PAIR H4: 5,7 BLK 6 G5: 5,7,4,6 # reduction candidate for 5,7 G5: 5,7 => SOLVED * 394165782765982134182347956641259378879634521523718649456871293218593467937426815 G5: 4,6 # 9 pairs I5: 5,7,1,9 # reduction candidate for 5,7 I5: 5,7 => CTR * 3...6.....6..8.1.4......9.66412.93.8...13.62....64.....568.1.432.4....6....4.6... I5: 1,9 # 9 pairs G6: 5,7,4,6 # reduction candidate for 5,7 G6: 5,7 => CTR * 39416..8..6.98.1.418..4.9.66412.93.8879534621523618749456871.93218.9.46.9..4.681. G6: 4,6 # 9 pairs I6: 5,7,1,9 # reduction candidate for 5,7 I6: 5,7 => CTR * 31..64....6..8.1.44...1.9.66412.93.8...63.42.....4.6...568.1.432.4....6.1..4.6.9. I6: 1,9 # 9 pairs * PAIR H4: 5,7 COL H H1: 5,7,8 # reduction candidate for 5,7 H1: 5,7 => CTR * 318964....6..8.1344...1.9866412.93.8...63.421....4.6...568.1.432.4....6.1..4.6.9. H1: 8 # 8 pairs H2: 5,7,3 # reduction candidate for 5,7 H2: 5,7 # 9 pairs H3: 5,7,3,8 # reduction candidate for 5,7 H3: 5,7 # 9 pairs * PAIR H7: 4,9 ROW 7 A7: 4,9,7 # reduction candidate for 4,9 A7: 7 => CTR * 31..64....6..8.1.44...1.9.66412.93.8....3.42.....4.61.756891243294...8611..426.9. A7: 4,9 # 11 pairs * PAIR H7: 4,9 COL H H6: 4,9,1 # reduction candidate for 4,9 H6: 1 => CTR * 3...64....6..8.1.44...1.9.66412.93.8...13..2........1..568.1.432.4....6....4.6.9. H6: 4,9 # 16 pairs * PAIR H9: 1,9 BLK 9 I8: 1,9,5,7 # reduction candidate for 1,9 I8: 1,9 => CTR * 31..64....6..8.1.44...1.9.66412.93.8...63.421....4.6...568.1.432.4....6.1..4.6.9. I8: 5,7 # 16 pairs I9: 1,9,2,5,7 # reduction candidate for 1,9 I9: 1,9 => CTR * 3...6...2.6..8.1.41...4.9.66412.93.8....3..2.....1..9.4568.1..32......6....4.6... I9: 2,5,7 # 8 pairs * PAIR H9: 1,9 ROW 9 A9: 1,9,7,8 # reduction candidate for 1,9 A9: 1,9 # 9 pairs B9: 1,9,3,7,8 # reduction candidate for 1,9 B9: 1,9 => CTR * 3.4.6.....6..821.412..4.9.66412.93.8....3..2..32.1....4568.1.932...9.46..934.681. B9: 3,7,8 # 8 pairs * PAIR H9: 1,9 COL H H6: 1,9,4 # reduction candidate for 1,9 H6: 1,9 => CTR * 31..64....6..8.1.44...1.9.66412.93.8...63.421....4.6...568.1.432.4....6.1..4.6.9. H6: 4 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-469-base-pr-000.dot * REASONING * DIS # A3: 5,7,8 => CTR => A3: 1,4 * DIS # D5: 5,7 => CTR => D5: 1,6 * DIS # F5: 5,7 => CTR => F5: 4,8 * PRF # D6: 5,7 => SOL * DIS # F6: 5,7 => CTR => F6: 4,8 * DIS # E8: 5,7 => CTR => E8: 9 * DIS # H6: 9 => CTR => H6: 1,4 * PRF # G5: 5,7 => SOL * DIS # I5: 5,7 => CTR => I5: 1,9 * DIS # G6: 5,7 => CTR => G6: 4,6 * DIS # I6: 5,7 => CTR => I6: 1,9 * DIS # H1: 5,7 => CTR => H1: 8 * DIS # A7: 7 => CTR => A7: 4,9 * DIS # H6: 1 => CTR => H6: 4,9 * DIS # I8: 1,9 => CTR => I8: 5,7 * DIS # I9: 1,9 => CTR => I9: 2,5,7 * DIS # B9: 1,9 => CTR => B9: 3,7,8 * DIS # H6: 1,9 => CTR => H6: 4 * CNT 18 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C6,E3,E4,E6,H4,H7,H9) * 3...6.....6..8.1.4......9.66412.93.8....3..2...........568.1..32......6....4.6... * PAIR E3: 1,4 ROW 3 A3: 1,4,5,7,8 # reduction candidate for 1,4 A3: 5,7,8 => CTR * 3...6.....6..8.1.4......9.66412.93.8....3..2..........4568.1.932.....46.1..4.6... * PAIR RESTART * PAIR E4: 5,7 BLK 5 D5: 5,7,1,6 # reduction candidate for 5,7 D5: 5,7 => CTR * 39416..8..6.98.1.418..4.9.66412.93.8879534621523618749456871.93218.9.46.9..4.681. F5: 5,7,4,8 # reduction candidate for 5,7 F5: 5,7 => CTR * 3...64....6..8.1.44...1.9.66412.93.8...63.421...14869..568.1.43214...86....4.6.1. D6: 5,7,1,6 # reduction candidate for 5,7 D6: 5,7 => SOLVED * 394165782765982134182347956641259378879634521523718649456871293218593467937426815 * DURATION: 0:00:07.616607 START: 18:45:09.612058 END: 18:45:17.228665 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-469-base-pr-001.dot * REASONING * DIS # A3: 5,7,8 => CTR => A3: 1,4 * DIS A3: 1,4 # D5: 5,7 => CTR => D5: 1,6 * DIS A3: 1,4 + D5: 1,6 # F5: 5,7 => CTR => F5: 4,8 * PRF A3: 1,4 + D5: 1,6 + F5: 4,8 # D6: 5,7 => SOL * STA A3: 1,4 + D5: 1,6 + F5: 4,8 + D6: 5,7 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 469 solution: 394165782765982134182347956641259378879634521523718649456871293218593467937426815 info: 95598 FNBHWK S8.f 29201 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 394165782765982134182347956641259378879634521523718649456871293218593467937426815 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 # A3: 1,4 => UNS * DIS # A3: 5,7,8 => CTR => A3: 1,4 * DIS # D5: 5,7 => CTR => D5: 1,6 * INC # D5: 1,6 => UNS * DIS # F5: 5,7 => CTR => F5: 4,8 * INC # F5: 4,8 => UNS * PRF # D6: 5,7 => SOL * INC # D6: 1,6 => UNS * DIS # F6: 5,7 => CTR => F6: 4,8 * INC # F6: 4,8 => UNS * DIS # E8: 5,7 => CTR => E8: 9 * INC # E8: 9 => UNS * INC # E9: 5,7 => UNS * INC # H6: 1,4 => UNS * DIS # H6: 9 => CTR => H6: 1,4 * PRF # G5: 5,7 => SOL * INC # G5: 4,6 => UNS * DIS # I5: 5,7 => CTR => I5: 1,9 * INC # I5: 1,9 => UNS * DIS # G6: 5,7 => CTR => G6: 4,6 * INC # G6: 4,6 => UNS * DIS # I6: 5,7 => CTR => I6: 1,9 * INC # I6: 1,9 => UNS * DIS # H1: 5,7 => CTR => H1: 8 * INC # H1: 8 => UNS * INC # H2: 5,7 => UNS * INC # H3: 5,7 => UNS * INC # A7: 4,9 => UNS * DIS # A7: 7 => CTR => A7: 4,9 * INC # H6: 4,9 => UNS * DIS # H6: 1 => CTR => H6: 4,9 * DIS # I8: 1,9 => CTR => I8: 5,7 * INC # I8: 5,7 => UNS * DIS # I9: 1,9 => CTR => I9: 2,5,7 * INC # I9: 2,5,7 => UNS * INC # A9: 1,9 => UNS * DIS # B9: 1,9 => CTR => B9: 3,7,8 * INC # B9: 3,7,8 => UNS * DIS # H6: 1,9 => CTR => H6: 4 * INC # H6: 4 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 1,4 => UNS * DIS # A3: 5,7,8 => CTR => A3: 1,4 * DIS A3: 1,4 # D5: 5,7 => CTR => D5: 1,6 * DIS A3: 1,4 + D5: 1,6 # F5: 5,7 => CTR => F5: 4,8 * PRF A3: 1,4 + D5: 1,6 + F5: 4,8 # D6: 5,7 => SOL * STA A3: 1,4 + D5: 1,6 + F5: 4,8 + D6: 5,7 * CNT 5 HDP CHAINS / 5 HYP OPENED