Analysis of xx-top500-265-base.sdk
Contents
Original Sudoku
level: medium
position: 6...2..7..4.5....3.........1.5....2....4..8.....3.........1.5..7.....9..........4 initial
Autosolve
position: 6.3.24175.415...935..13..48135...42....45.83.4..3..75.3.4.1.5.775..43912.1...53.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B7: 8,9 => CTR => B7: 2,6 * DIS # A9: 9 => CTR => A9: 2,8 * DIS # D4: 8,9 => CTR => D4: 6,7 * DIS # D7: 8,9 => CTR => D7: 2,6 * DIS # D9: 8,9 => CTR => D9: 2,6,7 * DIS # F4: 6,9 => CTR => F4: 7,8 * DIS # B6: 2,9 => CTR => B6: 6,8 * DIS # C6: 2,9 => CTR => C6: 6,8 * DIS # A9: 2,9 => CTR => A9: 8 * PRF # A9: 8 => SOL * DIS # F4: 6,9 => CTR => F4: 7,8 * PRF # B6: 6,9 => SOL * DIS # C6: 6,9 => CTR => C6: 2,8 * DIS # F4: 6,9 => CTR => F4: 7,8 * DIS # B7: 6,8 => CTR => B7: 2,9 * DIS # C9: 6,8 => CTR => C9: 2,9 * DIS # C6: 2,9 => CTR => C6: 6,8 * PRF # D7: 6,8 => SOL * DIS # D9: 6,8 => CTR => D9: 2,7,9 * DIS # E9: 6,8 => CTR => E9: 7,9 * DIS # D4: 6,8 => CTR => D4: 7,9 * DIS # B7: 6,8 => CTR => B7: 2,9 * PRF # D7: 6,8 => SOL * DIS # C9: 6,8 => CTR => C9: 2,9 * DIS # D9: 6,8 => CTR => D9: 2,7,9 * DIS # E9: 6,8 => CTR => E9: 7,9 * CNT 26 HDP CHAINS / 65 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B7: 8,9 => CTR => B7: 2,6 * PRF B7: 2,6 # B6: 2,6 => SOL * STA B7: 2,6 + B6: 2,6 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6...2..7..4.5....3.........1.5....2....4..8.....3.........1.5..7.....9..........4 | initial |
| 6.3.24175.415...935..13..48135...42....45.83.4..3..75.3.4.1.5.775..43912.1...53.4 | autosolve |
| 683924175241587693597136248135768429972451836468392751324619587756843912819275364 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B1: 8,9 A2: 2,8 D1: 8,9 F3: 6,9 G2: 2,6 G3: 2,6 A5: 2,9 F5: 1,2 E6: 6,9 F6: 1,2 I4: 6,9 C8: 6,8 D8: 6,8 H7: 6,8 H9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F5,F6: 1.. / F5 = 1 => 14 pairs (_) / F6 = 1 => 18 pairs (_) I5,I6: 1.. / I5 = 1 => 18 pairs (_) / I6 = 1 => 14 pairs (_) F5,I5: 1.. / F5 = 1 => 14 pairs (_) / I5 = 1 => 18 pairs (_) F6,I6: 1.. / F6 = 1 => 18 pairs (_) / I6 = 1 => 14 pairs (_) G2,G3: 2.. / G2 = 2 => 0 pairs (X) / G3 = 2 => 0 pairs (_) F5,F6: 2.. / F5 = 2 => 18 pairs (_) / F6 = 2 => 14 pairs (_) D7,D9: 2.. / D7 = 2 => 15 pairs (_) / D9 = 2 => 20 pairs (_) A2,G2: 2.. / A2 = 2 => 0 pairs (*) / G2 = 2 => 0 pairs (X) B7,D7: 2.. / B7 = 2 => 20 pairs (_) / D7 = 2 => 15 pairs (_) G2,G3: 6.. / G2 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) H7,H9: 6.. / H7 = 6 => 0 pairs (X) / H9 = 6 => 16 pairs (_) F3,G3: 6.. / F3 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) C8,D8: 6.. / C8 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) B3,C3: 7.. / B3 = 7 => 16 pairs (_) / C3 = 7 => 16 pairs (_) E2,F2: 7.. / E2 = 7 => 17 pairs (_) / F2 = 7 => 16 pairs (_) B5,C5: 7.. / B5 = 7 => 16 pairs (_) / C5 = 7 => 16 pairs (_) D9,E9: 7.. / D9 = 7 => 15 pairs (_) / E9 = 7 => 18 pairs (_) B3,B5: 7.. / B3 = 7 => 16 pairs (_) / B5 = 7 => 16 pairs (_) C3,C5: 7.. / C3 = 7 => 16 pairs (_) / C5 = 7 => 16 pairs (_) D4,D9: 7.. / D4 = 7 => 18 pairs (_) / D9 = 7 => 15 pairs (_) F2,F4: 7.. / F2 = 7 => 16 pairs (_) / F4 = 7 => 17 pairs (_) B1,A2: 8.. / B1 = 8 => 0 pairs (*) / A2 = 8 => 0 pairs (X) B6,C6: 8.. / B6 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) H7,H9: 8.. / H7 = 8 => 16 pairs (_) / H9 = 8 => 0 pairs (X) B1,D1: 8.. / B1 = 8 => 0 pairs (*) / D1 = 8 => 0 pairs (X) C8,D8: 8.. / C8 = 8 => 0 pairs (X) / D8 = 8 => 0 pairs (_) A2,A9: 8.. / A2 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) D1,F3: 9.. / D1 = 9 => 0 pairs (*) / F3 = 9 => 0 pairs (X) B1,D1: 9.. / B1 = 9 => 0 pairs (X) / D1 = 9 => 0 pairs (_) A5,A9: 9.. / A5 = 9 => 16 pairs (_) / A9 = 9 => 0 pairs (X) * DURATION: 0:00:55.565740 START: 11:55:32.783662 END: 11:56:28.349402 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B1,C8,D1,D8,E6,F3,F5,F6,G2,G3,H7,H9,I4) * 6.3.24175.415...935..13..48135...42....45.83.4..3..75.3.4.1.5.775..43912.1...53.4 * PAIR B1: 8,9 COL B B6: 8,9,2,6 # reduction candidate for 8,9 B6: 8,9 # 18 pairs B7: 8,9,2,6 # reduction candidate for 8,9 B7: 8,9 => CTR * 6839241752415..693579136248135...42.9.745.83.4.83..75.39421.5.7756843912.1...53.4 B7: 2,6 # 16 pairs * PAIR A2: 2,8 COL A A9: 2,8,9 # reduction candidate for 2,8 A9: 9 => CTR * 6938241758415672935.21396481357864292..45183.4..3.27513.491.5.775864391291.275384 A9: 2,8 # 16 pairs * PAIR D1: 8,9 COL D D4: 8,9,6,7 # reduction candidate for 8,9 D4: 8,9 => CTR * 6938241758415..2935..1396481359..426...45.83.48.36.75.3642185.7758643912.1.7.53.4 D4: 6,7 # 16 pairs D7: 8,9,2,6 # reduction candidate for 8,9 D7: 8,9 => CTR * 6.3.241758415672935.21396481357864292.74518364..3..75.324.1.5.775.643912.16275384 D7: 2,6 # 16 pairs D9: 8,9,2,6,7 # reduction candidate for 8,9 D9: 8,9 => CTR * 6.3.241758415672935..139648135786429...45.83.48.39.75.39421.5.7758643912.1..753.4 D9: 2,6,7 # 15 pairs * PAIR F3: 6,9 COL F F4: 6,9,7,8 # reduction candidate for 6,9 F4: 6,9 => CTR * 6938241758415672935..139648135786429.6.45.83.48.39.7563.4.18567758643912.16.75384 F4: 7,8 # 16 pairs F7: 6,9,8 # reduction candidate for 6,9 F7: 6,9 # 18 pairs * PAIR A5: 2,9 BLK 4 B5: 2,9,6,7 # reduction candidate for 2,9 B5: 2,9 # 16 pairs C5: 2,9,6,7 # reduction candidate for 2,9 C5: 2,9 # 16 pairs B6: 2,9,6,8 # reduction candidate for 2,9 B6: 2,9 => CTR * 6839241752415..6935..136248135...42.9674528314283.175.394.1.5.7756843912.1...53.4 B6: 6,8 # 16 pairs C6: 2,9,6,8 # reduction candidate for 2,9 C6: 2,9 => CTR * 6938241758415672935..1396481357864292.945.83.48.3..75.3.491.5.7758643912.1.275384 C6: 6,8 # 17 pairs * PAIR A5: 2,9 COL A A9: 2,9,8 # reduction candidate for 2,9 A9: 2,9 => CTR * 6938241758415672935..1396481357864292.94518364863..75.3.491.5.7758643912.1.275384 A9: 8 => SOLVED * 683924175241587693597136248135768429972451836468392751324619587756843912819275364 * PAIR E6: 6,9 BLK 5 D4: 6,9,7,8 # reduction candidate for 6,9 D4: 6,9 # 18 pairs E4: 6,9,7,8 # reduction candidate for 6,9 E4: 6,9 # 21 pairs F4: 6,9,7,8 # reduction candidate for 6,9 F4: 6,9 => CTR * 6938241758415672935..139648135786429.6.45.83.48.39.7563.4.18567758643912.16.75384 F4: 7,8 # 16 pairs * PAIR E6: 6,9 ROW 6 B6: 6,9,2,8 # reduction candidate for 6,9 B6: 6,9 => SOLVED * 683924175241587693597136248135768429972451836468392751324619587756843912819275364 B6: 2,8 # 16 pairs C6: 6,9,2,8 # reduction candidate for 6,9 C6: 6,9 => CTR * 6938241758415672935..1396481357864292.94518364863.27513.491.5.7758643912.1.275384 C6: 2,8 # 16 pairs I6: 6,9,1 # reduction candidate for 6,9 I6: 6,9 # 18 pairs * PAIR E6: 6,9 COL E E9: 6,9,7,8 # reduction candidate for 6,9 E9: 6,9 # 19 pairs E9: 7,8 # 16 pairs * PAIR I4: 6,9 BLK 6 I5: 6,9,1 # reduction candidate for 6,9 I5: 6,9 # 14 pairs I6: 6,9,1 # reduction candidate for 6,9 I6: 6,9 # 18 pairs * PAIR I4: 6,9 ROW 4 D4: 6,9,7,8 # reduction candidate for 6,9 D4: 6,9 # 18 pairs E4: 6,9,7,8 # reduction candidate for 6,9 E4: 6,9 # 21 pairs F4: 6,9,7,8 # reduction candidate for 6,9 F4: 6,9 => CTR * 6938241758415672935..139648135786429.6.45.83.48.39.7563.4.18567758643912.16.75384 F4: 7,8 # 16 pairs * PAIR C8: 6,8 BLK 7 B7: 6,8,2,9 # reduction candidate for 6,8 B7: 6,8 => CTR * 6839241752415..6935..136248135...42.9..45.83.4.83..75.3.42195.775..43912.1...53.4 B7: 2,9 # 16 pairs C9: 6,8,2,9 # reduction candidate for 6,8 C9: 6,8 => CTR * 6938241758415..2935..139648135.8.42..6745.83.489362751324918567758643912916275384 C9: 2,9 # 16 pairs * PAIR C8: 6,8 COL C C6: 6,8,2,9 # reduction candidate for 6,8 C6: 2,9 => CTR * 6938241758415672935..1396481357864292.945.83.48.3..75.3.491.5.7758643912.1.275384 C6: 6,8 # 17 pairs * PAIR D8: 6,8 BLK 8 D7: 6,8,2,9 # reduction candidate for 6,8 D7: 6,8 => SOLVED * 683924175241587693597136248135768429972451836468392751324619587756843912819275364 D7: 2,9 # 16 pairs F7: 6,8,9 # reduction candidate for 6,8 F7: 6,8 # 19 pairs D9: 6,8,2,7,9 # reduction candidate for 6,8 D9: 6,8 => CTR * 6839241752415876935..1362481357.842.9..45.83.4.83..75.3.42195.775..43912.1..753.4 D9: 2,7,9 # 15 pairs E9: 6,8,7,9 # reduction candidate for 6,8 E9: 6,8 => CTR * 6839241752415..6935..136248135...42.9..45.83.4.83..75.3.42195.775..43912.1.7.53.4 E9: 7,9 # 16 pairs * PAIR D8: 6,8 COL D D4: 6,8,7,9 # reduction candidate for 6,8 D4: 6,8 => CTR * 6839241752415..6935..136248135...42.9..45.83.4.83..75.3.421.5.77568439128127.53.4 D4: 7,9 # 17 pairs * PAIR H7: 6,8 ROW 7 B7: 6,8,2,9 # reduction candidate for 6,8 B7: 6,8 => CTR * 6839241752415..6935..136248135...42.9..45.83.4.83..75.3.42195.775..43912.1...53.4 B7: 2,9 # 16 pairs D7: 6,8,2,9 # reduction candidate for 6,8 D7: 6,8 => SOLVED * 683924175241587693597136248135768429972451836468392751324619587756843912819275364 D7: 2,9 # 16 pairs F7: 6,8,9 # reduction candidate for 6,8 F7: 6,8 # 19 pairs * PAIR H9: 6,8 ROW 9 C9: 6,8,2,9 # reduction candidate for 6,8 C9: 6,8 => CTR * 6938241758415..2935..139648135.8.42..6745.83.489362751324918567758643912916275384 C9: 2,9 # 16 pairs D9: 6,8,2,7,9 # reduction candidate for 6,8 D9: 6,8 => CTR * 6839241752415876935..1362481357.842.9..45.83.4.83..75.3.42195.775..43912.1..753.4 D9: 2,7,9 # 15 pairs E9: 6,8,7,9 # reduction candidate for 6,8 E9: 6,8 => CTR * 6839241752415..6935..136248135...42.9..45.83.4.83..75.3.42195.775..43912.1.7.53.4 E9: 7,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-265-base-pr-000.dot * REASONING * DIS # B7: 8,9 => CTR => B7: 2,6 * DIS # A9: 9 => CTR => A9: 2,8 * DIS # D4: 8,9 => CTR => D4: 6,7 * DIS # D7: 8,9 => CTR => D7: 2,6 * DIS # D9: 8,9 => CTR => D9: 2,6,7 * DIS # F4: 6,9 => CTR => F4: 7,8 * DIS # B6: 2,9 => CTR => B6: 6,8 * DIS # C6: 2,9 => CTR => C6: 6,8 * DIS # A9: 2,9 => CTR => A9: 8 * PRF # A9: 8 => SOL * DIS # F4: 6,9 => CTR => F4: 7,8 * PRF # B6: 6,9 => SOL * DIS # C6: 6,9 => CTR => C6: 2,8 * DIS # F4: 6,9 => CTR => F4: 7,8 * DIS # B7: 6,8 => CTR => B7: 2,9 * DIS # C9: 6,8 => CTR => C9: 2,9 * DIS # C6: 2,9 => CTR => C6: 6,8 * PRF # D7: 6,8 => SOL * DIS # D9: 6,8 => CTR => D9: 2,7,9 * DIS # E9: 6,8 => CTR => E9: 7,9 * DIS # D4: 6,8 => CTR => D4: 7,9 * DIS # B7: 6,8 => CTR => B7: 2,9 * PRF # D7: 6,8 => SOL * DIS # C9: 6,8 => CTR => C9: 2,9 * DIS # D9: 6,8 => CTR => D9: 2,7,9 * DIS # E9: 6,8 => CTR => E9: 7,9 * CNT 26 HDP CHAINS / 65 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B1,C8,D1,D8,E6,F3,F5,F6,G2,G3,H7,H9,I4) * 6.3.24175.415...935..13..48135...42....45.83.4..3..75.3.4.1.5.775..43912.1...53.4 * PAIR B1: 8,9 COL B B6: 8,9,2,6 # reduction candidate for 8,9 B6: 8,9 # 18 pairs B7: 8,9,2,6 # reduction candidate for 8,9 B7: 8,9 => CTR * 6839241752415..693579136248135...42.9.745.83.4.83..75.39421.5.7756843912.1...53.4 * RESTART * PAIR B1: 8,9 COL B B6: 8,9,2,6 # reduction candidate for 8,9 B6: 2,6 => SOLVED * 683924175241587693597136248135768429972451836468392751324619587756843912819275364 * DURATION: 0:00:05.598630 START: 11:57:34.273951 END: 11:57:39.872581 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-265-base-pr-001.dot * REASONING * DIS # B7: 8,9 => CTR => B7: 2,6 * PRF B7: 2,6 # B6: 2,6 => SOL * STA B7: 2,6 + B6: 2,6 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 265 solution: 683924175241587693597136248135768429972451836468392751324619587756843912819275364 info: 2132 FNBHWXY S8.f 34538 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 683924175241587693597136248135768429972451836468392751324619587756843912819275364 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 # B6: 8,9 => UNS * DIS # B7: 8,9 => CTR => B7: 2,6 * INC # B7: 2,6 => UNS * INC # A9: 2,8 => UNS * DIS # A9: 9 => CTR => A9: 2,8 * DIS # D4: 8,9 => CTR => D4: 6,7 * INC # D4: 6,7 => UNS * DIS # D7: 8,9 => CTR => D7: 2,6 * INC # D7: 2,6 => UNS * DIS # D9: 8,9 => CTR => D9: 2,6,7 * INC # D9: 2,6,7 => UNS * DIS # F4: 6,9 => CTR => F4: 7,8 * INC # F4: 7,8 => UNS * INC # F7: 6,9 => UNS * INC # B5: 2,9 => UNS * INC # C5: 2,9 => UNS * DIS # B6: 2,9 => CTR => B6: 6,8 * INC # B6: 6,8 => UNS * DIS # C6: 2,9 => CTR => C6: 6,8 * INC # C6: 6,8 => UNS * DIS # A9: 2,9 => CTR => A9: 8 * PRF # A9: 8 => SOL * INC # D4: 6,9 => UNS * INC # E4: 6,9 => UNS * DIS # F4: 6,9 => CTR => F4: 7,8 * INC # F4: 7,8 => UNS * PRF # B6: 6,9 => SOL * INC # B6: 2,8 => UNS * DIS # C6: 6,9 => CTR => C6: 2,8 * INC # C6: 2,8 => UNS * INC # I6: 6,9 => UNS * INC # E9: 6,9 => UNS * INC # E9: 7,8 => UNS * INC # I5: 6,9 => UNS * INC # I6: 6,9 => UNS * INC # D4: 6,9 => UNS * INC # E4: 6,9 => UNS * DIS # F4: 6,9 => CTR => F4: 7,8 * INC # F4: 7,8 => UNS * DIS # B7: 6,8 => CTR => B7: 2,9 * INC # B7: 2,9 => UNS * DIS # C9: 6,8 => CTR => C9: 2,9 * INC # C9: 2,9 => UNS * INC # C6: 6,8 => UNS * DIS # C6: 2,9 => CTR => C6: 6,8 * PRF # D7: 6,8 => SOL * INC # D7: 2,9 => UNS * INC # F7: 6,8 => UNS * DIS # D9: 6,8 => CTR => D9: 2,7,9 * INC # D9: 2,7,9 => UNS * DIS # E9: 6,8 => CTR => E9: 7,9 * INC # E9: 7,9 => UNS * DIS # D4: 6,8 => CTR => D4: 7,9 * INC # D4: 7,9 => UNS * DIS # B7: 6,8 => CTR => B7: 2,9 * INC # B7: 2,9 => UNS * PRF # D7: 6,8 => SOL * INC # D7: 2,9 => UNS * INC # F7: 6,8 => UNS * DIS # C9: 6,8 => CTR => C9: 2,9 * INC # C9: 2,9 => UNS * DIS # D9: 6,8 => CTR => D9: 2,7,9 * INC # D9: 2,7,9 => UNS * DIS # E9: 6,8 => CTR => E9: 7,9 * INC # E9: 7,9 => UNS * CNT 65 HDP CHAINS / 65 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B6: 8,9 => UNS * DIS # B7: 8,9 => CTR => B7: 2,6 * INC B7: 2,6 # B6: 8,9 => UNS * PRF B7: 2,6 # B6: 2,6 => SOL * STA B7: 2,6 + B6: 2,6 * CNT 4 HDP CHAINS / 4 HYP OPENED