Analysis of xx-top500-210-base.sdk
Contents
Original Sudoku
level: medium
position: .2.6..5....9....3.......8..4.1....9.7..5........2.....5.....6...3..9........1.... initial
Autosolve
position: .2.6..519..915..3..159..8..451.6.3927.25391..9.32417..59.3..6.113..9....2...1.9.3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 3,8 => CTR => F1: 4,7 * PRF # F1: 4,7 => SOL * PRF # F1: 4,7 => SOL * DIS # F1: 3,8 => CTR => F1: 4,7 * DIS # C8: 4,7 => CTR => C8: 6,8 * DIS # C9: 4,7 => CTR => C9: 6,8 * PRF # F2: 4,7 => SOL * DIS # I2: 4,7 => CTR => I2: 6 * PRF # I2: 6 => SOL * DIS # F1: 7,8 => CTR => F1: 3,4 * PRF # F2: 7,8 => SOL * DIS # F2: 2,4 => CTR => F2: 7,8 * PRF # E7: 7,8 => SOL * DIS # E7: 2 => CTR => E7: 7,8 * PRF # F2: 2,7 => SOL * DIS # F2: 4,8 => CTR => F2: 2,7 * DIS # F3: 2,7 => CTR => F3: 3,4 * DIS # H3: 4,6 => CTR => H3: 2,7 * PRF # E7: 2,7 => SOL * DIS # E7: 8 => CTR => E7: 2,7 * PRF # H3: 6,7 => SOL * DIS # F2: 2,4 => CTR => F2: 7,8 * PRF # F2: 7,8 => SOL * PRF # I5: 6,8 => SOL * PRF # D8: 7,8 => SOL * DIS # D8: 4 => CTR => D8: 7,8 * DIS # D9: 7,8 => CTR => D9: 4 * PRF # D9: 4 => SOL * DIS # F1: 7,8 => CTR => F1: 3,4 * PRF # F2: 7,8 => SOL * DIS # F2: 2,4 => CTR => F2: 7,8 * DIS # F7: 7,8 => CTR => F7: 2 * PRF # F7: 2 => SOL * DIS # C8: 4,7 => CTR => C8: 6,8 * DIS # C9: 4,7 => CTR => C9: 6,8 * DIS # H9: 4,7 => CTR => H9: 5,8 * PRF # H8: 2,4 => SOL * DIS # H8: 5,7,8 => CTR => H8: 2,4 * CNT 38 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 3,8 => CTR => F1: 4,7 * PRF F1: 4,7 => SOL * STA F1: 4,7 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.6..5....9....3.......8..4.1....9.7..5........2.....5.....6...3..9........1.... | initial |
| .2.6..519..915..3..159..8..451.6.3927.25391..9.32417..59.3..6.113..9....2...1.9.3 | autosolve |
| 327684519849157236615923874451768392762539148983241765594372681136895427278416953 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 3,8 C1: 4,7 A2: 6,8 B2: 4,7 A3: 3,6 E1: 7,8 E3: 2,7 G2: 2,4 B5: 6,8 B6: 6,8 D4: 7,8 F4: 7,8 B9: 4,7 F8: 5,6 F9: 5,6 G8: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,H3: 2.. / G2 = 2 => 0 pairs (*) / H3 = 2 => 0 pairs (X) E7,F7: 2.. / E7 = 2 => 0 pairs (X) / F7 = 2 => 0 pairs (_) G8,H8: 2.. / G8 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) F2,G2: 2.. / F2 = 2 => 0 pairs (X) / G2 = 2 => 0 pairs (_) E3,E7: 2.. / E3 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) G2,G8: 2.. / G2 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) H3,H8: 2.. / H3 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) A1,A3: 3.. / A1 = 3 => 0 pairs (*) / A3 = 3 => 0 pairs (X) F1,F3: 3.. / F1 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) A1,F1: 3.. / A1 = 3 => 0 pairs (*) / F1 = 3 => 0 pairs (X) A3,F3: 3.. / A3 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) C1,B2: 4.. / C1 = 4 => 0 pairs (X) / B2 = 4 => 0 pairs (_) H5,I5: 4.. / H5 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) D8,D9: 4.. / D8 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) C1,F1: 4.. / C1 = 4 => 0 pairs (X) / F1 = 4 => 0 pairs (_) C7,H7: 4.. / C7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) B2,B9: 4.. / B2 = 4 => 0 pairs (*) / B9 = 4 => 0 pairs (X) G2,G8: 4.. / G2 = 4 => 0 pairs (X) / G8 = 4 => 0 pairs (_) H6,I6: 5.. / H6 = 5 => 16 pairs (_) / I6 = 5 => 17 pairs (_) F8,F9: 5.. / F8 = 5 => 15 pairs (_) / F9 = 5 => 14 pairs (_) F9,H9: 5.. / F9 = 5 => 14 pairs (_) / H9 = 5 => 15 pairs (_) I6,I8: 5.. / I6 = 5 => 17 pairs (_) / I8 = 5 => 16 pairs (_) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 0 pairs (_) B5,B6: 6.. / B5 = 6 => 18 pairs (_) / B6 = 6 => 19 pairs (_) C8,C9: 6.. / C8 = 6 => 15 pairs (_) / C9 = 6 => 14 pairs (_) F8,F9: 6.. / F8 = 6 => 14 pairs (_) / F9 = 6 => 15 pairs (_) A2,I2: 6.. / A2 = 6 => 0 pairs (X) / I2 = 6 => 0 pairs (_) C8,F8: 6.. / C8 = 6 => 15 pairs (_) / F8 = 6 => 14 pairs (_) C9,F9: 6.. / C9 = 6 => 14 pairs (_) / F9 = 6 => 15 pairs (_) C1,B2: 7.. / C1 = 7 => 0 pairs (*) / B2 = 7 => 0 pairs (X) D4,F4: 7.. / D4 = 7 => 0 pairs (*) / F4 = 7 => 0 pairs (X) B2,B9: 7.. / B2 = 7 => 0 pairs (X) / B9 = 7 => 0 pairs (_) A1,A2: 8.. / A1 = 8 => 0 pairs (X) / A2 = 8 => 0 pairs (_) B5,B6: 8.. / B5 = 8 => 19 pairs (_) / B6 = 8 => 18 pairs (_) D4,F4: 8.. / D4 = 8 => 23 pairs (_) / F4 = 8 => 0 pairs (*) A2,F2: 8.. / A2 = 8 => 0 pairs (*) / F2 = 8 => 0 pairs (X) E1,E7: 8.. / E1 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) * DURATION: 0:01:06.145788 START: 10:00:12.969890 END: 10:01:19.115678 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A3,B2,B5,B6,B9,C1,D4,E1,E3,F4,F8,F9,G2,G8) * .2.6..519..915..3..159..8..451.6.3927.25391..9.32417..59.3..6.113..9....2...1.9.3 * PAIR A1: 3,8 ROW 1 F1: 3,8,4,7 # reduction candidate for 3,8 F1: 3,8 => CTR * .2467.519.7915..3..1592.8..451.6.3927.25391..9.32417..59.38264113.49.2..2...1.9.3 F1: 4,7 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 * PAIR C1: 4,7 ROW 1 F1: 4,7,3,8 # reduction candidate for 4,7 F1: 4,7 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 F1: 3,8 => CTR * .2467.519.7915..3..1592.8..451.6.3927.25391..9.32417..59.38264113.49.2..2...1.9.3 * PAIR C1: 4,7 COL C C7: 4,7,8 # reduction candidate for 4,7 C7: 4,7 # 19 pairs C8: 4,7,6,8 # reduction candidate for 4,7 C8: 4,7 => CTR * .2.68.5198.915243661597.8..451.6.3927.25391..9.32417..5983..64113..962..2.6.159.3 C8: 6,8 # 17 pairs C9: 4,7,6,8 # reduction candidate for 4,7 C9: 4,7 => CTR * .2.68.5198.915243661597.8..451.6.3927.25391..9.32417.55983..6411364952..2..816953 C9: 6,8 # 17 pairs * PAIR B2: 4,7 ROW 2 F2: 4,7,2,8 # reduction candidate for 4,7 F2: 4,7 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 F2: 2,8 # 20 pairs I2: 4,7,6 # reduction candidate for 4,7 I2: 4,7 => CTR * 82.6735196.915823.3159..8..4518673927.25391..9.32417..59.3826.113..9.42.2..41.9.3 I2: 6 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 * PAIR E1: 7,8 BLK 2 F1: 7,8,3,4 # reduction candidate for 7,8 F1: 7,8 => CTR * 3246..51987915..366159.38..451.6.3927.25391..9.32417..59.3..64113.49.2..24..1.9.3 F1: 3,4 # 17 pairs F2: 7,8,2,4 # reduction candidate for 7,8 F2: 7,8 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 F2: 2,4 => CTR * 3246..5198791542366159238..451.6.3927.25391..9.32417..59.3.264113..9....24..1.9.3 * PAIR E1: 7,8 COL E E7: 7,8,2 # reduction candidate for 7,8 E7: 7,8 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 E7: 2 => CTR * .2.68.5198.915..36615973824451.6.3927.25391..9.32417..59.3..6.113..9....2...1.9.3 * PAIR E3: 2,7 BLK 2 F2: 2,7,4,8 # reduction candidate for 2,7 F2: 2,7 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 F2: 4,8 => CTR * .2.6..519.49158237.159..8..4518673927.25391..9.32417..59438267113.79.42.27.41.9.3 F3: 2,7,3,4 # reduction candidate for 2,7 F3: 2,7 => CTR * .2.6.3519..915423.3159..8..451.6.3927.25391..9.32417..59.3..6.113..9.42.24..1.9.3 F3: 3,4 # 17 pairs * PAIR E3: 2,7 ROW 3 H3: 2,7,4,6 # reduction candidate for 2,7 H3: 4,6 => CTR * .276845198491572366159238474517683927.25391.49.32417..59437.6.113..9.42.27.41.9.3 H3: 2,7 # 21 pairs * PAIR E3: 2,7 COL E E7: 2,7,8 # reduction candidate for 2,7 E7: 2,7 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 E7: 8 => CTR * .2.67.519.7915.23..1592.8..4518673927.25391..9.32417..59.3826.113..9.42.24.71.9.3 * PAIR G2: 2,4 BLK 3 H3: 2,4,6,7 # reduction candidate for 2,4 H3: 6,7 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 H3: 2,4 # 21 pairs * PAIR G2: 2,4 ROW 2 F2: 2,4,7,8 # reduction candidate for 2,4 F2: 2,4 => CTR * 3246..5198791542366159238..451.6.3927.25391..9.32417..59.3.264113..9....24..1.9.3 F2: 7,8 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 * PAIR B5: 6,8 ROW 5 H5: 6,8,4 # reduction candidate for 6,8 H5: 6,8 # 22 pairs I5: 6,8,4 # reduction candidate for 6,8 I5: 6,8 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 I5: 4 # 22 pairs * PAIR B6: 6,8 ROW 6 H6: 6,8,5 # reduction candidate for 6,8 H6: 6,8 # 17 pairs I6: 6,8,5 # reduction candidate for 6,8 I6: 6,8 # 16 pairs * PAIR D4: 7,8 COL D D8: 7,8,4 # reduction candidate for 7,8 D8: 7,8 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 D8: 4 => CTR * .2.6..519..915243..15974826451.6.3927.25391.49.32417..59.32.6.113.49.2..24..1.9.3 D9: 7,8,4 # reduction candidate for 7,8 D9: 7,8 => CTR * .2.6..519..915243..15974826451.6.3927.25391.49.32417..59.32.6.113.49.2..24..1.9.3 D9: 4 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 * PAIR F4: 7,8 COL F F1: 7,8,3,4 # reduction candidate for 7,8 F1: 7,8 => CTR * 3246..51987915..366159.38..451.6.3927.25391..9.32417..59.3..64113.49.2..24..1.9.3 F1: 3,4 # 17 pairs F2: 7,8,2,4 # reduction candidate for 7,8 F2: 7,8 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 F2: 2,4 => CTR * 3246..5198791542366159238..451.6.3927.25391..9.32417..59.3.264113..9....24..1.9.3 F7: 7,8,2 # reduction candidate for 7,8 F7: 7,8 => CTR * .2.68.5198.915..36615973824451.6.3927.25391..9.32417..59.32.6.113..9....2...1.9.3 F7: 2 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 * PAIR B9: 4,7 BLK 7 C7: 4,7,8 # reduction candidate for 4,7 C7: 4,7 # 19 pairs C8: 4,7,6,8 # reduction candidate for 4,7 C8: 4,7 => CTR * .2.68.5198.915243661597.8..451.6.3927.25391..9.32417..5983..64113..962..2.6.159.3 C8: 6,8 # 17 pairs C9: 4,7,6,8 # reduction candidate for 4,7 C9: 4,7 => CTR * .2.68.5198.915243661597.8..451.6.3927.25391..9.32417.55983..6411364952..2..816953 C9: 6,8 # 17 pairs * PAIR B9: 4,7 ROW 9 D9: 4,7,8 # reduction candidate for 4,7 D9: 4,7 # 19 pairs H9: 4,7,5,8 # reduction candidate for 4,7 H9: 4,7 => CTR * 32.68.5198.91524366159738..4517683927.25391..9.32417..59.3..6.113.4962..2.68159.3 H9: 5,8 # 17 pairs * PAIR G8: 2,4 BLK 9 H8: 2,4,5,7,8 # reduction candidate for 2,4 H8: 2,4 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 H8: 5,7,8 => CTR * .2.68.5198.915243661597.82.451.6.3927.25391..9.32417..59.32.6.113..9.2..2...1.9.3 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-210-base-pr-000.dot * REASONING * DIS # F1: 3,8 => CTR => F1: 4,7 * PRF # F1: 4,7 => SOL * PRF # F1: 4,7 => SOL * DIS # F1: 3,8 => CTR => F1: 4,7 * DIS # C8: 4,7 => CTR => C8: 6,8 * DIS # C9: 4,7 => CTR => C9: 6,8 * PRF # F2: 4,7 => SOL * DIS # I2: 4,7 => CTR => I2: 6 * PRF # I2: 6 => SOL * DIS # F1: 7,8 => CTR => F1: 3,4 * PRF # F2: 7,8 => SOL * DIS # F2: 2,4 => CTR => F2: 7,8 * PRF # E7: 7,8 => SOL * DIS # E7: 2 => CTR => E7: 7,8 * PRF # F2: 2,7 => SOL * DIS # F2: 4,8 => CTR => F2: 2,7 * DIS # F3: 2,7 => CTR => F3: 3,4 * DIS # H3: 4,6 => CTR => H3: 2,7 * PRF # E7: 2,7 => SOL * DIS # E7: 8 => CTR => E7: 2,7 * PRF # H3: 6,7 => SOL * DIS # F2: 2,4 => CTR => F2: 7,8 * PRF # F2: 7,8 => SOL * PRF # I5: 6,8 => SOL * PRF # D8: 7,8 => SOL * DIS # D8: 4 => CTR => D8: 7,8 * DIS # D9: 7,8 => CTR => D9: 4 * PRF # D9: 4 => SOL * DIS # F1: 7,8 => CTR => F1: 3,4 * PRF # F2: 7,8 => SOL * DIS # F2: 2,4 => CTR => F2: 7,8 * DIS # F7: 7,8 => CTR => F7: 2 * PRF # F7: 2 => SOL * DIS # C8: 4,7 => CTR => C8: 6,8 * DIS # C9: 4,7 => CTR => C9: 6,8 * DIS # H9: 4,7 => CTR => H9: 5,8 * PRF # H8: 2,4 => SOL * DIS # H8: 5,7,8 => CTR => H8: 2,4 * CNT 38 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A3,B2,B5,B6,B9,C1,D4,E1,E3,F4,F8,F9,G2,G8) * .2.6..519..915..3..159..8..451.6.3927.25391..9.32417..59.3..6.113..9....2...1.9.3 * PAIR A1: 3,8 ROW 1 F1: 3,8,4,7 # reduction candidate for 3,8 F1: 3,8 => CTR * .2467.519.7915..3..1592.8..451.6.3927.25391..9.32417..59.38264113.49.2..2...1.9.3 F1: 4,7 => SOLVED * 327684519849157236615923874451768392762539148983241765594372681136895427278416953 * DURATION: 0:00:03.183256 START: 10:02:17.698404 END: 10:02:20.881660 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-210-base-pr-001.dot * REASONING * DIS # F1: 3,8 => CTR => F1: 4,7 * PRF F1: 4,7 => SOL * STA F1: 4,7 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 210 solution: 327684519849157236615923874451768392762539148983241765594372681136895427278416953 info: 1942 FNBHWY S8.f 16867 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 327684519849157236615923874451768392762539148983241765594372681136895427278416953 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 # F1: 3,8 => CTR => F1: 4,7 * PRF # F1: 4,7 => SOL * PRF # F1: 4,7 => SOL * DIS # F1: 3,8 => CTR => F1: 4,7 * INC # C7: 4,7 => UNS * DIS # C8: 4,7 => CTR => C8: 6,8 * INC # C8: 6,8 => UNS * DIS # C9: 4,7 => CTR => C9: 6,8 * INC # C9: 6,8 => UNS * PRF # F2: 4,7 => SOL * INC # F2: 2,8 => UNS * DIS # I2: 4,7 => CTR => I2: 6 * PRF # I2: 6 => SOL * DIS # F1: 7,8 => CTR => F1: 3,4 * INC # F1: 3,4 => UNS * PRF # F2: 7,8 => SOL * DIS # F2: 2,4 => CTR => F2: 7,8 * PRF # E7: 7,8 => SOL * DIS # E7: 2 => CTR => E7: 7,8 * PRF # F2: 2,7 => SOL * DIS # F2: 4,8 => CTR => F2: 2,7 * DIS # F3: 2,7 => CTR => F3: 3,4 * INC # F3: 3,4 => UNS * INC # H3: 2,7 => UNS * DIS # H3: 4,6 => CTR => H3: 2,7 * PRF # E7: 2,7 => SOL * DIS # E7: 8 => CTR => E7: 2,7 * INC # H3: 2,4 => UNS * PRF # H3: 6,7 => SOL * DIS # F2: 2,4 => CTR => F2: 7,8 * PRF # F2: 7,8 => SOL * INC # H5: 6,8 => UNS * PRF # I5: 6,8 => SOL * INC # I5: 4 => UNS * INC # H6: 6,8 => UNS * INC # I6: 6,8 => UNS * PRF # D8: 7,8 => SOL * DIS # D8: 4 => CTR => D8: 7,8 * DIS # D9: 7,8 => CTR => D9: 4 * PRF # D9: 4 => SOL * DIS # F1: 7,8 => CTR => F1: 3,4 * INC # F1: 3,4 => UNS * PRF # F2: 7,8 => SOL * DIS # F2: 2,4 => CTR => F2: 7,8 * DIS # F7: 7,8 => CTR => F7: 2 * PRF # F7: 2 => SOL * INC # C7: 4,7 => UNS * DIS # C8: 4,7 => CTR => C8: 6,8 * INC # C8: 6,8 => UNS * DIS # C9: 4,7 => CTR => C9: 6,8 * INC # C9: 6,8 => UNS * INC # D9: 4,7 => UNS * DIS # H9: 4,7 => CTR => H9: 5,8 * INC # H9: 5,8 => UNS * PRF # H8: 2,4 => SOL * DIS # H8: 5,7,8 => CTR => H8: 2,4 * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F1: 3,8 => CTR => F1: 4,7 * PRF F1: 4,7 => SOL * STA F1: 4,7 * CNT 2 HDP CHAINS / 1 HYP OPENED