Analysis of xx-top500-307-base.sdk
Contents
Original Sudoku
level: medium
position: ...2....6.4.....5..1.......6...3...5....741..2........5..8..........3.7.......4.. initial
Autosolve
position: 7..2.1.46.4.3.7.51.1.45...76.4132..5....741..2.1.....45.784..1.4...1357.1..7254.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 8,9 => CTR => E2: 6 * DIS # E2: 8,9 => CTR => E2: 6 * DIS # E6: 6 => CTR => E6: 8,9 * DIS # G4: 8,9 => CTR => G4: 7 * DIS # H5: 8,9 => CTR => H5: 2,3,6 * PRF # I5: 8,9 => SOL * DIS # B4: 7 => CTR => B4: 8,9 * PRF # H3: 8,9 => SOL * DIS # H9: 8,9 => CTR => H9: 3,6 * DIS # B8: 8,9 => CTR => B8: 2,6 * DIS # B9: 8,9 => CTR => B9: 3,6 * DIS # I8: 8,9 => CTR => I8: 2 * PRF # I8: 2 => SOL * DIS # B7: 6,9 => CTR => B7: 2,3 * PRF # G7: 6,9 => SOL * DIS # G7: 2,3 => CTR => G7: 6,9 * PRF # B8: 6,9 => SOL * DIS # B8: 2,8 => CTR => B8: 6,9 * DIS # D6: 6,9 => CTR => D6: 5 * CNT 19 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 8,9 => CTR => E2: 6 * DIS E2: 6 # G4: 8,9 => CTR => G4: 7 * DIS E2: 6 + G4: 7 # H5: 8,9 => CTR => H5: 2,6 * PRF E2: 6 + G4: 7 + H5: 2,6 # I5: 8,9 => SOL * STA E2: 6 + G4: 7 + H5: 2,6 + I5: 8,9 * CNT 4 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2....6.4.....5..1.......6...3...5....741..2........5..8..........3.7.......4.. | initial |
| 7..2.1.46.4.3.7.51.1.45...76.4132..5....741..2.1.....45.784..1.4...1357.1..7254.. | autosolve |
| 785291346942367851316458297694132785853674129271589634527846913468913572139725468 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A2: 8,9 C2: 2,6 C3: 2,6 E1: 8,9 H4: 8,9 C8: 8,9 F7: 6,9 D8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 2.. / C2 = 2 => 9 pairs (_) / C3 = 2 => 0 pairs (X) H5,I5: 2.. / H5 = 2 => 0 pairs (*) / I5 = 2 => 0 pairs (X) B7,B8: 2.. / B7 = 2 => 0 pairs (*) / B8 = 2 => 0 pairs (X) C2,G2: 2.. / C2 = 2 => 9 pairs (_) / G2 = 2 => 0 pairs (X) B8,I8: 2.. / B8 = 2 => 0 pairs (X) / I8 = 2 => 0 pairs (_) H3,H5: 2.. / H3 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) A3,A5: 3.. / A3 = 3 => 9 pairs (_) / A5 = 3 => 12 pairs (_) B1,C1: 5.. / B1 = 5 => 9 pairs (_) / C1 = 5 => 8 pairs (_) D5,D6: 5.. / D5 = 5 => 0 pairs (X) / D6 = 5 => 9 pairs (_) B6,D6: 5.. / B6 = 5 => 0 pairs (X) / D6 = 5 => 9 pairs (_) C1,C5: 5.. / C1 = 5 => 8 pairs (_) / C5 = 5 => 9 pairs (_) C2,C3: 6.. / C2 = 6 => 0 pairs (X) / C3 = 6 => 9 pairs (_) E2,F3: 6.. / E2 = 6 => 9 pairs (_) / F3 = 6 => 0 pairs (X) F7,D8: 6.. / F7 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) G7,H9: 6.. / G7 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) C2,E2: 6.. / C2 = 6 => 0 pairs (X) / E2 = 6 => 9 pairs (_) C3,F3: 6.. / C3 = 6 => 9 pairs (_) / F3 = 6 => 0 pairs (X) D5,H5: 6.. / D5 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) B8,D8: 6.. / B8 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) B9,H9: 6.. / B9 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) E2,E6: 6.. / E2 = 6 => 9 pairs (_) / E6 = 6 => 0 pairs (X) G6,G7: 6.. / G6 = 6 => 0 pairs (*) / G7 = 6 => 0 pairs (X) B4,B6: 7.. / B4 = 7 => 0 pairs (X) / B6 = 7 => 10 pairs (_) G4,G6: 7.. / G4 = 7 => 10 pairs (_) / G6 = 7 => 0 pairs (X) B4,G4: 7.. / B4 = 7 => 0 pairs (X) / G4 = 7 => 10 pairs (_) B6,G6: 7.. / B6 = 7 => 10 pairs (_) / G6 = 7 => 0 pairs (X) E6,F6: 8.. / E6 = 8 => 11 pairs (_) / F6 = 8 => 10 pairs (_) F3,F6: 8.. / F3 = 8 => 11 pairs (_) / F6 = 8 => 10 pairs (_) F7,D8: 9.. / F7 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) * DURATION: 0:00:46.298712 START: 13:28:15.220735 END: 13:29:01.519447 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C2,C3,C8,D8,E1,F7,H4) * 7..2.1.46.4.3.7.51.1.45...76.4132..5....741..2.1.....45.784..1.4...1357.1..7254.. * PAIR A2: 8,9 BLK 1 B1: 8,9,3,5 # reduction candidate for 8,9 B1: 8,9 # 10 pairs C1: 8,9,3,5 # reduction candidate for 8,9 C1: 8,9 # 12 pairs A3: 8,9,3 # reduction candidate for 8,9 A3: 8,9 # 12 pairs * PAIR A2: 8,9 ROW 2 E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 => CTR * 7..2.1.46.463.7251.12456..76.4132..5....7412.2.1.68..45.784961.4..61357.16.7254.. E2: 6 # 9 pairs G2: 8,9,2 # reduction candidate for 8,9 G2: 8,9 # 9 pairs * PAIR A2: 8,9 COL A A5: 8,9,3 # reduction candidate for 8,9 A5: 3 # 12 pairs A5: 8,9 # 9 pairs * PAIR E1: 8,9 BLK 2 E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 => CTR * 7..2.1.46.463.7251.12456..76.4132..5....7412.2.1.68..45.784961.4..61357.16.7254.. E2: 6 # 9 pairs F3: 8,9,6 # reduction candidate for 8,9 F3: 8,9 # 9 pairs * PAIR E1: 8,9 ROW 1 B1: 8,9,3,5 # reduction candidate for 8,9 B1: 8,9 # 10 pairs C1: 8,9,3,5 # reduction candidate for 8,9 C1: 8,9 # 12 pairs G1: 8,9,3 # reduction candidate for 8,9 G1: 8,9 # 12 pairs * PAIR E1: 8,9 COL E E6: 8,9,6 # reduction candidate for 8,9 E6: 6 => CTR * 7..2.1.46.463.7251.12456..76.4132..5....741..2.1.68..45.784.61.4..61357.16.7254.. E6: 8,9 # 9 pairs * PAIR H4: 8,9 BLK 6 G4: 8,9,7 # reduction candidate for 8,9 G4: 8,9 => CTR * 7..2.1.46.4.3.7.51.1.45...7674132..5....741622.1...7345278496134..61357.1637254.. G4: 7 # 10 pairs H5: 8,9,2,3,6 # reduction candidate for 8,9 H5: 8,9 => CTR * 7..2.1.46.4.3.7.51.1.45..276.4132..5...6741.22.15....45.784621.4...1357.1..7254.. H5: 2,3,6 # 8 pairs I5: 8,9,2,3 # reduction candidate for 8,9 I5: 8,9 => SOLVED * 785291346942367851316458297694132785853674129271589634527846913468913572139725468 I5: 2,3 # 10 pairs * PAIR H4: 8,9 ROW 4 B4: 8,9,7 # reduction candidate for 8,9 B4: 7 => CTR * 7..2.1.46.4.3.7.51.1.45...7674132..5....741622.1...7345278496134..61357.1637254.. B4: 8,9 # 10 pairs * PAIR H4: 8,9 COL H H3: 8,9,2,3 # reduction candidate for 8,9 H3: 8,9 => SOLVED * 785291346942367851316458297694132785853674129271589634527846913468913572139725468 H3: 2,3 # 13 pairs H9: 8,9,3,6 # reduction candidate for 8,9 H9: 8,9 => CTR * 7..2.1.46.4.3.7.51.1.45...76.4132..5....741622.1.....45278496134..61357.1637254.. H9: 3,6 # 9 pairs * PAIR C8: 8,9 BLK 7 B8: 8,9,2,6 # reduction candidate for 8,9 B8: 8,9 => CTR * 7..2.1.46.4.3.7.51.1.45...76.4132..5....741..2.1.....452784..1.4..6135721637254.. B8: 2,6 # 9 pairs B9: 8,9,3,6 # reduction candidate for 8,9 B9: 8,9 => CTR * 7..2.1.46.4.367.51.1645...76.41327.5...67412.2715..634527846.13468913572193725468 B9: 3,6 # 9 pairs C9: 8,9,3 # reduction candidate for 8,9 C9: 8,9 # 13 pairs * PAIR C8: 8,9 ROW 8 I8: 8,9,2 # reduction candidate for 8,9 I8: 8,9 => CTR * 7..2.1.46.4.3.7.51.1.45...76.4132..5....741622.1.....45.7849.1.42.61357.1..7254.. I8: 2 => SOLVED * 785291346942367851316458297694132785853674129271589634527846913468913572139725468 * PAIR C8: 8,9 COL C C1: 8,9,3,5 # reduction candidate for 8,9 C1: 8,9 # 12 pairs C5: 8,9,3,5 # reduction candidate for 8,9 C5: 8,9 # 10 pairs * PAIR F7: 6,9 ROW 7 B7: 6,9,2,3 # reduction candidate for 6,9 B7: 6,9 => CTR * 7..2.1.46.4.3.7.51.1.45...76.4132..5....741622.1.....45.7849.1.42.61357.1..7254.. B7: 2,3 # 9 pairs G7: 6,9,2,3 # reduction candidate for 6,9 G7: 6,9 => SOLVED * 785291346942367851316458297694132785853674129271589634527846913468913572139725468 G7: 2,3 => CTR * 7..2.1.46.4.367.51.1645...76.41327.5...6741..2715..6345.7846.1.46.9135721..725468 * PAIR F7: 6,9 COL F F3: 6,9,8 # reduction candidate for 6,9 F3: 6,9 # 10 pairs F6: 6,9,8 # reduction candidate for 6,9 F6: 6,9 # 11 pairs * PAIR D8: 6,9 ROW 8 B8: 6,9,2,8 # reduction candidate for 6,9 B8: 6,9 => SOLVED * 785291346942367851316458297694132785853674129271589634527846913468913572139725468 B8: 2,8 => CTR * 7..2.1.46.4.3.7.51.1.45...76.4132..5....741622.1.....45.7849.1.4..61357.1..7254.. * PAIR D8: 6,9 COL D D5: 6,9,5 # reduction candidate for 6,9 D5: 6,9 # 9 pairs D6: 6,9,5 # reduction candidate for 6,9 D6: 6,9 => CTR * 7..2.1.46.4.3.7.51.1.45...76.4132..5...574162251...7.45.784..1.4...1357.1..7254.. D6: 5 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-307-base-pr-000.dot * REASONING * DIS # E2: 8,9 => CTR => E2: 6 * DIS # E2: 8,9 => CTR => E2: 6 * DIS # E6: 6 => CTR => E6: 8,9 * DIS # G4: 8,9 => CTR => G4: 7 * DIS # H5: 8,9 => CTR => H5: 2,3,6 * PRF # I5: 8,9 => SOL * DIS # B4: 7 => CTR => B4: 8,9 * PRF # H3: 8,9 => SOL * DIS # H9: 8,9 => CTR => H9: 3,6 * DIS # B8: 8,9 => CTR => B8: 2,6 * DIS # B9: 8,9 => CTR => B9: 3,6 * DIS # I8: 8,9 => CTR => I8: 2 * PRF # I8: 2 => SOL * DIS # B7: 6,9 => CTR => B7: 2,3 * PRF # G7: 6,9 => SOL * DIS # G7: 2,3 => CTR => G7: 6,9 * PRF # B8: 6,9 => SOL * DIS # B8: 2,8 => CTR => B8: 6,9 * DIS # D6: 6,9 => CTR => D6: 5 * CNT 19 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C2,C3,C8,D8,E1,F7,H4) * 7..2.1.46.4.3.7.51.1.45...76.4132..5....741..2.1.....45.784..1.4...1357.1..7254.. * PAIR A2: 8,9 BLK 1 B1: 8,9,3,5 # reduction candidate for 8,9 B1: 8,9 # 10 pairs C1: 8,9,3,5 # reduction candidate for 8,9 C1: 8,9 # 12 pairs A3: 8,9,3 # reduction candidate for 8,9 A3: 8,9 # 12 pairs * PAIR A2: 8,9 ROW 2 E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 => CTR * 7..2.1.46.463.7251.12456..76.4132..5....7412.2.1.68..45.784961.4..61357.16.7254.. * RESTART * PAIR A2: 8,9 COL A A5: 8,9,3 # reduction candidate for 8,9 A5: 3 # 19 pairs A5: 8,9 # 10 pairs * PAIR RESTART * PAIR A2: 8,9 BLK 1 B1: 8,9,3,5 # reduction candidate for 8,9 B1: 8,9 # 11 pairs C1: 8,9,3,5 # reduction candidate for 8,9 C1: 8,9 # 13 pairs A3: 8,9,3 # reduction candidate for 8,9 A3: 8,9 # 19 pairs * PAIR A2: 8,9 COL A A5: 8,9,3 # reduction candidate for 8,9 A5: 3 # 19 pairs A5: 8,9 # 10 pairs * PAIR E1: 8,9 ROW 1 B1: 8,9,3,5 # reduction candidate for 8,9 B1: 8,9 # 11 pairs C1: 8,9,3,5 # reduction candidate for 8,9 C1: 8,9 # 13 pairs G1: 8,9,3 # reduction candidate for 8,9 G1: 8,9 # 19 pairs * PAIR H4: 8,9 BLK 6 G4: 8,9,7 # reduction candidate for 8,9 G4: 8,9 => CTR * 7..2.1.46.42367.51.1645.2.7674132..5....741..2.1...7.45.784.61.4..61357.16.7254.. H5: 8,9,2,6 # reduction candidate for 8,9 H5: 8,9 => CTR * 7..2.1.46.42367.51.1645..276.41327.5...6741.22715...345.784621.4...1357.1..7254.. I5: 8,9,2 # reduction candidate for 8,9 I5: 8,9 => SOLVED * 785291346942367851316458297694132785853674129271589634527846913468913572139725468 * DURATION: 0:00:17.303941 START: 13:29:44.515306 END: 13:30:01.819247 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-307-base-pr-001.dot * REASONING * DIS # E2: 8,9 => CTR => E2: 6 * DIS E2: 6 # G4: 8,9 => CTR => G4: 7 * DIS E2: 6 + G4: 7 # H5: 8,9 => CTR => H5: 2,6 * PRF E2: 6 + G4: 7 + H5: 2,6 # I5: 8,9 => SOL * STA E2: 6 + G4: 7 + H5: 2,6 + I5: 8,9 * CNT 4 HDP CHAINS / 17 HYP OPENED
Header Info
Top 500 Minimum 17 307 solution: 785291346942367851316458297694132785853674129271589634527846913468913572139725468 info: 2649 FNBHWY S8.f 43281 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 785291346942367851316458297694132785853674129271589634527846913468913572139725468 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 # B1: 8,9 => UNS * INC # C1: 8,9 => UNS * INC # A3: 8,9 => UNS * DIS # E2: 8,9 => CTR => E2: 6 * INC # E2: 6 => UNS * INC # G2: 8,9 => UNS * INC # A5: 8,9 => UNS * INC # A5: 3 => UNS * DIS # E2: 8,9 => CTR => E2: 6 * INC # E2: 6 => UNS * INC # F3: 8,9 => UNS * INC # B1: 8,9 => UNS * INC # C1: 8,9 => UNS * INC # G1: 8,9 => UNS * INC # E6: 8,9 => UNS * DIS # E6: 6 => CTR => E6: 8,9 * DIS # G4: 8,9 => CTR => G4: 7 * INC # G4: 7 => UNS * DIS # H5: 8,9 => CTR => H5: 2,3,6 * INC # H5: 2,3,6 => UNS * PRF # I5: 8,9 => SOL * INC # I5: 2,3 => UNS * INC # B4: 8,9 => UNS * DIS # B4: 7 => CTR => B4: 8,9 * PRF # H3: 8,9 => SOL * INC # H3: 2,3 => UNS * DIS # H9: 8,9 => CTR => H9: 3,6 * INC # H9: 3,6 => UNS * DIS # B8: 8,9 => CTR => B8: 2,6 * INC # B8: 2,6 => UNS * DIS # B9: 8,9 => CTR => B9: 3,6 * INC # B9: 3,6 => UNS * INC # C9: 8,9 => UNS * DIS # I8: 8,9 => CTR => I8: 2 * PRF # I8: 2 => SOL * INC # C1: 8,9 => UNS * INC # C5: 8,9 => UNS * DIS # B7: 6,9 => CTR => B7: 2,3 * INC # B7: 2,3 => UNS * PRF # G7: 6,9 => SOL * DIS # G7: 2,3 => CTR => G7: 6,9 * INC # F3: 6,9 => UNS * INC # F6: 6,9 => UNS * PRF # B8: 6,9 => SOL * DIS # B8: 2,8 => CTR => B8: 6,9 * INC # D5: 6,9 => UNS * DIS # D6: 6,9 => CTR => D6: 5 * INC # D6: 5 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 8,9 => UNS * INC # C1: 8,9 => UNS * INC # A3: 8,9 => UNS * DIS # E2: 8,9 => CTR => E2: 6 * INC E2: 6 # A5: 8,9 => UNS * INC E2: 6 # A5: 3 => UNS * INC E2: 6 # B1: 8,9 => UNS * INC E2: 6 # C1: 8,9 => UNS * INC E2: 6 # A3: 8,9 => UNS * INC E2: 6 # A5: 8,9 => UNS * INC E2: 6 # A5: 3 => UNS * INC E2: 6 # B1: 8,9 => UNS * INC E2: 6 # C1: 8,9 => UNS * INC E2: 6 # G1: 8,9 => UNS * DIS E2: 6 # G4: 8,9 => CTR => G4: 7 * DIS E2: 6 + G4: 7 # H5: 8,9 => CTR => H5: 2,6 * PRF E2: 6 + G4: 7 + H5: 2,6 # I5: 8,9 => SOL * STA E2: 6 + G4: 7 + H5: 2,6 + I5: 8,9 * CNT 17 HDP CHAINS / 17 HYP OPENED