Contents
level: medium
The following important HDP chains were detected:
* DIS # A3: 4,7 => CTR => A3: 5,8,9 * PRF # A3: 5,8,9 => SOL * DIS # B3: 4,7 => CTR => B3: 1,5,6,8,9 * DIS # H1: 4,7 => CTR => H1: 2 * PRF # H1: 2 => SOL * PRF # B8: 4,7 => SOL * PRF # H1: 2,4 => SOL * DIS # H1: 7 => CTR => H1: 2,4 * DIS # C9: 2,4 => CTR => C9: 5,6,8,9 * DIS # B5: 8,9 => CTR => B5: 1,4,5 * DIS # A2: 8,9 => CTR => A2: 2,5 * DIS # A3: 8,9 => CTR => A3: 4,5,7 * DIS # A8: 8,9 => CTR => A8: 4,7 * PRF # A9: 8,9 => SOL * DIS # E5: 2,9 => CTR => E5: 4 * PRF # E5: 4 => SOL * DIS # H5: 2,9 => CTR => H5: 8 * PRF # I5: 2,9 => SOL * DIS # F9: 2,9 => CTR => F9: 5,6,8 * DIS # F7: 5 => CTR => F7: 2,7 * PRF # F7: 5,7 => SOL * DIS # F7: 2 => CTR => F7: 5,7 * DIS # B3: 5,7 => CTR => B3: 1,4,6,8,9 * DIS # A9: 2,5 => CTR => A9: 4,8,9 * PRF # A9: 4,8,9 => SOL * DIS # C9: 2,5 => CTR => C9: 4,6,8,9 * DIS # F7: 2,5 => CTR => F7: 7 * PRF # F7: 7 => SOL * DIS # C2: 2,5 => CTR => C2: 1,6,8,9 * CNT 29 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
The following important HDP chains were detected:
* DIS # A3: 4,7 => CTR => A3: 5,8,9 * PRF A3: 5,8,9 => SOL * STA A3: 5,8,9 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
3.......1...7.4......2......2.5..4..6.7..........8..3.1...3..........25.......7.. | initial |
3.......1...7.43.....2.3....235.14..6.73.........8..3.1...3.......1..25.......71. | autosolve |
374958621281764395569213874823571469617349582495682137152837946748196253936425718 | solved |
level: medium
-------------------------------------------------- * PAIRS (8) B1: 4,7 C1: 2,4 A4: 8,9 F5: 2,9 F6: 2,7 I6: 2,7 B7: 5,7 C7: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 1.. / E2 = 1 => 8 pairs (_) / E3 = 1 => 8 pairs (_) G5,G6: 1.. / G5 = 1 => 8 pairs (_) / G6 = 1 => 0 pairs (*) B5,G5: 1.. / B5 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) C1,H1: 2.. / C1 = 2 => 0 pairs (X) / H1 = 2 => 0 pairs (_) F6,I6: 2.. / F6 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) C7,F7: 2.. / C7 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) A2,A9: 2.. / A2 = 2 => 0 pairs (*) / A9 = 2 => 0 pairs (X) E5,E9: 2.. / E5 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) B8,B9: 3.. / B8 = 3 => 8 pairs (_) / B9 = 3 => 8 pairs (_) I8,I9: 3.. / I8 = 3 => 8 pairs (_) / I9 = 3 => 8 pairs (_) B8,I8: 3.. / B8 = 3 => 8 pairs (_) / I8 = 3 => 8 pairs (_) B9,I9: 3.. / B9 = 3 => 8 pairs (_) / I9 = 3 => 8 pairs (_) E5,D6: 4.. / E5 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) B5,E5: 4.. / B5 = 4 => 0 pairs (X) / E5 = 4 => 0 pairs (_) E4,D6: 6.. / E4 = 6 => 0 pairs (X) / D6 = 6 => 0 pairs (_) D6,G6: 6.. / D6 = 6 => 0 pairs (*) / G6 = 6 => 0 pairs (X) E4,F6: 7.. / E4 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) B1,H1: 7.. / B1 = 7 => 0 pairs (*) / H1 = 7 => 0 pairs (X) F6,I6: 7.. / F6 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) B7,F7: 7.. / B7 = 7 => 0 pairs (X) / F7 = 7 => 0 pairs (_) A3,A8: 7.. / A3 = 7 => 0 pairs (X) / A8 = 7 => 0 pairs (_) E4,E8: 7.. / E4 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) D1,F1: 8.. / D1 = 8 => 8 pairs (_) / F1 = 8 => 9 pairs (_) A4,B5: 8.. / A4 = 8 => 7 pairs (_) / B5 = 8 => 0 pairs (X) * DURATION: 0:00:42.609743 START: 06:17:49.169547 END: 06:18:31.779290 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B7,C1,C7,F5,F6,I6) * 3.......1...7.43.....2.3....235.14..6.73.........8..3.1...3.......1..25.......71. * PAIR B1: 4,7 BLK 1 A3: 4,7,5,8,9 # reduction candidate for 4,7 A3: 4,7 => CTR * 342....71...7.432.7..2.3...823561497617329.85...487632175.32......17.25.2...4571. A3: 5,8,9 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 B3: 4,7,1,5,6,8,9 # reduction candidate for 4,7 B3: 4,7 => CTR * 3.2.....1...7.43.....2.3....235.14..6.734........8..3.15..3.......1..25.......71. B3: 1,5,6,8,9 # 8 pairs * PAIR B1: 4,7 ROW 1 H1: 4,7,2 # reduction candidate for 4,7 H1: 4,7 => CTR * 342....71...7.432.7..2.3...823561497617329.85...487632175.32......17.25.2...4571. H1: 2 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 * PAIR B1: 4,7 COL B B8: 4,7,3,6,8,9 # reduction candidate for 4,7 B8: 4,7 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 B8: 3,6,8,9 # 8 pairs * PAIR C1: 2,4 ROW 1 H1: 2,4,7 # reduction candidate for 2,4 H1: 2,4 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 H1: 7 => CTR * 342....71...7.43.....2.3....235.14..6.73.........8..3.1.5.32......1..25.2.....71. * PAIR C1: 2,4 COL C C9: 2,4,5,6,8,9 # reduction candidate for 2,4 C9: 2,4 => CTR * 342.....1...7.43.....2.3....235.14..6.7329.85...487632175.32......17.25.....4571. C9: 5,6,8,9 # 8 pairs * PAIR A4: 8,9 BLK 4 B5: 8,9,1,4,5 # reduction candidate for 8,9 B5: 8,9 => CTR * 3.4....212..7.43.....2.3....235.14..6.73421.5....87.32172.3.......1..25.....2.71. B5: 1,4,5 # 8 pairs * PAIR A4: 8,9 ROW 4 H4: 8,9,6,7 # reduction candidate for 8,9 H4: 8,9 # 11 pairs I4: 8,9,6,7 # reduction candidate for 8,9 I4: 8,9 # 11 pairs * PAIR A4: 8,9 COL A A2: 8,9,2,5 # reduction candidate for 8,9 A2: 8,9 => CTR * 342....71...7.432.7..2.3...823561497617329.85...487632175.32......17.25.2...4571. A2: 2,5 # 9 pairs A3: 8,9,4,5,7 # reduction candidate for 8,9 A3: 8,9 => CTR * 3.4....212..7.43.....2.3.74.235714..6.7349.8254.682.37152.37.4.7..1..25.4...2571. A3: 4,5,7 # 8 pairs A8: 8,9,4,7 # reduction candidate for 8,9 A8: 8,9 => CTR * 342....71...7.43..7..2.3....235.14..6.734........8..3.1.5.32......1..25.2.....71. A8: 4,7 # 9 pairs A9: 8,9,2,4,5 # reduction candidate for 8,9 A9: 8,9 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 A9: 2,4,5 # 8 pairs * PAIR F5: 2,9 BLK 5 E5: 2,9,4 # reduction candidate for 2,9 E5: 2,9 => CTR * 37......1...7.43.....2.3...8235614..6473..185...487632152.3.......1..25.......71. E5: 4 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 * PAIR F5: 2,9 ROW 5 H5: 2,9,8 # reduction candidate for 2,9 H5: 2,9 => CTR * 3.4....212..7.43.....2.3....235.14..6.7342.9.....87.32172.3.......1..25.....2.71. H5: 8 # 7 pairs I5: 2,9,5,8 # reduction candidate for 2,9 I5: 2,9 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 I5: 5,8 # 9 pairs * PAIR F5: 2,9 COL F F9: 2,9,5,6,8 # reduction candidate for 2,9 F9: 2,9 => CTR * 3.......1...7.43.....2.3....235.14..6.73.........87.32172.35......17.25.......71. F9: 5,6,8 # 8 pairs * PAIR F6: 2,7 COL F F7: 2,7,5 # reduction candidate for 2,7 F7: 5 => CTR * 3.......1...7.43.....2.3....235.14..6.73.........8..3.172.35......1..25.......71. F7: 2,7 # 13 pairs * PAIR B7: 5,7 ROW 7 F7: 5,7,2 # reduction candidate for 5,7 F7: 5,7 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 F7: 2 => CTR * 342....71...7.43..7..2.3....235.14..6.73.........8..3.175.32......1..25.......71. * PAIR B7: 5,7 COL B B3: 5,7,1,4,6,8,9 # reduction candidate for 5,7 B3: 5,7 => CTR * 342....71...7.43.....2.3....235.14..6.734........8..3.1.5.32......1..25.2.....71. B3: 1,4,6,8,9 # 8 pairs * PAIR C7: 2,5 BLK 7 A9: 2,5,4,8,9 # reduction candidate for 2,5 A9: 2,5 => CTR * 342....71...7.43..7..2.3....235.14..6.734........8..3.175.32......1..25.2.....71. A9: 4,8,9 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 C9: 2,5,4,6,8,9 # reduction candidate for 2,5 C9: 2,5 => CTR * 3.4....212..7.43.....2.3....235.14..6.73.........8..3.17..3.......1..25.......71. C9: 4,6,8,9 # 8 pairs * PAIR C7: 2,5 ROW 7 F7: 2,5,7 # reduction candidate for 2,5 F7: 2,5 => CTR * 342....71...7.43..7..2.3....235.14..6.734........8..3.175.32......1..25.2.....71. F7: 7 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 * PAIR C7: 2,5 COL C C2: 2,5,1,6,8,9 # reduction candidate for 2,5 C2: 2,5 => CTR * 374....212.57.43.....2.3.74.235714..6.734....5..682.37152.37...7..1..25.4...2571. C2: 1,6,8,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-103-base-pr-000.dot * REASONING * DIS # A3: 4,7 => CTR => A3: 5,8,9 * PRF # A3: 5,8,9 => SOL * DIS # B3: 4,7 => CTR => B3: 1,5,6,8,9 * DIS # H1: 4,7 => CTR => H1: 2 * PRF # H1: 2 => SOL * PRF # B8: 4,7 => SOL * PRF # H1: 2,4 => SOL * DIS # H1: 7 => CTR => H1: 2,4 * DIS # C9: 2,4 => CTR => C9: 5,6,8,9 * DIS # B5: 8,9 => CTR => B5: 1,4,5 * DIS # A2: 8,9 => CTR => A2: 2,5 * DIS # A3: 8,9 => CTR => A3: 4,5,7 * DIS # A8: 8,9 => CTR => A8: 4,7 * PRF # A9: 8,9 => SOL * DIS # E5: 2,9 => CTR => E5: 4 * PRF # E5: 4 => SOL * DIS # H5: 2,9 => CTR => H5: 8 * PRF # I5: 2,9 => SOL * DIS # F9: 2,9 => CTR => F9: 5,6,8 * DIS # F7: 5 => CTR => F7: 2,7 * PRF # F7: 5,7 => SOL * DIS # F7: 2 => CTR => F7: 5,7 * DIS # B3: 5,7 => CTR => B3: 1,4,6,8,9 * DIS # A9: 2,5 => CTR => A9: 4,8,9 * PRF # A9: 4,8,9 => SOL * DIS # C9: 2,5 => CTR => C9: 4,6,8,9 * DIS # F7: 2,5 => CTR => F7: 7 * PRF # F7: 7 => SOL * DIS # C2: 2,5 => CTR => C2: 1,6,8,9 * CNT 29 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B7,C1,C7,F5,F6,I6) * 3.......1...7.43.....2.3....235.14..6.73.........8..3.1...3.......1..25.......71. * PAIR B1: 4,7 BLK 1 A3: 4,7,5,8,9 # reduction candidate for 4,7 A3: 4,7 => CTR * 342....71...7.432.7..2.3...823561497617329.85...487632175.32......17.25.2...4571. A3: 5,8,9 => SOLVED * 374958621281764395569213874823571469617349582495682137152837946748196253936425718 * DURATION: 0:00:02.151520 START: 06:19:17.164985 END: 06:19:19.316505 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-103-base-pr-001.dot * REASONING * DIS # A3: 4,7 => CTR => A3: 5,8,9 * PRF A3: 5,8,9 => SOL * STA A3: 5,8,9 * CNT 2 HDP CHAINS / 1 HYP OPENED
Top 500 Minimum 17 103 solution: 374958621281764395569213874823571469617349582495682137152837946748196253936425718 info: 1613 FNBHXY S8.f 28614 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
See section Pair Reduction for the HDP chains leading to this result.
Full list of HDP chains traversed:
* DIS # A3: 4,7 => CTR => A3: 5,8,9 * PRF # A3: 5,8,9 => SOL * DIS # B3: 4,7 => CTR => B3: 1,5,6,8,9 * INC # B3: 1,5,6,8,9 => UNS * DIS # H1: 4,7 => CTR => H1: 2 * PRF # H1: 2 => SOL * PRF # B8: 4,7 => SOL * INC # B8: 3,6,8,9 => UNS * PRF # H1: 2,4 => SOL * DIS # H1: 7 => CTR => H1: 2,4 * DIS # C9: 2,4 => CTR => C9: 5,6,8,9 * INC # C9: 5,6,8,9 => UNS * DIS # B5: 8,9 => CTR => B5: 1,4,5 * INC # B5: 1,4,5 => UNS * INC # H4: 8,9 => UNS * INC # I4: 8,9 => UNS * DIS # A2: 8,9 => CTR => A2: 2,5 * INC # A2: 2,5 => UNS * DIS # A3: 8,9 => CTR => A3: 4,5,7 * INC # A3: 4,5,7 => UNS * DIS # A8: 8,9 => CTR => A8: 4,7 * INC # A8: 4,7 => UNS * PRF # A9: 8,9 => SOL * INC # A9: 2,4,5 => UNS * DIS # E5: 2,9 => CTR => E5: 4 * PRF # E5: 4 => SOL * DIS # H5: 2,9 => CTR => H5: 8 * INC # H5: 8 => UNS * PRF # I5: 2,9 => SOL * INC # I5: 5,8 => UNS * DIS # F9: 2,9 => CTR => F9: 5,6,8 * INC # F9: 5,6,8 => UNS * INC # F7: 2,7 => UNS * DIS # F7: 5 => CTR => F7: 2,7 * PRF # F7: 5,7 => SOL * DIS # F7: 2 => CTR => F7: 5,7 * DIS # B3: 5,7 => CTR => B3: 1,4,6,8,9 * INC # B3: 1,4,6,8,9 => UNS * DIS # A9: 2,5 => CTR => A9: 4,8,9 * PRF # A9: 4,8,9 => SOL * DIS # C9: 2,5 => CTR => C9: 4,6,8,9 * INC # C9: 4,6,8,9 => UNS * DIS # F7: 2,5 => CTR => F7: 7 * PRF # F7: 7 => SOL * DIS # C2: 2,5 => CTR => C2: 1,6,8,9 * INC # C2: 1,6,8,9 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
Full list of HDP chains traversed:
* DIS # A3: 4,7 => CTR => A3: 5,8,9 * PRF A3: 5,8,9 => SOL * STA A3: 5,8,9 * CNT 2 HDP CHAINS / 1 HYP OPENED