Analysis of xx-top500-073-base.sdk
Contents
Original Sudoku
level: medium
position: 4....6.5.......3.9...8........12.8..5..7.....6............5..4..8...3....1....... initial
Autosolve
position: 4....61588..5413.915.8......4.12583653876..1.62138....3...58.41.8..13....1.....83 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 7,9 => SOL * DIS # E1: 7,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # C2: 6,7 => CTR => C2: 2 * PRF # C2: 2 => SOL * PRF # B7: 6,7 => SOL * DIS # B7: 9 => CTR => B7: 6,7 * DIS # C1: 3,9 => CTR => C1: 2,7 * PRF # C1: 2,7 => SOL * DIS # C1: 2,9 => CTR => C1: 3,7 * PRF # C1: 3,7 => SOL * PRF # E1: 3,9 => SOL * DIS # E1: 7 => CTR => E1: 3,9 * PRF # H3: 2,7 => SOL * PRF # H3: 2,7 => SOL * DIS # C2: 6 => CTR => C2: 2,7 * DIS # A8: 7,9 => CTR => A8: 2 * PRF # A8: 2 => SOL * PRF # C1: 7,9 => SOL * DIS # C7: 7,9 => CTR => C7: 6 * DIS # G5: 2 => CTR => G5: 4,9 * DIS # G6: 4,9 => CTR => G6: 5,7 * DIS # G5: 9 => CTR => G5: 2,4 * DIS # I3: 7 => CTR => I3: 2,4 * DIS # H8: 7,9 => CTR => H8: 2,6 * PRF # A8: 2,9 => SOL * DIS # A8: 7 => CTR => A8: 2,9 * PRF # G7: 2,9 => SOL * DIS # G7: 7 => CTR => G7: 2,9 * DIS # E1: 7,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * CNT 32 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C1: 7,9 => SOL * STA C1: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4....6.5.......3.9...8........12.8..5..7.....6............5..4..8...3....1....... | initial |
| 4....61588..5413.915.8......4.12583653876..1.62138....3...58.41.8..13....1.....83 | autosolve |
| 497236158862541379153897624749125836538769412621384795376958241285413967914672583 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) B1: 7,9 B2: 6,7 C3: 3,9 D1: 2,9 E3: 3,9 F3: 2,7 H2: 2,7 A4: 7,9 C4: 7,9 F5: 4,9 F6: 4,9 I5: 2,4 H6: 7,9 C8: 4,5 A9: 2,9 C9: 4,5 D7: 2,9 D8: 4,6 D9: 4,6 E9: 7,9 F9: 2,7 G9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C2: 2.. / C1 = 2 => 0 pairs (X) / C2 = 2 => 0 pairs (_) D1,F3: 2.. / D1 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) G5,I5: 2.. / G5 = 2 => 0 pairs (X) / I5 = 2 => 24 pairs (_) A8,A9: 2.. / A8 = 2 => 0 pairs (*) / A9 = 2 => 0 pairs (X) D7,F9: 2.. / D7 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) C1,D1: 2.. / C1 = 2 => 0 pairs (X) / D1 = 2 => 0 pairs (_) C2,H2: 2.. / C2 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) D7,G7: 2.. / D7 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) A9,F9: 2.. / A9 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) D1,D7: 2.. / D1 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) F3,F9: 2.. / F3 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) C1,C3: 3.. / C1 = 3 => 0 pairs (X) / C3 = 3 => 0 pairs (_) E1,E3: 3.. / E1 = 3 => 0 pairs (*) / E3 = 3 => 0 pairs (X) C1,E1: 3.. / C1 = 3 => 0 pairs (X) / E1 = 3 => 0 pairs (_) C3,E3: 3.. / C3 = 3 => 0 pairs (*) / E3 = 3 => 0 pairs (X) G3,I3: 4.. / G3 = 4 => 24 pairs (_) / I3 = 4 => 24 pairs (_) F5,F6: 4.. / F5 = 4 => 0 pairs (X) / F6 = 4 => 22 pairs (_) C8,C9: 4.. / C8 = 4 => 17 pairs (_) / C9 = 4 => 18 pairs (_) D8,D9: 4.. / D8 = 4 => 18 pairs (_) / D9 = 4 => 17 pairs (_) C8,D8: 4.. / C8 = 4 => 17 pairs (_) / D8 = 4 => 18 pairs (_) C9,D9: 4.. / C9 = 4 => 18 pairs (_) / D9 = 4 => 17 pairs (_) G6,I6: 5.. / G6 = 5 => 18 pairs (_) / I6 = 5 => 23 pairs (_) C8,C9: 5.. / C8 = 5 => 18 pairs (_) / C9 = 5 => 17 pairs (_) C9,G9: 5.. / C9 = 5 => 17 pairs (_) / G9 = 5 => 18 pairs (_) I6,I8: 5.. / I6 = 5 => 23 pairs (_) / I8 = 5 => 18 pairs (_) B2,C2: 6.. / B2 = 6 => 23 pairs (_) / C2 = 6 => 0 pairs (X) G3,H3: 6.. / G3 = 6 => 0 pairs (*) / H3 = 6 => 0 pairs (X) B7,C7: 6.. / B7 = 6 => 0 pairs (X) / C7 = 6 => 23 pairs (_) D8,D9: 6.. / D8 = 6 => 17 pairs (_) / D9 = 6 => 18 pairs (_) D9,G9: 6.. / D9 = 6 => 18 pairs (_) / G9 = 6 => 17 pairs (_) B2,B7: 6.. / B2 = 6 => 23 pairs (_) / B7 = 6 => 0 pairs (X) C2,C7: 6.. / C2 = 6 => 0 pairs (X) / C7 = 6 => 23 pairs (_) H3,H8: 6.. / H3 = 6 => 22 pairs (_) / H8 = 6 => 0 pairs (*) E1,F3: 7.. / E1 = 7 => 0 pairs (X) / F3 = 7 => 0 pairs (_) A4,C4: 7.. / A4 = 7 => 0 pairs (*) / C4 = 7 => 0 pairs (X) E9,F9: 7.. / E9 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) A4,A8: 7.. / A4 = 7 => 0 pairs (*) / A8 = 7 => 0 pairs (X) E1,E9: 7.. / E1 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) F3,F9: 7.. / F3 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) A4,C4: 9.. / A4 = 9 => 0 pairs (X) / C4 = 9 => 0 pairs (_) F5,F6: 9.. / F5 = 9 => 22 pairs (_) / F6 = 9 => 0 pairs (X) D7,E9: 9.. / D7 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) C3,E3: 9.. / C3 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) F5,G5: 9.. / F5 = 9 => 22 pairs (_) / G5 = 9 => 0 pairs (X) A9,E9: 9.. / A9 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) B1,B7: 9.. / B1 = 9 => 0 pairs (*) / B7 = 9 => 0 pairs (X) D1,D7: 9.. / D1 = 9 => 0 pairs (X) / D7 = 9 => 0 pairs (_) H6,H8: 9.. / H6 = 9 => 22 pairs (_) / H8 = 9 => 0 pairs (X) * DURATION: 0:01:33.288810 START: 05:11:42.136671 END: 05:13:15.425481 2017-05-04 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B1,B2,C3,C4,C8,C9,D1,D7,D8,D9,E3,E9,F3,F5,F6,F9,G9,H2,H6,I5) * 4....61588..5413.915.8......4.12583653876..1.62138....3...58.41.8..13....1.....83 * PAIR B1: 7,9 BLK 1 C1: 7,9,2,3 # reduction candidate for 7,9 C1: 7,9 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 C1: 2,3 # 23 pairs * PAIR B1: 7,9 ROW 1 E1: 7,9,3 # reduction candidate for 7,9 E1: 7,9 => CTR * 4.32.61588.2541379159837...94712583653876..1.62138..9.39..58.41.8..13....1.....83 E1: 3 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 * PAIR B1: 7,9 COL B B7: 7,9,6 # reduction candidate for 7,9 B7: 6 => CTR * 49.2.615887.5413.915.8......4.12583653876..1.62138....3...58.41.8..13....1.....83 B7: 7,9 # 23 pairs * PAIR B2: 6,7 BLK 1 C2: 6,7,2 # reduction candidate for 6,7 C2: 6,7 => CTR * 4.29361588..5413.915.8......4.12583653876..1.62138....3...58.41.8..13....1.....83 C2: 2 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 * PAIR B2: 6,7 COL B B7: 6,7,9 # reduction candidate for 6,7 B7: 6,7 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 B7: 9 => CTR * 472..615886.5413.915.8......4.12583653876..1.62138....39625874178..13...21..97.83 * PAIR C3: 3,9 BLK 1 C1: 3,9,2,7 # reduction candidate for 3,9 C1: 3,9 => CTR * 4..2.61588.254137915.8.7....4.12583653876..1.62138..9.3.695824128..1396791.672583 C1: 2,7 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 * PAIR D1: 2,9 ROW 1 C1: 2,9,3,7 # reduction candidate for 2,9 C1: 2,9 => CTR * 4...361588..5413.9153897....4.12583653876..1.62138....3..95824128..13...91..72.83 C1: 3,7 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 * PAIR E3: 3,9 BLK 2 E1: 3,9,7 # reduction candidate for 3,9 E1: 3,9 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 E1: 7 => CTR * 4.32761588..5413.915.8......4.12583653876..1.62138....3...58.41.8..13....1.....83 * PAIR F3: 2,7 ROW 3 G3: 2,7,4,6 # reduction candidate for 2,7 G3: 2,7 # 25 pairs H3: 2,7,6 # reduction candidate for 2,7 H3: 2,7 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 H3: 6 # 22 pairs I3: 2,7,4 # reduction candidate for 2,7 I3: 2,7 # 24 pairs * PAIR H2: 2,7 BLK 3 G3: 2,7,4,6 # reduction candidate for 2,7 G3: 2,7 # 25 pairs H3: 2,7,6 # reduction candidate for 2,7 H3: 2,7 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 H3: 6 # 22 pairs I3: 2,7,4 # reduction candidate for 2,7 I3: 2,7 # 24 pairs * PAIR H2: 2,7 ROW 2 C2: 2,7,6 # reduction candidate for 2,7 C2: 6 => CTR * 4.29361588..5413.915.8......4.12583653876..1.62138....3...58.41.8..13....1.....83 C2: 2,7 # 23 pairs * PAIR H2: 2,7 COL H H8: 2,7,6,9 # reduction candidate for 2,7 H8: 6,9 # 24 pairs H8: 2,7 # 23 pairs * PAIR A4: 7,9 COL A A8: 7,9,2 # reduction candidate for 7,9 A8: 7,9 => CTR * 4..9761588..5413.915.8......4.12583653876..1.62138....3...58.41.8..13...21..97.83 A8: 2 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 * PAIR C4: 7,9 COL C C1: 7,9,2,3 # reduction candidate for 7,9 C1: 7,9 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 C1: 2,3 # 23 pairs C7: 7,9,6 # reduction candidate for 7,9 C7: 7,9 => CTR * 49...61588.654132915.8.2....4.12583653876..1.62138....36.258.41.8..13...21..97.83 C7: 6 # 23 pairs * PAIR F5: 4,9 ROW 5 G5: 4,9,2 # reduction candidate for 4,9 G5: 2 => CTR * 4.29.61588..5413.915.8......4.125836538769214621384...3..258.41.8..13...21..97.83 G5: 4,9 # 24 pairs * PAIR F6: 4,9 ROW 6 G6: 4,9,5,7 # reduction candidate for 4,9 G6: 4,9 => CTR * 4.29.61588..54132915.8.2.6..4.12583653876..1.62138..753..25874178..13.9221..97.83 G6: 5,7 # 23 pairs * PAIR I5: 2,4 BLK 6 G5: 2,4,9 # reduction candidate for 2,4 G5: 9 => CTR * 4.29.61588..54132915.8.2.6..4.125836538764912621389.7.3..25874178..13295215497683 G5: 2,4 # 22 pairs * PAIR I5: 2,4 COL I I3: 2,4,7 # reduction candidate for 2,4 I3: 7 => CTR * 4...761588..54132915.832467.4.12583653876..1.62138....3..258.41.8..13...21..97.83 I3: 2,4 # 25 pairs * PAIR H6: 7,9 BLK 6 G6: 7,9,4,5 # reduction candidate for 7,9 G6: 7,9 # 23 pairs G6: 4,5 # 23 pairs * PAIR H6: 7,9 COL H H8: 7,9,2,6 # reduction candidate for 7,9 H8: 7,9 => CTR * 4.29.61588..54132915.8.2.6..4.12583653876..1.62138....3..258.41.8..13...21..97.83 H8: 2,6 # 25 pairs * PAIR A9: 2,9 BLK 7 A8: 2,9,7 # reduction candidate for 2,9 A8: 2,9 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 A8: 7 => CTR * 4..9761588..5413.915.8......4.12583653876..1.62138....3...58.4178..13...21..97.83 * PAIR D7: 2,9 ROW 7 G7: 2,9,7 # reduction candidate for 2,9 G7: 2,9 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 G7: 7 => CTR * 4.29.61588..5413.915.8......4.12583653876..1.62138....3..25874178..13...21..97.83 * PAIR E9: 7,9 COL E E1: 7,9,3 # reduction candidate for 7,9 E1: 7,9 => CTR * 4.32.61588.2541379159837...94712583653876..1.62138..9.39..58.41.8..13....1.....83 E1: 3 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 * PAIR G9: 5,6 BLK 9 G8: 5,6,2,7,9 # reduction candidate for 5,6 G8: 5,6 # 24 pairs G8: 2,7,9 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-073-base-pr-000.dot * REASONING * PRF # C1: 7,9 => SOL * DIS # E1: 7,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * DIS # B7: 6 => CTR => B7: 7,9 * DIS # C2: 6,7 => CTR => C2: 2 * PRF # C2: 2 => SOL * PRF # B7: 6,7 => SOL * DIS # B7: 9 => CTR => B7: 6,7 * DIS # C1: 3,9 => CTR => C1: 2,7 * PRF # C1: 2,7 => SOL * DIS # C1: 2,9 => CTR => C1: 3,7 * PRF # C1: 3,7 => SOL * PRF # E1: 3,9 => SOL * DIS # E1: 7 => CTR => E1: 3,9 * PRF # H3: 2,7 => SOL * PRF # H3: 2,7 => SOL * DIS # C2: 6 => CTR => C2: 2,7 * DIS # A8: 7,9 => CTR => A8: 2 * PRF # A8: 2 => SOL * PRF # C1: 7,9 => SOL * DIS # C7: 7,9 => CTR => C7: 6 * DIS # G5: 2 => CTR => G5: 4,9 * DIS # G6: 4,9 => CTR => G6: 5,7 * DIS # G5: 9 => CTR => G5: 2,4 * DIS # I3: 7 => CTR => I3: 2,4 * DIS # H8: 7,9 => CTR => H8: 2,6 * PRF # A8: 2,9 => SOL * DIS # A8: 7 => CTR => A8: 2,9 * PRF # G7: 2,9 => SOL * DIS # G7: 7 => CTR => G7: 2,9 * DIS # E1: 7,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * CNT 32 HDP CHAINS / 54 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B1,B2,C3,C4,C8,C9,D1,D7,D8,D9,E3,E9,F3,F5,F6,F9,G9,H2,H6,I5) * 4....61588..5413.915.8......4.12583653876..1.62138....3...58.41.8..13....1.....83 * PAIR B1: 7,9 BLK 1 C1: 7,9,2,3 # reduction candidate for 7,9 C1: 7,9 => SOLVED * 497236158862541379153897624749125836538769412621384795376958241285413967914672583 * DURATION: 0:00:02.433765 START: 05:14:17.780094 END: 05:14:20.213859 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-073-base-pr-001.dot * REASONING * PRF # C1: 7,9 => SOL * STA C1: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 073 solution: 497236158862541379153897624749125836538769412621384795376958241285413967914672583 info: 1473 FNBTHWXY S8.f 30577 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 497236158862541379153897624749125836538769412621384795376958241285413967914672583 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:
* PRF # C1: 7,9 => SOL * INC # C1: 2,3 => UNS * DIS # E1: 7,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * INC # B7: 7,9 => UNS * DIS # B7: 6 => CTR => B7: 7,9 * DIS # C2: 6,7 => CTR => C2: 2 * PRF # C2: 2 => SOL * PRF # B7: 6,7 => SOL * DIS # B7: 9 => CTR => B7: 6,7 * DIS # C1: 3,9 => CTR => C1: 2,7 * PRF # C1: 2,7 => SOL * DIS # C1: 2,9 => CTR => C1: 3,7 * PRF # C1: 3,7 => SOL * PRF # E1: 3,9 => SOL * DIS # E1: 7 => CTR => E1: 3,9 * INC # G3: 2,7 => UNS * PRF # H3: 2,7 => SOL * INC # H3: 6 => UNS * INC # I3: 2,7 => UNS * INC # G3: 2,7 => UNS * PRF # H3: 2,7 => SOL * INC # H3: 6 => UNS * INC # I3: 2,7 => UNS * INC # C2: 2,7 => UNS * DIS # C2: 6 => CTR => C2: 2,7 * INC # H8: 2,7 => UNS * INC # H8: 6,9 => UNS * DIS # A8: 7,9 => CTR => A8: 2 * PRF # A8: 2 => SOL * PRF # C1: 7,9 => SOL * INC # C1: 2,3 => UNS * DIS # C7: 7,9 => CTR => C7: 6 * INC # C7: 6 => UNS * INC # G5: 4,9 => UNS * DIS # G5: 2 => CTR => G5: 4,9 * DIS # G6: 4,9 => CTR => G6: 5,7 * INC # G6: 5,7 => UNS * INC # G5: 2,4 => UNS * DIS # G5: 9 => CTR => G5: 2,4 * INC # I3: 2,4 => UNS * DIS # I3: 7 => CTR => I3: 2,4 * INC # G6: 7,9 => UNS * INC # G6: 4,5 => UNS * DIS # H8: 7,9 => CTR => H8: 2,6 * INC # H8: 2,6 => UNS * PRF # A8: 2,9 => SOL * DIS # A8: 7 => CTR => A8: 2,9 * PRF # G7: 2,9 => SOL * DIS # G7: 7 => CTR => G7: 2,9 * DIS # E1: 7,9 => CTR => E1: 3 * PRF # E1: 3 => SOL * INC # G8: 5,6 => UNS * INC # G8: 2,7,9 => UNS * CNT 54 HDP CHAINS / 54 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 7,9 => SOL * STA C1: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED