Analysis of xx-top500-201-base.sdk
Contents
Original Sudoku
level: medium
position: .8.....9.4...3..............9.8...6..5..4......1......2.....3.4...5..2..3..9..... initial
Autosolve
position: 5832..49.41..3982592.4...3.7948.2.6365234.9..831.9..422691..354148563279375924... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I3: 6,7 => CTR => I3: 1 * PRF # F1: 1,7 => SOL * DIS # F1: 6 => CTR => F1: 1,7 * PRF # F1: 6,7 => SOL * DIS # F1: 1 => CTR => F1: 6,7 * DIS # I3: 6,7 => CTR => I3: 1 * PRF # F1: 6,7 => SOL * DIS # F1: 1 => CTR => F1: 6,7 * DIS # I5: 8 => CTR => I5: 1,7 * PRF # F1: 1,7 => SOL * DIS # F1: 6 => CTR => F1: 1,7 * PRF # F6: 6,7 => SOL * DIS # F6: 5 => CTR => F6: 6,7 * DIS # I5: 1,8 => CTR => I5: 7 * PRF # I5: 7 => SOL * DIS # F6: 5,7 => CTR => F6: 6 * PRF # F6: 6 => SOL * DIS # I9: 1,6 => CTR => I9: 8 * DIS # G3: 1,6 => CTR => G3: 7 * PRF # G3: 7 => SOL * DIS # I9: 6 => CTR => I9: 1,8 * CNT 21 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I3: 6,7 => CTR => I3: 1 * PRF I3: 1 # F1: 1,7 => SOL * STA I3: 1 + F1: 1,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.....9.4...3..............9.8...6..5..4......1......2.....3.4...5..2..3..9..... | initial |
| 5832..49.41..3982592.4...3.7948.2.6365234.9..831.9..422691..354148563279375924... | autosolve |
| 583217496417639825926485731794852163652341987831796542269178354148563279375924618 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C2: 6,7 C3: 6,7 E1: 1,7 D2: 6,7 E3: 5,8 F3: 5,8 I1: 6,7 E4: 1,5 F5: 1,7 D6: 6,7 G4: 1,5 H5: 1,8 G6: 5,7 E7: 7,8 F7: 7,8 G9: 1,6 H9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 1.. / E1 = 1 => 0 pairs (*) / F1 = 1 => 0 pairs (X) G3,I3: 1.. / G3 = 1 => 0 pairs (X) / I3 = 1 => 20 pairs (_) E4,F5: 1.. / E4 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) E4,G4: 1.. / E4 = 1 => 0 pairs (X) / G4 = 1 => 0 pairs (_) E1,E4: 1.. / E1 = 1 => 0 pairs (*) / E4 = 1 => 0 pairs (X) F1,F5: 1.. / F1 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) H5,H9: 1.. / H5 = 1 => 0 pairs (X) / H9 = 1 => 16 pairs (_) E3,F3: 5.. / E3 = 5 => 0 pairs (X) / F3 = 5 => 0 pairs (_) E4,F6: 5.. / E4 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) G4,G6: 5.. / G4 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) E4,G4: 5.. / E4 = 5 => 0 pairs (*) / G4 = 5 => 0 pairs (X) F6,G6: 5.. / F6 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) E3,E4: 5.. / E3 = 5 => 0 pairs (X) / E4 = 5 => 0 pairs (_) F3,F6: 5.. / F3 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) C2,C3: 6.. / C2 = 6 => 0 pairs (X) / C3 = 6 => 0 pairs (_) F1,D2: 6.. / F1 = 6 => 0 pairs (X) / D2 = 6 => 0 pairs (_) D6,F6: 6.. / D6 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) G9,I9: 6.. / G9 = 6 => 18 pairs (_) / I9 = 6 => 0 pairs (X) F1,I1: 6.. / F1 = 6 => 0 pairs (X) / I1 = 6 => 0 pairs (_) C2,D2: 6.. / C2 = 6 => 0 pairs (X) / D2 = 6 => 0 pairs (_) D2,D6: 6.. / D2 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) F1,F6: 6.. / F1 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) G3,G9: 6.. / G3 = 6 => 0 pairs (X) / G9 = 6 => 18 pairs (_) C2,C3: 7.. / C2 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) I5,G6: 7.. / I5 = 7 => 0 pairs (*) / G6 = 7 => 0 pairs (X) E7,F7: 7.. / E7 = 7 => 0 pairs (*) / F7 = 7 => 0 pairs (X) C2,D2: 7.. / C2 = 7 => 0 pairs (*) / D2 = 7 => 0 pairs (X) F5,I5: 7.. / F5 = 7 => 0 pairs (X) / I5 = 7 => 0 pairs (_) D2,D6: 7.. / D2 = 7 => 0 pairs (X) / D6 = 7 => 0 pairs (_) E1,E7: 7.. / E1 = 7 => 0 pairs (X) / E7 = 7 => 0 pairs (_) G3,G6: 7.. / G3 = 7 => 0 pairs (*) / G6 = 7 => 0 pairs (X) E3,F3: 8.. / E3 = 8 => 0 pairs (*) / F3 = 8 => 0 pairs (X) H5,I5: 8.. / H5 = 8 => 16 pairs (_) / I5 = 8 => 0 pairs (X) E7,F7: 8.. / E7 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) H9,I9: 8.. / H9 = 8 => 0 pairs (X) / I9 = 8 => 16 pairs (_) E3,E7: 8.. / E3 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) F3,F7: 8.. / F3 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) H5,H9: 8.. / H5 = 8 => 16 pairs (_) / H9 = 8 => 0 pairs (X) I5,I9: 8.. / I5 = 8 => 0 pairs (X) / I9 = 8 => 16 pairs (_) * DURATION: 0:01:13.569464 START: 09:39:18.892712 END: 09:40:32.462176 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C3,D2,D6,E1,E3,E4,E7,F3,F5,F7,G4,G6,G9,H5,H9,I1) * 5832..49.41..3982592.4...3.7948.2.6365234.9..831.9..422691..354148563279375924... * PAIR C3: 6,7 ROW 3 G3: 6,7,1 # reduction candidate for 6,7 G3: 6,7 # 20 pairs I3: 6,7,1 # reduction candidate for 6,7 I3: 6,7 => CTR * 5832..49.41..3982592.4..13.7948125636523479..831695.422691..354148563279375924... I3: 1 # 20 pairs * PAIR E1: 1,7 BLK 2 F1: 1,7,6 # reduction candidate for 1,7 F1: 1,7 => SOLVED * 583217496417639825926485731794852163652341987831796542269178354148563279375924618 F1: 6 => CTR * 5832164974167398259274...3.794852.6365234.9..831.9..422691..354148563279375924... * PAIR D2: 6,7 BLK 2 F1: 6,7,1 # reduction candidate for 6,7 F1: 6,7 => SOLVED * 583217496417639825926485731794852163652341987831796542269178354148563279375924618 F1: 1 => CTR * 5832.149641.6398259264...3.7948125636523479..831.9..422691..354148563279375924... * PAIR I1: 6,7 BLK 3 G3: 6,7,1 # reduction candidate for 6,7 G3: 6,7 # 20 pairs I3: 6,7,1 # reduction candidate for 6,7 I3: 6,7 => CTR * 5832..49.41..3982592.4..13.7948125636523479..831695.422691..354148563279375924... I3: 1 # 20 pairs * PAIR I1: 6,7 ROW 1 F1: 6,7,1 # reduction candidate for 6,7 F1: 6,7 => SOLVED * 583217496417639825926485731794852163652341987831796542269178354148563279375924618 F1: 1 => CTR * 5832.149641.6398259264...3.7948125636523479..831.9..422691..354148563279375924... * PAIR F5: 1,7 ROW 5 I5: 1,7,8 # reduction candidate for 1,7 I5: 8 => CTR * 5832..49.41..3982592.4...3.7948.2.63652347918831695.422691..354148563279375924... I5: 1,7 # 16 pairs * PAIR F5: 1,7 COL F F1: 1,7,6 # reduction candidate for 1,7 F1: 1,7 => SOLVED * 583217496417639825926485731794852163652341987831796542269178354148563279375924618 F1: 6 => CTR * 5832164974167398259274...3.794852.6365234.9..831.9..422691..354148563279375924... * PAIR D6: 6,7 BLK 5 F6: 6,7,5 # reduction candidate for 6,7 F6: 6,7 => SOLVED * 583217496417639825926485731794852163652341987831796542269178354148563279375924618 F6: 5 => CTR * 5832.64974167398259274...3.7948.2.6365234.9..831.9..422691..354148563279375924... * PAIR H5: 1,8 BLK 6 I5: 1,8,7 # reduction candidate for 1,8 I5: 1,8 => CTR * 5832..49.41..3982592.4...3.7948.2.636523479..831695.422691..354148563279375924... I5: 7 => SOLVED * 583217496417639825926485731794852163652341987831796542269178354148563279375924618 * PAIR G6: 5,7 ROW 6 F6: 5,7,6 # reduction candidate for 5,7 F6: 5,7 => CTR * 5832.64974167398259274...3.7948.2.6365234.9..831.9..422691..354148563279375924... F6: 6 => SOLVED * 583217496417639825926485731794852163652341987831796542269178354148563279375924618 * PAIR G9: 1,6 BLK 9 I9: 1,6,8 # reduction candidate for 1,6 I9: 1,6 => CTR * 5832..49.41.7398259274...3.7948.25636523479188316957422691..354148563279375924.8. I9: 8 # 16 pairs * PAIR G9: 1,6 COL G G3: 1,6,7 # reduction candidate for 1,6 G3: 1,6 => CTR * 5832..49.41.7398259274...3.7948.25636523479..8316957422691..354148563279375924... G3: 7 => SOLVED * 583217496417639825926485731794852163652341987831796542269178354148563279375924618 * PAIR H9: 1,8 BLK 9 I9: 1,8,6 # reduction candidate for 1,8 I9: 6 => CTR * 5832.64974167398259274..6317948.256365234.9.8831.9.7422691..354148563279375924.86 I9: 1,8 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-201-base-pr-000.dot * REASONING * DIS # I3: 6,7 => CTR => I3: 1 * PRF # F1: 1,7 => SOL * DIS # F1: 6 => CTR => F1: 1,7 * PRF # F1: 6,7 => SOL * DIS # F1: 1 => CTR => F1: 6,7 * DIS # I3: 6,7 => CTR => I3: 1 * PRF # F1: 6,7 => SOL * DIS # F1: 1 => CTR => F1: 6,7 * DIS # I5: 8 => CTR => I5: 1,7 * PRF # F1: 1,7 => SOL * DIS # F1: 6 => CTR => F1: 1,7 * PRF # F6: 6,7 => SOL * DIS # F6: 5 => CTR => F6: 6,7 * DIS # I5: 1,8 => CTR => I5: 7 * PRF # I5: 7 => SOL * DIS # F6: 5,7 => CTR => F6: 6 * PRF # F6: 6 => SOL * DIS # I9: 1,6 => CTR => I9: 8 * DIS # G3: 1,6 => CTR => G3: 7 * PRF # G3: 7 => SOL * DIS # I9: 6 => CTR => I9: 1,8 * CNT 21 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C3,D2,D6,E1,E3,E4,E7,F3,F5,F7,G4,G6,G9,H5,H9,I1) * 5832..49.41..3982592.4...3.7948.2.6365234.9..831.9..422691..354148563279375924... * PAIR C3: 6,7 ROW 3 G3: 6,7,1 # reduction candidate for 6,7 G3: 6,7 # 20 pairs I3: 6,7,1 # reduction candidate for 6,7 I3: 6,7 => CTR * 5832..49.41..3982592.4..13.7948125636523479..831695.422691..354148563279375924... * RESTART * PAIR RESTART * PAIR E1: 1,7 BLK 2 F1: 1,7,6 # reduction candidate for 1,7 F1: 1,7 => SOLVED * 583217496417639825926485731794852163652341987831796542269178354148563279375924618 * DURATION: 0:00:04.268978 START: 09:41:04.838438 END: 09:41:09.107416 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-201-base-pr-001.dot * REASONING * DIS # I3: 6,7 => CTR => I3: 1 * PRF I3: 1 # F1: 1,7 => SOL * STA I3: 1 + F1: 1,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 201 solution: 583217496417639825926485731794852163652341987831796542269178354148563279375924618 info: 1890 FNBHWY S8.f 23347 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 583217496417639825926485731794852163652341987831796542269178354148563279375924618 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 # G3: 6,7 => UNS * DIS # I3: 6,7 => CTR => I3: 1 * INC # I3: 1 => UNS * PRF # F1: 1,7 => SOL * DIS # F1: 6 => CTR => F1: 1,7 * PRF # F1: 6,7 => SOL * DIS # F1: 1 => CTR => F1: 6,7 * INC # G3: 6,7 => UNS * DIS # I3: 6,7 => CTR => I3: 1 * INC # I3: 1 => UNS * PRF # F1: 6,7 => SOL * DIS # F1: 1 => CTR => F1: 6,7 * INC # I5: 1,7 => UNS * DIS # I5: 8 => CTR => I5: 1,7 * PRF # F1: 1,7 => SOL * DIS # F1: 6 => CTR => F1: 1,7 * PRF # F6: 6,7 => SOL * DIS # F6: 5 => CTR => F6: 6,7 * DIS # I5: 1,8 => CTR => I5: 7 * PRF # I5: 7 => SOL * DIS # F6: 5,7 => CTR => F6: 6 * PRF # F6: 6 => SOL * DIS # I9: 1,6 => CTR => I9: 8 * INC # I9: 8 => UNS * DIS # G3: 1,6 => CTR => G3: 7 * PRF # G3: 7 => SOL * INC # I9: 1,8 => UNS * DIS # I9: 6 => CTR => I9: 1,8 * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 6,7 => UNS * DIS # I3: 6,7 => CTR => I3: 1 * PRF I3: 1 # F1: 1,7 => SOL * STA I3: 1 + F1: 1,7 * CNT 3 HDP CHAINS / 3 HYP OPENED