Analysis of xx-top500-068-base.sdk
Contents
Original Sudoku
level: medium
position: ....182...4.....7......3....6.4....53.....1...........8.1...3.....65..4.......... initial
Autosolve
position: 6...18234.43...871.18.4365916.432.853248.51...8.1..423851..43...32651.484.638.512 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 6,9 => CTR => E2: 2 * PRF # F6: 6,9 => SOL * DIS # F6: 7 => CTR => F6: 6,9 * DIS # E6: 7,9 => CTR => E6: 6 * DIS # E7: 2 => CTR => E7: 7,9 * PRF # E7: 2,9 => SOL * DIS # E7: 7 => CTR => E7: 2,9 * DIS # E7: 2 => CTR => E7: 7,9 * DIS # F6: 6 => CTR => F6: 7,9 * CNT 9 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 6,9 => CTR => E2: 2 * PRF E2: 2 # C6: 7,9 => SOL * STA E2: 2 + C6: 7,9 * CNT 2 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....182...4.....7......3....6.4....53.....1...........8.1...3.....65..4.......... | initial |
| 6...18234.43...871.18.4365916.432.853248.51...8.1..423851..43...32651.484.638.512 | autosolve |
| 675918234943526871218743659169432785324875196587169423851294367732651948496387512 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B1: 7,9 A3: 2,7 F2: 6,9 D3: 2,7 C4: 7,9 E5: 7,9 G4: 7,9 H5: 6,9 I5: 6,7 A8: 7,9 B9: 7,9 D7: 2,9 F9: 7,9 H7: 6,9 I7: 6,7 G8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 2.. / A2 = 2 => 0 pairs (X) / A3 = 2 => 16 pairs (_) D7,E7: 2.. / D7 = 2 => 17 pairs (_) / E7 = 2 => 0 pairs (X) A3,D3: 2.. / A3 = 2 => 16 pairs (_) / D3 = 2 => 0 pairs (X) E2,E7: 2.. / E2 = 2 => 17 pairs (_) / E7 = 2 => 0 pairs (X) C1,A2: 5.. / C1 = 5 => 19 pairs (_) / A2 = 5 => 17 pairs (_) D1,D2: 5.. / D1 = 5 => 17 pairs (_) / D2 = 5 => 19 pairs (_) A6,C6: 5.. / A6 = 5 => 19 pairs (_) / C6 = 5 => 17 pairs (_) C1,D1: 5.. / C1 = 5 => 19 pairs (_) / D1 = 5 => 17 pairs (_) A2,D2: 5.. / A2 = 5 => 17 pairs (_) / D2 = 5 => 19 pairs (_) A2,A6: 5.. / A2 = 5 => 17 pairs (_) / A6 = 5 => 19 pairs (_) C1,C6: 5.. / C1 = 5 => 19 pairs (_) / C6 = 5 => 17 pairs (_) E2,F2: 6.. / E2 = 6 => 0 pairs (X) / F2 = 6 => 17 pairs (_) E6,F6: 6.. / E6 = 6 => 17 pairs (_) / F6 = 6 => 0 pairs (X) H5,I5: 6.. / H5 = 6 => 0 pairs (X) / I5 = 6 => 0 pairs (_) H7,I7: 6.. / H7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) E2,E6: 6.. / E2 = 6 => 0 pairs (X) / E6 = 6 => 17 pairs (_) F2,F6: 6.. / F2 = 6 => 17 pairs (_) / F6 = 6 => 0 pairs (X) H5,H7: 6.. / H5 = 6 => 0 pairs (X) / H7 = 6 => 0 pairs (_) I5,I7: 6.. / I5 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) D1,D3: 7.. / D1 = 7 => 0 pairs (X) / D3 = 7 => 16 pairs (_) G4,I5: 7.. / G4 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) A8,B9: 7.. / A8 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) E7,F9: 7.. / E7 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) I7,G8: 7.. / I7 = 7 => 0 pairs (*) / G8 = 7 => 0 pairs (X) A3,D3: 7.. / A3 = 7 => 0 pairs (X) / D3 = 7 => 16 pairs (_) C4,G4: 7.. / C4 = 7 => 0 pairs (X) / G4 = 7 => 0 pairs (_) E5,I5: 7.. / E5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) E7,I7: 7.. / E7 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) A8,G8: 7.. / A8 = 7 => 0 pairs (*) / G8 = 7 => 0 pairs (X) B9,F9: 7.. / B9 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) B1,B9: 7.. / B1 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) F6,F9: 7.. / F6 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) G4,G8: 7.. / G4 = 7 => 0 pairs (*) / G8 = 7 => 0 pairs (X) I5,I7: 7.. / I5 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) G4,H5: 9.. / G4 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) A8,B9: 9.. / A8 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) H7,G8: 9.. / H7 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) C4,G4: 9.. / C4 = 9 => 0 pairs (*) / G4 = 9 => 0 pairs (X) E5,H5: 9.. / E5 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) A8,G8: 9.. / A8 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) B9,F9: 9.. / B9 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) B1,B9: 9.. / B1 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) G4,G8: 9.. / G4 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) H5,H7: 9.. / H5 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) * DURATION: 0:01:40.552715 START: 04:59:22.177675 END: 05:01:02.730390 2017-05-04 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B1,B9,C4,D3,D7,E5,F2,F9,G4,G8,H5,H7,I5,I7) * 6...18234.43...871.18.4365916.432.853248.51...8.1..423851..43...32651.484.638.512 * PAIR B1: 7,9 BLK 1 C1: 7,9,5 # reduction candidate for 7,9 C1: 5 # 19 pairs C1: 7,9 # 17 pairs * PAIR B1: 7,9 ROW 1 D1: 7,9,5 # reduction candidate for 7,9 D1: 7,9 # 19 pairs D1: 5 # 17 pairs * PAIR F2: 6,9 BLK 2 E2: 6,9,2 # reduction candidate for 6,9 E2: 6,9 => CTR * 67..18234.43...8712187436591694327853248751965871..4238519243.7732651948496387512 E2: 2 # 17 pairs * PAIR F2: 6,9 COL F F6: 6,9,7 # reduction candidate for 6,9 F6: 6,9 => SOLVED * 675918234943526871218743659169432785324875196587169423851294367732651948496387512 F6: 7 => CTR * 69..18234.43926871.18.4365916.432.853248.51...8.167423851.743.6.32651748476389512 * PAIR C4: 7,9 BLK 4 A6: 7,9,5 # reduction candidate for 7,9 A6: 7,9 # 17 pairs C6: 7,9,5 # reduction candidate for 7,9 C6: 7,9 # 19 pairs * PAIR C4: 7,9 COL C C1: 7,9,5 # reduction candidate for 7,9 C1: 5 # 19 pairs C1: 7,9 # 17 pairs * PAIR E5: 7,9 BLK 5 E6: 7,9,6 # reduction candidate for 7,9 E6: 7,9 => CTR * 679518234543269871218743659167432.853248.51...8.1.6423851924367732651948496387512 E6: 6 # 17 pairs F6: 7,9,6 # reduction candidate for 7,9 F6: 7,9 # 17 pairs * PAIR E5: 7,9 COL E E7: 7,9,2 # reduction candidate for 7,9 E7: 2 => CTR * 67..18234.43...8712187436591694327853248751965871..4238519243.7732651948496387512 E7: 7,9 # 17 pairs * PAIR A8: 7,9 COL A A6: 7,9,5 # reduction candidate for 7,9 A6: 5 # 19 pairs A6: 7,9 # 17 pairs * PAIR D7: 2,9 BLK 8 E7: 2,9,7 # reduction candidate for 2,9 E7: 2,9 => SOLVED * 675918234943526871218743659169432785324875196587169423851294367732651948496387512 E7: 7 => CTR * 697518234543926871218743659169432.853248.51...8.16.423851274396932651748476389512 * PAIR D7: 2,9 COL D D2: 2,9,5 # reduction candidate for 2,9 D2: 5 # 19 pairs D2: 2,9 # 17 pairs * PAIR F9: 7,9 BLK 8 E7: 7,9,2 # reduction candidate for 7,9 E7: 2 => CTR * 67..18234.43...8712187436591694327853248751965871..4238519243.7732651948496387512 E7: 7,9 # 17 pairs * PAIR F9: 7,9 COL F F6: 7,9,6 # reduction candidate for 7,9 F6: 6 => CTR * 679518234543269871218743659167432.853248.51...8.1.6423851924367732651948496387512 F6: 7,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-068-base-pr-000.dot * REASONING * DIS # E2: 6,9 => CTR => E2: 2 * PRF # F6: 6,9 => SOL * DIS # F6: 7 => CTR => F6: 6,9 * DIS # E6: 7,9 => CTR => E6: 6 * DIS # E7: 2 => CTR => E7: 7,9 * PRF # E7: 2,9 => SOL * DIS # E7: 7 => CTR => E7: 2,9 * DIS # E7: 2 => CTR => E7: 7,9 * DIS # F6: 6 => CTR => F6: 7,9 * CNT 9 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B1,B9,C4,D3,D7,E5,F2,F9,G4,G8,H5,H7,I5,I7) * 6...18234.43...871.18.4365916.432.853248.51...8.1..423851..43...32651.484.638.512 * PAIR B1: 7,9 BLK 1 C1: 7,9,5 # reduction candidate for 7,9 C1: 5 # 19 pairs C1: 7,9 # 17 pairs * PAIR B1: 7,9 ROW 1 D1: 7,9,5 # reduction candidate for 7,9 D1: 7,9 # 19 pairs D1: 5 # 17 pairs * PAIR F2: 6,9 BLK 2 E2: 6,9,2 # reduction candidate for 6,9 E2: 6,9 => CTR * 67..18234.43...8712187436591694327853248751965871..4238519243.7732651948496387512 * PAIR C4: 7,9 BLK 4 A6: 7,9,5 # reduction candidate for 7,9 A6: 7,9 # 16 pairs C6: 7,9,5 # reduction candidate for 7,9 C6: 7,9 => SOLVED * 675918234943526871218743659169432785324875196587169423851294367732651948496387512 * DURATION: 0:00:11.368809 START: 05:01:38.401395 END: 05:01:49.770204 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-068-base-pr-001.dot * REASONING * DIS # E2: 6,9 => CTR => E2: 2 * PRF E2: 2 # C6: 7,9 => SOL * STA E2: 2 + C6: 7,9 * CNT 2 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 068 solution: 675918234943526871218743659169432785324875196587169423851294367732651948496387512 info: 1446 FNBHWX S8.f 3146 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 675918234943526871218743659169432785324875196587169423851294367732651948496387512 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 # C1: 7,9 => UNS * INC # C1: 5 => UNS * INC # D1: 7,9 => UNS * INC # D1: 5 => UNS * DIS # E2: 6,9 => CTR => E2: 2 * INC # E2: 2 => UNS * PRF # F6: 6,9 => SOL * DIS # F6: 7 => CTR => F6: 6,9 * INC # A6: 7,9 => UNS * INC # C6: 7,9 => UNS * INC # C1: 7,9 => UNS * INC # C1: 5 => UNS * DIS # E6: 7,9 => CTR => E6: 6 * INC # E6: 6 => UNS * INC # F6: 7,9 => UNS * INC # E7: 7,9 => UNS * DIS # E7: 2 => CTR => E7: 7,9 * INC # A6: 7,9 => UNS * INC # A6: 5 => UNS * PRF # E7: 2,9 => SOL * DIS # E7: 7 => CTR => E7: 2,9 * INC # D2: 2,9 => UNS * INC # D2: 5 => UNS * INC # E7: 7,9 => UNS * DIS # E7: 2 => CTR => E7: 7,9 * INC # F6: 7,9 => UNS * DIS # F6: 6 => CTR => F6: 7,9 * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 7,9 => UNS * INC # C1: 5 => UNS * INC # D1: 7,9 => UNS * INC # D1: 5 => UNS * DIS # E2: 6,9 => CTR => E2: 2 * INC E2: 2 # A6: 7,9 => UNS * PRF E2: 2 # C6: 7,9 => SOL * STA E2: 2 + C6: 7,9 * CNT 7 HDP CHAINS / 7 HYP OPENED