Analysis of xx-top500-053-base.sdk
Contents
Original Sudoku
level: medium
position: ......52.8..1.....2.....7...53....6....4....1.7..8........5.3..4..6.............. initial
Autosolve
position: 3178..52.8.51....324.5.37189537..8646..4359711749862357..25.3..43.6..15.5..3..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C7: 6,9 => SOL * PRF # E1: 4,9 => SOL * DIS # E1: 6 => CTR => E1: 4,9 * PRF # F9: 4,9 => SOL * DIS # E1: 6,9 => CTR => E1: 4 * PRF # E1: 4 => SOL * DIS # E1: 6,9 => CTR => E1: 4 * PRF # E1: 4 => SOL * DIS # H9: 4,9 => CTR => H9: 8 * DIS # C9: 2,8 => CTR => C9: 1,6,9 * PRF # E9: 7,9 => SOL * PRF # C7: 6,9 => SOL * CNT 12 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C7: 6,9 => SOL * STA C7: 6,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......52.8..1.....2.....7...53....6....4....1.7..8........5.3..4..6.............. | initial |
| 3178..52.8.51....324.5.37189537..8646..4359711749862357..25.3..43.6..15.5..3..... | autosolve |
| 317849526865127493249563718953712864628435971174986235786251349432698157591374682 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B2: 6,9 C3: 6,9 F1: 4,9 E2: 2,7 F2: 2,7 E3: 6,9 I1: 6,9 G2: 4,6 H2: 4,9 B5: 2,8 C5: 2,8 E4: 1,2 F4: 1,2 E8: 7,9 I7: 6,9 I8: 2,7 G9: 4,6 I9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,F4: 1.. / E4 = 1 => 15 pairs (_) / F4 = 1 => 0 pairs (X) C7,C9: 1.. / C7 = 1 => 18 pairs (_) / C9 = 1 => 0 pairs (*) C7,F7: 1.. / C7 = 1 => 18 pairs (_) / F7 = 1 => 0 pairs (*) E4,E9: 1.. / E4 = 1 => 15 pairs (_) / E9 = 1 => 0 pairs (X) E2,F2: 2.. / E2 = 2 => 15 pairs (_) / F2 = 2 => 0 pairs (X) B5,C5: 2.. / B5 = 2 => 17 pairs (_) / C5 = 2 => 18 pairs (_) E4,F4: 2.. / E4 = 2 => 0 pairs (X) / F4 = 2 => 15 pairs (_) I8,I9: 2.. / I8 = 2 => 17 pairs (_) / I9 = 2 => 0 pairs (*) C8,I8: 2.. / C8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) B5,B9: 2.. / B5 = 2 => 17 pairs (_) / B9 = 2 => 18 pairs (_) E2,E4: 2.. / E2 = 2 => 15 pairs (_) / E4 = 2 => 0 pairs (X) F2,F4: 2.. / F2 = 2 => 0 pairs (X) / F4 = 2 => 15 pairs (_) E1,F1: 4.. / E1 = 4 => 0 pairs (*) / F1 = 4 => 0 pairs (X) G2,H2: 4.. / G2 = 4 => 0 pairs (*) / H2 = 4 => 0 pairs (X) F7,H7: 4.. / F7 = 4 => 0 pairs (X) / H7 = 4 => 0 pairs (_) E1,E9: 4.. / E1 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) G2,G9: 4.. / G2 = 4 => 0 pairs (*) / G9 = 4 => 0 pairs (X) B2,C3: 6.. / B2 = 6 => 0 pairs (*) / C3 = 6 => 0 pairs (X) E1,E3: 6.. / E1 = 6 => 0 pairs (X) / E3 = 6 => 0 pairs (_) I1,G2: 6.. / I1 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) I7,G9: 6.. / I7 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) E1,I1: 6.. / E1 = 6 => 0 pairs (X) / I1 = 6 => 0 pairs (_) B2,G2: 6.. / B2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) C3,E3: 6.. / C3 = 6 => 0 pairs (X) / E3 = 6 => 0 pairs (_) G2,G9: 6.. / G2 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) I1,I7: 6.. / I1 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) E2,F2: 7.. / E2 = 7 => 0 pairs (X) / F2 = 7 => 15 pairs (_) I8,I9: 7.. / I8 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) B5,C5: 8.. / B5 = 8 => 18 pairs (_) / C5 = 8 => 17 pairs (_) H7,H9: 8.. / H7 = 8 => 0 pairs (X) / H9 = 8 => 20 pairs (_) C8,F8: 8.. / C8 = 8 => 20 pairs (_) / F8 = 8 => 19 pairs (_) B2,C3: 9.. / B2 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) I1,H2: 9.. / I1 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) B2,H2: 9.. / B2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) C3,E3: 9.. / C3 = 9 => 0 pairs (*) / E3 = 9 => 0 pairs (X) I1,I7: 9.. / I1 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) * DURATION: 0:01:16.170308 START: 04:28:10.228915 END: 04:29:26.399223 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B5,C3,C5,E2,E3,E4,E8,F1,F2,F4,G2,G9,H2,I1,I7,I8,I9) * 3178..52.8.51....324.5.37189537..8646..4359711749862357..25.3..43.6..15.5..3..... * PAIR B2: 6,9 COL B B7: 6,9,8 # reduction candidate for 6,9 B7: 6,9 # 22 pairs B9: 6,9,2,8 # reduction candidate for 6,9 B9: 6,9 # 21 pairs * PAIR C3: 6,9 COL C C7: 6,9,1,8 # reduction candidate for 6,9 C7: 6,9 => SOLVED * 317849526865127493249563718953712864628435971174986235786251349432698157591374682 C7: 1,8 # 19 pairs C9: 6,9,1,2,8 # reduction candidate for 6,9 C9: 6,9 # 21 pairs * PAIR F1: 4,9 BLK 2 E1: 4,9,6 # reduction candidate for 4,9 E1: 4,9 => SOLVED * 317849526865127493249563718953712864628435971174986235786251349432698157591374682 E1: 6 => CTR * 3178645298951..6432465937189537..8646..4359711749862357..25.3.643.67.15256234.... * PAIR F1: 4,9 COL F F7: 4,9,1,8 # reduction candidate for 4,9 F7: 4,9 # 20 pairs F9: 4,9,1,7,8 # reduction candidate for 4,9 F9: 4,9 => SOLVED * 317849526865127493249563718953712864628435971174986235786251349432698157591374682 F9: 1,7,8 # 18 pairs * PAIR E3: 6,9 BLK 2 E1: 6,9,4 # reduction candidate for 6,9 E1: 6,9 => CTR * 3178.45268651..4932495637189537128646..4359711749862357.625134943.6.815.59134768. E1: 4 => SOLVED * 317849526865127493249563718953712864628435971174986235786251349432698157591374682 * PAIR I1: 6,9 ROW 1 E1: 6,9,4 # reduction candidate for 6,9 E1: 6,9 => CTR * 3178.45268651..4932495637189537128646..4359711749862357.625134943.6.815.59134768. E1: 4 => SOLVED * 317849526865127493249563718953712864628435971174986235786251349432698157591374682 * PAIR H2: 4,9 COL H H7: 4,9,8 # reduction candidate for 4,9 H7: 4,9 # 20 pairs H9: 4,9,8 # reduction candidate for 4,9 H9: 4,9 => CTR * 3178495268651..4932495.37189537..8646..4359711749862357..25438.43.6..15.5..3..... H9: 8 # 20 pairs * PAIR B5: 2,8 COL B B9: 2,8,6,9 # reduction candidate for 2,8 B9: 2,8 # 22 pairs B9: 6,9 # 21 pairs * PAIR C5: 2,8 COL C C8: 2,8,9 # reduction candidate for 2,8 C8: 2,8 # 19 pairs C9: 2,8,1,6,9 # reduction candidate for 2,8 C9: 2,8 => CTR * 3178645298951276432465937189537128646..4359711749862357.12593864396781525..3....7 C9: 1,6,9 # 18 pairs * PAIR E8: 7,9 BLK 8 F8: 7,9,8 # reduction candidate for 7,9 F8: 7,9 # 20 pairs E9: 7,9,1,4 # reduction candidate for 7,9 E9: 7,9 => SOLVED * 317849526865127493249563718953712864628435971174986235786251349432698157591374682 E9: 1,4 # 19 pairs F9: 7,9,1,4,8 # reduction candidate for 7,9 F9: 7,9 # 22 pairs * PAIR I7: 6,9 ROW 7 B7: 6,9,8 # reduction candidate for 6,9 B7: 6,9 # 22 pairs C7: 6,9,1,8 # reduction candidate for 6,9 C7: 6,9 => SOLVED * 317849526865127493249563718953712864628435971174986235786251349432698157591374682 C7: 1,8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-053-base-pr-000.dot * REASONING * PRF # C7: 6,9 => SOL * PRF # E1: 4,9 => SOL * DIS # E1: 6 => CTR => E1: 4,9 * PRF # F9: 4,9 => SOL * DIS # E1: 6,9 => CTR => E1: 4 * PRF # E1: 4 => SOL * DIS # E1: 6,9 => CTR => E1: 4 * PRF # E1: 4 => SOL * DIS # H9: 4,9 => CTR => H9: 8 * DIS # C9: 2,8 => CTR => C9: 1,6,9 * PRF # E9: 7,9 => SOL * PRF # C7: 6,9 => SOL * CNT 12 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B5,C3,C5,E2,E3,E4,E8,F1,F2,F4,G2,G9,H2,I1,I7,I8,I9) * 3178..52.8.51....324.5.37189537..8646..4359711749862357..25.3..43.6..15.5..3..... * PAIR B2: 6,9 COL B B7: 6,9,8 # reduction candidate for 6,9 B7: 6,9 # 22 pairs B9: 6,9,2,8 # reduction candidate for 6,9 B9: 6,9 # 21 pairs * PAIR C3: 6,9 COL C C7: 6,9,1,8 # reduction candidate for 6,9 C7: 6,9 => SOLVED * 317849526865127493249563718953712864628435971174986235786251349432698157591374682 * DURATION: 0:00:04.609826 START: 04:30:03.555755 END: 04:30:08.165581 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-053-base-pr-001.dot * REASONING * PRF # C7: 6,9 => SOL * STA C7: 6,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 053 solution: 317849526865127493249563718953712864628435971174986235786251349432698157591374682 info: 1398 FNBTHWXY S8.f 1399 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 317849526865127493249563718953712864628435971174986235786251349432698157591374682 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 # B7: 6,9 => UNS * INC # B9: 6,9 => UNS * PRF # C7: 6,9 => SOL * INC # C7: 1,8 => UNS * INC # C9: 6,9 => UNS * PRF # E1: 4,9 => SOL * DIS # E1: 6 => CTR => E1: 4,9 * INC # F7: 4,9 => UNS * PRF # F9: 4,9 => SOL * INC # F9: 1,7,8 => UNS * DIS # E1: 6,9 => CTR => E1: 4 * PRF # E1: 4 => SOL * DIS # E1: 6,9 => CTR => E1: 4 * PRF # E1: 4 => SOL * INC # H7: 4,9 => UNS * DIS # H9: 4,9 => CTR => H9: 8 * INC # H9: 8 => UNS * INC # B9: 2,8 => UNS * INC # B9: 6,9 => UNS * INC # C8: 2,8 => UNS * DIS # C9: 2,8 => CTR => C9: 1,6,9 * INC # C9: 1,6,9 => UNS * INC # F8: 7,9 => UNS * PRF # E9: 7,9 => SOL * INC # E9: 1,4 => UNS * INC # F9: 7,9 => UNS * INC # B7: 6,9 => UNS * PRF # C7: 6,9 => SOL * INC # C7: 1,8 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B7: 6,9 => UNS * INC # B9: 6,9 => UNS * PRF # C7: 6,9 => SOL * STA C7: 6,9 * CNT 3 HDP CHAINS / 3 HYP OPENED