Analysis of xx-top500-398-base.sdk
Contents
Original Sudoku
level: medium
position: ....1.8...9.....3.2........4..5.3.6.7.1.....4..........5.2.......8...1.....3..... initial
Autosolve
position: 5.3.1.8..19.8...3.28..3..1.429583761731...5848651......5.2.1..8..8...1...123.8... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 4,7 => CTR => D1: 6,9 * DIS # F1: 4,7 => CTR => F1: 2,6,9 * DIS # D3: 6,9 => CTR => D3: 4,7 * DIS # D8: 6,9 => CTR => D8: 4,7 * DIS # E2: 4,7 => CTR => E2: 2,5,6 * PRF # E7: 4,7 => SOL * DIS # E8: 4,7 => CTR => E8: 5,6,9 * DIS # F1: 4,7 => CTR => F1: 2,6,9 * DIS # F8: 4,7 => CTR => F8: 5,6,9 * DIS # H1: 2,9 => CTR => H1: 4,7 * PRF # E7: 4,7 => SOL * DIS # E8: 4,7 => CTR => E8: 5,6,9 * DIS # F8: 4,7 => CTR => F8: 5,6,9 * DIS # H8: 4,7 => CTR => H8: 2,5,9 * DIS # E9: 6,9 => CTR => E9: 4,5,7 * PRF # G9: 6,9 => SOL * DIS # G9: 4 => CTR => G9: 6,9 * DIS # I9: 6,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * CNT 19 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 4,7 => CTR => D1: 6,9 * DIS D1: 6,9 # F1: 4,7 => CTR => F1: 2,6,9 * DIS D1: 6,9 + F1: 2,6,9 # H1: 2,9 => CTR => H1: 4,7 * DIS D1: 6,9 + F1: 2,6,9 + H1: 4,7 # E2: 4,7 => CTR => E2: 2,5,6 * PRF D1: 6,9 + F1: 2,6,9 + H1: 4,7 + E2: 2,5,6 # E7: 4,7 => SOL * STA D1: 6,9 + F1: 2,6,9 + H1: 4,7 + E2: 2,5,6 + E7: 4,7 * CNT 5 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....1.8...9.....3.2........4..5.3.6.7.1.....4..........5.2.......8...1.....3..... | initial |
| 5.3.1.8..19.8...3.28..3..1.429583761731...5848651......5.2.1..8..8...1...123.8... | autosolve |
| 543912876197864235286735419429583761731629584865147923654271398378496152912358647 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B1: 4,7 D5: 6,9 E6: 4,7 F6: 4,7 H6: 2,9 C7: 4,7 B8: 4,7 A9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E5,F5: 2.. / E5 = 2 => 9 pairs (_) / F5 = 2 => 12 pairs (_) H8,I8: 2.. / H8 = 2 => 16 pairs (_) / I8 = 2 => 21 pairs (_) E2,E5: 2.. / E2 = 2 => 12 pairs (_) / E5 = 2 => 9 pairs (_) G2,G6: 2.. / G2 = 2 => 12 pairs (_) / G6 = 2 => 11 pairs (_) G6,I6: 3.. / G6 = 3 => 20 pairs (_) / I6 = 3 => 10 pairs (_) A7,A8: 3.. / A7 = 3 => 20 pairs (_) / A8 = 3 => 10 pairs (_) G7,I8: 3.. / G7 = 3 => 10 pairs (_) / I8 = 3 => 20 pairs (_) A7,G7: 3.. / A7 = 3 => 20 pairs (_) / G7 = 3 => 10 pairs (_) A8,I8: 3.. / A8 = 3 => 10 pairs (_) / I8 = 3 => 20 pairs (_) G6,G7: 3.. / G6 = 3 => 20 pairs (_) / G7 = 3 => 10 pairs (_) I6,I8: 3.. / I6 = 3 => 10 pairs (_) / I8 = 3 => 20 pairs (_) E6,F6: 4.. / E6 = 4 => 0 pairs (*) / F6 = 4 => 0 pairs (X) C7,B8: 4.. / C7 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) B1,B8: 4.. / B1 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) I2,I3: 5.. / I2 = 5 => 8 pairs (_) / I3 = 5 => 8 pairs (_) H8,H9: 5.. / H8 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) F3,I3: 5.. / F3 = 5 => 8 pairs (_) / I3 = 5 => 8 pairs (_) E9,H9: 5.. / E9 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) C2,C3: 6.. / C2 = 6 => 10 pairs (_) / C3 = 6 => 10 pairs (_) E6,F6: 7.. / E6 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) C7,B8: 7.. / C7 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) B1,B8: 7.. / B1 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) * DURATION: 0:00:35.892433 START: 16:25:01.853354 END: 16:25:37.745787 2017-05-04 * CP COUNT: (22) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,B8,C7,D5,E6,F6,H6) * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651......5.2.1..8..8...1...123.8... * PAIR B1: 4,7 BLK 1 C2: 4,7,6 # reduction candidate for 4,7 C2: 4,7 # 10 pairs C3: 4,7,6 # reduction candidate for 4,7 C3: 4,7 # 10 pairs * PAIR B1: 4,7 ROW 1 D1: 4,7,6,9 # reduction candidate for 4,7 D1: 4,7 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651....3.5.2.13.83.8...1.2.123.8... D1: 6,9 # 11 pairs F1: 4,7,2,6,9 # reduction candidate for 4,7 F1: 4,7 => CTR * 5.3.1.82.19.8...3.28..3..1.429583761731...5848651..293.5.2.13.83.8...1.2.123.8... F1: 2,6,9 # 8 pairs H1: 4,7,2,9 # reduction candidate for 4,7 H1: 4,7 # 12 pairs * PAIR D5: 6,9 BLK 5 E5: 6,9,2 # reduction candidate for 6,9 E5: 6,9 # 12 pairs F5: 6,9,2 # reduction candidate for 6,9 F5: 6,9 # 9 pairs * PAIR D5: 6,9 COL D D1: 6,9,4,7 # reduction candidate for 6,9 D1: 6,9 # 11 pairs D3: 6,9,4,7 # reduction candidate for 6,9 D3: 6,9 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651....3.5.2.13.83.8...152.12358... D3: 4,7 # 9 pairs D8: 6,9,4,7 # reduction candidate for 6,9 D8: 6,9 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651....3.5.2.13.83.8...1.2.123.8... D8: 4,7 # 9 pairs * PAIR E6: 4,7 COL E E2: 4,7,2,5,6 # reduction candidate for 4,7 E2: 4,7 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731.2.5848651......5.2.1..8..8...1...123.8... E2: 2,5,6 # 8 pairs E7: 4,7,6,9 # reduction candidate for 4,7 E7: 4,7 => SOLVED * 543912876197864235286735419429583761731629584865147923654271398378496152912358647 E7: 6,9 # 9 pairs E8: 4,7,5,6,9 # reduction candidate for 4,7 E8: 4,7 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651......5.2.1..8..8...1...123.8... E8: 5,6,9 # 8 pairs E9: 4,7,5,6,9 # reduction candidate for 4,7 E9: 4,7 # 10 pairs * PAIR F6: 4,7 COL F F1: 4,7,2,6,9 # reduction candidate for 4,7 F1: 4,7 => CTR * 5.3.1.82.19.8...3.28..3..1.429583761731...5848651..293.5.2.13.83.8...1.2.123.8... F1: 2,6,9 # 8 pairs F2: 4,7,2,5,6 # reduction candidate for 4,7 F2: 4,7 # 9 pairs F3: 4,7,5,6,9 # reduction candidate for 4,7 F3: 4,7 # 9 pairs F8: 4,7,5,6,9 # reduction candidate for 4,7 F8: 4,7 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651....3.5.2.13.83.8...152.12358... F8: 5,6,9 # 8 pairs * PAIR H6: 2,9 BLK 6 G6: 2,9,3 # reduction candidate for 2,9 G6: 2,9 # 10 pairs I6: 2,9,3 # reduction candidate for 2,9 I6: 2,9 # 20 pairs * PAIR H6: 2,9 COL H H1: 2,9,4,7 # reduction candidate for 2,9 H1: 2,9 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651......5.2.1..8..8...1...123.8... H1: 4,7 # 12 pairs H8: 2,9,4,5,7 # reduction candidate for 2,9 H8: 2,9 # 16 pairs * PAIR C7: 4,7 ROW 7 E7: 4,7,6,9 # reduction candidate for 4,7 E7: 4,7 => SOLVED * 543912876197864235286735419429583761731629584865147923654271398378496152912358647 E7: 6,9 # 9 pairs H7: 4,7,9 # reduction candidate for 4,7 H7: 4,7 # 10 pairs * PAIR C7: 4,7 COL C C2: 4,7,6 # reduction candidate for 4,7 C2: 4,7 # 10 pairs C3: 4,7,6 # reduction candidate for 4,7 C3: 4,7 # 10 pairs * PAIR B8: 4,7 ROW 8 D8: 4,7,6,9 # reduction candidate for 4,7 D8: 4,7 # 9 pairs E8: 4,7,5,6,9 # reduction candidate for 4,7 E8: 4,7 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651......5.2.1..8..8...1...123.8... E8: 5,6,9 # 8 pairs F8: 4,7,5,6,9 # reduction candidate for 4,7 F8: 4,7 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651....3.5.2.13.83.8...152.12358... F8: 5,6,9 # 8 pairs H8: 4,7,2,5,9 # reduction candidate for 4,7 H8: 4,7 => CTR * 5.3.128..19.8..23.28..3..1.429583761731.2.5848651..92365.2.13983.8.951.29123.8.5. H8: 2,5,9 # 8 pairs * PAIR A9: 6,9 BLK 7 A7: 6,9,3 # reduction candidate for 6,9 A7: 6,9 # 10 pairs A8: 6,9,3 # reduction candidate for 6,9 A8: 6,9 # 20 pairs * PAIR A9: 6,9 ROW 9 E9: 6,9,4,5,7 # reduction candidate for 6,9 E9: 6,9 => CTR * 5.3.1.87.19.8...3.28..3..1.429583761731...5848651......5.2.1..8.78...1...123.8457 E9: 4,5,7 # 8 pairs G9: 6,9,4 # reduction candidate for 6,9 G9: 6,9 => SOLVED * 543912876197864235286735419429583761731629584865147923654271398378496152912358647 G9: 4 => CTR * 573.1.84.1948...3.28643.91.429583761731...584865174.29657241398.487..1...123.8476 I9: 6,9,7 # reduction candidate for 6,9 I9: 6,9 => CTR * 573.1.84.1948...3.28643.91.429583761731...584865174.29657241398.487..1..912358476 I9: 7 => SOLVED * 543912876197864235286735419429583761731629584865147923654271398378496152912358647 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-398-base-pr-000.dot * REASONING * DIS # D1: 4,7 => CTR => D1: 6,9 * DIS # F1: 4,7 => CTR => F1: 2,6,9 * DIS # D3: 6,9 => CTR => D3: 4,7 * DIS # D8: 6,9 => CTR => D8: 4,7 * DIS # E2: 4,7 => CTR => E2: 2,5,6 * PRF # E7: 4,7 => SOL * DIS # E8: 4,7 => CTR => E8: 5,6,9 * DIS # F1: 4,7 => CTR => F1: 2,6,9 * DIS # F8: 4,7 => CTR => F8: 5,6,9 * DIS # H1: 2,9 => CTR => H1: 4,7 * PRF # E7: 4,7 => SOL * DIS # E8: 4,7 => CTR => E8: 5,6,9 * DIS # F8: 4,7 => CTR => F8: 5,6,9 * DIS # H8: 4,7 => CTR => H8: 2,5,9 * DIS # E9: 6,9 => CTR => E9: 4,5,7 * PRF # G9: 6,9 => SOL * DIS # G9: 4 => CTR => G9: 6,9 * DIS # I9: 6,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * CNT 19 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,B8,C7,D5,E6,F6,H6) * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651......5.2.1..8..8...1...123.8... * PAIR B1: 4,7 BLK 1 C2: 4,7,6 # reduction candidate for 4,7 C2: 4,7 # 10 pairs C3: 4,7,6 # reduction candidate for 4,7 C3: 4,7 # 10 pairs * PAIR B1: 4,7 ROW 1 D1: 4,7,6,9 # reduction candidate for 4,7 D1: 4,7 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731...5848651....3.5.2.13.83.8...1.2.123.8... F1: 4,7,2,6,9 # reduction candidate for 4,7 F1: 4,7 => CTR * 5.3.1.82.19.8...3.28..3..1.429583761731...5848651..293.5.2.13.83.8...152.123.8... H1: 4,7,2,9 # reduction candidate for 4,7 H1: 4,7 # 12 pairs * RESTART * PAIR B1: 4,7 ROW 1 H1: 4,7,2,9 # reduction candidate for 4,7 H1: 2,9 => CTR * 543.1.8.719.8...3.28..3..1.429583761731...5848651......542.1..8.784..1...123.8.4. * PAIR RESTART * PAIR B1: 4,7 BLK 1 C2: 4,7,6 # reduction candidate for 4,7 C2: 4,7 # 14 pairs C3: 4,7,6 # reduction candidate for 4,7 C3: 4,7 # 17 pairs * PAIR D5: 6,9 BLK 5 E5: 6,9,2 # reduction candidate for 6,9 E5: 6,9 # 20 pairs F5: 6,9,2 # reduction candidate for 6,9 F5: 6,9 # 14 pairs * PAIR E6: 4,7 COL E E2: 4,7,2,5,6 # reduction candidate for 4,7 E2: 4,7 => CTR * 5.3.1.8..19.8...3.28..3..1.429583761731.2.5848651......5.2.1..8..8...1...123.8... E7: 4,7,6,9 # reduction candidate for 4,7 E7: 4,7 => SOLVED * 543912876197864235286735419429583761731629584865147923654271398378496152912358647 * DURATION: 0:00:13.635604 START: 16:26:21.372450 END: 16:26:35.008054 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-398-base-pr-001.dot * REASONING * DIS # D1: 4,7 => CTR => D1: 6,9 * DIS D1: 6,9 # F1: 4,7 => CTR => F1: 2,6,9 * DIS D1: 6,9 + F1: 2,6,9 # H1: 2,9 => CTR => H1: 4,7 * DIS D1: 6,9 + F1: 2,6,9 + H1: 4,7 # E2: 4,7 => CTR => E2: 2,5,6 * PRF D1: 6,9 + F1: 2,6,9 + H1: 4,7 + E2: 2,5,6 # E7: 4,7 => SOL * STA D1: 6,9 + F1: 2,6,9 + H1: 4,7 + E2: 2,5,6 + E7: 4,7 * CNT 5 HDP CHAINS / 13 HYP OPENED
Header Info
Top 500 Minimum 17 398 solution: 543912876197864235286735419429583761731629584865147923654271398378496152912358647 info: 90173 FNBX S8.f 2973 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 543912876197864235286735419429583761731629584865147923654271398378496152912358647 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 # C2: 4,7 => UNS * INC # C3: 4,7 => UNS * DIS # D1: 4,7 => CTR => D1: 6,9 * INC # D1: 6,9 => UNS * DIS # F1: 4,7 => CTR => F1: 2,6,9 * INC # F1: 2,6,9 => UNS * INC # H1: 4,7 => UNS * INC # E5: 6,9 => UNS * INC # F5: 6,9 => UNS * INC # D1: 6,9 => UNS * DIS # D3: 6,9 => CTR => D3: 4,7 * INC # D3: 4,7 => UNS * DIS # D8: 6,9 => CTR => D8: 4,7 * INC # D8: 4,7 => UNS * DIS # E2: 4,7 => CTR => E2: 2,5,6 * INC # E2: 2,5,6 => UNS * PRF # E7: 4,7 => SOL * INC # E7: 6,9 => UNS * DIS # E8: 4,7 => CTR => E8: 5,6,9 * INC # E8: 5,6,9 => UNS * INC # E9: 4,7 => UNS * DIS # F1: 4,7 => CTR => F1: 2,6,9 * INC # F1: 2,6,9 => UNS * INC # F2: 4,7 => UNS * INC # F3: 4,7 => UNS * DIS # F8: 4,7 => CTR => F8: 5,6,9 * INC # F8: 5,6,9 => UNS * INC # G6: 2,9 => UNS * INC # I6: 2,9 => UNS * DIS # H1: 2,9 => CTR => H1: 4,7 * INC # H1: 4,7 => UNS * INC # H8: 2,9 => UNS * PRF # E7: 4,7 => SOL * INC # E7: 6,9 => UNS * INC # H7: 4,7 => UNS * INC # C2: 4,7 => UNS * INC # C3: 4,7 => UNS * INC # D8: 4,7 => UNS * DIS # E8: 4,7 => CTR => E8: 5,6,9 * INC # E8: 5,6,9 => UNS * DIS # F8: 4,7 => CTR => F8: 5,6,9 * INC # F8: 5,6,9 => UNS * DIS # H8: 4,7 => CTR => H8: 2,5,9 * INC # H8: 2,5,9 => UNS * INC # A7: 6,9 => UNS * INC # A8: 6,9 => UNS * DIS # E9: 6,9 => CTR => E9: 4,5,7 * INC # E9: 4,5,7 => UNS * PRF # G9: 6,9 => SOL * DIS # G9: 4 => CTR => G9: 6,9 * DIS # I9: 6,9 => CTR => I9: 7 * PRF # I9: 7 => SOL * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 4,7 => UNS * INC # C3: 4,7 => UNS * DIS # D1: 4,7 => CTR => D1: 6,9 * DIS D1: 6,9 # F1: 4,7 => CTR => F1: 2,6,9 * INC D1: 6,9 + F1: 2,6,9 # H1: 4,7 => UNS * INC D1: 6,9 + F1: 2,6,9 # H1: 4,7 => UNS * DIS D1: 6,9 + F1: 2,6,9 # H1: 2,9 => CTR => H1: 4,7 * INC D1: 6,9 + F1: 2,6,9 + H1: 4,7 # C2: 4,7 => UNS * INC D1: 6,9 + F1: 2,6,9 + H1: 4,7 # C3: 4,7 => UNS * INC D1: 6,9 + F1: 2,6,9 + H1: 4,7 # E5: 6,9 => UNS * INC D1: 6,9 + F1: 2,6,9 + H1: 4,7 # F5: 6,9 => UNS * DIS D1: 6,9 + F1: 2,6,9 + H1: 4,7 # E2: 4,7 => CTR => E2: 2,5,6 * PRF D1: 6,9 + F1: 2,6,9 + H1: 4,7 + E2: 2,5,6 # E7: 4,7 => SOL * STA D1: 6,9 + F1: 2,6,9 + H1: 4,7 + E2: 2,5,6 + E7: 4,7 * CNT 13 HDP CHAINS / 13 HYP OPENED