Analysis of xx-top500-097-base.sdk
Contents
Original Sudoku
level: medium
position: .5.1..2..6...4......3..........6...7..1....4..2...7...7..4.8.........13.......... initial
Autosolve
position: .571.32646.274.3.1143...7.....264.17.713..642426.17..371.438.26..4.7.13......147. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A4: 8,9 => CTR => A4: 3,5 * DIS # A8: 8,9 => CTR => A8: 2,5 * DIS # A9: 8,9 => CTR => A9: 2,3,5 * PRF # H2: 5 => SOL * PRF # B8: 8,9 => SOL * DIS # B9: 8,9 => CTR => B9: 3,6 * DIS # E3: 8,9 => CTR => E3: 2,5 * DIS # E5: 5 => CTR => E5: 8,9 * DIS # D3: 5,9 => CTR => D3: 6,8 * PRF # E3: 5,9 => SOL * DIS # H2: 8 => CTR => H2: 5,9 * DIS # H3: 5,9 => CTR => H3: 8 * DIS # D3: 5,9 => CTR => D3: 6,8 * PRF # E3: 5,9 => SOL * DIS # I8: 5,9 => CTR => I8: 8 * DIS # D6: 5,9 => CTR => D6: 8 * DIS # A5: 5,9 => CTR => A5: 8 * DIS # G4: 5,9 => CTR => G4: 8 * DIS # D6: 5,9 => CTR => D6: 8 * DIS # H3: 5,9 => CTR => H3: 8 * DIS # A9: 5,9 => CTR => A9: 2,3,8 * DIS # C9: 5,9 => CTR => C9: 8 * DIS # C4: 8 => CTR => C4: 5,9 * DIS # I8: 5,9 => CTR => I8: 8 * DIS # G4: 5,9 => CTR => G4: 8 * CNT 25 HDP CHAINS / 61 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A4: 8,9 => CTR => A4: 3,5 * DIS A4: 3,5 # A8: 8,9 => CTR => A8: 2,5 * DIS A4: 3,5 + A8: 2,5 # A9: 8,9 => CTR => A9: 2,3,5 * DIS A4: 3,5 + A8: 2,5 + A9: 2,3,5 # H2: 8,9 => CTR => H2: 5 * PRF A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5 => SOL * STA A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5 * CNT 5 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.1..2..6...4......3..........6...7..1....4..2...7...7..4.8.........13.......... | initial |
| .571.32646.274.3.1143...7.....264.17.713..642426.17..371.438.26..4.7.13......147. | autosolve |
| 957183264682749351143652789539264817871395642426817593715438926294576138368921475 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A1: 8,9 B2: 8,9 E1: 8,9 F2: 5,9 F3: 2,6 I3: 5,9 F5: 5,9 H6: 5,9 C7: 5,9 F8: 2,6 G7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 2.. / E3 = 2 => 12 pairs (_) / F3 = 2 => 0 pairs (*) A8,A9: 2.. / A8 = 2 => 0 pairs (*) / A9 = 2 => 0 pairs (X) F8,E9: 2.. / F8 = 2 => 12 pairs (_) / E9 = 2 => 0 pairs (*) A8,F8: 2.. / A8 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) A9,E9: 2.. / A9 = 2 => 12 pairs (_) / E9 = 2 => 0 pairs (*) E3,E9: 2.. / E3 = 2 => 12 pairs (_) / E9 = 2 => 0 pairs (*) F3,F8: 2.. / F3 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) A4,B4: 3.. / A4 = 3 => 12 pairs (_) / B4 = 3 => 0 pairs (*) A9,B9: 3.. / A9 = 3 => 0 pairs (*) / B9 = 3 => 0 pairs (X) A4,A9: 3.. / A4 = 3 => 12 pairs (_) / A9 = 3 => 0 pairs (*) B4,B9: 3.. / B4 = 3 => 0 pairs (*) / B9 = 3 => 0 pairs (X) F2,H2: 5.. / F2 = 5 => 14 pairs (_) / H2 = 5 => 0 pairs (*) C7,G7: 5.. / C7 = 5 => 18 pairs (_) / G7 = 5 => 0 pairs (X) F2,F5: 5.. / F2 = 5 => 14 pairs (_) / F5 = 5 => 0 pairs (*) D3,F3: 6.. / D3 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) B8,B9: 6.. / B8 = 6 => 12 pairs (_) / B9 = 6 => 0 pairs (*) B9,D9: 6.. / B9 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) F3,F8: 6.. / F3 = 6 => 12 pairs (_) / F8 = 6 => 0 pairs (*) A1,B2: 8.. / A1 = 8 => 0 pairs (X) / B2 = 8 => 17 pairs (_) H2,H3: 8.. / H2 = 8 => 0 pairs (X) / H3 = 8 => 17 pairs (_) E5,D6: 8.. / E5 = 8 => 0 pairs (X) / D6 = 8 => 17 pairs (_) G4,G6: 8.. / G4 = 8 => 17 pairs (_) / G6 = 8 => 0 pairs (X) I8,I9: 8.. / I8 = 8 => 13 pairs (_) / I9 = 8 => 0 pairs (X) A1,E1: 8.. / A1 = 8 => 0 pairs (X) / E1 = 8 => 17 pairs (_) B2,H2: 8.. / B2 = 8 => 17 pairs (_) / H2 = 8 => 0 pairs (X) A5,E5: 8.. / A5 = 8 => 17 pairs (_) / E5 = 8 => 0 pairs (X) D6,G6: 8.. / D6 = 8 => 17 pairs (_) / G6 = 8 => 0 pairs (X) C4,C9: 8.. / C4 = 8 => 0 pairs (X) / C9 = 8 => 14 pairs (_) D3,D6: 8.. / D3 = 8 => 0 pairs (X) / D6 = 8 => 17 pairs (_) A1,B2: 9.. / A1 = 9 => 17 pairs (_) / B2 = 9 => 0 pairs (X) A1,E1: 9.. / A1 = 9 => 17 pairs (_) / E1 = 9 => 0 pairs (X) C7,G7: 9.. / C7 = 9 => 0 pairs (X) / G7 = 9 => 18 pairs (_) F2,F5: 9.. / F2 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) * DURATION: 0:00:59.382802 START: 06:05:00.002424 END: 06:05:59.385226 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,C7,E1,F2,F3,F5,F8,G7,H6,I3) * .571.32646.274.3.1143...7.....264.17.713..642426.17..371.438.26..4.7.13......147. * PAIR A1: 8,9 COL A A4: 8,9,3,5 # reduction candidate for 8,9 A4: 8,9 => CTR * .571.32646.274.3.11436.27...3.264.1757138.642426.17..371.438.262.4.7613.36..2147. A4: 3,5 # 12 pairs A5: 8,9,5 # reduction candidate for 8,9 A5: 8,9 # 16 pairs A8: 8,9,2,5 # reduction candidate for 8,9 A8: 8,9 => CTR * .571.32646.274.3.1143.267..3..264.1757138964242651789371.438926.64972135239651478 A8: 2,5 # 12 pairs A9: 8,9,2,3,5 # reduction candidate for 8,9 A9: 8,9 => CTR * .571.32646.274.3.1143...7..3..264.17.713..642426.17..371.438.262.4.7613......147. A9: 2,3,5 # 11 pairs * PAIR B2: 8,9 ROW 2 H2: 8,9,5 # reduction candidate for 8,9 H2: 5 => SOLVED * 957183264682749351143652789539264817871395642426817593715438926294576138368921475 H2: 8,9 # 14 pairs * PAIR B2: 8,9 COL B B4: 8,9,3 # reduction candidate for 8,9 B4: 8,9 # 12 pairs B8: 8,9,6 # reduction candidate for 8,9 B8: 8,9 => SOLVED * 957183264682749351143652789539264817871395642426817593715438926294576138368921475 B8: 6 # 12 pairs B9: 8,9,3,6 # reduction candidate for 8,9 B9: 8,9 => CTR * .571.32646.274.3.1143...7...3.264.17.713..642426.17..371.438.26.64.7213......147. B9: 3,6 # 12 pairs * PAIR E1: 8,9 BLK 2 D3: 8,9,5,6 # reduction candidate for 8,9 D3: 8,9 # 16 pairs E3: 8,9,2,5 # reduction candidate for 8,9 E3: 8,9 => CTR * 9571832646827453911436.27..539264817871359642426817..3715438926294576138368921475 E3: 2,5 # 12 pairs * PAIR E1: 8,9 COL E E5: 8,9,5 # reduction candidate for 8,9 E5: 5 => CTR * 957183264682745391143...785...264817871359642426817953719438526.64.72138238..147. E5: 8,9 # 18 pairs * PAIR F2: 5,9 BLK 2 D3: 5,9,6,8 # reduction candidate for 5,9 D3: 5,9 => CTR * .571.32646.274.3.1143.2678.3..2648178713..642426817..371.438.26564972138238651479 D3: 6,8 # 12 pairs E3: 5,9,2,8 # reduction candidate for 5,9 E3: 5,9 => SOLVED * 957183264682749351143652789539264817871395642426817593715438926294576138368921475 E3: 2,8 # 12 pairs * PAIR F2: 5,9 ROW 2 H2: 5,9,8 # reduction candidate for 5,9 H2: 8 => CTR * 857193264692745381143826759..8264517571389642426517893715438926.846721352...51478 H2: 5,9 # 17 pairs * PAIR I3: 5,9 BLK 3 H2: 5,9,8 # reduction candidate for 5,9 H2: 5,9 # 17 pairs H3: 5,9,8 # reduction candidate for 5,9 H3: 5,9 => CTR * 857193264692745381143826759..8264517571389642426517893715438926.846721352...51478 H3: 8 # 17 pairs * PAIR I3: 5,9 ROW 3 D3: 5,9,6,8 # reduction candidate for 5,9 D3: 5,9 => CTR * .571.32646.274.3.1143.2678.3..2648178713..642426817..371.438.26564972138238651479 D3: 6,8 # 12 pairs E3: 5,9,2,8 # reduction candidate for 5,9 E3: 5,9 => SOLVED * 957183264682749351143652789539264817871395642426817593715438926294576138368921475 E3: 2,8 # 12 pairs * PAIR I3: 5,9 COL I I8: 5,9,8 # reduction candidate for 5,9 I8: 5,9 => CTR * 8571932646927453811438267...38264.1757138.642426.178.371.438.26..4.7.13......1478 I8: 8 # 13 pairs I9: 5,9,8 # reduction candidate for 5,9 I9: 5,9 # 13 pairs * PAIR F5: 5,9 BLK 5 E5: 5,9,8 # reduction candidate for 5,9 E5: 5,9 # 17 pairs D6: 5,9,8 # reduction candidate for 5,9 D6: 5,9 => CTR * 8571932646927453811438267..38.264.1757138964242651789371.438926..4.7213.23.6.147. D6: 8 # 17 pairs * PAIR F5: 5,9 ROW 5 A5: 5,9,8 # reduction candidate for 5,9 A5: 5,9 => CTR * 8571932646927453811438267.....264.1757138964242651789371.438926..4.7213523.651478 A5: 8 # 17 pairs * PAIR H6: 5,9 BLK 6 G4: 5,9,8 # reduction candidate for 5,9 G4: 5,9 => CTR * 8571932646927453811438267..38.264.1757138964242651789371.438926..4.7213.23.6.147. G4: 8 # 17 pairs G6: 5,9,8 # reduction candidate for 5,9 G6: 5,9 # 17 pairs * PAIR H6: 5,9 ROW 6 D6: 5,9,8 # reduction candidate for 5,9 D6: 5,9 => CTR * 8571932646927453811438267..38.264.1757138964242651789371.438926..4.7213.23.6.147. D6: 8 # 17 pairs * PAIR H6: 5,9 COL H H2: 5,9,8 # reduction candidate for 5,9 H2: 5,9 # 17 pairs H3: 5,9,8 # reduction candidate for 5,9 H3: 5,9 => CTR * 857193264692745381143826759..8264517571389642426517893715438926.846721352...51478 H3: 8 # 17 pairs * PAIR C7: 5,9 BLK 7 A8: 5,9,2,8 # reduction candidate for 5,9 A8: 5,9 # 15 pairs A9: 5,9,2,3,8 # reduction candidate for 5,9 A9: 5,9 => CTR * .571.32646.274.3.1143...7..3..264.17.713..642426.17..371.438.262.4.7613......147. A9: 2,3,8 # 11 pairs C9: 5,9,8 # reduction candidate for 5,9 C9: 5,9 => CTR * 8571932646927453811438267...38264.1757138.642426.178.371.438.26..4.7.13......147. C9: 8 # 14 pairs * PAIR C7: 5,9 COL C C4: 5,9,8 # reduction candidate for 5,9 C4: 8 => CTR * 8571932646927453811438267...38264.1757138.642426.178.371.438.26..4.7.13......147. C4: 5,9 # 14 pairs * PAIR G7: 5,9 BLK 9 I8: 5,9,8 # reduction candidate for 5,9 I8: 5,9 => CTR * 8571932646927453811438267...38264.1757138.642426.178.371.438.26..4.7.13......1478 I8: 8 # 13 pairs I9: 5,9,8 # reduction candidate for 5,9 I9: 5,9 # 13 pairs * PAIR G7: 5,9 COL G G4: 5,9,8 # reduction candidate for 5,9 G4: 5,9 => CTR * 8571932646927453811438267..38.264.1757138964242651789371.438926..4.7213.23.6.147. G4: 8 # 17 pairs G6: 5,9,8 # reduction candidate for 5,9 G6: 5,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-097-base-pr-000.dot * REASONING * DIS # A4: 8,9 => CTR => A4: 3,5 * DIS # A8: 8,9 => CTR => A8: 2,5 * DIS # A9: 8,9 => CTR => A9: 2,3,5 * PRF # H2: 5 => SOL * PRF # B8: 8,9 => SOL * DIS # B9: 8,9 => CTR => B9: 3,6 * DIS # E3: 8,9 => CTR => E3: 2,5 * DIS # E5: 5 => CTR => E5: 8,9 * DIS # D3: 5,9 => CTR => D3: 6,8 * PRF # E3: 5,9 => SOL * DIS # H2: 8 => CTR => H2: 5,9 * DIS # H3: 5,9 => CTR => H3: 8 * DIS # D3: 5,9 => CTR => D3: 6,8 * PRF # E3: 5,9 => SOL * DIS # I8: 5,9 => CTR => I8: 8 * DIS # D6: 5,9 => CTR => D6: 8 * DIS # A5: 5,9 => CTR => A5: 8 * DIS # G4: 5,9 => CTR => G4: 8 * DIS # D6: 5,9 => CTR => D6: 8 * DIS # H3: 5,9 => CTR => H3: 8 * DIS # A9: 5,9 => CTR => A9: 2,3,8 * DIS # C9: 5,9 => CTR => C9: 8 * DIS # C4: 8 => CTR => C4: 5,9 * DIS # I8: 5,9 => CTR => I8: 8 * DIS # G4: 5,9 => CTR => G4: 8 * CNT 25 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,C7,E1,F2,F3,F5,F8,G7,H6,I3) * .571.32646.274.3.1143...7.....264.17.713..642426.17..371.438.26..4.7.13......147. * PAIR A1: 8,9 COL A A4: 8,9,3,5 # reduction candidate for 8,9 A4: 8,9 => CTR * .571.32646.274.3.11436.27...3.264.1757138.642426.17..371.438.262.4.7613.36..2147. A5: 8,9,5 # reduction candidate for 8,9 A5: 8,9 # 16 pairs A8: 8,9,2,5 # reduction candidate for 8,9 A8: 8,9 => CTR * .571.32646.274.3.1143.267..3..264.1757138964242651789371.438926.64972135239651478 A9: 8,9,2,3,5 # reduction candidate for 8,9 A9: 8,9 => CTR * .571.32646.274.3.1143...7..3..264.17.713..642426.17..371.438.262.4.7613......147. * RESTART * PAIR RESTART * PAIR B2: 8,9 ROW 2 H2: 8,9,5 # reduction candidate for 8,9 H2: 8,9 => CTR * 957183264682745391143...785...264817871359642426817953719438526.64.72138238..147. H2: 5 => SOLVED * 957183264682749351143652789539264817871395642426817593715438926294576138368921475 * DURATION: 0:00:07.310846 START: 06:06:56.828576 END: 06:07:04.139422 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-097-base-pr-001.dot * REASONING * DIS # A4: 8,9 => CTR => A4: 3,5 * DIS A4: 3,5 # A8: 8,9 => CTR => A8: 2,5 * DIS A4: 3,5 + A8: 2,5 # A9: 8,9 => CTR => A9: 2,3,5 * DIS A4: 3,5 + A8: 2,5 + A9: 2,3,5 # H2: 8,9 => CTR => H2: 5 * PRF A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5 => SOL * STA A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5 * CNT 5 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 097 solution: 957183264682749351143652789539264817871395642426817593715438926294576138368921475 info: 1574 FNBTWXY S8.f 20107 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 957183264682749351143652789539264817871395642426817593715438926294576138368921475 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:
* DIS # A4: 8,9 => CTR => A4: 3,5 * INC # A4: 3,5 => UNS * INC # A5: 8,9 => UNS * DIS # A8: 8,9 => CTR => A8: 2,5 * INC # A8: 2,5 => UNS * DIS # A9: 8,9 => CTR => A9: 2,3,5 * INC # A9: 2,3,5 => UNS * INC # H2: 8,9 => UNS * PRF # H2: 5 => SOL * INC # B4: 8,9 => UNS * PRF # B8: 8,9 => SOL * INC # B8: 6 => UNS * DIS # B9: 8,9 => CTR => B9: 3,6 * INC # B9: 3,6 => UNS * INC # D3: 8,9 => UNS * DIS # E3: 8,9 => CTR => E3: 2,5 * INC # E3: 2,5 => UNS * INC # E5: 8,9 => UNS * DIS # E5: 5 => CTR => E5: 8,9 * DIS # D3: 5,9 => CTR => D3: 6,8 * INC # D3: 6,8 => UNS * PRF # E3: 5,9 => SOL * INC # E3: 2,8 => UNS * INC # H2: 5,9 => UNS * DIS # H2: 8 => CTR => H2: 5,9 * INC # H2: 5,9 => UNS * DIS # H3: 5,9 => CTR => H3: 8 * INC # H3: 8 => UNS * DIS # D3: 5,9 => CTR => D3: 6,8 * INC # D3: 6,8 => UNS * PRF # E3: 5,9 => SOL * INC # E3: 2,8 => UNS * DIS # I8: 5,9 => CTR => I8: 8 * INC # I8: 8 => UNS * INC # I9: 5,9 => UNS * INC # E5: 5,9 => UNS * DIS # D6: 5,9 => CTR => D6: 8 * INC # D6: 8 => UNS * DIS # A5: 5,9 => CTR => A5: 8 * INC # A5: 8 => UNS * DIS # G4: 5,9 => CTR => G4: 8 * INC # G4: 8 => UNS * INC # G6: 5,9 => UNS * DIS # D6: 5,9 => CTR => D6: 8 * INC # D6: 8 => UNS * INC # H2: 5,9 => UNS * DIS # H3: 5,9 => CTR => H3: 8 * INC # H3: 8 => UNS * INC # A8: 5,9 => UNS * DIS # A9: 5,9 => CTR => A9: 2,3,8 * INC # A9: 2,3,8 => UNS * DIS # C9: 5,9 => CTR => C9: 8 * INC # C9: 8 => UNS * INC # C4: 5,9 => UNS * DIS # C4: 8 => CTR => C4: 5,9 * DIS # I8: 5,9 => CTR => I8: 8 * INC # I8: 8 => UNS * INC # I9: 5,9 => UNS * DIS # G4: 5,9 => CTR => G4: 8 * INC # G4: 8 => UNS * INC # G6: 5,9 => UNS * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A4: 8,9 => CTR => A4: 3,5 * INC A4: 3,5 # A5: 8,9 => UNS * DIS A4: 3,5 # A8: 8,9 => CTR => A8: 2,5 * DIS A4: 3,5 + A8: 2,5 # A9: 8,9 => CTR => A9: 2,3,5 * DIS A4: 3,5 + A8: 2,5 + A9: 2,3,5 # H2: 8,9 => CTR => H2: 5 * PRF A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5 => SOL * STA A4: 3,5 + A8: 2,5 + A9: 2,3,5 + H2: 5 * CNT 6 HDP CHAINS / 5 HYP OPENED