Analysis of xx-top500-192-base.sdk
Contents
Original Sudoku
level: medium
position: 3.5.....8....21...............4...5379..6..............2....61.4..3...........2.. initial
Autosolve
position: 3.56...2864..213.5....354.....4...5379.563.425342......23.5.61.4..3.258..571.623. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 1,7 => CTR => B3: 8 * PRF # B3: 8 => SOL * DIS # G1: 9 => CTR => G1: 1,7 * DIS # C3: 8,9 => CTR => C3: 1,2 * PRF # C3: 1,2 => SOL * DIS # D2: 7 => CTR => D2: 8,9 * PRF # C3: 1,2 => SOL * DIS # C3: 8,9 => CTR => C3: 1,2 * DIS # G1: 7,9 => CTR => G1: 1 * PRF # G1: 1 => SOL * PRF # H3: 7,9 => SOL * DIS # H3: 6 => CTR => H3: 7,9 * DIS # D2: 7,9 => CTR => D2: 8 * DIS # H6: 7,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * DIS # C4: 1,2 => CTR => C4: 6,8 * PRF # C4: 6,8 => SOL * DIS # B4: 1,8 => CTR => B4: 6 * PRF # B4: 6 => SOL * PRF # C4: 1,8 => SOL * DIS # C3: 1,8 => CTR => C3: 2,9 * DIS # G4: 1,8 => CTR => G4: 7,9 * DIS # G6: 1,8 => CTR => G6: 7,9 * PRF # B4: 1,6 => SOL * DIS # B4: 8 => CTR => B4: 1,6 * DIS # C4: 1,6 => CTR => C4: 2,8 * PRF # C4: 2,8 => SOL * DIS # I7: 4 => CTR => I7: 7,9 * DIS # D2: 7,9 => CTR => D2: 8 * DIS # E1: 7,9 => CTR => E1: 4 * DIS # E4: 7,9 => CTR => E4: 1,8 * PRF # E6: 7,9 => SOL * DIS # I7: 4 => CTR => I7: 7,9 * DIS # I7: 4,9 => CTR => I7: 7 * CNT 34 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 1,7 => CTR => B3: 8 * PRF B3: 8 => SOL * STA B3: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.5.....8....21...............4...5379..6..............2....61.4..3...........2.. | initial |
| 3.56...2864..213.5....354.....4...5379.563.425342......23.5.61.4..3.258..571.623. | autosolve |
| 375649128649821375182735496268417953791563842534298761823954617416372589957186234 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B1: 1,7 C2: 8,9 A3: 1,2 H2: 7,9 I3: 1,6 A4: 1,2 C5: 1,8 G5: 1,8 I6: 1,6 A7: 8,9 B8: 1,6 C8: 1,6 A9: 8,9 D7: 7,9 F7: 4,8 E8: 7,9 E9: 4,8 I8: 7,9 I9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,I3: 1.. / G1 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) E4,E6: 1.. / E4 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) B8,C8: 1.. / B8 = 1 => 0 pairs (*) / C8 = 1 => 0 pairs (X) B1,G1: 1.. / B1 = 1 => 0 pairs (X) / G1 = 1 => 0 pairs (_) C5,G5: 1.. / C5 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) A3,A4: 1.. / A3 = 1 => 0 pairs (*) / A4 = 1 => 0 pairs (X) I3,I6: 1.. / I3 = 1 => 0 pairs (X) / I6 = 1 => 0 pairs (_) A3,C3: 2.. / A3 = 2 => 0 pairs (X) / C3 = 2 => 0 pairs (_) A4,C4: 2.. / A4 = 2 => 0 pairs (*) / C4 = 2 => 0 pairs (X) A3,A4: 2.. / A3 = 2 => 0 pairs (X) / A4 = 2 => 0 pairs (_) C3,C4: 2.. / C3 = 2 => 0 pairs (*) / C4 = 2 => 0 pairs (X) E1,F1: 4.. / E1 = 4 => 16 pairs (_) / F1 = 4 => 0 pairs (X) F7,E9: 4.. / F7 = 4 => 16 pairs (_) / E9 = 4 => 0 pairs (X) I7,I9: 4.. / I7 = 4 => 0 pairs (X) / I9 = 4 => 16 pairs (_) F7,I7: 4.. / F7 = 4 => 16 pairs (_) / I7 = 4 => 0 pairs (X) E9,I9: 4.. / E9 = 4 => 0 pairs (X) / I9 = 4 => 16 pairs (_) E1,E9: 4.. / E1 = 4 => 16 pairs (_) / E9 = 4 => 0 pairs (X) F1,F7: 4.. / F1 = 4 => 0 pairs (X) / F7 = 4 => 16 pairs (_) H3,I3: 6.. / H3 = 6 => 0 pairs (X) / I3 = 6 => 0 pairs (_) B4,C4: 6.. / B4 = 6 => 0 pairs (*) / C4 = 6 => 0 pairs (X) H6,I6: 6.. / H6 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) B8,C8: 6.. / B8 = 6 => 0 pairs (X) / C8 = 6 => 0 pairs (_) B4,B8: 6.. / B4 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) C4,C8: 6.. / C4 = 6 => 0 pairs (X) / C8 = 6 => 0 pairs (_) H3,H6: 6.. / H3 = 6 => 0 pairs (X) / H6 = 6 => 0 pairs (_) I3,I6: 6.. / I3 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) B1,B3: 7.. / B1 = 7 => 0 pairs (*) / B3 = 7 => 0 pairs (X) D7,E8: 7.. / D7 = 7 => 0 pairs (X) / E8 = 7 => 19 pairs (_) I7,I8: 7.. / I7 = 7 => 19 pairs (_) / I8 = 7 => 0 pairs (X) D2,H2: 7.. / D2 = 7 => 0 pairs (X) / H2 = 7 => 22 pairs (_) D7,I7: 7.. / D7 = 7 => 0 pairs (X) / I7 = 7 => 19 pairs (_) E8,I8: 7.. / E8 = 7 => 19 pairs (_) / I8 = 7 => 0 pairs (X) D2,D3: 8.. / D2 = 8 => 21 pairs (_) / D3 = 8 => 0 pairs (X) A7,A9: 8.. / A7 = 8 => 16 pairs (_) / A9 = 8 => 0 pairs (X) F7,E9: 8.. / F7 = 8 => 0 pairs (X) / E9 = 8 => 16 pairs (_) C2,D2: 8.. / C2 = 8 => 0 pairs (X) / D2 = 8 => 21 pairs (_) C5,G5: 8.. / C5 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) A7,F7: 8.. / A7 = 8 => 16 pairs (_) / F7 = 8 => 0 pairs (X) A9,E9: 8.. / A9 = 8 => 0 pairs (X) / E9 = 8 => 16 pairs (_) B3,B4: 8.. / B3 = 8 => 0 pairs (*) / B4 = 8 => 0 pairs (X) C2,C3: 9.. / C2 = 9 => 21 pairs (_) / C3 = 9 => 0 pairs (X) A7,A9: 9.. / A7 = 9 => 0 pairs (X) / A9 = 9 => 16 pairs (_) D7,E8: 9.. / D7 = 9 => 19 pairs (_) / E8 = 9 => 0 pairs (X) E8,I8: 9.. / E8 = 9 => 0 pairs (X) / I8 = 9 => 19 pairs (_) A9,I9: 9.. / A9 = 9 => 16 pairs (_) / I9 = 9 => 0 pairs (X) * DURATION: 0:01:24.593997 START: 09:17:47.204595 END: 09:19:11.798592 2017-05-04 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A7,A9,B1,B8,C2,C5,C8,D7,E8,E9,F7,G5,H2,I3,I6,I8,I9) * 3.56...2864..213.5....354.....4...5379.563.425342......23.5.61.4..3.258..571.623. * PAIR B1: 1,7 BLK 1 B3: 1,7,8 # reduction candidate for 1,7 B3: 1,7 => CTR * 3.56...2864..213.5....354...864...53791563.425342......23.5.61.4..3.258..571.623. B3: 8 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 * PAIR B1: 1,7 ROW 1 G1: 1,7,9 # reduction candidate for 1,7 G1: 9 => CTR * 3156..92864..2137527..3546118.4...5379.563.425342......23.5.61.4..3.258..571.623. G1: 1,7 # 19 pairs * PAIR C2: 8,9 BLK 1 C3: 8,9,1,2 # reduction candidate for 8,9 C3: 8,9 => CTR * 3.56...2864..213.52...354..1.24...53798563.425342......23.5.61.4..3.258..571.623. C3: 1,2 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 * PAIR C2: 8,9 ROW 2 D2: 8,9,7 # reduction candidate for 8,9 D2: 7 => CTR * 3.56...28648721395..98354...8.4...5379.563.425342......23.5.61.4..3.258..571.623. D2: 8,9 # 22 pairs * PAIR A3: 1,2 BLK 1 C3: 1,2,8,9 # reduction candidate for 1,2 C3: 1,2 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 C3: 8,9 => CTR * 3.56...2864..213.52...354..1.24...53798563.425342......23.5.61.4..3.258..571.623. * PAIR H2: 7,9 BLK 3 G1: 7,9,1 # reduction candidate for 7,9 G1: 7,9 => CTR * 3156...2864..213.527..354.118.4...5379.563.425342......23.5.61.4..3.258..571.623. G1: 1 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 H3: 7,9,6 # reduction candidate for 7,9 H3: 7,9 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 H3: 6 => CTR * 3.56...2864..213.5....354611.24...53798563.425342......23.5.61.4..3.258..571.623. * PAIR H2: 7,9 ROW 2 D2: 7,9,8 # reduction candidate for 7,9 D2: 7,9 => CTR * 3.56...28648.213.5..98354...8.4...5379.563.425342......23.5.61.4..3.258..571.623. D2: 8 # 21 pairs * PAIR H2: 7,9 COL H H6: 7,9,6 # reduction candidate for 7,9 H6: 7,9 => CTR * 3.56...2864..213.5....354611.24...53798563.425342......23.5.61.4..3.258..571.623. H6: 6 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 * PAIR A4: 1,2 BLK 4 C4: 1,2,6,8 # reduction candidate for 1,2 C4: 1,2 => CTR * 3.56...2864..213.5....354...6.4...5379856314253421...6.23.5.61.4163.258..571.623. C4: 6,8 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 * PAIR C5: 1,8 BLK 4 B4: 1,8,6 # reduction candidate for 1,8 B4: 1,8 => CTR * 3.56...2864..213.5..2.354..2164...5379856314253421...6.23.5.61.4613.258..571.623. B4: 6 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 C4: 1,8,2,6 # reduction candidate for 1,8 C4: 1,8 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 C4: 2,6 # 20 pairs * PAIR C5: 1,8 COL C C3: 1,8,2,9 # reduction candidate for 1,8 C3: 1,8 => CTR * 3.56...286498213752...354..1.24...5379856314253421...6.23.5.61.4.63.258..571.623. C3: 2,9 # 20 pairs * PAIR G5: 1,8 BLK 6 G4: 1,8,7,9 # reduction candidate for 1,8 G4: 1,8 => CTR * 3.564..2864..213.5....354611.24..853798563.42534218..6823.5461.4..3.258.957186234 G4: 7,9 # 20 pairs G6: 1,8,7,9 # reduction candidate for 1,8 G6: 1,8 => CTR * 3156...2864..213.527..3546118.4...5379.563.425342......23.5.61.4..3.258..571.623. G6: 7,9 # 21 pairs * PAIR B8: 1,6 COL B B4: 1,6,8 # reduction candidate for 1,6 B4: 1,6 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 B4: 8 => CTR * 3.56...2864..213.5....354...864...53791563.425342......23.5.61.4..3.258..571.623. * PAIR C8: 1,6 COL C C4: 1,6,2,8 # reduction candidate for 1,6 C4: 1,6 => CTR * 3.56...286498213751827354962..4...537985631425342......23.5.61.4..3.258..571.623. C4: 2,8 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 * PAIR D7: 7,9 ROW 7 I7: 7,9,4 # reduction candidate for 7,9 I7: 4 => CTR * 3.567492864..21375.7..3546118.4...5379.563.425342......2375.6144..392587.57146239 I7: 7,9 # 16 pairs * PAIR D7: 7,9 COL D D2: 7,9,8 # reduction candidate for 7,9 D2: 7,9 => CTR * 3.56...28648.213.5..98354...8.4...5379.563.425342......23.5.61.4..3.258..571.623. D2: 8 # 21 pairs D3: 7,9,8 # reduction candidate for 7,9 D3: 7,9 # 21 pairs * PAIR E8: 7,9 COL E E1: 7,9,4 # reduction candidate for 7,9 E1: 7,9 => CTR * 3.567492864..21375.7..3546118.4...5379.563.425342.....9237586144..392587857146239 E1: 4 # 16 pairs E4: 7,9,1,8 # reduction candidate for 7,9 E4: 7,9 => CTR * 3.564..2864..213.5....354611.24...53798563.4253421...6.23.5.61.4..3.258..57186234 E4: 1,8 # 22 pairs E6: 7,9,1,8 # reduction candidate for 7,9 E6: 7,9 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 E6: 1,8 # 20 pairs * PAIR I8: 7,9 BLK 9 I7: 7,9,4 # reduction candidate for 7,9 I7: 4 => CTR * 3.567492864..21375.7..3546118.4...5379.563.425342......2375.6144..392587.57146239 I7: 7,9 # 16 pairs * PAIR I9: 4,9 BLK 9 I7: 4,9,7 # reduction candidate for 4,9 I7: 4,9 => CTR * 3.56...2864..21375.7..354...864...53791563.425342......2375.61.4..392587.571.623. I7: 7 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-192-base-pr-000.dot * REASONING * DIS # B3: 1,7 => CTR => B3: 8 * PRF # B3: 8 => SOL * DIS # G1: 9 => CTR => G1: 1,7 * DIS # C3: 8,9 => CTR => C3: 1,2 * PRF # C3: 1,2 => SOL * DIS # D2: 7 => CTR => D2: 8,9 * PRF # C3: 1,2 => SOL * DIS # C3: 8,9 => CTR => C3: 1,2 * DIS # G1: 7,9 => CTR => G1: 1 * PRF # G1: 1 => SOL * PRF # H3: 7,9 => SOL * DIS # H3: 6 => CTR => H3: 7,9 * DIS # D2: 7,9 => CTR => D2: 8 * DIS # H6: 7,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * DIS # C4: 1,2 => CTR => C4: 6,8 * PRF # C4: 6,8 => SOL * DIS # B4: 1,8 => CTR => B4: 6 * PRF # B4: 6 => SOL * PRF # C4: 1,8 => SOL * DIS # C3: 1,8 => CTR => C3: 2,9 * DIS # G4: 1,8 => CTR => G4: 7,9 * DIS # G6: 1,8 => CTR => G6: 7,9 * PRF # B4: 1,6 => SOL * DIS # B4: 8 => CTR => B4: 1,6 * DIS # C4: 1,6 => CTR => C4: 2,8 * PRF # C4: 2,8 => SOL * DIS # I7: 4 => CTR => I7: 7,9 * DIS # D2: 7,9 => CTR => D2: 8 * DIS # E1: 7,9 => CTR => E1: 4 * DIS # E4: 7,9 => CTR => E4: 1,8 * PRF # E6: 7,9 => SOL * DIS # I7: 4 => CTR => I7: 7,9 * DIS # I7: 4,9 => CTR => I7: 7 * CNT 34 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A7,A9,B1,B8,C2,C5,C8,D7,E8,E9,F7,G5,H2,I3,I6,I8,I9) * 3.56...2864..213.5....354.....4...5379.563.425342......23.5.61.4..3.258..571.623. * PAIR B1: 1,7 BLK 1 B3: 1,7,8 # reduction candidate for 1,7 B3: 1,7 => CTR * 3.56...2864..213.5....354...864...53791563.425342......23.5.61.4..3.258..571.623. B3: 8 => SOLVED * 375649128649821375182735496268417953791563842534298761823954617416372589957186234 * DURATION: 0:00:03.248439 START: 09:20:06.391527 END: 09:20:09.639966 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-192-base-pr-001.dot * REASONING * DIS # B3: 1,7 => CTR => B3: 8 * PRF B3: 8 => SOL * STA B3: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 192 solution: 375649128649821375182735496268417953791563842534298761823954617416372589957186234 info: 1844 FNBTWY S8.f 29754 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 375649128649821375182735496268417953791563842534298761823954617416372589957186234 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 # B3: 1,7 => CTR => B3: 8 * PRF # B3: 8 => SOL * INC # G1: 1,7 => UNS * DIS # G1: 9 => CTR => G1: 1,7 * DIS # C3: 8,9 => CTR => C3: 1,2 * PRF # C3: 1,2 => SOL * INC # D2: 8,9 => UNS * DIS # D2: 7 => CTR => D2: 8,9 * PRF # C3: 1,2 => SOL * DIS # C3: 8,9 => CTR => C3: 1,2 * DIS # G1: 7,9 => CTR => G1: 1 * PRF # G1: 1 => SOL * PRF # H3: 7,9 => SOL * DIS # H3: 6 => CTR => H3: 7,9 * DIS # D2: 7,9 => CTR => D2: 8 * INC # D2: 8 => UNS * DIS # H6: 7,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * DIS # C4: 1,2 => CTR => C4: 6,8 * PRF # C4: 6,8 => SOL * DIS # B4: 1,8 => CTR => B4: 6 * PRF # B4: 6 => SOL * PRF # C4: 1,8 => SOL * INC # C4: 2,6 => UNS * DIS # C3: 1,8 => CTR => C3: 2,9 * INC # C3: 2,9 => UNS * DIS # G4: 1,8 => CTR => G4: 7,9 * INC # G4: 7,9 => UNS * DIS # G6: 1,8 => CTR => G6: 7,9 * INC # G6: 7,9 => UNS * PRF # B4: 1,6 => SOL * DIS # B4: 8 => CTR => B4: 1,6 * DIS # C4: 1,6 => CTR => C4: 2,8 * PRF # C4: 2,8 => SOL * INC # I7: 7,9 => UNS * DIS # I7: 4 => CTR => I7: 7,9 * DIS # D2: 7,9 => CTR => D2: 8 * INC # D2: 8 => UNS * INC # D3: 7,9 => UNS * DIS # E1: 7,9 => CTR => E1: 4 * INC # E1: 4 => UNS * DIS # E4: 7,9 => CTR => E4: 1,8 * INC # E4: 1,8 => UNS * PRF # E6: 7,9 => SOL * INC # E6: 1,8 => UNS * INC # I7: 7,9 => UNS * DIS # I7: 4 => CTR => I7: 7,9 * DIS # I7: 4,9 => CTR => I7: 7 * INC # I7: 7 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 1,7 => CTR => B3: 8 * PRF B3: 8 => SOL * STA B3: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED