Analysis of xx-top500-273-base.sdk
Contents
Original Sudoku
level: medium
position: .836.........7..4...........6.1.8..........27...3.....4.2.5....7.....8........1.. initial
Autosolve
position: .836.........7..48.74.8.....671.8..........27...3.7.814.285....7.....8.....7..1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 5,9 => CTR => G1: 2,7 * PRF # G2: 5,9 => SOL * DIS # I3: 5,9 => CTR => I3: 3,6 * DIS # F1: 5,9 => CTR => F1: 1,2,4 * DIS # I4: 3 => CTR => I4: 5,9 * DIS # A4: 5,9 => CTR => A4: 2,3 * DIS # B6: 5,9 => CTR => B6: 2,4 * DIS # G6: 5,9 => CTR => G6: 4,6 * DIS # C8: 5,9 => CTR => C8: 1,6 * PRF # C9: 5,9 => SOL * DIS # G4: 3,9 => CTR => G4: 4,5 * DIS # I4: 3,9 => CTR => I4: 5 * DIS # A4: 2,5 => CTR => A4: 3,9 * PRF # H3: 3,9 => SOL * DIS # H7: 3,9 => CTR => H7: 6,7 * DIS # F8: 2,4 => CTR => F8: 1,6,9 * DIS # F9: 6,9 => CTR => F9: 2,4 * CNT 17 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G1: 5,9 => CTR => G1: 2,7 * PRF G1: 2,7 # G2: 5,9 => SOL * STA G1: 2,7 + G2: 5,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .836.........7..4...........6.1.8..........27...3.....4.2.5....7.....8........1.. | initial |
| .836.........7..48.74.8.....671.8..........27...3.7.814.285....7.....8.....7..1.. | autosolve |
| 583642719621973548974581236367128495198465327245397681412856973736219854859734162 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) I1: 5,9 C6: 5,9 H4: 3,9 I8: 2,4 I9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H3: 1.. / H1 = 1 => 0 pairs (*) / H3 = 1 => 0 pairs (X) B7,F7: 1.. / B7 = 1 => 8 pairs (_) / F7 = 1 => 0 pairs (X) E1,E8: 1.. / E1 = 1 => 0 pairs (X) / E8 = 1 => 0 pairs (_) E4,E6: 2.. / E4 = 2 => 5 pairs (_) / E6 = 2 => 0 pairs (X) I8,I9: 2.. / I8 = 2 => 4 pairs (_) / I9 = 2 => 10 pairs (_) A4,E4: 2.. / A4 = 2 => 0 pairs (X) / E4 = 2 => 5 pairs (_) F9,I9: 2.. / F9 = 2 => 4 pairs (_) / I9 = 2 => 10 pairs (_) B2,B6: 2.. / B2 = 2 => 6 pairs (_) / B6 = 2 => 0 pairs (X) F2,F3: 3.. / F2 = 3 => 0 pairs (*) / F3 = 3 => 0 pairs (X) E8,E9: 3.. / E8 = 3 => 0 pairs (X) / E9 = 3 => 7 pairs (_) F2,G2: 3.. / F2 = 3 => 0 pairs (*) / G2 = 3 => 0 pairs (X) E1,F1: 4.. / E1 = 4 => 0 pairs (*) / F1 = 4 => 0 pairs (X) B5,B6: 4.. / B5 = 4 => 0 pairs (X) / B6 = 4 => 6 pairs (_) I8,I9: 4.. / I8 = 4 => 10 pairs (_) / I9 = 4 => 4 pairs (_) E4,G4: 4.. / E4 = 4 => 0 pairs (X) / G4 = 4 => 6 pairs (_) D5,D8: 4.. / D5 = 4 => 11 pairs (_) / D8 = 4 => 4 pairs (_) D5,F5: 5.. / D5 = 5 => 6 pairs (_) / F5 = 5 => 6 pairs (_) H8,H9: 5.. / H8 = 5 => 5 pairs (_) / H9 = 5 => 6 pairs (_) A2,C2: 6.. / A2 = 6 => 5 pairs (_) / C2 = 6 => 0 pairs (X) H3,I3: 6.. / H3 = 6 => 0 pairs (X) / I3 = 6 => 6 pairs (_) G5,G6: 6.. / G5 = 6 => 0 pairs (X) / G6 = 6 => 5 pairs (_) E6,G6: 6.. / E6 = 6 => 0 pairs (X) / G6 = 6 => 5 pairs (_) A2,A9: 6.. / A2 = 6 => 5 pairs (_) / A9 = 6 => 0 pairs (X) I3,I7: 6.. / I3 = 6 => 6 pairs (_) / I7 = 6 => 0 pairs (X) G1,H1: 7.. / G1 = 7 => 7 pairs (_) / H1 = 7 => 0 pairs (X) G7,H7: 7.. / G7 = 7 => 0 pairs (X) / H7 = 7 => 7 pairs (_) G1,G7: 7.. / G1 = 7 => 7 pairs (_) / G7 = 7 => 0 pairs (X) H1,H7: 7.. / H1 = 7 => 0 pairs (X) / H7 = 7 => 7 pairs (_) A5,C5: 8.. / A5 = 8 => 6 pairs (_) / C5 = 8 => 5 pairs (_) A9,C9: 8.. / A9 = 8 => 5 pairs (_) / C9 = 8 => 6 pairs (_) A5,A9: 8.. / A5 = 8 => 6 pairs (_) / A9 = 8 => 5 pairs (_) C5,C9: 8.. / C5 = 8 => 5 pairs (_) / C9 = 8 => 6 pairs (_) * DURATION: 0:00:51.235247 START: 12:15:10.921703 END: 12:16:02.156950 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,H4,I1,I8,I9) * .836.........7..48.74.8.....671.8..........27...3.7.814.285....7.....8.....7..1.. * PAIR I1: 5,9 BLK 3 G1: 5,9,2,7 # reduction candidate for 5,9 G1: 5,9 => CTR * 183642.7.62..71348.74.83216.671.84..3....5.27.4.3.7.8141285.7..7..21.8.4...7341.2 G1: 2,7 # 6 pairs G2: 5,9,2,3 # reduction candidate for 5,9 G2: 5,9 => SOLVED * 583642719621973548974581236367128495198465327245397681412856973736219854859734162 G2: 2,3 # 6 pairs G3: 5,9,2,3 # reduction candidate for 5,9 G3: 5,9 # 10 pairs I3: 5,9,3,6 # reduction candidate for 5,9 I3: 5,9 => CTR * .836..71.....7..48.74.8..6..671.8.933.8....27...3.7.81412859.767...1.8.....73.1.. I3: 3,6 # 6 pairs * PAIR I1: 5,9 ROW 1 A1: 5,9,1,2 # reduction candidate for 5,9 A1: 5,9 # 9 pairs F1: 5,9,1,2,4 # reduction candidate for 5,9 F1: 5,9 => CTR * .8364.27..2..7..48.74.8..16.671.84...9..6.327.453.768141285.73973..1.85..5.73.16. F1: 1,2,4 # 5 pairs * PAIR I1: 5,9 COL I I4: 5,9,3 # reduction candidate for 5,9 I4: 3 => CTR * .836.....62..71348.74.83....671.8.93.......27.4.3.7.81412856.397.6...8.....7..1.. I4: 5,9 # 8 pairs * PAIR C6: 5,9 BLK 4 A4: 5,9,2,3 # reduction candidate for 5,9 A4: 5,9 => CTR * .836.....62..71348.74.83....671284.........2724.3.7.8141285....7.6.1.8....873.1.. A4: 2,3 # 6 pairs A6: 5,9,2 # reduction candidate for 5,9 A6: 5,9 # 10 pairs B6: 5,9,2,4 # reduction candidate for 5,9 B6: 5,9 => CTR * .836.427..2..7..48.7428..16.671.8...34.....27...3.7.814.285.7..7..4..8.2...7.21.4 B6: 2,4 # 6 pairs * PAIR C6: 5,9 ROW 6 G6: 5,9,4,6 # reduction candidate for 5,9 G6: 5,9 => CTR * .836.....62..71348.74.83....671284........62724.367.8141285....7.6.1.8....873.1.. G6: 4,6 # 6 pairs * PAIR C6: 5,9 COL C C2: 5,9,1,6 # reduction candidate for 5,9 C2: 5,9 # 9 pairs C8: 5,9,1,6 # reduction candidate for 5,9 C8: 5,9 => CTR * .8364.719....73.48.74.81.36367128495....6.327.4.39768141285697373..1.86....73.15. C8: 1,6 # 6 pairs C9: 5,9,6,8 # reduction candidate for 5,9 C9: 5,9 => SOLVED * 583642719621973548974581236367128495198465327245397681412856973736219854859734162 C9: 6,8 # 6 pairs * PAIR H4: 3,9 BLK 6 G4: 3,9,4,5 # reduction candidate for 3,9 G4: 3,9 => CTR * 583614279.2..7..4897428..16267148..5......427.4.3276814.285.7.37..4..8.2...7.21.4 G4: 4,5 # 6 pairs I4: 3,9,5 # reduction candidate for 3,9 I4: 3,9 => CTR * .836.....62..71348.74.83....671.8..........27.4.3.7.8141285....7.6.1.8....873.1.. I4: 5 # 8 pairs G5: 3,9,4,6 # reduction candidate for 3,9 G5: 3,9 # 10 pairs * PAIR H4: 3,9 ROW 4 A4: 3,9,2,5 # reduction candidate for 3,9 A4: 2,5 => CTR * .836.....62..71348.74.83....671.8..........27.4.3.7.8141285....7.6.1.8....873.1.. A4: 3,9 # 10 pairs * PAIR H4: 3,9 COL H H3: 3,9,1,6 # reduction candidate for 3,9 H3: 3,9 => SOLVED * 583642719621973548974581236367128495198465327245397681412856973736219854859734162 H3: 1,6 # 6 pairs H7: 3,9,6,7 # reduction candidate for 3,9 H7: 3,9 => CTR * 1836...7.62..71348.74.83.16.671.8...831....27.4.3.7.814128567..7.....8.....7..1.. H7: 6,7 # 6 pairs H8: 3,9,5,6 # reduction candidate for 3,9 H8: 3,9 # 11 pairs H9: 3,9,5,6 # reduction candidate for 3,9 H9: 3,9 # 10 pairs * PAIR I8: 2,4 ROW 8 D8: 2,4,9 # reduction candidate for 2,4 D8: 2,4 # 6 pairs F8: 2,4,1,6,9 # reduction candidate for 2,4 F8: 2,4 => CTR * 5836..279.2.57.348974283516.671.8435...4.5.272453.7.814.285.7.37..9..8.....7..1.. F8: 1,6,9 # 5 pairs * PAIR I9: 2,4 ROW 9 F9: 2,4,6,9 # reduction candidate for 2,4 F9: 6,9 => CTR * .8361427..2..7..48.74.8..16.671.84.....4.5.27.4.3.7.814.285.7..7...3.8.4...74.1.2 F9: 2,4 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-273-base-pr-000.dot * REASONING * DIS # G1: 5,9 => CTR => G1: 2,7 * PRF # G2: 5,9 => SOL * DIS # I3: 5,9 => CTR => I3: 3,6 * DIS # F1: 5,9 => CTR => F1: 1,2,4 * DIS # I4: 3 => CTR => I4: 5,9 * DIS # A4: 5,9 => CTR => A4: 2,3 * DIS # B6: 5,9 => CTR => B6: 2,4 * DIS # G6: 5,9 => CTR => G6: 4,6 * DIS # C8: 5,9 => CTR => C8: 1,6 * PRF # C9: 5,9 => SOL * DIS # G4: 3,9 => CTR => G4: 4,5 * DIS # I4: 3,9 => CTR => I4: 5 * DIS # A4: 2,5 => CTR => A4: 3,9 * PRF # H3: 3,9 => SOL * DIS # H7: 3,9 => CTR => H7: 6,7 * DIS # F8: 2,4 => CTR => F8: 1,6,9 * DIS # F9: 6,9 => CTR => F9: 2,4 * CNT 17 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,H4,I1,I8,I9) * .836.........7..48.74.8.....671.8..........27...3.7.814.285....7.....8.....7..1.. * PAIR I1: 5,9 BLK 3 G1: 5,9,2,7 # reduction candidate for 5,9 G1: 5,9 => CTR * 183642.7.62..71348.74.83216.671.84..3....5.27.4.3.7.8141285.7..7..21.8.4...7341.2 G2: 5,9,2,3 # reduction candidate for 5,9 G2: 5,9 => SOLVED * 583642719621973548974581236367128495198465327245397681412856973736219854859734162 * DURATION: 0:00:04.008084 START: 12:16:40.186596 END: 12:16:44.194680 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-273-base-pr-001.dot * REASONING * DIS # G1: 5,9 => CTR => G1: 2,7 * PRF G1: 2,7 # G2: 5,9 => SOL * STA G1: 2,7 + G2: 5,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 273 solution: 583642719621973548974581236367128495198465327245397681412856973736219854859734162 info: 2201 FNBHXYK S8.f 24153 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 583642719621973548974581236367128495198465327245397681412856973736219854859734162 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 # G1: 5,9 => CTR => G1: 2,7 * INC # G1: 2,7 => UNS * PRF # G2: 5,9 => SOL * INC # G2: 2,3 => UNS * INC # G3: 5,9 => UNS * DIS # I3: 5,9 => CTR => I3: 3,6 * INC # I3: 3,6 => UNS * INC # A1: 5,9 => UNS * DIS # F1: 5,9 => CTR => F1: 1,2,4 * INC # F1: 1,2,4 => UNS * INC # I4: 5,9 => UNS * DIS # I4: 3 => CTR => I4: 5,9 * DIS # A4: 5,9 => CTR => A4: 2,3 * INC # A4: 2,3 => UNS * INC # A6: 5,9 => UNS * DIS # B6: 5,9 => CTR => B6: 2,4 * INC # B6: 2,4 => UNS * DIS # G6: 5,9 => CTR => G6: 4,6 * INC # G6: 4,6 => UNS * INC # C2: 5,9 => UNS * DIS # C8: 5,9 => CTR => C8: 1,6 * INC # C8: 1,6 => UNS * PRF # C9: 5,9 => SOL * INC # C9: 6,8 => UNS * DIS # G4: 3,9 => CTR => G4: 4,5 * INC # G4: 4,5 => UNS * DIS # I4: 3,9 => CTR => I4: 5 * INC # I4: 5 => UNS * INC # G5: 3,9 => UNS * INC # A4: 3,9 => UNS * DIS # A4: 2,5 => CTR => A4: 3,9 * PRF # H3: 3,9 => SOL * INC # H3: 1,6 => UNS * DIS # H7: 3,9 => CTR => H7: 6,7 * INC # H7: 6,7 => UNS * INC # H8: 3,9 => UNS * INC # H9: 3,9 => UNS * INC # D8: 2,4 => UNS * DIS # F8: 2,4 => CTR => F8: 1,6,9 * INC # F8: 1,6,9 => UNS * INC # F9: 2,4 => UNS * DIS # F9: 6,9 => CTR => F9: 2,4 * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G1: 5,9 => CTR => G1: 2,7 * PRF G1: 2,7 # G2: 5,9 => SOL * STA G1: 2,7 + G2: 5,9 * CNT 2 HDP CHAINS / 2 HYP OPENED