Analysis of xx-top500-059-base.sdk
Contents
Original Sudoku
level: medium
position: ...8....12.....5...........41..5......3....8.......7.....1.8.4..2.3.....5.....6.. initial
Autosolve
position: ..58....12.....5.....5.....418753...753...184..2481753...1.8.45.2.3.5...5.....6.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 6,9 => CTR => B2: 3,4,7,8 * PRF # I2: 6,9 => SOL * DIS # D5: 6,9 => CTR => D5: 2 * DIS # A1: 6,9 => CTR => A1: 3 * DIS # B2: 6,9 => CTR => B2: 3,4,7,8 * DIS # F5: 2,9 => CTR => F5: 6 * DIS # E1: 2,9 => CTR => E1: 3,4,7 * DIS # E3: 2,9 => CTR => E3: 1,3,4,7 * DIS # E9: 2,9 => CTR => E9: 4,7 * DIS # G1: 2,9 => CTR => G1: 3,4 * DIS # G3: 2,9 => CTR => G3: 3,4,8 * DIS # E9: 2,9 => CTR => E9: 4,7 * DIS # F9: 2,9 => CTR => F9: 4,7 * DIS # D5: 6 => CTR => D5: 2,9 * PRF # H9: 2,3 => SOL * DIS # H9: 1 => CTR => H9: 2,3 * DIS # G1: 2,3 => CTR => G1: 4,9 * DIS # G3: 2,3 => CTR => G3: 4,8,9 * DIS # I8: 8,9 => CTR => I8: 7 * PRF # G3: 8,9 => SOL * DIS # G3: 2,3,4 => CTR => G3: 8,9 * PRF # I3: 2,8 => SOL * CNT 22 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 6,9 => CTR => B2: 3,4,7,8 * PRF B2: 3,4,7,8 # I2: 6,9 => SOL * STA B2: 3,4,7,8 + I2: 6,9 * CNT 2 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8....12.....5...........41..5......3....8.......7.....1.8.4..2.3.....5.....6.. | initial |
| ..58....12.....5.....5.....418753...753...184..2481753...1.8.45.2.3.5...5.....6.. | autosolve |
| 395872461287614539146539872418753296753296184962481753679128345824365917531947628 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A3: 1,8 D2: 6,9 A6: 6,9 B6: 6,9 E5: 2,9 G4: 2,9 A8: 1,8 C8: 4,6 E8: 4,6 D9: 2,9 G7: 2,3 G8: 8,9 I9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 1.. / E2 = 1 => 13 pairs (_) / E3 = 1 => 0 pairs (X) A8,C9: 1.. / A8 = 1 => 0 pairs (X) / C9 = 1 => 0 pairs (_) H8,H9: 1.. / H8 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) C2,E2: 1.. / C2 = 1 => 0 pairs (X) / E2 = 1 => 13 pairs (_) A8,H8: 1.. / A8 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) C9,H9: 1.. / C9 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) A3,A8: 1.. / A3 = 1 => 0 pairs (*) / A8 = 1 => 0 pairs (X) E7,G7: 2.. / E7 = 2 => 0 pairs (*) / G7 = 2 => 0 pairs (X) D5,D9: 2.. / D5 = 2 => 10 pairs (_) / D9 = 2 => 0 pairs (X) G7,H9: 3.. / G7 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) B9,H9: 3.. / B9 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) A1,A7: 3.. / A1 = 3 => 16 pairs (_) / A7 = 3 => 0 pairs (X) G1,G3: 4.. / G1 = 4 => 13 pairs (_) / G3 = 4 => 0 pairs (X) C8,E8: 4.. / C8 = 4 => 11 pairs (_) / E8 = 4 => 0 pairs (X) A6,B6: 6.. / A6 = 6 => 13 pairs (_) / B6 = 6 => 13 pairs (_) D5,F5: 6.. / D5 = 6 => 0 pairs (X) / F5 = 6 => 13 pairs (_) H4,I4: 6.. / H4 = 6 => 14 pairs (_) / I4 = 6 => 14 pairs (_) E7,E8: 6.. / E7 = 6 => 0 pairs (X) / E8 = 6 => 11 pairs (_) C8,E8: 6.. / C8 = 6 => 0 pairs (X) / E8 = 6 => 11 pairs (_) D2,D5: 6.. / D2 = 6 => 13 pairs (_) / D5 = 6 => 0 pairs (X) H8,I8: 7.. / H8 = 7 => 0 pairs (X) / I8 = 7 => 14 pairs (_) A8,B9: 8.. / A8 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) B2,I2: 8.. / B2 = 8 => 0 pairs (*) / I2 = 8 => 0 pairs (X) B9,I9: 8.. / B9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) A3,A8: 8.. / A3 = 8 => 0 pairs (X) / A8 = 8 => 0 pairs (_) G3,G8: 8.. / G3 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) A6,B6: 9.. / A6 = 9 => 13 pairs (_) / B6 = 9 => 13 pairs (_) * DURATION: 0:00:40.885239 START: 04:41:11.210037 END: 04:41:52.095276 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,A8,B6,C8,D2,D9,E5,E8,G4,G7,G8,I9) * ..58....12.....5.....5.....418753...753...184..2481753...1.8.45.2.3.5...5.....6.. * PAIR D2: 6,9 BLK 2 F1: 6,9,2,4,7 # reduction candidate for 6,9 F1: 6,9 # 15 pairs F2: 6,9,4,7 # reduction candidate for 6,9 F2: 6,9 # 16 pairs F3: 6,9,2,4,7 # reduction candidate for 6,9 F3: 6,9 # 15 pairs * PAIR D2: 6,9 ROW 2 B2: 6,9,3,4,7,8 # reduction candidate for 6,9 B2: 6,9 => CTR * ..58....12.....5.8...5.....418753...753...184..2481753...1.8.45.2.3.58..58....632 B2: 3,4,7,8 # 13 pairs C2: 6,9,1,4,7 # reduction candidate for 6,9 C2: 6,9 # 17 pairs H2: 6,9,3,7 # reduction candidate for 6,9 H2: 6,9 # 16 pairs I2: 6,9,7,8 # reduction candidate for 6,9 I2: 6,9 => SOLVED * 395872461287614539146539872418753296753296184962481753679128345824365917531947628 I2: 7,8 # 14 pairs * PAIR D2: 6,9 COL D D5: 6,9,2 # reduction candidate for 6,9 D5: 6,9 => CTR * ..58....128....5..1..5..8..418753...753...184..2481753...1.824582.3.59..5..2..6.8 D5: 2 # 10 pairs * PAIR A6: 6,9 COL A A1: 6,9,3 # reduction candidate for 6,9 A1: 6,9 => CTR * ..58....12.....5.....5.....418753...753...184..24817533..1.8245.2.3.5...5.....638 A1: 3 # 16 pairs A7: 6,9,3 # reduction candidate for 6,9 A7: 6,9 # 16 pairs * PAIR B6: 6,9 COL B B1: 6,9,3,4,7 # reduction candidate for 6,9 B1: 6,9 # 15 pairs B2: 6,9,3,4,7,8 # reduction candidate for 6,9 B2: 6,9 => CTR * ..58....12.....5.8...5.....418753...753...184..2481753...1.8.45.2.3.58..58....632 B2: 3,4,7,8 # 13 pairs B3: 6,9,3,4,7,8 # reduction candidate for 6,9 B3: 6,9 # 15 pairs B7: 6,9,3,7 # reduction candidate for 6,9 B7: 6,9 # 14 pairs * PAIR E5: 2,9 BLK 5 D5: 2,9,6 # reduction candidate for 2,9 D5: 2,9 # 13 pairs F5: 2,9,6 # reduction candidate for 2,9 F5: 2,9 => CTR * ..58....128.9..5..1..5..8..418753...7536..184..2481753...1.824582.3.59..5..2..6.8 F5: 6 # 13 pairs * PAIR E5: 2,9 COL E E1: 2,9,3,4,7 # reduction candidate for 2,9 E1: 2,9 => CTR * ..58....12.....5.....5.....418753...753...184..2481753...1.8245.2.3.5...5.....638 E1: 3,4,7 # 13 pairs E3: 2,9,1,3,4,7 # reduction candidate for 2,9 E3: 2,9 => CTR * ..583...12...1.5.....5.....418753...753...184..24817533..1.8245.2.3.5...5.....638 E3: 1,3,4,7 # 13 pairs E7: 2,9,6,7 # reduction candidate for 2,9 E7: 2,9 # 16 pairs E9: 2,9,4,7 # reduction candidate for 2,9 E9: 2,9 => CTR * ..58....12.....5.....5.....418753...753...184..2481753...1.8245.2.3.5...5.....638 E9: 4,7 # 14 pairs * PAIR G4: 2,9 BLK 6 H4: 2,9,6 # reduction candidate for 2,9 H4: 2,9 # 14 pairs I4: 2,9,6 # reduction candidate for 2,9 I4: 2,9 # 14 pairs * PAIR G4: 2,9 COL G G1: 2,9,3,4 # reduction candidate for 2,9 G1: 2,9 => CTR * ..58....12.....5.....5..4..418753...753...184..2481753...1.8345.2.3.58..5.....6.. G1: 3,4 # 14 pairs G3: 2,9,3,4,8 # reduction candidate for 2,9 G3: 2,9 => CTR * ..58..4.12.....5.....5.....418753...753...184..2481753...1.8345.2.3.58..5.....6.. G3: 3,4,8 # 13 pairs * PAIR C8: 4,6 COL C C2: 4,6,1,7,9 # reduction candidate for 4,6 C2: 4,6 # 15 pairs C3: 4,6,1,7,9 # reduction candidate for 4,6 C3: 4,6 # 15 pairs * PAIR D9: 2,9 BLK 8 E7: 2,9,6,7 # reduction candidate for 2,9 E7: 2,9 # 16 pairs E9: 2,9,4,7 # reduction candidate for 2,9 E9: 2,9 => CTR * ..58....12.....5.....5.....418753...753...184..2481753...1.8245.2.3.5...5.....638 E9: 4,7 # 14 pairs F9: 2,9,4,7 # reduction candidate for 2,9 F9: 2,9 => CTR * ..58....12.....5.....5.....418753...753...184..2481753...1.8245.2.3.5...5.....638 F9: 4,7 # 14 pairs * PAIR D9: 2,9 COL D D5: 2,9,6 # reduction candidate for 2,9 D5: 6 => CTR * ..58....128.9..5..1..5..8..418753...7536..184..2481753...1.824582.3.59..5..2..6.8 D5: 2,9 # 13 pairs * PAIR G7: 2,3 BLK 9 H9: 2,3,1 # reduction candidate for 2,3 H9: 2,3 => SOLVED * 395872461287614539146539872418753296753296184962481753679128345824365917531947628 H9: 1 => CTR * ..58....12.....5.....5.....418753...753...184..2481753...1.8345.2.3.5...53....61. * PAIR G7: 2,3 COL G G1: 2,3,4,9 # reduction candidate for 2,3 G1: 2,3 => CTR * ..58....12.....5.....5..4..418753...753...184..2481753...1.8.45.2.3.58..58....632 G1: 4,9 # 14 pairs G3: 2,3,4,8,9 # reduction candidate for 2,3 G3: 2,3 => CTR * ..58..4.12.....5.....5.....418753...753...184..2481753...1.8.45.2.3.58..58....632 G3: 4,8,9 # 13 pairs * PAIR G8: 8,9 BLK 9 I8: 8,9,7 # reduction candidate for 8,9 I8: 8,9 => CTR * ..58....12.....5.....5.....418753...753...184..2481753...1.834512.3.5.7.5.....61. I8: 7 # 14 pairs * PAIR G8: 8,9 COL G G3: 8,9,2,3,4 # reduction candidate for 8,9 G3: 8,9 => SOLVED * 395872461287614539146539872418753296753296184962481753679128345824365917531947628 G3: 2,3,4 => CTR * ..58....12.....5.....5.....418753...753...184..2481753...1.8.45.2.3.58..58....632 * PAIR I9: 2,8 COL I I3: 2,8,6,7,9 # reduction candidate for 2,8 I3: 2,8 => SOLVED * 395872461287614539146539872418753296753296184962481753679128345824365917531947628 I3: 6,7,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-059-base-pr-000.dot * REASONING * DIS # B2: 6,9 => CTR => B2: 3,4,7,8 * PRF # I2: 6,9 => SOL * DIS # D5: 6,9 => CTR => D5: 2 * DIS # A1: 6,9 => CTR => A1: 3 * DIS # B2: 6,9 => CTR => B2: 3,4,7,8 * DIS # F5: 2,9 => CTR => F5: 6 * DIS # E1: 2,9 => CTR => E1: 3,4,7 * DIS # E3: 2,9 => CTR => E3: 1,3,4,7 * DIS # E9: 2,9 => CTR => E9: 4,7 * DIS # G1: 2,9 => CTR => G1: 3,4 * DIS # G3: 2,9 => CTR => G3: 3,4,8 * DIS # E9: 2,9 => CTR => E9: 4,7 * DIS # F9: 2,9 => CTR => F9: 4,7 * DIS # D5: 6 => CTR => D5: 2,9 * PRF # H9: 2,3 => SOL * DIS # H9: 1 => CTR => H9: 2,3 * DIS # G1: 2,3 => CTR => G1: 4,9 * DIS # G3: 2,3 => CTR => G3: 4,8,9 * DIS # I8: 8,9 => CTR => I8: 7 * PRF # G3: 8,9 => SOL * DIS # G3: 2,3,4 => CTR => G3: 8,9 * PRF # I3: 2,8 => SOL * CNT 22 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,A8,B6,C8,D2,D9,E5,E8,G4,G7,G8,I9) * ..58....12.....5.....5.....418753...753...184..2481753...1.8.45.2.3.5...5.....6.. * PAIR D2: 6,9 BLK 2 F1: 6,9,2,4,7 # reduction candidate for 6,9 F1: 6,9 # 15 pairs F2: 6,9,4,7 # reduction candidate for 6,9 F2: 6,9 # 16 pairs F3: 6,9,2,4,7 # reduction candidate for 6,9 F3: 6,9 # 15 pairs * PAIR D2: 6,9 ROW 2 B2: 6,9,3,4,7,8 # reduction candidate for 6,9 B2: 6,9 => CTR * ..58....12.....5.8...5.....418753...753...184..2481753...1.8.45.2.3.58..58....632 C2: 6,9,1,4,7 # reduction candidate for 6,9 C2: 6,9 # 17 pairs H2: 6,9,3,7 # reduction candidate for 6,9 H2: 6,9 # 16 pairs I2: 6,9,7,8 # reduction candidate for 6,9 I2: 6,9 => SOLVED * 395872461287614539146539872418753296753296184962481753679128345824365917531947628 * DURATION: 0:00:07.319533 START: 04:42:38.285514 END: 04:42:45.605047 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-059-base-pr-001.dot * REASONING * DIS # B2: 6,9 => CTR => B2: 3,4,7,8 * PRF B2: 3,4,7,8 # I2: 6,9 => SOL * STA B2: 3,4,7,8 + I2: 6,9 * CNT 2 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 059 solution: 395872461287614539146539872418753296753296184962481753679128345824365917531947628 info: 1430 FNBHWXY S8.f 11943 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 395872461287614539146539872418753296753296184962481753679128345824365917531947628 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 # F1: 6,9 => UNS * INC # F2: 6,9 => UNS * INC # F3: 6,9 => UNS * DIS # B2: 6,9 => CTR => B2: 3,4,7,8 * INC # B2: 3,4,7,8 => UNS * INC # C2: 6,9 => UNS * INC # H2: 6,9 => UNS * PRF # I2: 6,9 => SOL * INC # I2: 7,8 => UNS * DIS # D5: 6,9 => CTR => D5: 2 * INC # D5: 2 => UNS * DIS # A1: 6,9 => CTR => A1: 3 * INC # A1: 3 => UNS * INC # A7: 6,9 => UNS * INC # B1: 6,9 => UNS * DIS # B2: 6,9 => CTR => B2: 3,4,7,8 * INC # B2: 3,4,7,8 => UNS * INC # B3: 6,9 => UNS * INC # B7: 6,9 => UNS * INC # D5: 2,9 => UNS * DIS # F5: 2,9 => CTR => F5: 6 * INC # F5: 6 => UNS * DIS # E1: 2,9 => CTR => E1: 3,4,7 * INC # E1: 3,4,7 => UNS * DIS # E3: 2,9 => CTR => E3: 1,3,4,7 * INC # E3: 1,3,4,7 => UNS * INC # E7: 2,9 => UNS * DIS # E9: 2,9 => CTR => E9: 4,7 * INC # E9: 4,7 => UNS * INC # H4: 2,9 => UNS * INC # I4: 2,9 => UNS * DIS # G1: 2,9 => CTR => G1: 3,4 * INC # G1: 3,4 => UNS * DIS # G3: 2,9 => CTR => G3: 3,4,8 * INC # G3: 3,4,8 => UNS * INC # C2: 4,6 => UNS * INC # C3: 4,6 => UNS * INC # E7: 2,9 => UNS * DIS # E9: 2,9 => CTR => E9: 4,7 * INC # E9: 4,7 => UNS * DIS # F9: 2,9 => CTR => F9: 4,7 * INC # F9: 4,7 => UNS * INC # D5: 2,9 => UNS * DIS # D5: 6 => CTR => D5: 2,9 * PRF # H9: 2,3 => SOL * DIS # H9: 1 => CTR => H9: 2,3 * DIS # G1: 2,3 => CTR => G1: 4,9 * INC # G1: 4,9 => UNS * DIS # G3: 2,3 => CTR => G3: 4,8,9 * INC # G3: 4,8,9 => UNS * DIS # I8: 8,9 => CTR => I8: 7 * INC # I8: 7 => UNS * PRF # G3: 8,9 => SOL * DIS # G3: 2,3,4 => CTR => G3: 8,9 * PRF # I3: 2,8 => SOL * INC # I3: 6,7,9 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 6,9 => UNS * INC # F2: 6,9 => UNS * INC # F3: 6,9 => UNS * DIS # B2: 6,9 => CTR => B2: 3,4,7,8 * INC B2: 3,4,7,8 # C2: 6,9 => UNS * INC B2: 3,4,7,8 # H2: 6,9 => UNS * PRF B2: 3,4,7,8 # I2: 6,9 => SOL * STA B2: 3,4,7,8 + I2: 6,9 * CNT 7 HDP CHAINS / 7 HYP OPENED