Analysis of xx-top500-354-base.sdk
Contents
Original Sudoku
level: medium
position: 9..6.1....3......8.......4..4..8..3....3..1..2...........52....1.....9......4.... initial
Autosolve
position: 9846.12.3.3249..18.1.238.49.41982.3.8..3.419229371.48.4.85293.11..8.39.43.914.8.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 5,6 => CTR => A3: 7 * DIS # G3: 7 => CTR => G3: 5,6 * DIS # C5: 5,6 => CTR => C5: 7 * DIS # G2: 5,7 => CTR => G2: 6 * DIS # G2: 5,7 => CTR => G2: 6 * PRF # H9: 5,7 => SOL * DIS # C5: 5,6 => CTR => C5: 7 * PRF # I4: 5,6 => SOL * DIS # I4: 7 => CTR => I4: 5,6 * DIS # A3: 5,6 => CTR => A3: 7 * DIS # C5: 5,6 => CTR => C5: 7 * PRF # I4: 5,7 => SOL * DIS # I4: 6 => CTR => I4: 5,7 * DIS # G2: 5,7 => CTR => G2: 6 * PRF # I4: 5,6 => SOL * DIS # I4: 7 => CTR => I4: 5,6 * PRF # B8: 6,7 => SOL * DIS # B9: 6,7 => CTR => B9: 2,5 * PRF # B5: 5 => SOL * PRF # B8: 6,7 => SOL * DIS # H8: 6,7 => CTR => H8: 2,5 * DIS # B9: 6,7 => CTR => B9: 2,5 * DIS # H9: 6,7 => CTR => H9: 2,5 * DIS # H8: 6,7 => CTR => H8: 2,5 * DIS # H9: 6,7 => CTR => H9: 2,5 * PRF # H9: 5,7 => SOL * DIS # B9: 5,7 => CTR => B9: 2,6 * PRF # I4: 5,7 => SOL * DIS # I4: 6 => CTR => I4: 5,7 * CNT 29 HDP CHAINS / 62 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 5,6 => CTR => A3: 7 * DIS A3: 7 # C5: 5,6 => CTR => C5: 7 * DIS A3: 7 + C5: 7 # G2: 5,7 => CTR => G2: 6 * PRF A3: 7 + C5: 7 + G2: 6 => SOL * STA A3: 7 + C5: 7 + G2: 6 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9..6.1....3......8.......4..4..8..3....3..1..2...........52....1.....9......4.... | initial |
| 9846.12.3.3249..18.1.238.49.41982.3.8..3.419229371.48.4.85293.11..8.39.43.914.8.. | autosolve |
| 984651273532497618716238549641982735857364192293715486478529361165873924329146857 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C3: 5,6 E1: 5,7 F2: 5,7 H1: 5,7 A4: 5,6 E5: 5,6 F6: 5,6 G4: 5,7 I6: 5,6 B7: 6,7 E8: 6,7 F9: 6,7 H7: 6,7 I9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B8,B9: 2.. / B8 = 2 => 14 pairs (_) / B9 = 2 => 14 pairs (_) H8,H9: 2.. / H8 = 2 => 14 pairs (_) / H9 = 2 => 14 pairs (_) B8,H8: 2.. / B8 = 2 => 14 pairs (_) / H8 = 2 => 14 pairs (_) B9,H9: 2.. / B9 = 2 => 14 pairs (_) / H9 = 2 => 14 pairs (_) E1,F2: 5.. / E1 = 5 => 0 pairs (*) / F2 = 5 => 0 pairs (X) E5,F6: 5.. / E5 = 5 => 0 pairs (X) / F6 = 5 => 0 pairs (_) E1,H1: 5.. / E1 = 5 => 0 pairs (*) / H1 = 5 => 0 pairs (X) F6,I6: 5.. / F6 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) E1,E5: 5.. / E1 = 5 => 0 pairs (*) / E5 = 5 => 0 pairs (X) F2,F6: 5.. / F2 = 5 => 0 pairs (X) / F6 = 5 => 0 pairs (_) G2,G3: 6.. / G2 = 6 => 16 pairs (_) / G3 = 6 => 0 pairs (X) E5,F6: 6.. / E5 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) I4,I6: 6.. / I4 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) E8,F9: 6.. / E8 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) A2,G2: 6.. / A2 = 6 => 0 pairs (X) / G2 = 6 => 16 pairs (_) A4,I4: 6.. / A4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) F6,I6: 6.. / F6 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) B7,H7: 6.. / B7 = 6 => 0 pairs (X) / H7 = 6 => 14 pairs (_) E5,E8: 6.. / E5 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) F6,F9: 6.. / F6 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) A2,A3: 7.. / A2 = 7 => 0 pairs (X) / A3 = 7 => 16 pairs (_) E1,F2: 7.. / E1 = 7 => 0 pairs (X) / F2 = 7 => 0 pairs (_) B5,C5: 7.. / B5 = 7 => 0 pairs (X) / C5 = 7 => 16 pairs (_) G4,I4: 7.. / G4 = 7 => 0 pairs (*) / I4 = 7 => 0 pairs (X) E8,F9: 7.. / E8 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) E1,H1: 7.. / E1 = 7 => 0 pairs (X) / H1 = 7 => 0 pairs (_) A3,G3: 7.. / A3 = 7 => 16 pairs (_) / G3 = 7 => 0 pairs (X) B7,H7: 7.. / B7 = 7 => 14 pairs (_) / H7 = 7 => 0 pairs (X) C5,C8: 7.. / C5 = 7 => 16 pairs (_) / C8 = 7 => 0 pairs (X) E1,E8: 7.. / E1 = 7 => 0 pairs (X) / E8 = 7 => 0 pairs (_) F2,F9: 7.. / F2 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) I4,I9: 7.. / I4 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) * DURATION: 0:00:54.106478 START: 14:50:55.475033 END: 14:51:49.581511 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,C3,E1,E5,E8,F2,F6,F9,G4,H1,H7,I6,I9) * 9846.12.3.3249..18.1.238.49.41982.3.8..3.419229371.48.4.85293.11..8.39.43.914.8.. * PAIR C3: 5,6 BLK 1 A2: 5,6,7 # reduction candidate for 5,6 A2: 5,6 # 16 pairs A3: 5,6,7 # reduction candidate for 5,6 A3: 5,6 => CTR * 9846.12.3732495618.1.238749.419825378..35419229371648.4.85293.11..8.39.43.914.8.. A3: 7 # 16 pairs * PAIR C3: 5,6 ROW 3 G3: 5,6,7 # reduction candidate for 5,6 G3: 7 => CTR * 9846.12.3.3249.618.1.238749.419825378..3.41922937154864.85293.11..8.39.43.91468.5 G3: 5,6 # 16 pairs * PAIR C3: 5,6 COL C C5: 5,6,7 # reduction candidate for 5,6 C5: 5,6 => CTR * 9846.12.3.3249..18.1.238.49.41982.3.87.3.419229371.48.4685293711.78639.43.9147865 C5: 7 # 16 pairs C8: 5,6,7 # reduction candidate for 5,6 C8: 5,6 # 16 pairs * PAIR F2: 5,7 ROW 2 A2: 5,7,6 # reduction candidate for 5,7 A2: 5,7 # 16 pairs G2: 5,7,6 # reduction candidate for 5,7 G2: 5,7 => CTR * 9846.12.363249..187152386495419827368..35419229371648.4.85293.11..8.39.43.914.8.. G2: 6 # 16 pairs * PAIR H1: 5,7 BLK 3 G2: 5,7,6 # reduction candidate for 5,7 G2: 5,7 => CTR * 9846.12.363249..187152386495419827368..35419229371648.4.85293.11..8.39.43.914.8.. G2: 6 # 16 pairs G3: 5,7,6 # reduction candidate for 5,7 G3: 5,7 # 16 pairs * PAIR H1: 5,7 COL H H8: 5,7,2,6 # reduction candidate for 5,7 H8: 5,7 # 16 pairs H9: 5,7,2,6 # reduction candidate for 5,7 H9: 5,7 => SOLVED * 984651273532497618716238549641982735857364192293715486478529361165873924329146857 H9: 2,6 # 15 pairs * PAIR A4: 5,6 BLK 4 B5: 5,6,7 # reduction candidate for 5,6 B5: 5,6 # 16 pairs C5: 5,6,7 # reduction candidate for 5,6 C5: 5,6 => CTR * 9846.12.3.3249..18.1.238.49.41982.3.87.3.419229371.48.4685293711.78639.43.9147865 C5: 7 # 16 pairs * PAIR A4: 5,6 ROW 4 I4: 5,6,7 # reduction candidate for 5,6 I4: 5,6 => SOLVED * 984651273532497618716238549641982735857364192293715486478529361165873924329146857 I4: 7 => CTR * 9846.12.3.3249..18.1.238.496419825378..3641922937154864.85293.11..8739.43.91468.5 * PAIR A4: 5,6 COL A A2: 5,6,7 # reduction candidate for 5,6 A2: 5,6 # 16 pairs A3: 5,6,7 # reduction candidate for 5,6 A3: 5,6 => CTR * 9846.12.3732495618.1.238749.419825378..35419229371648.4.85293.11..8.39.43.914.8.. A3: 7 # 16 pairs * PAIR E5: 5,6 ROW 5 B5: 5,6,7 # reduction candidate for 5,6 B5: 5,6 # 16 pairs C5: 5,6,7 # reduction candidate for 5,6 C5: 5,6 => CTR * 9846.12.3.3249..18.1.238.49.41982.3.87.3.419229371.48.4685293711.78639.43.9147865 C5: 7 # 16 pairs * PAIR G4: 5,7 BLK 6 I4: 5,7,6 # reduction candidate for 5,7 I4: 5,7 => SOLVED * 984651273532497618716238549641982735857364192293715486478529361165873924329146857 I4: 6 => CTR * 9846.12.3.3249..18.1.238.49.419827368..3.41922937164854.85293.11..8639.43.91478.. * PAIR G4: 5,7 COL G G2: 5,7,6 # reduction candidate for 5,7 G2: 5,7 => CTR * 9846.12.363249..187152386495419827368..35419229371648.4.85293.11..8.39.43.914.8.. G2: 6 # 16 pairs G3: 5,7,6 # reduction candidate for 5,7 G3: 5,7 # 16 pairs * PAIR I6: 5,6 BLK 6 I4: 5,6,7 # reduction candidate for 5,6 I4: 5,6 => SOLVED * 984651273532497618716238549641982735857364192293715486478529361165873924329146857 I4: 7 => CTR * 9846.12.3.3249..18.1.238.496419825378..3641922937154864.85293.11..8739.43.91468.5 * PAIR B7: 6,7 BLK 7 B8: 6,7,2,5 # reduction candidate for 6,7 B8: 6,7 => SOLVED * 984651273532497618716238549641982735857364192293715486478529361165873924329146857 B8: 2,5 # 15 pairs C8: 6,7,5 # reduction candidate for 6,7 C8: 6,7 # 19 pairs B9: 6,7,2,5 # reduction candidate for 6,7 B9: 6,7 => CTR * 9846.1253.32495.1851623874964198253785.3.419229371.48.4.85293.11258.39.43.914.825 B9: 2,5 # 15 pairs * PAIR B7: 6,7 COL B B5: 6,7,5 # reduction candidate for 6,7 B5: 5 => SOLVED * 984651273532497618716238549641982735857364192293715486478529361165873924329146857 B5: 6,7 # 19 pairs * PAIR E8: 6,7 ROW 8 B8: 6,7,2,5 # reduction candidate for 6,7 B8: 6,7 => SOLVED * 984651273532497618716238549641982735857364192293715486478529361165873924329146857 B8: 2,5 # 15 pairs C8: 6,7,5 # reduction candidate for 6,7 C8: 6,7 # 19 pairs H8: 6,7,2,5 # reduction candidate for 6,7 H8: 6,7 => CTR * 9846.1253.32495.1851623874964198253785.3.419229371.48.4.85293.11258.39.43.914.825 H8: 2,5 # 15 pairs * PAIR F9: 6,7 ROW 9 B9: 6,7,2,5 # reduction candidate for 6,7 B9: 6,7 => CTR * 9846.1253.32495.1851623874964198253785.3.419229371.48.4.85293.11258.39.43.914.825 B9: 2,5 # 15 pairs H9: 6,7,2,5 # reduction candidate for 6,7 H9: 6,7 => CTR * 9846.1253.32495.18.1.238.49.419825378..35419229371648.4.85293.11..8.392432914.8.5 H9: 2,5 # 15 pairs * PAIR H7: 6,7 BLK 9 H8: 6,7,2,5 # reduction candidate for 6,7 H8: 6,7 => CTR * 9846.1253.32495.1851623874964198253785.3.419229371.48.4.85293.11258.39.43.914.825 H8: 2,5 # 15 pairs H9: 6,7,2,5 # reduction candidate for 6,7 H9: 6,7 => CTR * 9846.1253.32495.18.1.238.49.419825378..35419229371648.4.85293.11..8.392432914.8.5 H9: 2,5 # 15 pairs * PAIR I9: 5,7 BLK 9 H8: 5,7,2,6 # reduction candidate for 5,7 H8: 5,7 # 16 pairs H9: 5,7,2,6 # reduction candidate for 5,7 H9: 5,7 => SOLVED * 984651273532497618716238549641982735857364192293715486478529361165873924329146857 H9: 2,6 # 15 pairs * PAIR I9: 5,7 ROW 9 B9: 5,7,2,6 # reduction candidate for 5,7 B9: 5,7 => CTR * 9846.12.3.32497.1871.238.49.4198273.8..36419229371548646852937112.873964379146825 B9: 2,6 # 15 pairs * PAIR I9: 5,7 COL I I4: 5,7,6 # reduction candidate for 5,7 I4: 5,7 => SOLVED * 984651273532497618716238549641982735857364192293715486478529361165873924329146857 I4: 6 => CTR * 9846.12.3.3249..18.1.238.49.419827368..3.41922937164854.85293.11..8639.43.91478.. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-354-base-pr-000.dot * REASONING * DIS # A3: 5,6 => CTR => A3: 7 * DIS # G3: 7 => CTR => G3: 5,6 * DIS # C5: 5,6 => CTR => C5: 7 * DIS # G2: 5,7 => CTR => G2: 6 * DIS # G2: 5,7 => CTR => G2: 6 * PRF # H9: 5,7 => SOL * DIS # C5: 5,6 => CTR => C5: 7 * PRF # I4: 5,6 => SOL * DIS # I4: 7 => CTR => I4: 5,6 * DIS # A3: 5,6 => CTR => A3: 7 * DIS # C5: 5,6 => CTR => C5: 7 * PRF # I4: 5,7 => SOL * DIS # I4: 6 => CTR => I4: 5,7 * DIS # G2: 5,7 => CTR => G2: 6 * PRF # I4: 5,6 => SOL * DIS # I4: 7 => CTR => I4: 5,6 * PRF # B8: 6,7 => SOL * DIS # B9: 6,7 => CTR => B9: 2,5 * PRF # B5: 5 => SOL * PRF # B8: 6,7 => SOL * DIS # H8: 6,7 => CTR => H8: 2,5 * DIS # B9: 6,7 => CTR => B9: 2,5 * DIS # H9: 6,7 => CTR => H9: 2,5 * DIS # H8: 6,7 => CTR => H8: 2,5 * DIS # H9: 6,7 => CTR => H9: 2,5 * PRF # H9: 5,7 => SOL * DIS # B9: 5,7 => CTR => B9: 2,6 * PRF # I4: 5,7 => SOL * DIS # I4: 6 => CTR => I4: 5,7 * CNT 29 HDP CHAINS / 62 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,C3,E1,E5,E8,F2,F6,F9,G4,H1,H7,I6,I9) * 9846.12.3.3249..18.1.238.49.41982.3.8..3.419229371.48.4.85293.11..8.39.43.914.8.. * PAIR C3: 5,6 BLK 1 A2: 5,6,7 # reduction candidate for 5,6 A2: 5,6 # 16 pairs A3: 5,6,7 # reduction candidate for 5,6 A3: 5,6 => CTR * 9846.12.3732495618.1.238749.419825378..35419229371648.4.85293.11..8.39.43.914.8.. * RESTART * PAIR C3: 5,6 COL C C5: 5,6,7 # reduction candidate for 5,6 C5: 5,6 => CTR * 9846.12.3.3249..1871.238.49.41982.3.87.3.419229371.48.4685293711.78639.43.9147865 * RESTART * PAIR RESTART * PAIR F2: 5,7 ROW 2 G2: 5,7,6 # reduction candidate for 5,7 G2: 5,7 => CTR * 9846.12.363249..1871523864954198273686735419229371648.4.85293.11..8.39.43.914.8.. G2: 6 => SOLVED * 984651273532497618716238549641982735857364192293715486478529361165873924329146857 * DURATION: 0:00:06.058202 START: 14:52:50.092642 END: 14:52:56.150844 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-354-base-pr-001.dot * REASONING * DIS # A3: 5,6 => CTR => A3: 7 * DIS A3: 7 # C5: 5,6 => CTR => C5: 7 * DIS A3: 7 + C5: 7 # G2: 5,7 => CTR => G2: 6 * PRF A3: 7 + C5: 7 + G2: 6 => SOL * STA A3: 7 + C5: 7 + G2: 6 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 354 solution: 984651273532497618716238549641982735857364192293715486478529361165873924329146857 info: 4885 FNBWX S8.f 39072 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 984651273532497618716238549641982735857364192293715486478529361165873924329146857 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 # A2: 5,6 => UNS * DIS # A3: 5,6 => CTR => A3: 7 * INC # A3: 7 => UNS * INC # G3: 5,6 => UNS * DIS # G3: 7 => CTR => G3: 5,6 * DIS # C5: 5,6 => CTR => C5: 7 * INC # C5: 7 => UNS * INC # C8: 5,6 => UNS * INC # A2: 5,7 => UNS * DIS # G2: 5,7 => CTR => G2: 6 * INC # G2: 6 => UNS * DIS # G2: 5,7 => CTR => G2: 6 * INC # G2: 6 => UNS * INC # G3: 5,7 => UNS * INC # H8: 5,7 => UNS * PRF # H9: 5,7 => SOL * INC # H9: 2,6 => UNS * INC # B5: 5,6 => UNS * DIS # C5: 5,6 => CTR => C5: 7 * INC # C5: 7 => UNS * PRF # I4: 5,6 => SOL * DIS # I4: 7 => CTR => I4: 5,6 * INC # A2: 5,6 => UNS * DIS # A3: 5,6 => CTR => A3: 7 * INC # A3: 7 => UNS * INC # B5: 5,6 => UNS * DIS # C5: 5,6 => CTR => C5: 7 * INC # C5: 7 => UNS * PRF # I4: 5,7 => SOL * DIS # I4: 6 => CTR => I4: 5,7 * DIS # G2: 5,7 => CTR => G2: 6 * INC # G2: 6 => UNS * INC # G3: 5,7 => UNS * PRF # I4: 5,6 => SOL * DIS # I4: 7 => CTR => I4: 5,6 * PRF # B8: 6,7 => SOL * INC # B8: 2,5 => UNS * INC # C8: 6,7 => UNS * DIS # B9: 6,7 => CTR => B9: 2,5 * INC # B9: 2,5 => UNS * INC # B5: 6,7 => UNS * PRF # B5: 5 => SOL * PRF # B8: 6,7 => SOL * INC # B8: 2,5 => UNS * INC # C8: 6,7 => UNS * DIS # H8: 6,7 => CTR => H8: 2,5 * INC # H8: 2,5 => UNS * DIS # B9: 6,7 => CTR => B9: 2,5 * INC # B9: 2,5 => UNS * DIS # H9: 6,7 => CTR => H9: 2,5 * INC # H9: 2,5 => UNS * DIS # H8: 6,7 => CTR => H8: 2,5 * INC # H8: 2,5 => UNS * DIS # H9: 6,7 => CTR => H9: 2,5 * INC # H9: 2,5 => UNS * INC # H8: 5,7 => UNS * PRF # H9: 5,7 => SOL * INC # H9: 2,6 => UNS * DIS # B9: 5,7 => CTR => B9: 2,6 * INC # B9: 2,6 => UNS * PRF # I4: 5,7 => SOL * DIS # I4: 6 => CTR => I4: 5,7 * CNT 62 HDP CHAINS / 62 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 5,6 => UNS * DIS # A3: 5,6 => CTR => A3: 7 * DIS A3: 7 # C5: 5,6 => CTR => C5: 7 * DIS A3: 7 + C5: 7 # G2: 5,7 => CTR => G2: 6 * PRF A3: 7 + C5: 7 + G2: 6 => SOL * STA A3: 7 + C5: 7 + G2: 6 * CNT 5 HDP CHAINS / 4 HYP OPENED