Analysis of xx-top500-275-base.sdk
Contents
Original Sudoku
level: medium
position: ...3...1..6..5....2........3..6........5..7..1.........7....4.8.5...26......1.... initial
Autosolve
position: 5..327.1676315.2..21..6.3..3..6..1.2.265.17.31..2.3.6.671935428.5.7.2631.32.16... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 8,9 => CTR => C1: 4 * DIS # F3: 4 => CTR => F3: 8,9 * DIS # C8: 4 => CTR => C8: 8,9 * DIS # F3: 4 => CTR => F3: 8,9 * DIS # H2: 4 => CTR => H2: 8,9 * DIS # F3: 9 => CTR => F3: 4,8 * DIS # H2: 4 => CTR => H2: 8,9 * DIS # C1: 8,9 => CTR => C1: 4 * DIS # G6: 5 => CTR => G6: 8,9 * DIS # H2: 4,9 => CTR => H2: 8 * DIS # F3: 9 => CTR => F3: 4,8 * DIS # A8: 4,8 => CTR => A8: 9 * DIS # A5: 9 => CTR => A5: 4,8 * DIS # A8: 4,8 => CTR => A8: 9 * DIS # G6: 5,9 => CTR => G6: 8 * CNT 15 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 8,9 => CTR => C1: 4 * DIS C1: 4 # F3: 4 => CTR => F3: 8,9 * DIS C1: 4 + F3: 8,9 # G6: 5 => CTR => G6: 8,9 * PRF C1: 4 + F3: 8,9 + G6: 8,9 # H4: 5 => SOL * STA C1: 4 + F3: 8,9 + G6: 8,9 + H4: 5 * CNT 4 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...3...1..6..5....2........3..6........5..7..1.........7....4.8.5...26......1.... | initial |
| 5..327.1676315.2..21..6.3..3..6..1.2.265.17.31..2.3.6.671935428.5.7.2631.32.16... | autosolve |
| 584327916763159284219468375397684152826591743145273869671935428958742631432816597 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C3: 8,9 F2: 8,9 D3: 4,8 G1: 8,9 I2: 4,9 H3: 5,7 I3: 5,7 C4: 5,7 C6: 5,7 F4: 4,8 A9: 4,8 E8: 4,8 D9: 4,8 G9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 4.. / B1 = 4 => 0 pairs (X) / C1 = 4 => 17 pairs (_) D3,F3: 4.. / D3 = 4 => 17 pairs (_) / F3 = 4 => 0 pairs (X) H2,I2: 4.. / H2 = 4 => 0 pairs (X) / I2 = 4 => 15 pairs (_) E8,D9: 4.. / E8 = 4 => 17 pairs (_) / D9 = 4 => 0 pairs (X) A9,D9: 4.. / A9 = 4 => 17 pairs (_) / D9 = 4 => 0 pairs (X) C1,C8: 4.. / C1 = 4 => 17 pairs (_) / C8 = 4 => 0 pairs (X) D3,D9: 4.. / D3 = 4 => 17 pairs (_) / D9 = 4 => 0 pairs (X) F3,F4: 4.. / F3 = 4 => 0 pairs (X) / F4 = 4 => 17 pairs (_) I2,I6: 4.. / I2 = 4 => 15 pairs (_) / I6 = 4 => 0 pairs (X) H3,I3: 5.. / H3 = 5 => 11 pairs (_) / I3 = 5 => 14 pairs (_) C4,C6: 5.. / C4 = 5 => 13 pairs (_) / C6 = 5 => 14 pairs (_) C4,H4: 5.. / C4 = 5 => 13 pairs (_) / H4 = 5 => 14 pairs (_) G6,G9: 5.. / G6 = 5 => 0 pairs (X) / G9 = 5 => 16 pairs (_) H3,I3: 7.. / H3 = 7 => 14 pairs (_) / I3 = 7 => 11 pairs (_) C4,C6: 7.. / C4 = 7 => 14 pairs (_) / C6 = 7 => 13 pairs (_) E4,E6: 7.. / E4 = 7 => 13 pairs (_) / E6 = 7 => 14 pairs (_) H9,I9: 7.. / H9 = 7 => 11 pairs (_) / I9 = 7 => 14 pairs (_) C4,E4: 7.. / C4 = 7 => 14 pairs (_) / E4 = 7 => 13 pairs (_) C6,E6: 7.. / C6 = 7 => 13 pairs (_) / E6 = 7 => 14 pairs (_) H3,H9: 7.. / H3 = 7 => 14 pairs (_) / H9 = 7 => 11 pairs (_) I3,I9: 7.. / I3 = 7 => 11 pairs (_) / I9 = 7 => 14 pairs (_) G1,H2: 8.. / G1 = 8 => 0 pairs (X) / H2 = 8 => 19 pairs (_) E8,D9: 8.. / E8 = 8 => 0 pairs (X) / D9 = 8 => 17 pairs (_) F2,H2: 8.. / F2 = 8 => 0 pairs (X) / H2 = 8 => 19 pairs (_) A9,D9: 8.. / A9 = 8 => 0 pairs (X) / D9 = 8 => 17 pairs (_) D3,D9: 8.. / D3 = 8 => 0 pairs (X) / D9 = 8 => 17 pairs (_) G1,G6: 8.. / G1 = 8 => 0 pairs (X) / G6 = 8 => 19 pairs (_) F2,F3: 9.. / F2 = 9 => 19 pairs (_) / F3 = 9 => 0 pairs (X) A8,C8: 9.. / A8 = 9 => 17 pairs (_) / C8 = 9 => 0 pairs (X) C3,F3: 9.. / C3 = 9 => 19 pairs (_) / F3 = 9 => 0 pairs (X) A5,A8: 9.. / A5 = 9 => 0 pairs (X) / A8 = 9 => 17 pairs (_) * DURATION: 0:01:04.346147 START: 12:19:41.647972 END: 12:20:45.994119 2017-05-04 * CP COUNT: (31) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C3,C4,C6,D3,D9,E8,F2,F4,G1,G9,H3,I2,I3) * 5..327.1676315.2..21..6.3..3..6..1.2.265.17.31..2.3.6.671935428.5.7.2631.32.16... * PAIR C3: 8,9 BLK 1 B1: 8,9,4 # reduction candidate for 8,9 B1: 8,9 # 17 pairs C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 => CTR * 54.327.1676315.2..21.8643..3..6.81.242659178318.2.3.6.671935428954782631832416... C1: 4 # 17 pairs * PAIR C3: 8,9 ROW 3 F3: 8,9,4 # reduction candidate for 8,9 F3: 4 => CTR * 5..327.167631592842198643..3..6.81.28265.17.31..2.386.671935428958742631.32.16... F3: 8,9 # 17 pairs * PAIR C3: 8,9 COL C C8: 8,9,4 # reduction candidate for 8,9 C8: 4 => CTR * 54.327.1676315.2..21.8643..3..6.81.242659178318.2.3.6.671935428954782631832416... C8: 8,9 # 17 pairs * PAIR F2: 8,9 BLK 2 F3: 8,9,4 # reduction candidate for 8,9 F3: 4 => CTR * 5..327.167631592842198643..3..6.81.28265.17.31..2.386.671935428958742631.32.16... F3: 8,9 # 17 pairs * PAIR F2: 8,9 ROW 2 H2: 8,9,4 # reduction candidate for 8,9 H2: 4 => CTR * 5..3278167631582492184693..3..6.41.24265.17.31..2.3.646719354289547.2631.32.16... H2: 8,9 # 15 pairs * PAIR D3: 4,8 BLK 2 F3: 4,8,9 # reduction candidate for 4,8 F3: 9 => CTR * 5943278167631582942184693..38.69415292658174314.2.3.6.671935428859742631432816... F3: 4,8 # 19 pairs * PAIR G1: 8,9 BLK 3 H2: 8,9,4 # reduction candidate for 8,9 H2: 4 => CTR * 5..3278167631582492184693..3..6.41.24265.17.31..2.3.646719354289547.2631.32.16... H2: 8,9 # 15 pairs * PAIR G1: 8,9 ROW 1 B1: 8,9,4 # reduction candidate for 8,9 B1: 8,9 # 17 pairs C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 => CTR * 54.327.1676315.2..21.8643..3..6.81.242659178318.2.3.6.671935428954782631832416... C1: 4 # 17 pairs * PAIR G1: 8,9 COL G G6: 8,9,5 # reduction candidate for 8,9 G6: 5 => CTR * 5.43278167631582..2184693..3.56741.2.265.17431472835696719354288597426314328169.. G6: 8,9 # 16 pairs * PAIR I2: 4,9 BLK 3 H2: 4,9,8 # reduction candidate for 4,9 H2: 4,9 => CTR * 5.43278167631582..2184693..3..6.41.2.265.174314.283.6.671935428859742631432816... H2: 8 # 19 pairs * PAIR I2: 4,9 COL I I6: 4,9,5 # reduction candidate for 4,9 I6: 4,9 # 16 pairs I6: 5 # 10 pairs * PAIR H3: 5,7 COL H H9: 5,7,9 # reduction candidate for 5,7 H9: 9 # 14 pairs H9: 5,7 # 13 pairs * PAIR I3: 5,7 COL I I9: 5,7,9 # reduction candidate for 5,7 I9: 5,7 # 16 pairs I9: 9 # 10 pairs * PAIR F4: 4,8 BLK 5 E4: 4,8,7,9 # reduction candidate for 4,8 E4: 4,8 # 18 pairs E5: 4,8,9 # reduction candidate for 4,8 E5: 4,8 # 17 pairs E6: 4,8,7,9 # reduction candidate for 4,8 E6: 4,8 # 18 pairs * PAIR F4: 4,8 ROW 4 B4: 4,8,9 # reduction candidate for 4,8 B4: 4,8 # 19 pairs H4: 4,8,5,9 # reduction candidate for 4,8 H4: 4,8 # 18 pairs * PAIR F4: 4,8 COL F F3: 4,8,9 # reduction candidate for 4,8 F3: 9 => CTR * 5943278167631582942184693..38.69415292658174314.2.3.6.671935428859742631432816... F3: 4,8 # 19 pairs * PAIR A9: 4,8 BLK 7 A8: 4,8,9 # reduction candidate for 4,8 A8: 4,8 => CTR * 5943278167631582..2184693..3..6.41.29265817431..2.3.6.671935428.597.2631.32.16... A8: 9 # 17 pairs C8: 4,8,9 # reduction candidate for 4,8 C8: 4,8 # 17 pairs * PAIR A9: 4,8 COL A A5: 4,8,9 # reduction candidate for 4,8 A5: 9 => CTR * 5943278167631582..2184693..3..6.41.29265817431..2.3.6.671935428.597.2631.32.16... A5: 4,8 # 17 pairs * PAIR E8: 4,8 ROW 8 A8: 4,8,9 # reduction candidate for 4,8 A8: 4,8 => CTR * 5943278167631582..2184693..3..6.41.29265817431..2.3.6.671935428.597.2631.32.16... A8: 9 # 17 pairs C8: 4,8,9 # reduction candidate for 4,8 C8: 4,8 # 17 pairs * PAIR E8: 4,8 COL E E4: 4,8,7,9 # reduction candidate for 4,8 E4: 4,8 # 18 pairs E5: 4,8,9 # reduction candidate for 4,8 E5: 4,8 # 17 pairs E6: 4,8,7,9 # reduction candidate for 4,8 E6: 4,8 # 18 pairs * PAIR G9: 5,9 BLK 9 H9: 5,9,7 # reduction candidate for 5,9 H9: 5,9 # 14 pairs I9: 5,9,7 # reduction candidate for 5,9 I9: 5,9 # 11 pairs * PAIR G9: 5,9 COL G G6: 5,9,8 # reduction candidate for 5,9 G6: 5,9 => CTR * 5.43278167631582..2184693..3..6.41.2.265.174314.283.6.671935428859742631432816... G6: 8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-275-base-pr-000.dot * REASONING * DIS # C1: 8,9 => CTR => C1: 4 * DIS # F3: 4 => CTR => F3: 8,9 * DIS # C8: 4 => CTR => C8: 8,9 * DIS # F3: 4 => CTR => F3: 8,9 * DIS # H2: 4 => CTR => H2: 8,9 * DIS # F3: 9 => CTR => F3: 4,8 * DIS # H2: 4 => CTR => H2: 8,9 * DIS # C1: 8,9 => CTR => C1: 4 * DIS # G6: 5 => CTR => G6: 8,9 * DIS # H2: 4,9 => CTR => H2: 8 * DIS # F3: 9 => CTR => F3: 4,8 * DIS # A8: 4,8 => CTR => A8: 9 * DIS # A5: 9 => CTR => A5: 4,8 * DIS # A8: 4,8 => CTR => A8: 9 * DIS # G6: 5,9 => CTR => G6: 8 * CNT 15 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C3,C4,C6,D3,D9,E8,F2,F4,G1,G9,H3,I2,I3) * 5..327.1676315.2..21..6.3..3..6..1.2.265.17.31..2.3.6.671935428.5.7.2631.32.16... * PAIR C3: 8,9 BLK 1 B1: 8,9,4 # reduction candidate for 8,9 B1: 8,9 # 17 pairs C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 => CTR * 54.327.1676315.2..21.8643..3..6.81.242659178318.2.3.6.671935428954782631832416... * RESTART * PAIR C3: 8,9 ROW 3 F3: 8,9,4 # reduction candidate for 8,9 F3: 4 => CTR * 5.4327.167631592842198643..3..6.81.28265.17.31..2.386.6719354289587.2631.32.16... * PAIR RESTART * PAIR G1: 8,9 COL G G6: 8,9,5 # reduction candidate for 8,9 G6: 5 => CTR * 5.43278167631582942184693..38.694152.265.174314.2.3.6.671935428.5.742631432816... * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,A8,B1,B4,C3,C4,C6,C8,E5,F2,F3,G1,G6,H2,H3,H9,I3,I6,I9) * 5.4327.1676315.2.421.46.3..3..6.41.2.265.174314.2.3.6.671935428.5.7426314328165.. * PAIR H2: 8,9 COL H H4: 8,9,5 # reduction candidate for 8,9 H4: 5 => SOLVED * 584327916763159284219468375397684152826591743145273869671935428958742631432816597 * DURATION: 0:00:11.469503 START: 12:21:40.914805 END: 12:21:52.384308 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-275-base-pr-001.dot * REASONING * DIS # C1: 8,9 => CTR => C1: 4 * DIS C1: 4 # F3: 4 => CTR => F3: 8,9 * DIS C1: 4 + F3: 8,9 # G6: 5 => CTR => G6: 8,9 * PRF C1: 4 + F3: 8,9 + G6: 8,9 # H4: 5 => SOL * STA C1: 4 + F3: 8,9 + G6: 8,9 + H4: 5 * CNT 4 HDP CHAINS / 8 HYP OPENED
Header Info
Top 500 Minimum 17 275 solution: 584327916763159284219468375397684152826591743145273869671935428958742631432816597 info: 2204 FNBHWXY S8.f 48985 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 584327916763159284219468375397684152826591743145273869671935428958742631432816597 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 # B1: 8,9 => UNS * DIS # C1: 8,9 => CTR => C1: 4 * INC # C1: 4 => UNS * INC # F3: 8,9 => UNS * DIS # F3: 4 => CTR => F3: 8,9 * INC # C8: 8,9 => UNS * DIS # C8: 4 => CTR => C8: 8,9 * INC # F3: 8,9 => UNS * DIS # F3: 4 => CTR => F3: 8,9 * INC # H2: 8,9 => UNS * DIS # H2: 4 => CTR => H2: 8,9 * INC # F3: 4,8 => UNS * DIS # F3: 9 => CTR => F3: 4,8 * INC # H2: 8,9 => UNS * DIS # H2: 4 => CTR => H2: 8,9 * INC # B1: 8,9 => UNS * DIS # C1: 8,9 => CTR => C1: 4 * INC # C1: 4 => UNS * INC # G6: 8,9 => UNS * DIS # G6: 5 => CTR => G6: 8,9 * DIS # H2: 4,9 => CTR => H2: 8 * INC # H2: 8 => UNS * INC # I6: 4,9 => UNS * INC # I6: 5 => UNS * INC # H9: 5,7 => UNS * INC # H9: 9 => UNS * INC # I9: 5,7 => UNS * INC # I9: 9 => UNS * INC # E4: 4,8 => UNS * INC # E5: 4,8 => UNS * INC # E6: 4,8 => UNS * INC # B4: 4,8 => UNS * INC # H4: 4,8 => UNS * INC # F3: 4,8 => UNS * DIS # F3: 9 => CTR => F3: 4,8 * DIS # A8: 4,8 => CTR => A8: 9 * INC # A8: 9 => UNS * INC # C8: 4,8 => UNS * INC # A5: 4,8 => UNS * DIS # A5: 9 => CTR => A5: 4,8 * DIS # A8: 4,8 => CTR => A8: 9 * INC # A8: 9 => UNS * INC # C8: 4,8 => UNS * INC # E4: 4,8 => UNS * INC # E5: 4,8 => UNS * INC # E6: 4,8 => UNS * INC # H9: 5,9 => UNS * INC # I9: 5,9 => UNS * DIS # G6: 5,9 => CTR => G6: 8 * INC # G6: 8 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 8,9 => UNS * DIS # C1: 8,9 => CTR => C1: 4 * INC C1: 4 # F3: 8,9 => UNS * DIS C1: 4 # F3: 4 => CTR => F3: 8,9 * INC C1: 4 + F3: 8,9 # G6: 8,9 => UNS * DIS C1: 4 + F3: 8,9 # G6: 5 => CTR => G6: 8,9 * INC C1: 4 + F3: 8,9 + G6: 8,9 # H4: 8,9 => UNS * PRF C1: 4 + F3: 8,9 + G6: 8,9 # H4: 5 => SOL * STA C1: 4 + F3: 8,9 + G6: 8,9 + H4: 5 * CNT 8 HDP CHAINS / 8 HYP OPENED