Analysis of xx-top500-095-base.sdk
Contents
Original Sudoku
level: medium
position: ...76.2..4..8.....15............1.4..3....8...2..........2....36......1.....8.... initial
Autosolve
position: 3897642514.2815...15...24.88...21.4..314..826.246.81...1.24..83648..3.122.318.5.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H2: 6,7 => CTR => H2: 3,9 * DIS # B4: 9 => CTR => B4: 6,7 * DIS # C4: 5 => CTR => C4: 6,7 * DIS # H2: 6,7 => CTR => H2: 3,9 * DIS # H9: 9 => CTR => H9: 6,7 * DIS # F9: 7,9 => CTR => F9: 6 * DIS # A7: 9 => CTR => A7: 5,7 * DIS # C4: 5,7 => CTR => C4: 6 * DIS # A7: 5 => CTR => A7: 7,9 * DIS # F9: 7,9 => CTR => F9: 6 * DIS # B4: 6 => CTR => B4: 7,9 * DIS # G7: 7,9 => CTR => G7: 6 * CNT 12 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 # H2: 6,7 => CTR => H2: 3,9 * DIS H2: 3,9 # B4: 9 => CTR => B4: 6,7 * PRF H2: 3,9 + B4: 6,7 # G2: 6,7 => SOL * STA H2: 3,9 + B4: 6,7 + G2: 6,7 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...76.2..4..8.....15............1.4..3....8...2..........2....36......1.....8.... | initial |
| 3897642514.2815...15...24.88...21.4..314..826.246.81...1.24..83648..3.122.318.5.4 | autosolve |
| 389764251462815739157392468876921345931457826524638197715249683648573912293186574 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) B2: 6,7 C3: 6,7 D3: 3,9 E3: 3,9 I2: 7,9 H3: 6,7 F5: 7,9 C7: 5,7 B9: 7,9 D8: 5,9 G8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,E3: 3.. / D3 = 3 => 14 pairs (_) / E3 = 3 => 12 pairs (_) G2,H2: 3.. / G2 = 3 => 12 pairs (_) / H2 = 3 => 14 pairs (_) D4,E6: 3.. / D4 = 3 => 12 pairs (_) / E6 = 3 => 14 pairs (_) G4,H6: 3.. / G4 = 3 => 14 pairs (_) / H6 = 3 => 12 pairs (_) D4,G4: 3.. / D4 = 3 => 12 pairs (_) / G4 = 3 => 14 pairs (_) E6,H6: 3.. / E6 = 3 => 14 pairs (_) / H6 = 3 => 12 pairs (_) D3,D4: 3.. / D3 = 3 => 14 pairs (_) / D4 = 3 => 12 pairs (_) E3,E6: 3.. / E3 = 3 => 12 pairs (_) / E6 = 3 => 14 pairs (_) G2,G4: 3.. / G2 = 3 => 12 pairs (_) / G4 = 3 => 14 pairs (_) H2,H6: 3.. / H2 = 3 => 14 pairs (_) / H6 = 3 => 12 pairs (_) I4,I6: 5.. / I4 = 5 => 14 pairs (_) / I6 = 5 => 13 pairs (_) A7,C7: 5.. / A7 = 5 => 0 pairs (X) / C7 = 5 => 12 pairs (_) D8,E8: 5.. / D8 = 5 => 12 pairs (_) / E8 = 5 => 15 pairs (_) A5,E5: 5.. / A5 = 5 => 16 pairs (_) / E5 = 5 => 13 pairs (_) C4,C7: 5.. / C4 = 5 => 0 pairs (X) / C7 = 5 => 12 pairs (_) D4,D8: 5.. / D4 = 5 => 15 pairs (_) / D8 = 5 => 12 pairs (_) B2,C3: 6.. / B2 = 6 => 11 pairs (_) / C3 = 6 => 0 pairs (X) B4,C4: 6.. / B4 = 6 => 0 pairs (X) / C4 = 6 => 11 pairs (_) F7,F9: 6.. / F7 = 6 => 0 pairs (X) / F9 = 6 => 13 pairs (_) G7,H9: 6.. / G7 = 6 => 13 pairs (_) / H9 = 6 => 0 pairs (X) C3,H3: 6.. / C3 = 6 => 0 pairs (X) / H3 = 6 => 11 pairs (_) F7,G7: 6.. / F7 = 6 => 0 pairs (X) / G7 = 6 => 13 pairs (_) F9,H9: 6.. / F9 = 6 => 13 pairs (_) / H9 = 6 => 0 pairs (X) B2,B4: 6.. / B2 = 6 => 11 pairs (_) / B4 = 6 => 0 pairs (X) C3,C4: 6.. / C3 = 6 => 0 pairs (X) / C4 = 6 => 11 pairs (_) G2,G7: 6.. / G2 = 6 => 0 pairs (X) / G7 = 6 => 13 pairs (_) B2,C3: 7.. / B2 = 7 => 0 pairs (X) / C3 = 7 => 11 pairs (_) C3,H3: 7.. / C3 = 7 => 11 pairs (_) / H3 = 7 => 0 pairs (X) E8,G8: 7.. / E8 = 7 => 18 pairs (_) / G8 = 7 => 18 pairs (_) D3,E3: 9.. / D3 = 9 => 12 pairs (_) / E3 = 9 => 14 pairs (_) A7,B9: 9.. / A7 = 9 => 0 pairs (X) / B9 = 9 => 19 pairs (_) B4,B9: 9.. / B4 = 9 => 0 pairs (X) / B9 = 9 => 19 pairs (_) * DURATION: 0:00:55.596383 START: 06:01:21.516915 END: 06:02:17.113298 2017-05-04 * CP COUNT: (32) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B9,C3,C7,D3,D8,E3,F5,G8,H3,I2) * 3897642514.2815...15...24.88...21.4..314..826.246.81...1.24..83648..3.122.318.5.4 * PAIR B2: 6,7 ROW 2 G2: 6,7,3,9 # reduction candidate for 6,7 G2: 6,7 # 17 pairs H2: 6,7,3,9 # reduction candidate for 6,7 H2: 6,7 => CTR * 3897642514.28153.915.9324.889632174..314..826.246.813..1.24.6836485.3.122.3186594 H2: 3,9 # 12 pairs * PAIR B2: 6,7 COL B B4: 6,7,9 # reduction candidate for 6,7 B4: 9 => CTR * 389764251462815937157..2468896.21.4..314..826.246.81..91524.683648..3.12273186594 B4: 6,7 # 19 pairs * PAIR C3: 6,7 COL C C4: 6,7,5 # reduction candidate for 6,7 C4: 5 => CTR * 389764251472815639156..2478865.21347731459826.246.81.551724..836485.3712293187564 C4: 6,7 # 12 pairs * PAIR D3: 3,9 COL D D4: 3,9,5 # reduction candidate for 3,9 D4: 5 # 15 pairs D4: 3,9 # 12 pairs * PAIR E3: 3,9 COL E E6: 3,9,5,7 # reduction candidate for 3,9 E6: 3,9 # 15 pairs E6: 5,7 # 14 pairs * PAIR I2: 7,9 BLK 3 G2: 7,9,3,6 # reduction candidate for 7,9 G2: 7,9 # 15 pairs H2: 7,9,3,6 # reduction candidate for 7,9 H2: 7,9 # 12 pairs * PAIR I2: 7,9 COL I I4: 7,9,5 # reduction candidate for 7,9 I4: 7,9 # 13 pairs I6: 7,9,5 # reduction candidate for 7,9 I6: 7,9 # 14 pairs * PAIR H3: 6,7 BLK 3 G2: 6,7,3,9 # reduction candidate for 6,7 G2: 6,7 # 17 pairs H2: 6,7,3,9 # reduction candidate for 6,7 H2: 6,7 => CTR * 3897642514.28153.915.9324.889632174..314..826.246.813..1.24.6836485.3.122.3186594 H2: 3,9 # 12 pairs * PAIR H3: 6,7 COL H H9: 6,7,9 # reduction candidate for 6,7 H9: 9 => CTR * 3897642514.2815...15...24.8896.21347.314..826.246.81...1.24.683648..37122.3186594 H9: 6,7 # 15 pairs * PAIR F5: 7,9 BLK 5 E5: 7,9,5 # reduction candidate for 7,9 E5: 7,9 # 16 pairs E6: 7,9,3,5 # reduction candidate for 7,9 E6: 7,9 # 14 pairs * PAIR F5: 7,9 ROW 5 A5: 7,9,5 # reduction candidate for 7,9 A5: 5 # 16 pairs A5: 7,9 # 13 pairs * PAIR F5: 7,9 COL F F7: 7,9,6 # reduction candidate for 7,9 F7: 7,9 # 13 pairs F9: 7,9,6 # reduction candidate for 7,9 F9: 7,9 => CTR * 38976425147281563915639247886.92134..314..826.2463819..1.246.83648..3.12293187564 F9: 6 # 13 pairs * PAIR C7: 5,7 BLK 7 A7: 5,7,9 # reduction candidate for 5,7 A7: 9 => CTR * 389764251462815937157..2468896.21345.314..826.246.81..91524.683648..3712273186594 A7: 5,7 # 19 pairs * PAIR C7: 5,7 COL C C4: 5,7,6 # reduction candidate for 5,7 C4: 5,7 => CTR * 389764251472815639156..247886..2134..314.98269246.81...1.24..83648..3.12293187564 C4: 6 # 11 pairs * PAIR B9: 7,9 BLK 7 A7: 7,9,5 # reduction candidate for 7,9 A7: 5 => CTR * 389764251472815..9156..2478865.21.47.3145.826.246.819551724..836485.3712293187564 A7: 7,9 # 12 pairs * PAIR B9: 7,9 ROW 9 F9: 7,9,6 # reduction candidate for 7,9 F9: 7,9 => CTR * 38976425147281563915639247886.92134..314..826.2463819..1.246.83648..3.12293187564 F9: 6 # 13 pairs H9: 7,9,6 # reduction candidate for 7,9 H9: 7,9 # 13 pairs * PAIR B9: 7,9 COL B B4: 7,9,6 # reduction candidate for 7,9 B4: 6 => CTR * 389764251472815639156..247886.921.4..314..826.246.819..1.24..83648..3.12293187564 B4: 7,9 # 11 pairs * PAIR D8: 5,9 BLK 8 E8: 5,9,7 # reduction candidate for 5,9 E8: 7 # 18 pairs E8: 5,9 # 18 pairs * PAIR D8: 5,9 COL D D4: 5,9,3 # reduction candidate for 5,9 D4: 5,9 # 14 pairs D4: 3 # 12 pairs * PAIR G8: 7,9 BLK 9 G7: 7,9,6 # reduction candidate for 7,9 G7: 7,9 => CTR * 38976425147281563915639247886.92134..314..826.2463819..1.246.83648..3.12293187564 G7: 6 # 13 pairs H9: 7,9,6 # reduction candidate for 7,9 H9: 7,9 # 13 pairs * PAIR G8: 7,9 ROW 8 E8: 7,9,5 # reduction candidate for 7,9 E8: 5 # 15 pairs E8: 7,9 # 12 pairs * PAIR G8: 7,9 COL G G2: 7,9,3,6 # reduction candidate for 7,9 G2: 7,9 # 15 pairs G4: 7,9,3 # reduction candidate for 7,9 G4: 7,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-095-base-pr-000.dot * REASONING * DIS # H2: 6,7 => CTR => H2: 3,9 * DIS # B4: 9 => CTR => B4: 6,7 * DIS # C4: 5 => CTR => C4: 6,7 * DIS # H2: 6,7 => CTR => H2: 3,9 * DIS # H9: 9 => CTR => H9: 6,7 * DIS # F9: 7,9 => CTR => F9: 6 * DIS # A7: 9 => CTR => A7: 5,7 * DIS # C4: 5,7 => CTR => C4: 6 * DIS # A7: 5 => CTR => A7: 7,9 * DIS # F9: 7,9 => CTR => F9: 6 * DIS # B4: 6 => CTR => B4: 7,9 * DIS # G7: 7,9 => CTR => G7: 6 * CNT 12 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B9,C3,C7,D3,D8,E3,F5,G8,H3,I2) * 3897642514.2815...15...24.88...21.4..314..826.246.81...1.24..83648..3.122.318.5.4 * PAIR B2: 6,7 ROW 2 G2: 6,7,3,9 # reduction candidate for 6,7 G2: 6,7 # 17 pairs H2: 6,7,3,9 # reduction candidate for 6,7 H2: 6,7 => CTR * 3897642514.28153.915.9324.889632174..314..826.246.813..1.24.6836485.3.122.3186594 * RESTART * PAIR B2: 6,7 ROW 2 G2: 6,7,3,9 # reduction candidate for 6,7 G2: 6,7 # 17 pairs G2: 3,9 # 16 pairs * PAIR B2: 6,7 COL B B4: 6,7,9 # reduction candidate for 6,7 B4: 9 => CTR * 389764251462815937157..2468896.21.4..314..826.246.81..91524.683648..3.12273186594 * PAIR RESTART * PAIR B2: 6,7 ROW 2 G2: 6,7,3 # reduction candidate for 6,7 G2: 6,7 => SOLVED * 389764251462815739157392468876921345931457826524638197715249683648573912293186574 * DURATION: 0:00:08.124482 START: 06:03:02.736914 END: 06:03:10.861396 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-095-base-pr-001.dot * REASONING * DIS # H2: 6,7 => CTR => H2: 3,9 * DIS H2: 3,9 # B4: 9 => CTR => B4: 6,7 * PRF H2: 3,9 + B4: 6,7 # G2: 6,7 => SOL * STA H2: 3,9 + B4: 6,7 + G2: 6,7 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 095 solution: 389764251462815739157392468876921345931457826524638197715249683648573912293186574 info: 1573 FNBTWXY S8.f 11907 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 389764251462815739157392468876921345931457826524638197715249683648573912293186574 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 # G2: 6,7 => UNS * DIS # H2: 6,7 => CTR => H2: 3,9 * INC # H2: 3,9 => UNS * INC # B4: 6,7 => UNS * DIS # B4: 9 => CTR => B4: 6,7 * INC # C4: 6,7 => UNS * DIS # C4: 5 => CTR => C4: 6,7 * INC # D4: 3,9 => UNS * INC # D4: 5 => UNS * INC # E6: 3,9 => UNS * INC # E6: 5,7 => UNS * INC # G2: 7,9 => UNS * INC # H2: 7,9 => UNS * INC # I4: 7,9 => UNS * INC # I6: 7,9 => UNS * INC # G2: 6,7 => UNS * DIS # H2: 6,7 => CTR => H2: 3,9 * INC # H2: 3,9 => UNS * INC # H9: 6,7 => UNS * DIS # H9: 9 => CTR => H9: 6,7 * INC # E5: 7,9 => UNS * INC # E6: 7,9 => UNS * INC # A5: 7,9 => UNS * INC # A5: 5 => UNS * INC # F7: 7,9 => UNS * DIS # F9: 7,9 => CTR => F9: 6 * INC # F9: 6 => UNS * INC # A7: 5,7 => UNS * DIS # A7: 9 => CTR => A7: 5,7 * DIS # C4: 5,7 => CTR => C4: 6 * INC # C4: 6 => UNS * INC # A7: 7,9 => UNS * DIS # A7: 5 => CTR => A7: 7,9 * DIS # F9: 7,9 => CTR => F9: 6 * INC # F9: 6 => UNS * INC # H9: 7,9 => UNS * INC # B4: 7,9 => UNS * DIS # B4: 6 => CTR => B4: 7,9 * INC # E8: 5,9 => UNS * INC # E8: 7 => UNS * INC # D4: 5,9 => UNS * INC # D4: 3 => UNS * DIS # G7: 7,9 => CTR => G7: 6 * INC # G7: 6 => UNS * INC # H9: 7,9 => UNS * INC # E8: 7,9 => UNS * INC # E8: 5 => UNS * INC # G2: 7,9 => UNS * INC # G4: 7,9 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 6,7 => UNS * DIS # H2: 6,7 => CTR => H2: 3,9 * INC H2: 3,9 # G2: 6,7 => UNS * INC H2: 3,9 # G2: 3,9 => UNS * INC H2: 3,9 # B4: 6,7 => UNS * DIS H2: 3,9 # B4: 9 => CTR => B4: 6,7 * PRF H2: 3,9 + B4: 6,7 # G2: 6,7 => SOL * STA H2: 3,9 + B4: 6,7 + G2: 6,7 * CNT 7 HDP CHAINS / 7 HYP OPENED