Analysis of xx-top500-454-base.sdk
Contents
Original Sudoku
level: medium
position: ...76.2..4..8.....15............1.4..3....8...2..........2....37......1.....8.... initial
Autosolve
position: 3897642514.2815...15...24.88...21.4..314..82..24..81...1.24..83748..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 * PRF # B4: 9 => SOL * DIS # C4: 5 => CTR => C4: 6,7 * DIS # H2: 6,7 => CTR => H2: 3,9 * PRF # H6: 6,7 => SOL * DIS # F9: 6,9 => CTR => F9: 7 * PRF # A7: 9 => SOL * DIS # C4: 5,6 => CTR => C4: 7 * DIS # A7: 5 => CTR => A7: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * DIS # B4: 7 => CTR => B4: 6,9 * DIS # G7: 6,9 => CTR => G7: 7 * CNT 12 HDP CHAINS / 48 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 * PRF H2: 3,9 # B4: 9 => SOL * STA H2: 3,9 + B4: 9 * CNT 2 HDP CHAINS / 5 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....37......1.....8.... | initial |
| 3897642514.2815...15...24.88...21.4..314..82..24..81...1.24..83748..3.122.318.5.4 | autosolve |
| 389764251472815936156932478897621345631459827524378169915246783748593612263187594 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B2: 6,7 C3: 6,7 D3: 3,9 E3: 3,9 H3: 6,7 F5: 6,9 C7: 5,6 B9: 6,9 E8: 5,9 G8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,E3: 3.. / D3 = 3 => 8 pairs (_) / E3 = 3 => 9 pairs (_) G2,H2: 3.. / G2 = 3 => 14 pairs (_) / H2 = 3 => 10 pairs (_) G4,H6: 3.. / G4 = 3 => 10 pairs (_) / H6 = 3 => 14 pairs (_) D4,G4: 3.. / D4 = 3 => 14 pairs (_) / G4 = 3 => 10 pairs (_) E3,E6: 3.. / E3 = 3 => 9 pairs (_) / E6 = 3 => 8 pairs (_) G2,G4: 3.. / G2 = 3 => 14 pairs (_) / G4 = 3 => 10 pairs (_) H2,H6: 3.. / H2 = 3 => 10 pairs (_) / H6 = 3 => 14 pairs (_) A7,C7: 5.. / A7 = 5 => 0 pairs (X) / C7 = 5 => 11 pairs (_) D8,E8: 5.. / D8 = 5 => 15 pairs (_) / E8 = 5 => 11 pairs (_) C4,C7: 5.. / C4 = 5 => 0 pairs (X) / C7 = 5 => 11 pairs (_) B2,C3: 6.. / B2 = 6 => 0 pairs (X) / C3 = 6 => 11 pairs (_) C3,H3: 6.. / C3 = 6 => 11 pairs (_) / H3 = 6 => 0 pairs (X) D8,G8: 6.. / D8 = 6 => 17 pairs (_) / G8 = 6 => 16 pairs (_) B2,C3: 7.. / B2 = 7 => 11 pairs (_) / C3 = 7 => 0 pairs (X) B4,C4: 7.. / B4 = 7 => 0 pairs (X) / C4 = 7 => 11 pairs (_) E5,E6: 7.. / E5 = 7 => 10 pairs (_) / E6 = 7 => 12 pairs (_) F7,F9: 7.. / F7 = 7 => 0 pairs (X) / F9 = 7 => 12 pairs (_) G7,H9: 7.. / G7 = 7 => 12 pairs (_) / H9 = 7 => 0 pairs (X) C3,H3: 7.. / C3 = 7 => 0 pairs (X) / H3 = 7 => 11 pairs (_) E5,I5: 7.. / E5 = 7 => 10 pairs (_) / I5 = 7 => 12 pairs (_) F7,G7: 7.. / F7 = 7 => 0 pairs (X) / G7 = 7 => 12 pairs (_) F9,H9: 7.. / F9 = 7 => 12 pairs (_) / H9 = 7 => 0 pairs (X) B2,B4: 7.. / B2 = 7 => 11 pairs (_) / B4 = 7 => 0 pairs (X) C3,C4: 7.. / C3 = 7 => 0 pairs (X) / C4 = 7 => 11 pairs (_) G2,G7: 7.. / G2 = 7 => 0 pairs (X) / G7 = 7 => 12 pairs (_) D3,E3: 9.. / D3 = 9 => 9 pairs (_) / E3 = 9 => 8 pairs (_) A7,B9: 9.. / A7 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) B4,B9: 9.. / B4 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) * DURATION: 0:00:46.527441 START: 18:14:58.213080 END: 18:15:44.740521 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B9,C3,C7,D3,E3,E8,F5,G8,H3) * 3897642514.2815...15...24.88...21.4..314..82..24..81...1.24..83748..3.122.318.5.4 * PAIR B2: 6,7 ROW 2 G2: 6,7,3,9 # reduction candidate for 6,7 G2: 6,7 # 14 pairs H2: 6,7,3,9 # reduction candidate for 6,7 H2: 6,7 => CTR * 3897642514.28153.915.9324.889732164..314..82..24..813..1.24.783748..3.122.3187594 H2: 3,9 # 11 pairs I2: 6,7,9 # reduction candidate for 6,7 I2: 6,7 # 16 pairs * PAIR B2: 6,7 COL B B4: 6,7,9 # reduction candidate for 6,7 B4: 9 => SOLVED * 389764251472815936156932478897621345631459827524378169915246783748593612263187594 B4: 6,7 # 19 pairs * PAIR C3: 6,7 COL C C4: 6,7,5 # reduction candidate for 6,7 C4: 5 => CTR * 389764251462815739157..2468875.213466314.982..24..81..51624..83748..3612293186574 C4: 6,7 # 11 pairs * PAIR D3: 3,9 COL D D4: 3,9,5,6 # reduction candidate for 3,9 D4: 3,9 # 13 pairs D6: 3,9,5,6 # reduction candidate for 3,9 D6: 3,9 # 13 pairs * PAIR E3: 3,9 COL E E6: 3,9,5,7 # reduction candidate for 3,9 E6: 5,7 # 11 pairs E6: 3,9 # 11 pairs * PAIR H3: 6,7 BLK 3 G2: 6,7,3,9 # reduction candidate for 6,7 G2: 6,7 # 14 pairs H2: 6,7,3,9 # reduction candidate for 6,7 H2: 6,7 => CTR * 3897642514.28153.915.9324.889732164..314..82..24..813..1.24.783748..3.122.3187594 H2: 3,9 # 11 pairs I2: 6,7,9 # reduction candidate for 6,7 I2: 6,7 # 16 pairs * PAIR H3: 6,7 COL H H6: 6,7,3,9 # reduction candidate for 6,7 H6: 6,7 => SOLVED * 389764251472815936156932478897621345631459827524378169915246783748593612263187594 H6: 3,9 # 12 pairs H9: 6,7,9 # reduction candidate for 6,7 H9: 6,7 # 15 pairs * PAIR F5: 6,9 BLK 5 D4: 6,9,3,5 # reduction candidate for 6,9 D4: 6,9 # 13 pairs D6: 6,9,3,5 # reduction candidate for 6,9 D6: 6,9 # 13 pairs * PAIR F5: 6,9 ROW 5 A5: 6,9,5 # reduction candidate for 6,9 A5: 6,9 # 13 pairs I5: 6,9,5,7 # reduction candidate for 6,9 I5: 6,9 # 13 pairs * PAIR F5: 6,9 COL F F7: 6,9,7 # reduction candidate for 6,9 F7: 6,9 # 12 pairs F9: 6,9,7 # reduction candidate for 6,9 F9: 6,9 => CTR * 389764251462815739157..246887.92134..314..82..24..819..1.247.83748..3.12293186574 F9: 7 # 12 pairs * PAIR C7: 5,6 BLK 7 A7: 5,6,9 # reduction candidate for 5,6 A7: 9 => SOLVED * 389764251472815936156932478897621345631459827524378169915246783748593612263187594 A7: 5,6 # 19 pairs * PAIR C7: 5,6 COL C C4: 5,6,7 # reduction candidate for 5,6 C4: 5,6 => CTR * 389764251462815739157..246887..2134..314.982.924..81...1.24..83748..3.12293186574 C4: 7 # 11 pairs * PAIR B9: 6,9 BLK 7 A7: 6,9,5 # reduction candidate for 6,9 A7: 5 => CTR * 389764251462815739157..2468875.213466314.982..24..81..51624..83748..3612293186574 A7: 6,9 # 11 pairs * PAIR B9: 6,9 ROW 9 F9: 6,9,7 # reduction candidate for 6,9 F9: 6,9 => CTR * 389764251462815739157..246887.92134..314..82..24..819..1.247.83748..3.12293186574 F9: 7 # 12 pairs H9: 6,9,7 # reduction candidate for 6,9 H9: 6,9 # 12 pairs * PAIR B9: 6,9 COL B B4: 6,9,7 # reduction candidate for 6,9 B4: 7 => CTR * 389764251462815739157..246887..2134..314.982.924..81...1.24..83748..3.12293186574 B4: 6,9 # 11 pairs * PAIR E8: 5,9 BLK 8 D8: 5,9,6 # reduction candidate for 5,9 D8: 6 # 17 pairs D8: 5,9 # 16 pairs * PAIR E8: 5,9 COL E E5: 5,9,7 # reduction candidate for 5,9 E5: 5,9 # 12 pairs E6: 5,9,3,7 # reduction candidate for 5,9 E6: 5,9 # 10 pairs * PAIR G8: 6,9 BLK 9 G7: 6,9,7 # reduction candidate for 6,9 G7: 6,9 => CTR * 389764251462815739157..246887.92134..314..82..24..819..1.247.83748..3.12293186574 G7: 7 # 12 pairs H9: 6,9,7 # reduction candidate for 6,9 H9: 6,9 # 12 pairs * PAIR G8: 6,9 ROW 8 D8: 6,9,5 # reduction candidate for 6,9 D8: 5 # 15 pairs D8: 6,9 # 11 pairs * PAIR G8: 6,9 COL G G2: 6,9,3,7 # reduction candidate for 6,9 G2: 6,9 # 13 pairs G4: 6,9,3 # reduction candidate for 6,9 G4: 6,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-454-base-pr-000.dot * REASONING * DIS # H2: 6,7 => CTR => H2: 3,9 * PRF # B4: 9 => SOL * DIS # C4: 5 => CTR => C4: 6,7 * DIS # H2: 6,7 => CTR => H2: 3,9 * PRF # H6: 6,7 => SOL * DIS # F9: 6,9 => CTR => F9: 7 * PRF # A7: 9 => SOL * DIS # C4: 5,6 => CTR => C4: 7 * DIS # A7: 5 => CTR => A7: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * DIS # B4: 7 => CTR => B4: 6,9 * DIS # G7: 6,9 => CTR => G7: 7 * CNT 12 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B9,C3,C7,D3,E3,E8,F5,G8,H3) * 3897642514.2815...15...24.88...21.4..314..82..24..81...1.24..83748..3.122.318.5.4 * PAIR B2: 6,7 ROW 2 G2: 6,7,3,9 # reduction candidate for 6,7 G2: 6,7 # 14 pairs H2: 6,7,3,9 # reduction candidate for 6,7 H2: 6,7 => CTR * 3897642514.28153.915.9324.889732164..314..82..24..813..1.24.783748..3.122.3187594 I2: 6,7,9 # reduction candidate for 6,7 I2: 6,7 # 16 pairs * PAIR B2: 6,7 COL B B4: 6,7,9 # reduction candidate for 6,7 B4: 9 => SOLVED * 389764251472815936156932478897621345631459827524378169915246783748593612263187594 * DURATION: 0:00:05.904511 START: 18:16:29.416502 END: 18:16:35.321013 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-454-base-pr-001.dot * REASONING * DIS # H2: 6,7 => CTR => H2: 3,9 * PRF H2: 3,9 # B4: 9 => SOL * STA H2: 3,9 + B4: 9 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 454 solution: 389764251472815936156932478897621345631459827524378169915246783748593612263187594 info: 95477 FNBXK S8.f 11908 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 389764251472815936156932478897621345631459827524378169915246783748593612263187594 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 # I2: 6,7 => UNS * INC # B4: 6,7 => UNS * PRF # B4: 9 => SOL * INC # C4: 6,7 => UNS * DIS # C4: 5 => CTR => C4: 6,7 * INC # D4: 3,9 => UNS * INC # D6: 3,9 => UNS * INC # E6: 3,9 => UNS * INC # E6: 5,7 => UNS * INC # G2: 6,7 => UNS * DIS # H2: 6,7 => CTR => H2: 3,9 * INC # H2: 3,9 => UNS * INC # I2: 6,7 => UNS * PRF # H6: 6,7 => SOL * INC # H6: 3,9 => UNS * INC # H9: 6,7 => UNS * INC # D4: 6,9 => UNS * INC # D6: 6,9 => UNS * INC # A5: 6,9 => UNS * INC # I5: 6,9 => UNS * INC # F7: 6,9 => UNS * DIS # F9: 6,9 => CTR => F9: 7 * INC # F9: 7 => UNS * INC # A7: 5,6 => UNS * PRF # A7: 9 => SOL * DIS # C4: 5,6 => CTR => C4: 7 * INC # C4: 7 => UNS * INC # A7: 6,9 => UNS * DIS # A7: 5 => CTR => A7: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * INC # F9: 7 => UNS * INC # H9: 6,9 => UNS * INC # B4: 6,9 => UNS * DIS # B4: 7 => CTR => B4: 6,9 * INC # D8: 5,9 => UNS * INC # D8: 6 => UNS * INC # E5: 5,9 => UNS * INC # E6: 5,9 => UNS * DIS # G7: 6,9 => CTR => G7: 7 * INC # G7: 7 => UNS * INC # H9: 6,9 => UNS * INC # D8: 6,9 => UNS * INC # D8: 5 => UNS * INC # G2: 6,9 => UNS * INC # G4: 6,9 => UNS * CNT 48 HDP CHAINS / 48 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 # I2: 6,7 => UNS * INC H2: 3,9 # B4: 6,7 => UNS * PRF H2: 3,9 # B4: 9 => SOL * STA H2: 3,9 + B4: 9 * CNT 5 HDP CHAINS / 5 HYP OPENED