Analysis of xx-top500-054-base.sdk
Contents
Original Sudoku
level: medium
position: 3...48.........1......3.....2.1..7..5.4.........6.....6......43...2...5..1....... initial
Autosolve
position: 39174852674....13.2.6.314...231..76.5643...1.1..6..3..6..81..4343.2...51.1.4.3... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C6: 7 => SOL * DIS # E4: 5 => CTR => E4: 8,9 * PRF # C6: 7,8 => SOL * DIS # C6: 9 => CTR => C6: 7,8 * PRF # E5: 7,9 => SOL * DIS # E5: 8 => CTR => E5: 7,9 * PRF # F8: 7,9 => SOL * DIS # F4: 9 => CTR => F4: 4,5 * PRF # C6: 7 => SOL * PRF # F6: 2 => SOL * DIS # C9: 8,9 => CTR => C9: 2,5 * DIS # G9: 8,9 => CTR => G9: 2,6 * DIS # G9: 2,9 => CTR => G9: 6,8 * DIS # G5: 8 => CTR => G5: 2,9 * CNT 14 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C6: 7 => SOL * STA C6: 7 * CNT 1 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3...48.........1......3.....2.1..7..5.4.........6.....6......43...2...5..1....... | initial |
| 39174852674....13.2.6.314...231..76.5643...1.1..6..3..6..81..4343.2...51.1.4.3... | autosolve |
| 391748526748526139256931487923184765564379218187652394672815943439267851815493672 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C2: 5,8 B3: 5,8 D2: 5,9 E2: 2,6 F2: 2,6 D3: 5,9 I2: 8,9 A4: 8,9 B6: 7,8 F5: 7,9 E6: 2,5 I4: 4,5 H6: 8,9 I6: 4,5 B7: 5,7 A9: 8,9 G7: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 2.. / E2 = 2 => 0 pairs (*) / F2 = 2 => 0 pairs (X) E6,F6: 2.. / E6 = 2 => 18 pairs (_) / F6 = 2 => 0 pairs (*) G5,I5: 2.. / G5 = 2 => 21 pairs (_) / I5 = 2 => 21 pairs (_) C7,C9: 2.. / C7 = 2 => 20 pairs (_) / C9 = 2 => 20 pairs (_) C7,G7: 2.. / C7 = 2 => 20 pairs (_) / G7 = 2 => 20 pairs (_) E2,E6: 2.. / E2 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) F2,F6: 2.. / F2 = 2 => 18 pairs (_) / F6 = 2 => 0 pairs (*) I5,I9: 2.. / I5 = 2 => 21 pairs (_) / I9 = 2 => 21 pairs (_) F4,F6: 4.. / F4 = 4 => 17 pairs (_) / F6 = 4 => 16 pairs (_) I4,I6: 4.. / I4 = 4 => 16 pairs (_) / I6 = 4 => 17 pairs (_) F4,I4: 4.. / F4 = 4 => 17 pairs (_) / I4 = 4 => 16 pairs (_) F6,I6: 4.. / F6 = 4 => 16 pairs (_) / I6 = 4 => 17 pairs (_) C2,B3: 5.. / C2 = 5 => 17 pairs (_) / B3 = 5 => 0 pairs (*) D2,D3: 5.. / D2 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) I4,I6: 5.. / I4 = 5 => 17 pairs (_) / I6 = 5 => 16 pairs (_) F7,E9: 5.. / F7 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) C2,D2: 5.. / C2 = 5 => 17 pairs (_) / D2 = 5 => 0 pairs (*) B3,D3: 5.. / B3 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) C9,E9: 5.. / C9 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) B3,B7: 5.. / B3 = 5 => 0 pairs (*) / B7 = 5 => 0 pairs (X) E2,F2: 6.. / E2 = 6 => 18 pairs (_) / F2 = 6 => 0 pairs (*) G8,G9: 6.. / G8 = 6 => 0 pairs (X) / G9 = 6 => 19 pairs (_) E9,G9: 6.. / E9 = 6 => 0 pairs (X) / G9 = 6 => 19 pairs (_) F2,F8: 6.. / F2 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) H3,I3: 7.. / H3 = 7 => 23 pairs (_) / I3 = 7 => 18 pairs (_) B6,C6: 7.. / B6 = 7 => 17 pairs (_) / C6 = 7 => 0 pairs (*) E5,F5: 7.. / E5 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) H9,I9: 7.. / H9 = 7 => 18 pairs (_) / I9 = 7 => 23 pairs (_) B6,B7: 7.. / B6 = 7 => 17 pairs (_) / B7 = 7 => 0 pairs (*) E5,E8: 7.. / E5 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) H3,H9: 7.. / H3 = 7 => 23 pairs (_) / H9 = 7 => 18 pairs (_) I3,I9: 7.. / I3 = 7 => 18 pairs (_) / I9 = 7 => 23 pairs (_) C2,B3: 8.. / C2 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) E4,E5: 8.. / E4 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) C2,I2: 8.. / C2 = 8 => 0 pairs (*) / I2 = 8 => 0 pairs (X) A4,E4: 8.. / A4 = 8 => 0 pairs (X) / E4 = 8 => 0 pairs (_) C8,G8: 8.. / C8 = 8 => 0 pairs (X) / G8 = 8 => 21 pairs (_) A4,A9: 8.. / A4 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) B3,B6: 8.. / B3 = 8 => 17 pairs (_) / B6 = 8 => 0 pairs (*) D2,D3: 9.. / D2 = 9 => 17 pairs (_) / D3 = 9 => 0 pairs (*) A4,C6: 9.. / A4 = 9 => 0 pairs (*) / C6 = 9 => 0 pairs (X) D2,I2: 9.. / D2 = 9 => 17 pairs (_) / I2 = 9 => 0 pairs (*) C6,H6: 9.. / C6 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) A4,A9: 9.. / A4 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) * DURATION: 0:01:33.177805 START: 04:30:23.540652 END: 04:31:56.718457 2017-05-04 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B3,B6,B7,C2,D2,D3,E2,E6,F2,F5,G7,H6,I2,I4,I6) * 39174852674....13.2.6.314...231..76.5643...1.1..6..3..6..81..4343.2...51.1.4.3... * PAIR C2: 5,8 COL C C9: 5,8,2,9 # reduction candidate for 5,8 C9: 5,8 # 23 pairs C9: 2,9 # 21 pairs * PAIR I2: 8,9 BLK 3 H3: 8,9,7 # reduction candidate for 8,9 H3: 8,9 # 18 pairs I3: 8,9,7 # reduction candidate for 8,9 I3: 8,9 # 23 pairs * PAIR I2: 8,9 COL I I5: 8,9,2 # reduction candidate for 8,9 I5: 8,9 # 21 pairs I9: 8,9,2,7 # reduction candidate for 8,9 I9: 8,9 # 23 pairs * PAIR A4: 8,9 BLK 4 C6: 8,9,7 # reduction candidate for 8,9 C6: 7 => SOLVED * 391748526748526139256931487923184765564379218187652394672815943439267851815493672 C6: 8,9 # 17 pairs * PAIR A4: 8,9 ROW 4 E4: 8,9,5 # reduction candidate for 8,9 E4: 5 => CTR * 39174852674....13.2.6.314..823159764564387.1.17962438565.81..4343.2...51.1.4.3... E4: 8,9 # 19 pairs * PAIR B6: 7,8 BLK 4 C6: 7,8,9 # reduction candidate for 7,8 C6: 7,8 => SOLVED * 391748526748526139256931487923184765564379218187652394672815943439267851815493672 C6: 9 => CTR * 3917485267459..13828653149782319.76.564387.1917962.38.65781924343.2...5191.45367. * PAIR F5: 7,9 BLK 5 E5: 7,9,8 # reduction candidate for 7,9 E5: 7,9 => SOLVED * 391748526748526139256931487923184765564379218187652394672815943439267851815493672 E5: 8 => CTR * 39174852674....13.2865314..8231..76.564387.1.1796..38.657819243438276951.1.4.3... * PAIR F5: 7,9 COL F F7: 7,9,5 # reduction candidate for 7,9 F7: 7,9 # 20 pairs F8: 7,9,6 # reduction candidate for 7,9 F8: 7,9 => SOLVED * 391748526748526139256931487923184765564379218187652394672815943439267851815493672 F8: 6 # 18 pairs * PAIR E6: 2,5 BLK 5 F6: 2,5,4 # reduction candidate for 2,5 F6: 2,5 # 17 pairs F6: 4 # 16 pairs * PAIR I4: 4,5 ROW 4 F4: 4,5,9 # reduction candidate for 4,5 F4: 9 => CTR * 39174852674....13.2.6.314...231.97645643.7.1.1.96.43856..81594343.2...51.1.4.3... F4: 4,5 # 19 pairs * PAIR H6: 8,9 BLK 6 G5: 8,9,2 # reduction candidate for 8,9 G5: 8,9 # 21 pairs I5: 8,9,2 # reduction candidate for 8,9 I5: 8,9 # 21 pairs * PAIR H6: 8,9 ROW 6 C6: 8,9,7 # reduction candidate for 8,9 C6: 7 => SOLVED * 391748526748526139256931487923184765564379218187652394672815943439267851815493672 C6: 8,9 # 17 pairs * PAIR H6: 8,9 COL H H3: 8,9,7 # reduction candidate for 8,9 H3: 8,9 # 18 pairs H9: 8,9,7 # reduction candidate for 8,9 H9: 8,9 # 23 pairs * PAIR I6: 4,5 ROW 6 F6: 4,5,2 # reduction candidate for 4,5 F6: 2 => SOLVED * 391748526748526139256931487923184765564379218187652394672815943439267851815493672 F6: 4,5 # 18 pairs * PAIR B7: 5,7 BLK 7 C7: 5,7,2,9 # reduction candidate for 5,7 C7: 5,7 # 20 pairs C7: 2,9 # 19 pairs * PAIR B7: 5,7 ROW 7 F7: 5,7,9 # reduction candidate for 5,7 F7: 9 # 20 pairs F7: 5,7 # 19 pairs * PAIR A9: 8,9 BLK 7 C8: 8,9,7 # reduction candidate for 8,9 C8: 8,9 # 20 pairs C9: 8,9,2,5 # reduction candidate for 8,9 C9: 8,9 => CTR * 3917485267459..1382865314.7.231..76.5643..21917962.38.65281794343.2...51.1.4536.2 C9: 2,5 # 18 pairs * PAIR A9: 8,9 ROW 9 G9: 8,9,2,6 # reduction candidate for 8,9 G9: 8,9 => CTR * 39174852674..2613.2.6.314...231..76.5643...1.1..6523.46..815.434382..651915463... G9: 2,6 # 18 pairs H9: 8,9,7 # reduction candidate for 8,9 H9: 8,9 # 23 pairs I9: 8,9,2,7 # reduction candidate for 8,9 I9: 8,9 # 23 pairs * PAIR G7: 2,9 BLK 9 G9: 2,9,6,8 # reduction candidate for 2,9 G9: 2,9 => CTR * 39174852674..2613.2.6.314...231..76.5643..8121..6523946..815.434382..65191.463... G9: 6,8 # 18 pairs I9: 2,9,7,8 # reduction candidate for 2,9 I9: 2,9 # 22 pairs * PAIR G7: 2,9 ROW 7 C7: 2,9,5,7 # reduction candidate for 2,9 C7: 5,7 # 20 pairs C7: 2,9 # 19 pairs * PAIR G7: 2,9 COL G G5: 2,9,8 # reduction candidate for 2,9 G5: 8 => CTR * 39174852674....13.2.6.314...231..76.5643..8121..6..39.6..81..434382...5191.4.3... G5: 2,9 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-054-base-pr-000.dot * REASONING * PRF # C6: 7 => SOL * DIS # E4: 5 => CTR => E4: 8,9 * PRF # C6: 7,8 => SOL * DIS # C6: 9 => CTR => C6: 7,8 * PRF # E5: 7,9 => SOL * DIS # E5: 8 => CTR => E5: 7,9 * PRF # F8: 7,9 => SOL * DIS # F4: 9 => CTR => F4: 4,5 * PRF # C6: 7 => SOL * PRF # F6: 2 => SOL * DIS # C9: 8,9 => CTR => C9: 2,5 * DIS # G9: 8,9 => CTR => G9: 2,6 * DIS # G9: 2,9 => CTR => G9: 6,8 * DIS # G5: 8 => CTR => G5: 2,9 * CNT 14 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B3,B6,B7,C2,D2,D3,E2,E6,F2,F5,G7,H6,I2,I4,I6) * 39174852674....13.2.6.314...231..76.5643...1.1..6..3..6..81..4343.2...51.1.4.3... * PAIR C2: 5,8 COL C C9: 5,8,2,9 # reduction candidate for 5,8 C9: 5,8 # 23 pairs C9: 2,9 # 21 pairs * PAIR I2: 8,9 BLK 3 H3: 8,9,7 # reduction candidate for 8,9 H3: 8,9 # 18 pairs I3: 8,9,7 # reduction candidate for 8,9 I3: 8,9 # 23 pairs * PAIR I2: 8,9 COL I I5: 8,9,2 # reduction candidate for 8,9 I5: 8,9 # 21 pairs I9: 8,9,2,7 # reduction candidate for 8,9 I9: 8,9 # 23 pairs * PAIR A4: 8,9 BLK 4 C6: 8,9,7 # reduction candidate for 8,9 C6: 7 => SOLVED * 391748526748526139256931487923184765564379218187652394672815943439267851815493672 * DURATION: 0:00:11.021937 START: 04:32:53.659537 END: 04:33:04.681474 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-054-base-pr-001.dot * REASONING * PRF # C6: 7 => SOL * STA C6: 7 * CNT 1 HDP CHAINS / 8 HYP OPENED
Header Info
Top 500 Minimum 17 054 solution: 391748526748526139256931487923184765564379218187652394672815943439267851815493672 info: 1405 FNBTHWXY S8.f 29162 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 391748526748526139256931487923184765564379218187652394672815943439267851815493672 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 # C9: 5,8 => UNS * INC # C9: 2,9 => UNS * INC # H3: 8,9 => UNS * INC # I3: 8,9 => UNS * INC # I5: 8,9 => UNS * INC # I9: 8,9 => UNS * INC # C6: 8,9 => UNS * PRF # C6: 7 => SOL * INC # E4: 8,9 => UNS * DIS # E4: 5 => CTR => E4: 8,9 * PRF # C6: 7,8 => SOL * DIS # C6: 9 => CTR => C6: 7,8 * PRF # E5: 7,9 => SOL * DIS # E5: 8 => CTR => E5: 7,9 * INC # F7: 7,9 => UNS * PRF # F8: 7,9 => SOL * INC # F8: 6 => UNS * INC # F6: 2,5 => UNS * INC # F6: 4 => UNS * INC # F4: 4,5 => UNS * DIS # F4: 9 => CTR => F4: 4,5 * INC # G5: 8,9 => UNS * INC # I5: 8,9 => UNS * INC # C6: 8,9 => UNS * PRF # C6: 7 => SOL * INC # H3: 8,9 => UNS * INC # H9: 8,9 => UNS * INC # F6: 4,5 => UNS * PRF # F6: 2 => SOL * INC # C7: 5,7 => UNS * INC # C7: 2,9 => UNS * INC # F7: 5,7 => UNS * INC # F7: 9 => UNS * INC # C8: 8,9 => UNS * DIS # C9: 8,9 => CTR => C9: 2,5 * INC # C9: 2,5 => UNS * DIS # G9: 8,9 => CTR => G9: 2,6 * INC # G9: 2,6 => UNS * INC # H9: 8,9 => UNS * INC # I9: 8,9 => UNS * DIS # G9: 2,9 => CTR => G9: 6,8 * INC # G9: 6,8 => UNS * INC # I9: 2,9 => UNS * INC # C7: 2,9 => UNS * INC # C7: 5,7 => UNS * INC # G5: 2,9 => UNS * DIS # G5: 8 => CTR => G5: 2,9 * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C9: 5,8 => UNS * INC # C9: 2,9 => UNS * INC # H3: 8,9 => UNS * INC # I3: 8,9 => UNS * INC # I5: 8,9 => UNS * INC # I9: 8,9 => UNS * INC # C6: 8,9 => UNS * PRF # C6: 7 => SOL * STA C6: 7 * CNT 8 HDP CHAINS / 8 HYP OPENED