Analysis of xx-top500-215-base.sdk
Contents
Original Sudoku
level: medium
position: 6.1.3.......5...7...........7.....4.5....1.......6...82.....6.....7..3...5.4..... initial
Autosolve
position: 641.375.....5...767.56...3..76..5.4.5.4.71.6..1..647582.71536.446.7..3151534.6..7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G3: 1,4 => CTR => G3: 2,8,9 * DIS # H1: 2,9 => CTR => H1: 8 * PRF # H1: 8 => SOL * PRF # G3: 2,9 => SOL * DIS # I3: 2,9 => CTR => I3: 1 * PRF # D1: 2,9 => SOL * DIS # D1: 8 => CTR => D1: 2,9 * DIS # G3: 1,4 => CTR => G3: 2,8,9 * DIS # A4: 3,9 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # B5: 3,9 => SOL * DIS # D6: 2 => CTR => D6: 3,9 * PRF # A2: 3,9 => SOL * DIS # A2: 8 => CTR => A2: 3,9 * DIS # B5: 2,9 => CTR => B5: 3,8 * DIS # C2: 2,9 => CTR => C2: 8 * PRF # C2: 8 => SOL * DIS # G4: 2,9 => CTR => G4: 1 * DIS # B5: 2,9 => CTR => B5: 3,8 * DIS # D5: 2,9 => CTR => D5: 3,8 * PRF # G3: 2,9 => SOL * DIS # G9: 2,9 => CTR => G9: 8 * PRF # G9: 8 => SOL * DIS # B2: 8,9 => CTR => B2: 2,3 * PRF # B3: 8,9 => SOL * PRF # E8: 8,9 => SOL * DIS # C2: 2 => CTR => C2: 8,9 * PRF # E8: 8,9 => SOL * DIS # H9: 8,9 => CTR => H9: 2 * PRF # E4: 2 => SOL * DIS # H9: 8,9 => CTR => H9: 2 * DIS # H1: 2 => CTR => H1: 8,9 * CNT 32 HDP CHAINS / 63 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G3: 1,4 => CTR => G3: 2,8,9 * DIS G3: 2,8,9 # H1: 2,9 => CTR => H1: 8 * PRF G3: 2,8,9 + H1: 8 => SOL * STA G3: 2,8,9 + H1: 8 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.1.3.......5...7...........7.....4.5....1.......6...82.....6.....7..3...5.4..... | initial |
| 641.375.....5...767.56...3..76..5.4.5.4.71.6..1..647582.71536.446.7..3151534.6..7 | autosolve |
| 641237589328519476795648231876925143534871962912364758287153694469782315153496827 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) E2: 1,4 E3: 1,4 I1: 2,9 G2: 1,4 A6: 3,9 C6: 2,9 G5: 2,9 B7: 8,9 C8: 8,9 E9: 8,9 H7: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 1.. / E2 = 1 => 8 pairs (_) / E3 = 1 => 0 pairs (X) G4,I4: 1.. / G4 = 1 => 8 pairs (_) / I4 = 1 => 0 pairs (X) E2,G2: 1.. / E2 = 1 => 8 pairs (_) / G2 = 1 => 0 pairs (X) I3,I4: 1.. / I3 = 1 => 8 pairs (_) / I4 = 1 => 0 pairs (X) B5,C6: 2.. / B5 = 2 => 0 pairs (X) / C6 = 2 => 12 pairs (_) E8,F8: 2.. / E8 = 2 => 15 pairs (_) / F8 = 2 => 0 pairs (*) G9,H9: 2.. / G9 = 2 => 0 pairs (X) / H9 = 2 => 13 pairs (_) C6,D6: 2.. / C6 = 2 => 12 pairs (_) / D6 = 2 => 0 pairs (X) C2,C6: 2.. / C2 = 2 => 0 pairs (X) / C6 = 2 => 12 pairs (_) E4,E8: 2.. / E4 = 2 => 0 pairs (*) / E8 = 2 => 0 pairs (X) H1,H9: 2.. / H1 = 2 => 0 pairs (X) / H9 = 2 => 13 pairs (_) A2,B2: 3.. / A2 = 3 => 0 pairs (*) / B2 = 3 => 0 pairs (X) I4,I5: 3.. / I4 = 3 => 14 pairs (_) / I5 = 3 => 12 pairs (_) A6,D6: 3.. / A6 = 3 => 13 pairs (_) / D6 = 3 => 13 pairs (_) B2,B5: 3.. / B2 = 3 => 12 pairs (_) / B5 = 3 => 0 pairs (*) E2,E3: 4.. / E2 = 4 => 0 pairs (X) / E3 = 4 => 8 pairs (_) G2,G3: 4.. / G2 = 4 => 8 pairs (_) / G3 = 4 => 0 pairs (X) E2,G2: 4.. / E2 = 4 => 0 pairs (X) / G2 = 4 => 8 pairs (_) E3,G3: 4.. / E3 = 4 => 8 pairs (_) / G3 = 4 => 0 pairs (X) H1,G3: 8.. / H1 = 8 => 0 pairs (*) / G3 = 8 => 0 pairs (X) A4,B5: 8.. / A4 = 8 => 0 pairs (*) / B5 = 8 => 0 pairs (X) B7,C8: 8.. / B7 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) D1,H1: 8.. / D1 = 8 => 0 pairs (X) / H1 = 8 => 0 pairs (_) B5,D5: 8.. / B5 = 8 => 0 pairs (X) / D5 = 8 => 0 pairs (_) B7,H7: 8.. / B7 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) A2,A4: 8.. / A2 = 8 => 0 pairs (X) / A4 = 8 => 0 pairs (_) C2,C8: 8.. / C2 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) G3,G9: 8.. / G3 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) B7,C8: 9.. / B7 = 9 => 0 pairs (X) / C8 = 9 => 0 pairs (_) B7,H7: 9.. / B7 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) * DURATION: 0:00:56.178449 START: 10:09:14.187703 END: 10:10:10.366152 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,C6,C8,E2,E3,E9,G2,G5,H7,I1) * 641.375.....5...767.56...3..76..5.4.5.4.71.6..1..647582.71536.446.7..3151534.6..7 * PAIR E3: 1,4 ROW 3 G3: 1,4,2,8,9 # reduction candidate for 1,4 G3: 1,4 => CTR * 641237589.285.9.767956.8.3.876.25.4.5.487126..12.64758287153694469782315153496827 G3: 2,8,9 # 8 pairs * PAIR I1: 2,9 BLK 3 H1: 2,9,8 # reduction candidate for 2,9 H1: 2,9 => CTR * 6418375.....5...767.56..83..76.85.4.584.71.6..12.647582971536844687293151534.6..7 H1: 8 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 G3: 2,9,1,4,8 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 G3: 1,4,8 # 11 pairs I3: 2,9,1 # reduction candidate for 2,9 I3: 2,9 => CTR * 641.3758..385.2.767256...3..76..5.415.4.71.63.1..647582871536944697..315153496827 I3: 1 # 8 pairs * PAIR I1: 2,9 ROW 1 D1: 2,9,8 # reduction candidate for 2,9 D1: 2,9 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 D1: 8 => CTR * 6418375.....5...767.56..83..76.85.4.584.71.6..12.647582971536844687293151534.6..7 * PAIR I1: 2,9 COL I I4: 2,9,1,3 # reduction candidate for 2,9 I4: 2,9 # 10 pairs I5: 2,9,3 # reduction candidate for 2,9 I5: 2,9 # 14 pairs * PAIR G2: 1,4 BLK 3 G3: 1,4,2,8,9 # reduction candidate for 1,4 G3: 1,4 => CTR * 641237589.285.9.767956.8.3.876.25.4.5.487126..12.64758287153694469782315153496827 G3: 2,8,9 # 8 pairs * PAIR A6: 3,9 BLK 4 A4: 3,9,8 # reduction candidate for 3,9 A4: 3,9 => CTR * 6418375..8395.2.767256.9.3..76..5.4.584.71.6..12.647582971536844687..315153486..7 A4: 8 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 B5: 3,9,2,8 # reduction candidate for 3,9 B5: 3,9 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 B5: 2,8 # 13 pairs * PAIR A6: 3,9 ROW 6 D6: 3,9,2 # reduction candidate for 3,9 D6: 2 => CTR * 641.375.....5...767.56...3..76..5.4.5.4.71.6.319264758297153684468729315153486..7 D6: 3,9 # 12 pairs * PAIR A6: 3,9 COL A A2: 3,9,8 # reduction candidate for 3,9 A2: 3,9 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 A2: 8 => CTR * 6418375..8395.2.767256.9.3..76..5.4.584.71.6..12.647582971536844687..315153486..7 * PAIR C6: 2,9 BLK 4 B5: 2,9,3,8 # reduction candidate for 2,9 B5: 2,9 => CTR * 641.3758.93.5...767.56...3.8763.5.4.5.4871.6331..647582871536944697..315153496827 B5: 3,8 # 14 pairs * PAIR C6: 2,9 ROW 6 D6: 2,9,3 # reduction candidate for 2,9 D6: 3 # 13 pairs D6: 2,9 # 13 pairs * PAIR C6: 2,9 COL C C2: 2,9,8 # reduction candidate for 2,9 C2: 2,9 => CTR * 6418375.....5..476725649831876..514.534.71.6.912364758297153684468792315153486..7 C2: 8 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 * PAIR G5: 2,9 BLK 6 G4: 2,9,1 # reduction candidate for 2,9 G4: 2,9 => CTR * 641.3758..385.2.767256...3..76..5.415.4.71.63.1..647582871536944697..315153496827 G4: 1 # 8 pairs I4: 2,9,1,3 # reduction candidate for 2,9 I4: 2,9 # 10 pairs I5: 2,9,3 # reduction candidate for 2,9 I5: 2,9 # 14 pairs * PAIR G5: 2,9 ROW 5 B5: 2,9,3,8 # reduction candidate for 2,9 B5: 2,9 => CTR * 641.3758.93.5...767.56...3.8763.5.4.5.4871.6331..647582871536944697..315153496827 B5: 3,8 # 14 pairs D5: 2,9,3,8 # reduction candidate for 2,9 D5: 2,9 => CTR * 6418375..8395.2.767256.9.3..76..5.4.584.71.63.12.647582971536844687..315153486..7 D5: 3,8 # 12 pairs * PAIR G5: 2,9 COL G G3: 2,9,1,4,8 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 G3: 1,4,8 # 11 pairs G9: 2,9,8 # reduction candidate for 2,9 G9: 2,9 => CTR * 6418375.....5..4767.564.831.76.8514.584.71.6..12.647582971536844687293151534.6..7 G9: 8 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 * PAIR B7: 8,9 COL B B2: 8,9,2,3 # reduction candidate for 8,9 B2: 8,9 => CTR * 641.3758.3..5.2.767256.8.3.876295143534871.6.9123647582871536944697..3151534.6..7 B2: 2,3 # 12 pairs B3: 8,9,2 # reduction candidate for 8,9 B3: 8,9 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 B3: 2 # 17 pairs B5: 8,9,2,3 # reduction candidate for 8,9 B5: 8,9 # 19 pairs * PAIR C8: 8,9 ROW 8 E8: 8,9,2 # reduction candidate for 8,9 E8: 8,9 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 E8: 2 # 15 pairs F8: 8,9,2 # reduction candidate for 8,9 F8: 8,9 # 15 pairs * PAIR C8: 8,9 COL C C2: 8,9,2 # reduction candidate for 8,9 C2: 2 => CTR * 641.375....25...767.56...3..76..5.4.524871963.19264758297153684468729315153486297 C2: 8,9 # 12 pairs * PAIR E9: 8,9 BLK 8 E8: 8,9,2 # reduction candidate for 8,9 E8: 8,9 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 E8: 2 # 15 pairs F8: 8,9,2 # reduction candidate for 8,9 F8: 8,9 # 15 pairs * PAIR E9: 8,9 ROW 9 G9: 8,9,2 # reduction candidate for 8,9 G9: 8,9 # 13 pairs H9: 8,9,2 # reduction candidate for 8,9 H9: 8,9 => CTR * 641837529...51.4767.564.831.76.8514.584.7196..12.6475829715368446.7..3151534.62.7 H9: 2 # 13 pairs * PAIR E9: 8,9 COL E E4: 8,9,2 # reduction candidate for 8,9 E4: 2 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 E4: 8,9 # 15 pairs * PAIR H7: 8,9 BLK 9 G9: 8,9,2 # reduction candidate for 8,9 G9: 8,9 # 13 pairs H9: 8,9,2 # reduction candidate for 8,9 H9: 8,9 => CTR * 641837529...51.4767.564.831.76.8514.584.7196..12.6475829715368446.7..3151534.62.7 H9: 2 # 13 pairs * PAIR H7: 8,9 COL H H1: 8,9,2 # reduction candidate for 8,9 H1: 2 => CTR * 641837529...5...767.56..831.76.8514.584.7196..12.6475829715368446.7..3151534.6..7 H1: 8,9 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-215-base-pr-000.dot * REASONING * DIS # G3: 1,4 => CTR => G3: 2,8,9 * DIS # H1: 2,9 => CTR => H1: 8 * PRF # H1: 8 => SOL * PRF # G3: 2,9 => SOL * DIS # I3: 2,9 => CTR => I3: 1 * PRF # D1: 2,9 => SOL * DIS # D1: 8 => CTR => D1: 2,9 * DIS # G3: 1,4 => CTR => G3: 2,8,9 * DIS # A4: 3,9 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # B5: 3,9 => SOL * DIS # D6: 2 => CTR => D6: 3,9 * PRF # A2: 3,9 => SOL * DIS # A2: 8 => CTR => A2: 3,9 * DIS # B5: 2,9 => CTR => B5: 3,8 * DIS # C2: 2,9 => CTR => C2: 8 * PRF # C2: 8 => SOL * DIS # G4: 2,9 => CTR => G4: 1 * DIS # B5: 2,9 => CTR => B5: 3,8 * DIS # D5: 2,9 => CTR => D5: 3,8 * PRF # G3: 2,9 => SOL * DIS # G9: 2,9 => CTR => G9: 8 * PRF # G9: 8 => SOL * DIS # B2: 8,9 => CTR => B2: 2,3 * PRF # B3: 8,9 => SOL * PRF # E8: 8,9 => SOL * DIS # C2: 2 => CTR => C2: 8,9 * PRF # E8: 8,9 => SOL * DIS # H9: 8,9 => CTR => H9: 2 * PRF # E4: 2 => SOL * DIS # H9: 8,9 => CTR => H9: 2 * DIS # H1: 2 => CTR => H1: 8,9 * CNT 32 HDP CHAINS / 63 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,C6,C8,E2,E3,E9,G2,G5,H7,I1) * 641.375.....5...767.56...3..76..5.4.5.4.71.6..1..647582.71536.446.7..3151534.6..7 * PAIR E3: 1,4 ROW 3 G3: 1,4,2,8,9 # reduction candidate for 1,4 G3: 1,4 => CTR * 641237589.285.9.767956.8.3.876.25.4.5.487126..12.64758287153694469782315153496827 * PAIR RESTART * PAIR I1: 2,9 BLK 3 H1: 2,9,8 # reduction candidate for 2,9 H1: 2,9 => CTR * 6418375.....51.4767.564.831.76.8514.584.71.6..12.647582971536844687293151534.6..7 H1: 8 => SOLVED * 641237589328519476795648231876925143534871962912364758287153694469782315153496827 * DURATION: 0:00:04.151020 START: 10:11:18.918811 END: 10:11:23.069831 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-215-base-pr-001.dot * REASONING * DIS # G3: 1,4 => CTR => G3: 2,8,9 * DIS G3: 2,8,9 # H1: 2,9 => CTR => H1: 8 * PRF G3: 2,8,9 + H1: 8 => SOL * STA G3: 2,8,9 + H1: 8 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 215 solution: 641237589328519476795648231876925143534871962912364758287153694469782315153496827 info: 1948 FNBHWX S8.f 35341 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 641237589328519476795648231876925143534871962912364758287153694469782315153496827 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:
* DIS # G3: 1,4 => CTR => G3: 2,8,9 * INC # G3: 2,8,9 => UNS * DIS # H1: 2,9 => CTR => H1: 8 * PRF # H1: 8 => SOL * PRF # G3: 2,9 => SOL * INC # G3: 1,4,8 => UNS * DIS # I3: 2,9 => CTR => I3: 1 * INC # I3: 1 => UNS * PRF # D1: 2,9 => SOL * DIS # D1: 8 => CTR => D1: 2,9 * INC # I4: 2,9 => UNS * INC # I5: 2,9 => UNS * DIS # G3: 1,4 => CTR => G3: 2,8,9 * INC # G3: 2,8,9 => UNS * DIS # A4: 3,9 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # B5: 3,9 => SOL * INC # B5: 2,8 => UNS * INC # D6: 3,9 => UNS * DIS # D6: 2 => CTR => D6: 3,9 * PRF # A2: 3,9 => SOL * DIS # A2: 8 => CTR => A2: 3,9 * DIS # B5: 2,9 => CTR => B5: 3,8 * INC # B5: 3,8 => UNS * INC # D6: 2,9 => UNS * INC # D6: 3 => UNS * DIS # C2: 2,9 => CTR => C2: 8 * PRF # C2: 8 => SOL * DIS # G4: 2,9 => CTR => G4: 1 * INC # G4: 1 => UNS * INC # I4: 2,9 => UNS * INC # I5: 2,9 => UNS * DIS # B5: 2,9 => CTR => B5: 3,8 * INC # B5: 3,8 => UNS * DIS # D5: 2,9 => CTR => D5: 3,8 * INC # D5: 3,8 => UNS * PRF # G3: 2,9 => SOL * INC # G3: 1,4,8 => UNS * DIS # G9: 2,9 => CTR => G9: 8 * PRF # G9: 8 => SOL * DIS # B2: 8,9 => CTR => B2: 2,3 * INC # B2: 2,3 => UNS * PRF # B3: 8,9 => SOL * INC # B3: 2 => UNS * INC # B5: 8,9 => UNS * PRF # E8: 8,9 => SOL * INC # E8: 2 => UNS * INC # F8: 8,9 => UNS * INC # C2: 8,9 => UNS * DIS # C2: 2 => CTR => C2: 8,9 * PRF # E8: 8,9 => SOL * INC # E8: 2 => UNS * INC # F8: 8,9 => UNS * INC # G9: 8,9 => UNS * DIS # H9: 8,9 => CTR => H9: 2 * INC # H9: 2 => UNS * INC # E4: 8,9 => UNS * PRF # E4: 2 => SOL * INC # G9: 8,9 => UNS * DIS # H9: 8,9 => CTR => H9: 2 * INC # H9: 2 => UNS * INC # H1: 8,9 => UNS * DIS # H1: 2 => CTR => H1: 8,9 * CNT 63 HDP CHAINS / 63 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G3: 1,4 => CTR => G3: 2,8,9 * DIS G3: 2,8,9 # H1: 2,9 => CTR => H1: 8 * PRF G3: 2,8,9 + H1: 8 => SOL * STA G3: 2,8,9 + H1: 8 * CNT 3 HDP CHAINS / 2 HYP OPENED