Analysis of xx-top500-005-base.sdk
Contents
Original Sudoku
level: medium
position: ....6...8.4.3......1....5.....1.5.4.6.....2..7....3...2...7...........1.......6.. initial
Autosolve
position: ...5641.854.31.9...1....5.4...1.57466.1.4.2.37.46.38.12639714854...5631.1.543.6.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 3,9 => CTR => B1: 2,7 * DIS # A4: 3,9 => CTR => A4: 8 * DIS # A4: 9 => CTR => A4: 3,8 * DIS # F3: 2,7 => CTR => F3: 8,9 * DIS # H1: 2,7 => CTR => H1: 3 * DIS # H2: 2,7 => CTR => H2: 6 * DIS # C2: 2,7 => CTR => C2: 6,8 * PRF # I9: 2,7 => SOL * DIS # F5: 9 => CTR => F5: 7,8 * PRF # D3: 7,8 => SOL * DIS # D3: 2 => CTR => D3: 7,8 * DIS # E4: 8 => CTR => E4: 2,9 * DIS # B5: 8 => CTR => B5: 5,9 * PRF # D3: 7 => SOL * DIS # F3: 2,8 => CTR => F3: 7,9 * PRF # I9: 2,7 => SOL * DIS # H1: 2,7 => CTR => H1: 3 * DIS # H2: 2,7 => CTR => H2: 6 * CNT 18 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 3,9 => CTR => B1: 2,7 * DIS B1: 2,7 # F3: 2,7 => CTR => F3: 8,9 * PRF B1: 2,7 + F3: 8,9 # I9: 2,7 => SOL * STA B1: 2,7 + F3: 8,9 + I9: 2,7 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....6...8.4.3......1....5.....1.5.4.6.....2..7....3...2...7...........1.......6.. | initial |
| ...5641.854.31.9...1....5.4...1.57466.1.4.2.37.46.38.12639714854...5631.1.543.6.. | autosolve |
| 972564138548312967316789524839125746651847293724693851263971485487256319195438672 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A1: 3,9 A3: 3,8 E3: 8,9 I2: 2,7 D5: 7,8 E6: 2,9 H5: 5,9 H6: 5,9 D8: 2,8 F9: 2,8 H9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,E6: 2.. / E4 = 2 => 12 pairs (_) / E6 = 2 => 15 pairs (_) D8,F9: 2.. / D8 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) B6,E6: 2.. / B6 = 2 => 12 pairs (_) / E6 = 2 => 15 pairs (_) D8,I8: 2.. / D8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) D3,D8: 2.. / D3 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) H1,H3: 3.. / H1 = 3 => 18 pairs (_) / H3 = 3 => 0 pairs (X) A4,B4: 3.. / A4 = 3 => 0 pairs (X) / B4 = 3 => 12 pairs (_) A3,H3: 3.. / A3 = 3 => 18 pairs (_) / H3 = 3 => 0 pairs (X) B1,B4: 3.. / B1 = 3 => 0 pairs (X) / B4 = 3 => 12 pairs (_) B5,B6: 5.. / B5 = 5 => 16 pairs (_) / B6 = 5 => 13 pairs (_) H5,H6: 5.. / H5 = 5 => 13 pairs (_) / H6 = 5 => 16 pairs (_) B5,H5: 5.. / B5 = 5 => 16 pairs (_) / H5 = 5 => 13 pairs (_) B6,H6: 5.. / B6 = 5 => 13 pairs (_) / H6 = 5 => 16 pairs (_) C2,C3: 6.. / C2 = 6 => 0 pairs (X) / C3 = 6 => 11 pairs (_) H2,H3: 6.. / H2 = 6 => 11 pairs (_) / H3 = 6 => 0 pairs (X) C2,H2: 6.. / C2 = 6 => 0 pairs (X) / H2 = 6 => 11 pairs (_) C3,H3: 6.. / C3 = 6 => 11 pairs (_) / H3 = 6 => 0 pairs (X) D5,F5: 7.. / D5 = 7 => 12 pairs (_) / F5 = 7 => 0 pairs (*) D3,D5: 7.. / D3 = 7 => 0 pairs (*) / D5 = 7 => 0 pairs (X) D8,F9: 8.. / D8 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) C2,F2: 8.. / C2 = 8 => 18 pairs (_) / F2 = 8 => 0 pairs (X) B9,F9: 8.. / B9 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) A3,A4: 8.. / A3 = 8 => 0 pairs (X) / A4 = 8 => 18 pairs (_) E3,E4: 8.. / E3 = 8 => 18 pairs (_) / E4 = 8 => 0 pairs (X) E3,F3: 9.. / E3 = 9 => 0 pairs (X) / F3 = 9 => 18 pairs (_) H5,H6: 9.. / H5 = 9 => 16 pairs (_) / H6 = 9 => 13 pairs (_) I8,I9: 9.. / I8 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) B9,I9: 9.. / B9 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) A1,A4: 9.. / A1 = 9 => 12 pairs (_) / A4 = 9 => 0 pairs (X) F3,F5: 9.. / F3 = 9 => 18 pairs (_) / F5 = 9 => 0 pairs (X) * DURATION: 0:00:49.263561 START: 02:44:55.070597 END: 02:45:44.334158 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,D5,D8,E3,E6,F9,H5,H6,H9,I2) * ...5641.854.31.9...1....5.4...1.57466.1.4.2.37.46.38.12639714854...5631.1.543.6.. * PAIR A1: 3,9 BLK 1 B1: 3,9,2,7 # reduction candidate for 3,9 B1: 3,9 => CTR * ...5641.854.31896.816.9.534...1857466817492537546238912639714854.825631.1.543.6.. B1: 2,7 # 13 pairs * PAIR A1: 3,9 COL A A4: 3,9,8 # reduction candidate for 3,9 A4: 3,9 => CTR * ...5641.854.31.9..81..9.534...1857466817492537546238912639714854.825631.1.543.6.. A4: 8 # 18 pairs * PAIR A3: 3,8 COL A A4: 3,8,9 # reduction candidate for 3,8 A4: 9 => CTR * ...5641.854.31.9..81..9.53493.1857466817492537546238912639714854.825631.1.543.6.. A4: 3,8 # 12 pairs * PAIR E3: 8,9 BLK 2 F3: 8,9,2,7 # reduction candidate for 8,9 F3: 2,7 => CTR * ...5641.854.31.9...1..9.5.4...1857466817492537546238912639714854.825631.1.54386.. F3: 8,9 # 18 pairs * PAIR E3: 8,9 COL E E4: 8,9,2 # reduction candidate for 8,9 E4: 8,9 # 15 pairs E4: 2 # 12 pairs * PAIR I2: 2,7 BLK 3 H1: 2,7,3 # reduction candidate for 2,7 H1: 2,7 => CTR * ...5641.854.31.96.816.9.534...1857466817492537546238912639714854.825631.1.543.6.. H1: 3 # 18 pairs H2: 2,7,6 # reduction candidate for 2,7 H2: 2,7 => CTR * ...5641.85463189...1..9.564...1857466817492537546238912639714854.825631.1.543.6.. H2: 6 # 11 pairs H3: 2,7,3,6 # reduction candidate for 2,7 H3: 2,7 # 18 pairs * PAIR I2: 2,7 ROW 2 C2: 2,7,6,8 # reduction candidate for 2,7 C2: 2,7 => CTR * ...5641.854.31896..16.9.5.4...1857466817492537546238912639714854.825631.1.543.6.. C2: 6,8 # 12 pairs F2: 2,7,8 # reduction candidate for 2,7 F2: 2,7 # 18 pairs * PAIR I2: 2,7 COL I I8: 2,7,9 # reduction candidate for 2,7 I8: 2,7 # 13 pairs I9: 2,7,9 # reduction candidate for 2,7 I9: 2,7 => SOLVED * 972564138548312967316789524839125746651847293724693851263971485487256319195438672 I9: 9 # 13 pairs * PAIR D5: 7,8 BLK 5 F5: 7,8,9 # reduction candidate for 7,8 F5: 9 => CTR * ...5641.854.31.9...1..9.5.4...1857466817492537546238912639714854.825631.1.54386.. F5: 7,8 # 18 pairs * PAIR D5: 7,8 COL D D3: 7,8,2 # reduction candidate for 7,8 D3: 7,8 => SOLVED * 972564138548312967316789524839125746651847293724693851263971485487256319195438672 D3: 2 => CTR * ...5641.854.31.9.7.1.2.75.4...1.57466.174.2.37.46.38.12639714854..856312185432679 * PAIR E6: 2,9 BLK 5 E4: 2,9,8 # reduction candidate for 2,9 E4: 8 => CTR * ...5641.854.31.9...1....5.4...1857466817492537546238912639714854.825631.1.54386.. E4: 2,9 # 18 pairs * PAIR E6: 2,9 ROW 6 B6: 2,9,5 # reduction candidate for 2,9 B6: 2,9 # 16 pairs B6: 5 # 13 pairs * PAIR H5: 5,9 ROW 5 B5: 5,9,8 # reduction candidate for 5,9 B5: 8 => CTR * ...5641.854.31.9...1....5.4...1.57466817492537546238912639714854.825631.1.54386.. B5: 5,9 # 18 pairs * PAIR H6: 5,9 ROW 6 B6: 5,9,2 # reduction candidate for 5,9 B6: 5,9 # 15 pairs B6: 2 # 12 pairs * PAIR D8: 2,8 COL D D3: 2,8,7 # reduction candidate for 2,8 D3: 7 => SOLVED * 972564138548312967316789524839125746651847293724693851263971485487256319195438672 D3: 2,8 # 12 pairs * PAIR F9: 2,8 COL F F2: 2,8,7 # reduction candidate for 2,8 F2: 2,8 # 14 pairs F3: 2,8,7,9 # reduction candidate for 2,8 F3: 2,8 => CTR * ...5641.854.31.9...1..9.5.4...1857466817492537546238912639714854.825631.1.54386.. F3: 7,9 # 12 pairs * PAIR H9: 2,7 BLK 9 I8: 2,7,9 # reduction candidate for 2,7 I8: 2,7 # 13 pairs I9: 2,7,9 # reduction candidate for 2,7 I9: 2,7 => SOLVED * 972564138548312967316789524839125746651847293724693851263971485487256319195438672 I9: 9 # 13 pairs * PAIR H9: 2,7 COL H H1: 2,7,3 # reduction candidate for 2,7 H1: 2,7 => CTR * ...5641.854.31.96.816.9.534...1857466817492537546238912639714854.825631.1.543.6.. H1: 3 # 18 pairs H2: 2,7,6 # reduction candidate for 2,7 H2: 2,7 => CTR * ...5641.85463189...1..9.564...1857466817492537546238912639714854.825631.1.543.6.. H2: 6 # 11 pairs H3: 2,7,3,6 # reduction candidate for 2,7 H3: 2,7 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-005-base-pr-000.dot * REASONING * DIS # B1: 3,9 => CTR => B1: 2,7 * DIS # A4: 3,9 => CTR => A4: 8 * DIS # A4: 9 => CTR => A4: 3,8 * DIS # F3: 2,7 => CTR => F3: 8,9 * DIS # H1: 2,7 => CTR => H1: 3 * DIS # H2: 2,7 => CTR => H2: 6 * DIS # C2: 2,7 => CTR => C2: 6,8 * PRF # I9: 2,7 => SOL * DIS # F5: 9 => CTR => F5: 7,8 * PRF # D3: 7,8 => SOL * DIS # D3: 2 => CTR => D3: 7,8 * DIS # E4: 8 => CTR => E4: 2,9 * DIS # B5: 8 => CTR => B5: 5,9 * PRF # D3: 7 => SOL * DIS # F3: 2,8 => CTR => F3: 7,9 * PRF # I9: 2,7 => SOL * DIS # H1: 2,7 => CTR => H1: 3 * DIS # H2: 2,7 => CTR => H2: 6 * CNT 18 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,D5,D8,E3,E6,F9,H5,H6,H9,I2) * ...5641.854.31.9...1....5.4...1.57466.1.4.2.37.46.38.12639714854...5631.1.543.6.. * PAIR A1: 3,9 BLK 1 B1: 3,9,2,7 # reduction candidate for 3,9 B1: 3,9 => CTR * ...5641.854.31896.816.9.534...1857466817492537546238912639714854.825631.1.543.6.. * PAIR E3: 8,9 BLK 2 F3: 8,9,2,7 # reduction candidate for 8,9 F3: 2,7 => CTR * ...5641.854.31.9...1..9.5.4.3.1857466817492537546238912639714854.825631.1.54386.. * PAIR I2: 2,7 COL I I8: 2,7,9 # reduction candidate for 2,7 I8: 2,7 # 20 pairs I9: 2,7,9 # reduction candidate for 2,7 I9: 2,7 => SOLVED * 972564138548312967316789524839125746651847293724693851263971485487256319195438672 * DURATION: 0:00:07.249894 START: 02:46:26.452251 END: 02:46:33.702145 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-005-base-pr-001.dot * REASONING * DIS # B1: 3,9 => CTR => B1: 2,7 * DIS B1: 2,7 # F3: 2,7 => CTR => F3: 8,9 * PRF B1: 2,7 + F3: 8,9 # I9: 2,7 => SOL * STA B1: 2,7 + F3: 8,9 + I9: 2,7 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 005 solution: 972564138548312967316789524839125746651847293724693851263971485487256319195438672 info: 1305 FNBWX S8.f 43167 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 972564138548312967316789524839125746651847293724693851263971485487256319195438672 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 # B1: 3,9 => CTR => B1: 2,7 * INC # B1: 2,7 => UNS * DIS # A4: 3,9 => CTR => A4: 8 * INC # A4: 8 => UNS * INC # A4: 3,8 => UNS * DIS # A4: 9 => CTR => A4: 3,8 * INC # F3: 8,9 => UNS * DIS # F3: 2,7 => CTR => F3: 8,9 * INC # E4: 8,9 => UNS * INC # E4: 2 => UNS * DIS # H1: 2,7 => CTR => H1: 3 * INC # H1: 3 => UNS * DIS # H2: 2,7 => CTR => H2: 6 * INC # H2: 6 => UNS * INC # H3: 2,7 => UNS * DIS # C2: 2,7 => CTR => C2: 6,8 * INC # C2: 6,8 => UNS * INC # F2: 2,7 => UNS * INC # I8: 2,7 => UNS * PRF # I9: 2,7 => SOL * INC # I9: 9 => UNS * INC # F5: 7,8 => UNS * DIS # F5: 9 => CTR => F5: 7,8 * PRF # D3: 7,8 => SOL * DIS # D3: 2 => CTR => D3: 7,8 * INC # E4: 2,9 => UNS * DIS # E4: 8 => CTR => E4: 2,9 * INC # B6: 2,9 => UNS * INC # B6: 5 => UNS * INC # B5: 5,9 => UNS * DIS # B5: 8 => CTR => B5: 5,9 * INC # B6: 5,9 => UNS * INC # B6: 2 => UNS * INC # D3: 2,8 => UNS * PRF # D3: 7 => SOL * INC # F2: 2,8 => UNS * DIS # F3: 2,8 => CTR => F3: 7,9 * INC # F3: 7,9 => UNS * INC # I8: 2,7 => UNS * PRF # I9: 2,7 => SOL * INC # I9: 9 => UNS * DIS # H1: 2,7 => CTR => H1: 3 * INC # H1: 3 => UNS * DIS # H2: 2,7 => CTR => H2: 6 * INC # H2: 6 => UNS * INC # H3: 2,7 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 3,9 => CTR => B1: 2,7 * INC B1: 2,7 # F3: 8,9 => UNS * DIS B1: 2,7 # F3: 2,7 => CTR => F3: 8,9 * INC B1: 2,7 + F3: 8,9 # I8: 2,7 => UNS * PRF B1: 2,7 + F3: 8,9 # I9: 2,7 => SOL * STA B1: 2,7 + F3: 8,9 + I9: 2,7 * CNT 5 HDP CHAINS / 5 HYP OPENED