Analysis of xx-top500-441-base.sdk
Contents
Original Sudoku
level: medium
position: ....3...26.....5...1.4.........527...74...........1......8...1.2.3......5........ initial
Autosolve
position: ....3...26.....5...1.4.........527...74.........741......8...1.2.3......5.1...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 7,8,9 => CTR => C3: 2,5 * DIS # A4: 3,9 => CTR => A4: 1,8 * DIS # H4: 3,9 => CTR => H4: 4,8 * DIS # I4: 3,9 => CTR => I4: 1,4,8 * DIS # D9: 3,9 => CTR => D9: 2,6 * CNT 5 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 7,8,9 => CTR => C3: 2,5 * DIS C3: 2,5 # A4: 3,9 => CTR => A4: 1,8 * DIS C3: 2,5 + A4: 1,8 # H4: 3,9 => CTR => H4: 4,8 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 # I4: 3,9 => CTR => I4: 1,4,8 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 # B4: 6 => CTR => B4: 3,9 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 # D9: 3,9 => CTR => D9: 2,6 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 # D5: 6 => CTR => D5: 3,9 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 # E2: 1,2 => CTR => E2: 7,8,9 * PRF C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # A6: 3,9 => SOL * STA C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 + A6: 3,9 * CNT 9 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....3...26.....5...1.4.........527...74...........1......8...1.2.3......5........ | initial |
| ....3...26.....5...1.4.........527...74.........741......8...1.2.3......5.1...... | autosolve |
| 748536192629187534315429678836952741174368925952741386467895213293614857581273469 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) B6: 2,5 C6: 2,5 D4: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,I2: 1.. / G1 = 1 => 3 pairs (_) / I2 = 1 => 0 pairs (X) A4,A5: 1.. / A4 = 1 => 7 pairs (_) / A5 = 1 => 4 pairs (_) D8,E8: 1.. / D8 = 1 => 0 pairs (X) / E8 = 1 => 3 pairs (_) D1,G1: 1.. / D1 = 1 => 0 pairs (X) / G1 = 1 => 3 pairs (_) A4,I4: 1.. / A4 = 1 => 7 pairs (_) / I4 = 1 => 4 pairs (_) E2,E8: 1.. / E2 = 1 => 0 pairs (X) / E8 = 1 => 3 pairs (_) G1,G5: 1.. / G1 = 1 => 3 pairs (_) / G5 = 1 => 0 pairs (X) B6,C6: 2.. / B6 = 2 => 0 pairs (X) / C6 = 2 => 0 pairs (_) G5,H5: 2.. / G5 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) C3,E3: 2.. / C3 = 2 => 0 pairs (X) / E3 = 2 => 0 pairs (_) E7,G7: 2.. / E7 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) B2,B6: 2.. / B2 = 2 => 0 pairs (*) / B6 = 2 => 0 pairs (X) D2,D9: 2.. / D2 = 2 => 0 pairs (X) / D9 = 2 => 0 pairs (_) H5,H9: 2.. / H5 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) B2,A3: 3.. / B2 = 3 => 0 pairs (X) / A3 = 3 => 12 pairs (_) B2,B4: 3.. / B2 = 3 => 0 pairs (X) / B4 = 3 => 12 pairs (_) H4,I4: 4.. / H4 = 4 => 5 pairs (_) / I4 = 4 => 7 pairs (_) A1,A7: 4.. / A1 = 4 => 5 pairs (_) / A7 = 4 => 12 pairs (_) B6,C6: 5.. / B6 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) H5,I5: 5.. / H5 = 5 => 0 pairs (X) / I5 = 5 => 0 pairs (_) C3,F3: 5.. / C3 = 5 => 0 pairs (*) / F3 = 5 => 0 pairs (X) F7,I7: 5.. / F7 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) B1,B6: 5.. / B1 = 5 => 0 pairs (X) / B6 = 5 => 0 pairs (_) D1,D8: 5.. / D1 = 5 => 0 pairs (*) / D8 = 5 => 0 pairs (X) H5,H8: 5.. / H5 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) B4,C4: 6.. / B4 = 6 => 0 pairs (X) / C4 = 6 => 7 pairs (_) C4,C7: 6.. / C4 = 6 => 7 pairs (_) / C7 = 6 => 0 pairs (X) A7,C7: 7.. / A7 = 7 => 5 pairs (_) / C7 = 7 => 10 pairs (_) E5,F5: 8.. / E5 = 8 => 3 pairs (_) / F5 = 8 => 5 pairs (_) B8,B9: 8.. / B8 = 8 => 3 pairs (_) / B9 = 8 => 3 pairs (_) * DURATION: 0:00:47.477465 START: 17:50:39.494246 END: 17:51:26.971711 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C6,D4) * ....3...26.....5...1.4.........527...74.........741......8...1.2.3......5.1...... * PAIR C6: 2,5 COL C C3: 2,5,7,8,9 # reduction candidate for 2,5 C3: 7,8,9 => CTR * ....3...26.....5...1.425.......527...74.........741......8..2152.351....5.12..... C3: 2,5 # 4 pairs * PAIR D4: 3,9 BLK 5 D5: 3,9,6 # reduction candidate for 3,9 D5: 3,9 # 8 pairs F5: 3,9,6,8 # reduction candidate for 3,9 F5: 3,9 # 4 pairs * PAIR D4: 3,9 ROW 4 A4: 3,9,1,8 # reduction candidate for 3,9 A4: 3,9 => CTR * 45..3.1.263.1..5.481.4.5....68.52741174....5..25741...7.68...152.351....5.12..... A4: 1,8 # 4 pairs B4: 3,9,6 # reduction candidate for 3,9 B4: 3,9 # 7 pairs H4: 3,9,4,8 # reduction candidate for 3,9 H4: 3,9 => CTR * 45..3...263.2..5418124.5...168.527.4.74....5..25741...7.68...152.351....5.1....2. H4: 4,8 # 4 pairs I4: 3,9,1,4,8 # reduction candidate for 3,9 I4: 3,9 => CTR * 45..3.1.263....5.481.4.5...168.5274..74....51.25741...7.68...152.351....5.1....2. I4: 1,4,8 # 3 pairs * PAIR D4: 3,9 COL D D9: 3,9,2,6 # reduction candidate for 3,9 D9: 3,9 => CTR * .5.13...26..2..5.1.124.5...1...527...746..1...25741......8...152.351....5.1...... D9: 2,6 # 4 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-441-base-pr-000.dot * REASONING * DIS # C3: 7,8,9 => CTR => C3: 2,5 * DIS # A4: 3,9 => CTR => A4: 1,8 * DIS # H4: 3,9 => CTR => H4: 4,8 * DIS # I4: 3,9 => CTR => I4: 1,4,8 * DIS # D9: 3,9 => CTR => D9: 2,6 * CNT 5 HDP CHAINS / 13 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C6,D4) * ....3...26.....5...1.4.........527...74.........741......8...1.2.3......5.1...... * PAIR C6: 2,5 COL C C3: 2,5,7,8,9 # reduction candidate for 2,5 C3: 7,8,9 => CTR * ....3...26.....5...1.425.......527...74.........741......8..2152.351....5.12..... * PAIR RESTART * PAIR D4: 3,9 BLK 5 D5: 3,9,6 # reduction candidate for 3,9 D5: 3,9 # 9 pairs F5: 3,9,6,8 # reduction candidate for 3,9 F5: 3,9 # 5 pairs * PAIR D4: 3,9 ROW 4 A4: 3,9,1,8 # reduction candidate for 3,9 A4: 3,9 => CTR * 45..3.1.263.12.5.48124.5....68.52741174.8..5..25741...7.689.2152.351....5.12..... B4: 3,9,6 # reduction candidate for 3,9 B4: 3,9 # 8 pairs H4: 3,9,4,8 # reduction candidate for 3,9 H4: 3,9 => CTR * 45..3...263.2..5418124.5...168.527.4.74....5..25741...7.68...152.351....5.1....2. I4: 3,9,1,4,8 # reduction candidate for 3,9 I4: 3,9 => CTR * 45..3.1.263.12.5.48124.5...168.5274..74.8..51.25741...7.689.2152.351....5.12..... * RESTART * PAIR D4: 3,9 ROW 4 B4: 3,9,6 # reduction candidate for 3,9 B4: 6 => CTR * 45..3...263.2..5.19124.5...1693527..374....5..25741...7.68...152.351....5.1....2. * PAIR D4: 3,9 COL D D9: 3,9,2,6 # reduction candidate for 3,9 D9: 3,9 => CTR * .5.13...26..2..5.1.124.5...1.6.527...746..1...25741......8...152.351....5.1...... * PAIR RESTART * PAIR D4: 3,9 BLK 5 D5: 3,9,6 # reduction candidate for 3,9 D5: 6 => CTR * ....3...263..2.5...124.5....963527...746...25.25741......8..21.2.351....5.12..... * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,B4,B6,C3,C6,C7,D2,D4,D5,D9,E5,F5,H4) * ....3...26.....5...1.4.......6.527...74.........741......8...1.2.3......5.1...... * PAIR D2: 1,2 BLK 2 E2: 1,2,7,8,9 # reduction candidate for 1,2 E2: 1,2 => CTR * .5.63.1.26..12.5...124.5.....6.527...74....5..25741......8..2152.351....5.12..... * PAIR A4: 1,8 ROW 4 I4: 1,8,4 # reduction candidate for 1,8 I4: 4 # 18 pairs I4: 1,8 # 18 pairs * PAIR B4: 3,9 BLK 4 A5: 3,9,1 # reduction candidate for 3,9 A5: 3,9 # 19 pairs A6: 3,9,8 # reduction candidate for 3,9 A6: 3,9 => SOLVED * 748536192629187534315429678836952741174368925952741386467895213293614857581273469 * DURATION: 0:00:20.597232 START: 17:51:36.869219 END: 17:51:57.466451 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-441-base-pr-001.dot * REASONING * DIS # C3: 7,8,9 => CTR => C3: 2,5 * DIS C3: 2,5 # A4: 3,9 => CTR => A4: 1,8 * DIS C3: 2,5 + A4: 1,8 # H4: 3,9 => CTR => H4: 4,8 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 # I4: 3,9 => CTR => I4: 1,4,8 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 # B4: 6 => CTR => B4: 3,9 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 # D9: 3,9 => CTR => D9: 2,6 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 # D5: 6 => CTR => D5: 3,9 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 # E2: 1,2 => CTR => E2: 7,8,9 * PRF C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # A6: 3,9 => SOL * STA C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 + A6: 3,9 * CNT 9 HDP CHAINS / 18 HYP OPENED
Header Info
Top 500 Minimum 17 441 solution: 748536192629187534315429678836952741174368925952741386467895213293614857581273469 info: 95272 FNBHYK S8.f 40763 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 748536192629187534315429678836952741174368925952741386467895213293614857581273469 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 # C3: 2,5 => UNS * DIS # C3: 7,8,9 => CTR => C3: 2,5 * INC # D5: 3,9 => UNS * INC # F5: 3,9 => UNS * DIS # A4: 3,9 => CTR => A4: 1,8 * INC # A4: 1,8 => UNS * INC # B4: 3,9 => UNS * DIS # H4: 3,9 => CTR => H4: 4,8 * INC # H4: 4,8 => UNS * DIS # I4: 3,9 => CTR => I4: 1,4,8 * INC # I4: 1,4,8 => UNS * DIS # D9: 3,9 => CTR => D9: 2,6 * INC # D9: 2,6 => UNS * CNT 13 HDP CHAINS / 13 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 2,5 => UNS * DIS # C3: 7,8,9 => CTR => C3: 2,5 * INC C3: 2,5 # D5: 3,9 => UNS * INC C3: 2,5 # F5: 3,9 => UNS * DIS C3: 2,5 # A4: 3,9 => CTR => A4: 1,8 * INC C3: 2,5 + A4: 1,8 # B4: 3,9 => UNS * DIS C3: 2,5 + A4: 1,8 # H4: 3,9 => CTR => H4: 4,8 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 # I4: 3,9 => CTR => I4: 1,4,8 * INC C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 # B4: 3,9 => UNS * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 # B4: 6 => CTR => B4: 3,9 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 # D9: 3,9 => CTR => D9: 2,6 * INC C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 # D5: 3,9 => UNS * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 # D5: 6 => CTR => D5: 3,9 * DIS C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 # E2: 1,2 => CTR => E2: 7,8,9 * INC C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # I4: 1,8 => UNS * INC C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # I4: 4 => UNS * INC C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # A5: 3,9 => UNS * PRF C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 # A6: 3,9 => SOL * STA C3: 2,5 + A4: 1,8 + H4: 4,8 + I4: 1,4,8 + B4: 3,9 + D9: 2,6 + D5: 3,9 + E2: 7,8,9 + A6: 3,9 * CNT 18 HDP CHAINS / 18 HYP OPENED