Analysis of xx-top500-491-base.sdk
Contents
Original Sudoku
level: medium
position: ...8...1.2.6......5.........4...3...7...5........62....1.7...........2.5..3...6.. initial
Autosolve
position: ...8...1.2.6......5.1.......4..73...7...58.......62....1.7...........2.5..3...671 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C4: 2,9 => SOL * PRF # H5: 2,9 => SOL * DIS # I5: 2,9 => CTR => I5: 3,4,6 * DIS # G6: 1,3 => CTR => G6: 4,5,7,8,9 * DIS # G6: 3,5 => CTR => G6: 1,4,7,8,9 * DIS # H6: 3,5 => CTR => H6: 4,8,9 * DIS # G4: 1,9 => CTR => G4: 5,8 * DIS # D3: 3,6 => CTR => D3: 2 * PRF # D3: 2 => SOL * DIS # E7: 4,9 => CTR => E7: 2,3,8 * PRF # F7: 4,9 => SOL * CNT 11 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C4: 2,9 => SOL * STA C4: 2,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8...1.2.6......5.........4...3...7...5........62....1.7...........2.5..3...6.. | initial |
| ...8...1.2.6......5.1.......4..73...7...58.......62....1.7...........2.5..3...671 | autosolve |
| 437896512296315784581247369142973856769458123358162947615729438874631295923584671 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C1: 4,7 D2: 3,5 A4: 1,6 C5: 2,9 A6: 1,3 B6: 3,5 D4: 1,9 C7: 2,5 C8: 4,7 B9: 2,5 D8: 3,6 D9: 2,5 F9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 1.. / E2 = 1 => 13 pairs (_) / F2 = 1 => 13 pairs (_) A4,A6: 1.. / A4 = 1 => 0 pairs (*) / A6 = 1 => 0 pairs (X) E8,F8: 1.. / E8 = 1 => 13 pairs (_) / F8 = 1 => 13 pairs (_) D5,G5: 1.. / D5 = 1 => 12 pairs (_) / G5 = 1 => 14 pairs (_) E2,E8: 1.. / E2 = 1 => 13 pairs (_) / E8 = 1 => 13 pairs (_) F2,F8: 1.. / F2 = 1 => 13 pairs (_) / F8 = 1 => 13 pairs (_) C7,B9: 2.. / C7 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) E7,D9: 2.. / E7 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) E1,I1: 2.. / E1 = 2 => 0 pairs (X) / I1 = 2 => 0 pairs (_) C7,E7: 2.. / C7 = 2 => 0 pairs (X) / E7 = 2 => 0 pairs (_) B9,D9: 2.. / B9 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) B5,B9: 2.. / B5 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) D3,D9: 2.. / D3 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) A1,A6: 3.. / A1 = 3 => 0 pairs (X) / A6 = 3 => 0 pairs (_) A1,C1: 4.. / A1 = 4 => 0 pairs (*) / C1 = 4 => 0 pairs (X) D5,D6: 4.. / D5 = 4 => 14 pairs (_) / D6 = 4 => 14 pairs (_) C1,C8: 4.. / C1 = 4 => 13 pairs (_) / C8 = 4 => 0 pairs (*) C7,B9: 5.. / C7 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) F7,D9: 5.. / F7 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) F1,G1: 5.. / F1 = 5 => 0 pairs (X) / G1 = 5 => 13 pairs (_) C7,F7: 5.. / C7 = 5 => 0 pairs (*) / F7 = 5 => 0 pairs (X) B9,D9: 5.. / B9 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) B6,B9: 5.. / B6 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) D2,D9: 5.. / D2 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) A4,B5: 6.. / A4 = 6 => 0 pairs (X) / B5 = 6 => 0 pairs (_) F1,I1: 6.. / F1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) A7,F7: 6.. / A7 = 6 => 0 pairs (*) / F7 = 6 => 0 pairs (X) B5,B8: 6.. / B5 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) D3,D8: 6.. / D3 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) G6,I6: 7.. / G6 = 7 => 13 pairs (_) / I6 = 7 => 13 pairs (_) B8,C8: 7.. / B8 = 7 => 0 pairs (*) / C8 = 7 => 0 pairs (X) C1,C8: 7.. / C1 = 7 => 0 pairs (*) / C8 = 7 => 0 pairs (X) B2,B3: 8.. / B2 = 8 => 13 pairs (_) / B3 = 8 => 13 pairs (_) C4,C6: 8.. / C4 = 8 => 14 pairs (_) / C6 = 8 => 13 pairs (_) A9,E9: 8.. / A9 = 8 => 16 pairs (_) / E9 = 8 => 14 pairs (_) * DURATION: 0:01:00.895486 START: 19:27:05.746720 END: 19:28:06.642206 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B6,B9,C1,C5,C7,C8,D2,D4,D8,D9,F9) * ...8...1.2.6......5.1.......4..73...7...58.......62....1.7...........2.5..3...671 * PAIR D2: 3,5 ROW 2 G2: 3,5,4,7,8,9 # reduction candidate for 3,5 G2: 3,5 # 14 pairs H2: 3,5,4,8,9 # reduction candidate for 3,5 H2: 3,5 # 14 pairs * PAIR C5: 2,9 BLK 4 C4: 2,9,5,8 # reduction candidate for 2,9 C4: 2,9 => SOLVED * 437896512296315784581247369142973856769458123358162947615729438874631295923584671 C4: 5,8 # 14 pairs * PAIR C5: 2,9 ROW 5 H5: 2,9,3,4,6 # reduction candidate for 2,9 H5: 2,9 => SOLVED * 437896512296315784581247369142973856769458123358162947615729438874631295923584671 H5: 3,4,6 # 13 pairs I5: 2,9,3,4,6 # reduction candidate for 2,9 I5: 2,9 => CTR * ...89..122.631..5.5.124.....4..73.2.7.2.58..9.5..62....1572.......6312.5.2358.671 I5: 3,4,6 # 13 pairs * PAIR A6: 1,3 ROW 6 G6: 1,3,4,5,7,8,9 # reduction candidate for 1,3 G6: 1,3 => CTR * 4378965122.63157..5.1247.6.142973856769158.2.358462197615729.388746312.5923584671 G6: 4,5,7,8,9 # 13 pairs * PAIR B6: 3,5 ROW 6 G6: 3,5,1,4,7,8,9 # reduction candidate for 3,5 G6: 3,5 => CTR * 3.48...1.2.6......5.1......64..73...7...58...1...62..7.1.7.6....673..2.5..35..671 G6: 1,4,7,8,9 # 13 pairs H6: 3,5,4,8,9 # reduction candidate for 3,5 H6: 3,5 => CTR * 3.48...1.2.6......5.1......64..73...7...58...1...62....1.7.6....673..2.5..35..671 H6: 4,8,9 # 13 pairs * PAIR D4: 1,9 BLK 5 D5: 1,9,4 # reduction candidate for 1,9 D5: 1,9 # 14 pairs D6: 1,9,4 # reduction candidate for 1,9 D6: 1,9 # 14 pairs * PAIR D4: 1,9 ROW 4 G4: 1,9,5,8 # reduction candidate for 1,9 G4: 1,9 => CTR * ...8...1.2.6......5.1......64..73...7...58...1...62....1.7.6....673..2.5..35..671 G4: 5,8 # 14 pairs * PAIR C7: 2,5 COL C C4: 2,5,8,9 # reduction candidate for 2,5 C4: 8,9 # 14 pairs C4: 2,5 # 14 pairs * PAIR D8: 3,6 COL D D3: 3,6,2 # reduction candidate for 3,6 D3: 3,6 => CTR * ...8...1.2.65.....5.1.......4..73...729.58.......62....127.5....673..2.5.532..671 D3: 2 => SOLVED * 437896512296315784581247369142973856769458123358162947615729438874631295923584671 * PAIR F9: 4,9 BLK 8 E7: 4,9,2,3,8 # reduction candidate for 4,9 E7: 4,9 => CTR * ...8..51.2.65.....5.1.......4..73...729.58....3..62...6127.5.........2.5.532..671 E7: 2,3,8 # 13 pairs F7: 4,9,5,6 # reduction candidate for 4,9 F7: 4,9 => SOLVED * 437896512296315784581247369142973856769458123358162947615729438874631295923584671 F7: 5,6 # 14 pairs E8: 4,9,1,3,8 # reduction candidate for 4,9 E8: 4,9 # 17 pairs F8: 4,9,1,6 # reduction candidate for 4,9 F8: 4,9 # 18 pairs E9: 4,9,8 # reduction candidate for 4,9 E9: 4,9 # 16 pairs * PAIR F9: 4,9 ROW 9 A9: 4,9,8 # reduction candidate for 4,9 A9: 8 # 16 pairs A9: 4,9 # 14 pairs * PAIR F9: 4,9 COL F F2: 4,9,1,5,7 # reduction candidate for 4,9 F2: 4,9 # 16 pairs F3: 4,9,6,7 # reduction candidate for 4,9 F3: 4,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-491-base-pr-000.dot * REASONING * PRF # C4: 2,9 => SOL * PRF # H5: 2,9 => SOL * DIS # I5: 2,9 => CTR => I5: 3,4,6 * DIS # G6: 1,3 => CTR => G6: 4,5,7,8,9 * DIS # G6: 3,5 => CTR => G6: 1,4,7,8,9 * DIS # H6: 3,5 => CTR => H6: 4,8,9 * DIS # G4: 1,9 => CTR => G4: 5,8 * DIS # D3: 3,6 => CTR => D3: 2 * PRF # D3: 2 => SOL * DIS # E7: 4,9 => CTR => E7: 2,3,8 * PRF # F7: 4,9 => SOL * CNT 11 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B6,B9,C1,C5,C7,C8,D2,D4,D8,D9,F9) * ...8...1.2.6......5.1.......4..73...7...58.......62....1.7...........2.5..3...671 * PAIR D2: 3,5 ROW 2 G2: 3,5,4,7,8,9 # reduction candidate for 3,5 G2: 3,5 # 14 pairs H2: 3,5,4,8,9 # reduction candidate for 3,5 H2: 3,5 # 14 pairs * PAIR C5: 2,9 BLK 4 C4: 2,9,5,8 # reduction candidate for 2,9 C4: 2,9 => SOLVED * 437896512296315784581247369142973856769458123358162947615729438874631295923584671 * DURATION: 0:00:04.414419 START: 19:28:36.506617 END: 19:28:40.921036 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-491-base-pr-001.dot * REASONING * PRF # C4: 2,9 => SOL * STA C4: 2,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 491 solution: 437896512296315784581247369142973856769458123358162947615729438874631295923584671 info: 96251 FNBTHXYK S8.f 11989 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 437896512296315784581247369142973856769458123358162947615729438874631295923584671 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: 3,5 => UNS * INC # H2: 3,5 => UNS * PRF # C4: 2,9 => SOL * INC # C4: 5,8 => UNS * PRF # H5: 2,9 => SOL * INC # H5: 3,4,6 => UNS * DIS # I5: 2,9 => CTR => I5: 3,4,6 * INC # I5: 3,4,6 => UNS * DIS # G6: 1,3 => CTR => G6: 4,5,7,8,9 * INC # G6: 4,5,7,8,9 => UNS * DIS # G6: 3,5 => CTR => G6: 1,4,7,8,9 * INC # G6: 1,4,7,8,9 => UNS * DIS # H6: 3,5 => CTR => H6: 4,8,9 * INC # H6: 4,8,9 => UNS * INC # D5: 1,9 => UNS * INC # D6: 1,9 => UNS * DIS # G4: 1,9 => CTR => G4: 5,8 * INC # G4: 5,8 => UNS * INC # C4: 2,5 => UNS * INC # C4: 8,9 => UNS * DIS # D3: 3,6 => CTR => D3: 2 * PRF # D3: 2 => SOL * DIS # E7: 4,9 => CTR => E7: 2,3,8 * INC # E7: 2,3,8 => UNS * PRF # F7: 4,9 => SOL * INC # F7: 5,6 => UNS * INC # E8: 4,9 => UNS * INC # F8: 4,9 => UNS * INC # E9: 4,9 => UNS * INC # A9: 4,9 => UNS * INC # A9: 8 => UNS * INC # F2: 4,9 => UNS * INC # F3: 4,9 => UNS * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 3,5 => UNS * INC # H2: 3,5 => UNS * PRF # C4: 2,9 => SOL * STA C4: 2,9 * CNT 3 HDP CHAINS / 3 HYP OPENED