Analysis of xx-top500-218-base.sdk
Contents
Original Sudoku
level: medium
position: ...7..6...24.......8.......6....41......2...7....58..........28...3...5.1........ initial
Autosolve
position: ...7..6...24.......86......6..9741......23..7....58..........28...3...511........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G2: 3,7,9 => CTR => G2: 5,8 * PRF # D9: 5,8 => SOL * DIS # D9: 2,4 => CTR => D9: 5,8 * DIS # C4: 3,5 => CTR => C4: 2,8 * PRF # I4: 3,5 => SOL * DIS # I4: 2 => CTR => I4: 3,5 * DIS # C4: 3,8 => CTR => C4: 2,5 * PRF # C4: 2,5 => SOL * DIS # H2: 3,8 => CTR => H2: 1,7,9 * DIS # D9: 4,5 => CTR => D9: 2,8 * DIS # D3: 4,5 => CTR => D3: 2 * PRF # D3: 2 => SOL * CNT 12 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G2: 3,7,9 => CTR => G2: 5,8 * PRF G2: 5,8 # D9: 5,8 => SOL * STA G2: 5,8 + D9: 5,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...7..6...24.......8.......6....41......2...7....58..........28...3...5.1........ | initial |
| ...7..6...24.......86......6..9741......23..7....58..........28...3...511........ | autosolve |
| 513789642724536819986241573632974185851623497497158236369415728248367951175892364 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) D2: 5,8 B4: 3,5 D5: 1,6 D6: 1,6 H4: 3,8 D7: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 1.. / B1 = 1 => 6 pairs (_) / C1 = 1 => 6 pairs (_) H2,H3: 1.. / H2 = 1 => 6 pairs (_) / H3 = 1 => 8 pairs (_) D5,D6: 1.. / D5 = 1 => 6 pairs (_) / D6 = 1 => 4 pairs (_) E7,F7: 1.. / E7 = 1 => 6 pairs (_) / F7 = 1 => 6 pairs (_) F1,I1: 2.. / F1 = 2 => 0 pairs (X) / I1 = 2 => 0 pairs (_) C4,I4: 2.. / C4 = 2 => 0 pairs (*) / I4 = 2 => 0 pairs (X) A6,A8: 2.. / A6 = 2 => 0 pairs (X) / A8 = 2 => 0 pairs (_) D3,D9: 2.. / D3 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) G3,G6: 2.. / G3 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) I4,G5: 5.. / I4 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) E2,F2: 6.. / E2 = 6 => 6 pairs (_) / F2 = 6 => 6 pairs (_) D5,D6: 6.. / D5 = 6 => 4 pairs (_) / D6 = 6 => 6 pairs (_) B7,B8: 6.. / B7 = 6 => 6 pairs (_) / B8 = 6 => 8 pairs (_) H9,I9: 6.. / H9 = 6 => 6 pairs (_) / I9 = 6 => 6 pairs (_) D5,H5: 6.. / D5 = 6 => 4 pairs (_) / H5 = 6 => 6 pairs (_) I6,I9: 6.. / I6 = 6 => 6 pairs (_) / I9 = 6 => 6 pairs (_) A2,A3: 7.. / A2 = 7 => 6 pairs (_) / A3 = 7 => 6 pairs (_) B6,C6: 7.. / B6 = 7 => 6 pairs (_) / C6 = 7 => 6 pairs (_) E1,H1: 8.. / E1 = 8 => 0 pairs (*) / H1 = 8 => 0 pairs (X) C4,H4: 8.. / C4 = 8 => 0 pairs (X) / H4 = 8 => 0 pairs (_) A5,A8: 8.. / A5 = 8 => 0 pairs (*) / A8 = 8 => 0 pairs (X) D2,D9: 8.. / D2 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) G2,G5: 8.. / G2 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) * DURATION: 0:00:30.128958 START: 10:14:25.016988 END: 10:14:55.145946 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,D2,D5,D6,D7,H4) * ...7..6...24.......86......6..9741......23..7....58..........28...3...511........ * PAIR D2: 5,8 ROW 2 G2: 5,8,3,7,9 # reduction candidate for 5,8 G2: 3,7,9 => CTR * ...7..6...24.......86...5..6.897413.....238.7....58..........288..3...511........ G2: 5,8 # 8 pairs * PAIR D2: 5,8 COL D D9: 5,8,2,4 # reduction candidate for 5,8 D9: 5,8 => SOLVED * 513789642724536819986241573632974185851623497497158236369415728248367951175892364 D9: 2,4 => CTR * ...7..68..248......86......6.897413.....238.7....58..........288..3...511...8.... * PAIR B4: 3,5 BLK 4 C4: 3,5,2,8 # reduction candidate for 3,5 C4: 3,5 => CTR * ...7826...245......86......6..974182....235.7....58..........28...3...511........ C4: 2,8 # 7 pairs * PAIR B4: 3,5 ROW 4 I4: 3,5,2 # reduction candidate for 3,5 I4: 3,5 => SOLVED * 513789642724536819986241573632974185851623497497158236369415728248367951175892364 I4: 2 => CTR * ...7.26...24...8...86...2..6..9741.2....235.7....58..........28...3...511........ * PAIR B4: 3,5 COL B B1: 3,5,1,9 # reduction candidate for 3,5 B1: 3,5 # 7 pairs B7: 3,5,4,6,7,9 # reduction candidate for 3,5 B7: 3,5 # 10 pairs B9: 3,5,4,7,9 # reduction candidate for 3,5 B9: 3,5 # 8 pairs * PAIR H4: 3,8 ROW 4 C4: 3,8,2,5 # reduction candidate for 3,8 C4: 3,8 => CTR * ...7.26...24...8...86...2..65.9741.2....235.7....58..........28...3...511........ C4: 2,5 => SOLVED * 513789642724536819986241573632974185851623497497158236369415728248367951175892364 * PAIR H4: 3,8 COL H H1: 3,8,4,9 # reduction candidate for 3,8 H1: 3,8 # 7 pairs H2: 3,8,1,7,9 # reduction candidate for 3,8 H2: 3,8 => CTR * ...78.6...245..839.86.3.71.6529741838...235.7....582.44......282..3...511......76 H2: 1,7,9 # 6 pairs * PAIR D7: 4,5 BLK 8 D9: 4,5,2,8 # reduction candidate for 4,5 D9: 4,5 => CTR * ...7..6...248......862.....6..9741......238.7....582.........28...3...511........ D9: 2,8 # 7 pairs * PAIR D7: 4,5 ROW 7 A7: 4,5,3,9 # reduction candidate for 4,5 A7: 4,5 # 7 pairs B7: 4,5,3,6,7,9 # reduction candidate for 4,5 B7: 4,5 # 12 pairs * PAIR D7: 4,5 COL D D3: 4,5,2 # reduction candidate for 4,5 D3: 4,5 => CTR * ...7..6...248......86......6..9741......238.7....58..........288.23...511..28.... D3: 2 => SOLVED * 513789642724536819986241573632974185851623497497158236369415728248367951175892364 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-218-base-pr-000.dot * REASONING * DIS # G2: 3,7,9 => CTR => G2: 5,8 * PRF # D9: 5,8 => SOL * DIS # D9: 2,4 => CTR => D9: 5,8 * DIS # C4: 3,5 => CTR => C4: 2,8 * PRF # I4: 3,5 => SOL * DIS # I4: 2 => CTR => I4: 3,5 * DIS # C4: 3,8 => CTR => C4: 2,5 * PRF # C4: 2,5 => SOL * DIS # H2: 3,8 => CTR => H2: 1,7,9 * DIS # D9: 4,5 => CTR => D9: 2,8 * DIS # D3: 4,5 => CTR => D3: 2 * PRF # D3: 2 => SOL * CNT 12 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,D2,D5,D6,D7,H4) * ...7..6...24.......86......6..9741......23..7....58..........28...3...511........ * PAIR D2: 5,8 ROW 2 G2: 5,8,3,7,9 # reduction candidate for 5,8 G2: 3,7,9 => CTR * ...7..6...24.......86...5..6.897413.....238.7....58..........288..3...511........ * PAIR D2: 5,8 COL D D9: 5,8,2,4 # reduction candidate for 5,8 D9: 5,8 => SOLVED * 513789642724536819986241573632974185851623497497158236369415728248367951175892364 * DURATION: 0:00:03.761314 START: 10:15:11.698675 END: 10:15:15.459989 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-218-base-pr-001.dot * REASONING * DIS # G2: 3,7,9 => CTR => G2: 5,8 * PRF G2: 5,8 # D9: 5,8 => SOL * STA G2: 5,8 + D9: 5,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 218 solution: 513789642724536819986241573632974185851623497497158236369415728248367951175892364 info: 1954 FNBHXY S8.f 11556 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 513789642724536819986241573632974185851623497497158236369415728248367951175892364 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: 5,8 => UNS * DIS # G2: 3,7,9 => CTR => G2: 5,8 * PRF # D9: 5,8 => SOL * DIS # D9: 2,4 => CTR => D9: 5,8 * DIS # C4: 3,5 => CTR => C4: 2,8 * INC # C4: 2,8 => UNS * PRF # I4: 3,5 => SOL * DIS # I4: 2 => CTR => I4: 3,5 * INC # B1: 3,5 => UNS * INC # B7: 3,5 => UNS * INC # B9: 3,5 => UNS * DIS # C4: 3,8 => CTR => C4: 2,5 * PRF # C4: 2,5 => SOL * INC # H1: 3,8 => UNS * DIS # H2: 3,8 => CTR => H2: 1,7,9 * INC # H2: 1,7,9 => UNS * DIS # D9: 4,5 => CTR => D9: 2,8 * INC # D9: 2,8 => UNS * INC # A7: 4,5 => UNS * INC # B7: 4,5 => UNS * DIS # D3: 4,5 => CTR => D3: 2 * PRF # D3: 2 => SOL * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 5,8 => UNS * DIS # G2: 3,7,9 => CTR => G2: 5,8 * PRF G2: 5,8 # D9: 5,8 => SOL * STA G2: 5,8 + D9: 5,8 * CNT 3 HDP CHAINS / 3 HYP OPENED