Analysis of xx-top500-049-base.sdk
Contents
Original Sudoku
level: medium
position: 7......1....4....3.........14.....6.....9.2...8..3....6..1.5........28........3.. initial
Autosolve
position: 7....3.1....4....33........143..79685..891234.8.63417563.1.5......3.28........3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H3: 2,9 => SOL * DIS # I3: 2,9 => CTR => I3: 7 * DIS # B1: 2,9 => CTR => B1: 5,6 * DIS # C1: 2,9 => CTR => C1: 4,5,6,8 * DIS # I7: 7 => CTR => I7: 2,9 * DIS # A2: 8 => CTR => A2: 2,9 * DIS # C1: 2,9 => CTR => C1: 4,5,6,8 * DIS # C2: 2,9 => CTR => C2: 1,5,6,8 * DIS # C3: 2,9 => CTR => C3: 1,4,5,6,8 * PRF # D3: 2,5 => SOL * DIS # E2: 2,5 => CTR => E2: 1,6,7,8 * DIS # E3: 2,5 => CTR => E3: 1,6,7,8 * PRF # D3: 2,5 => SOL * DIS # G3: 4,7 => CTR => G3: 5,6 * CNT 14 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H3: 2,9 => SOL * STA H3: 2,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7......1....4....3.........14.....6.....9.2...8..3....6..1.5........28........3.. | initial |
| 7....3.1....4....33........143..79685..891234.8.63417563.1.5......3.28........3.. | autosolve |
| 768953412921476583354218697143527968576891234289634175632185749497362851815749326 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) I1: 2,9 B5: 6,7 C5: 6,7 A6: 2,9 C6: 2,9 D4: 2,5 E4: 2,5 A8: 4,9 E7: 4,8 D9: 7,9 G7: 4,7 I8: 1,6 I9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 1.. / E2 = 1 => 0 pairs (X) / E3 = 1 => 13 pairs (_) I8,I9: 1.. / I8 = 1 => 12 pairs (_) / I9 = 1 => 12 pairs (_) A6,C6: 2.. / A6 = 2 => 15 pairs (_) / C6 = 2 => 16 pairs (_) D4,E4: 2.. / D4 = 2 => 12 pairs (_) / E4 = 2 => 13 pairs (_) C1,C3: 4.. / C1 = 4 => 0 pairs (X) / C3 = 4 => 19 pairs (_) A8,A9: 4.. / A8 = 4 => 15 pairs (_) / A9 = 4 => 0 pairs (X) C1,G1: 4.. / C1 = 4 => 0 pairs (X) / G1 = 4 => 19 pairs (_) D4,E4: 5.. / D4 = 5 => 13 pairs (_) / E4 = 5 => 12 pairs (_) H8,H9: 5.. / H8 = 5 => 15 pairs (_) / H9 = 5 => 17 pairs (_) B5,C5: 6.. / B5 = 6 => 0 pairs (X) / C5 = 6 => 11 pairs (_) I8,I9: 6.. / I8 = 6 => 12 pairs (_) / I9 = 6 => 12 pairs (_) E8,I8: 6.. / E8 = 6 => 12 pairs (_) / I8 = 6 => 12 pairs (_) B5,C5: 7.. / B5 = 7 => 11 pairs (_) / C5 = 7 => 0 pairs (X) G7,I7: 7.. / G7 = 7 => 19 pairs (_) / I7 = 7 => 0 pairs (X) E2,G2: 7.. / E2 = 7 => 19 pairs (_) / G2 = 7 => 0 pairs (X) D3,D9: 7.. / D3 = 7 => 0 pairs (X) / D9 = 7 => 19 pairs (_) I3,I7: 7.. / I3 = 7 => 19 pairs (_) / I7 = 7 => 0 pairs (X) H2,H3: 8.. / H2 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) C1,E1: 8.. / C1 = 8 => 19 pairs (_) / E1 = 8 => 0 pairs (X) C7,E7: 8.. / C7 = 8 => 0 pairs (X) / E7 = 8 => 19 pairs (_) A2,A9: 8.. / A2 = 8 => 0 pairs (X) / A9 = 8 => 19 pairs (_) A6,C6: 9.. / A6 = 9 => 16 pairs (_) / C6 = 9 => 15 pairs (_) D9,F9: 9.. / D9 = 9 => 0 pairs (X) / F9 = 9 => 19 pairs (_) * DURATION: 0:00:39.265067 START: 04:20:28.614745 END: 04:21:07.879812 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B5,C5,C6,D4,D9,E4,E7,G7,I1,I8,I9) * 7....3.1....4....33........143..79685..891234.8.63417563.1.5......3.28........3.. * PAIR I1: 2,9 BLK 3 H2: 2,9,8 # reduction candidate for 2,9 H2: 2,9 # 18 pairs H3: 2,9,4,8 # reduction candidate for 2,9 H3: 2,9 => SOLVED * 768953412921476583354218697143527968576891234289634175632185749497362851815749326 H3: 4,8 # 14 pairs I3: 2,9,7 # reduction candidate for 2,9 I3: 2,9 => CTR * 7.4.83.1....4....33........143..79685..891234.8.63417563.1.54.7...3.28........3.. I3: 7 # 19 pairs * PAIR I1: 2,9 ROW 1 B1: 2,9,5,6 # reduction candidate for 2,9 B1: 2,9 => CTR * 7.4583.1....4..7.33..7..5..1432579685..891234.8.63417563.1.54.7...3.28.....9..3.. B1: 5,6 # 14 pairs C1: 2,9,4,5,6,8 # reduction candidate for 2,9 C1: 2,9 => CTR * 76.58341.8..47...33.4.1..871432.79685..891234.8.6341756381457.....3.28.......83.. C1: 4,5,6,8 # 13 pairs D1: 2,9,5 # reduction candidate for 2,9 D1: 2,9 # 15 pairs * PAIR I1: 2,9 COL I I7: 2,9,7 # reduction candidate for 2,9 I7: 7 => CTR * 7.4.83.1....4....33........143..79685..891234.8.63417563.1.54.7...3.28........3.. I7: 2,9 # 19 pairs * PAIR A6: 2,9 COL A A2: 2,9,8 # reduction candidate for 2,9 A2: 8 => CTR * 7...83.1.8..47...33...1..87143..79685..891234.8.6341756381457.....3.28.....9.83.. A2: 2,9 # 19 pairs * PAIR C6: 2,9 COL C C1: 2,9,4,5,6,8 # reduction candidate for 2,9 C1: 2,9 => CTR * 76.58341.8..47...33.4.1..871432.79685..891234.8.6341756381457.....3.28.......83.. C1: 4,5,6,8 # 13 pairs C2: 2,9,1,5,6,8 # reduction candidate for 2,9 C2: 2,9 => CTR * 7...83.1.8..4765.33...19.87143..79685..891234.8.6341756381457.....3.28........3.. C2: 1,5,6,8 # 13 pairs C3: 2,9,1,4,5,6,8 # reduction candidate for 2,9 C3: 2,9 => CTR * 7.4.83.1.8..47...33...1.487143..79685..891234.8.6341756381457.....3.28.......83.. C3: 1,4,5,6,8 # 13 pairs C7: 2,9,8 # reduction candidate for 2,9 C7: 2,9 # 19 pairs * PAIR D4: 2,5 COL D D1: 2,5,9 # reduction candidate for 2,5 D1: 2,5 # 15 pairs D3: 2,5,7,9 # reduction candidate for 2,5 D3: 2,5 => SOLVED * 768953412921476583354218697143527968576891234289634175632185749497362851815749326 D3: 7,9 # 15 pairs * PAIR E4: 2,5 COL E E1: 2,5,6,8 # reduction candidate for 2,5 E1: 2,5 # 19 pairs E2: 2,5,1,6,7,8 # reduction candidate for 2,5 E2: 2,5 => CTR * 7.4.83.1....4..7.33...1....143..79685..891234.8.63417563.1.54.7...3.28........3.. E2: 1,6,7,8 # 13 pairs E3: 2,5,1,6,7,8 # reduction candidate for 2,5 E3: 2,5 => CTR * 7.4.83.1....41.7.33..7.....143..79685..891234.8.63417563.1.54.7...3.28.....9..3.. E3: 1,6,7,8 # 13 pairs * PAIR A8: 4,9 ROW 8 H8: 4,9,5 # reduction candidate for 4,9 H8: 4,9 # 17 pairs H8: 5 # 15 pairs * PAIR E7: 4,8 BLK 8 E9: 4,8,6,7 # reduction candidate for 4,8 E9: 4,8 # 19 pairs E9: 6,7 # 14 pairs * PAIR D9: 7,9 COL D D3: 7,9,2,5 # reduction candidate for 7,9 D3: 2,5 => SOLVED * 768953412921476583354218697143527968576891234289634175632185749497362851815749326 D3: 7,9 # 15 pairs * PAIR G7: 4,7 COL G G3: 4,7,5,6 # reduction candidate for 4,7 G3: 4,7 => CTR * 7.4.83.1....47...33...1....143..79685..891234.8.63417563.1.5......3.28........3.. G3: 5,6 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-049-base-pr-000.dot * REASONING * PRF # H3: 2,9 => SOL * DIS # I3: 2,9 => CTR => I3: 7 * DIS # B1: 2,9 => CTR => B1: 5,6 * DIS # C1: 2,9 => CTR => C1: 4,5,6,8 * DIS # I7: 7 => CTR => I7: 2,9 * DIS # A2: 8 => CTR => A2: 2,9 * DIS # C1: 2,9 => CTR => C1: 4,5,6,8 * DIS # C2: 2,9 => CTR => C2: 1,5,6,8 * DIS # C3: 2,9 => CTR => C3: 1,4,5,6,8 * PRF # D3: 2,5 => SOL * DIS # E2: 2,5 => CTR => E2: 1,6,7,8 * DIS # E3: 2,5 => CTR => E3: 1,6,7,8 * PRF # D3: 2,5 => SOL * DIS # G3: 4,7 => CTR => G3: 5,6 * CNT 14 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B5,C5,C6,D4,D9,E4,E7,G7,I1,I8,I9) * 7....3.1....4....33........143..79685..891234.8.63417563.1.5......3.28........3.. * PAIR I1: 2,9 BLK 3 H2: 2,9,8 # reduction candidate for 2,9 H2: 2,9 # 18 pairs H3: 2,9,4,8 # reduction candidate for 2,9 H3: 2,9 => SOLVED * 768953412921476583354218697143527968576891234289634175632185749497362851815749326 * DURATION: 0:00:03.821465 START: 04:21:44.703389 END: 04:21:48.524854 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-049-base-pr-001.dot * REASONING * PRF # H3: 2,9 => SOL * STA H3: 2,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 049 solution: 768953412921476583354218697143527968576891234289634175632185749497362851815749326 info: 1384 FNBTHWXY S8.f 42645 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 768953412921476583354218697143527968576891234289634175632185749497362851815749326 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 # H2: 2,9 => UNS * PRF # H3: 2,9 => SOL * INC # H3: 4,8 => UNS * DIS # I3: 2,9 => CTR => I3: 7 * INC # I3: 7 => UNS * DIS # B1: 2,9 => CTR => B1: 5,6 * INC # B1: 5,6 => UNS * DIS # C1: 2,9 => CTR => C1: 4,5,6,8 * INC # C1: 4,5,6,8 => UNS * INC # D1: 2,9 => UNS * INC # I7: 2,9 => UNS * DIS # I7: 7 => CTR => I7: 2,9 * INC # A2: 2,9 => UNS * DIS # A2: 8 => CTR => A2: 2,9 * DIS # C1: 2,9 => CTR => C1: 4,5,6,8 * INC # C1: 4,5,6,8 => UNS * DIS # C2: 2,9 => CTR => C2: 1,5,6,8 * INC # C2: 1,5,6,8 => UNS * DIS # C3: 2,9 => CTR => C3: 1,4,5,6,8 * INC # C3: 1,4,5,6,8 => UNS * INC # C7: 2,9 => UNS * INC # D1: 2,5 => UNS * PRF # D3: 2,5 => SOL * INC # D3: 7,9 => UNS * INC # E1: 2,5 => UNS * DIS # E2: 2,5 => CTR => E2: 1,6,7,8 * INC # E2: 1,6,7,8 => UNS * DIS # E3: 2,5 => CTR => E3: 1,6,7,8 * INC # E3: 1,6,7,8 => UNS * INC # H8: 4,9 => UNS * INC # H8: 5 => UNS * INC # E9: 4,8 => UNS * INC # E9: 6,7 => UNS * INC # D3: 7,9 => UNS * PRF # D3: 2,5 => SOL * DIS # G3: 4,7 => CTR => G3: 5,6 * INC # G3: 5,6 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H2: 2,9 => UNS * PRF # H3: 2,9 => SOL * STA H3: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED