Analysis of xx-top500-477-base.sdk
Contents
Original Sudoku
level: medium
position: .6.7...8..34...............5......2.....41......6.3.........1.49..8.........5.3.. initial
Autosolve
position: .6.7...8..34...............5..9...2....541......623.........1.49..8.........5.3.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 1,2 => CTR => A2: 7,8 * PRF # I1: 1,2 => SOL * DIS # A9: 1,2 => CTR => A9: 4,6,7 * DIS # D3: 1,2 => CTR => D3: 3,4 * DIS # A2: 1,2 => CTR => A2: 7,8 * DIS # I2: 1,2 => CTR => I2: 5,6,7,9 * PRF # D9: 1,2 => SOL * DIS # D9: 4 => CTR => D9: 1,2 * DIS # B6: 1,4 => CTR => B6: 7,8,9 * DIS # B9: 1,4 => CTR => B9: 2,7 * DIS # G3: 4,6 => CTR => G3: 2,5,7,9 * DIS # C7: 2,3 => CTR => C7: 5,6,7,8 * DIS # D3: 2,3 => CTR => D3: 1,4 * PRF # D3: 1,4 => SOL * CNT 14 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 1,2 => CTR => A2: 7,8 * PRF A2: 7,8 # I1: 1,2 => SOL * STA A2: 7,8 + I1: 1,2 * CNT 2 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.7...8..34...............5......2.....41......6.3.........1.49..8.........5.3.. | initial |
| .6.7...8..34...............5..9...2....541......623.........1.49..8.........5.3.8 | autosolve |
| 169735482834296715257418936541987623326541879798623541685372194913864257472159368 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A1: 1,2 D2: 1,2 B4: 1,4 E4: 7,8 F4: 7,8 G4: 4,6 D7: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E8,D9: 1.. / E8 = 1 => 0 pairs (X) / D9 = 1 => 0 pairs (_) G8,I8: 2.. / G8 = 2 => 7 pairs (_) / I8 = 2 => 7 pairs (_) E1,I1: 3.. / E1 = 3 => 0 pairs (*) / I1 = 3 => 0 pairs (X) C4,I4: 3.. / C4 = 3 => 0 pairs (X) / I4 = 3 => 0 pairs (_) C8,E8: 3.. / C8 = 3 => 0 pairs (*) / E8 = 3 => 0 pairs (X) A5,A7: 3.. / A5 = 3 => 0 pairs (*) / A7 = 3 => 0 pairs (X) D3,D7: 3.. / D3 = 3 => 0 pairs (X) / D7 = 3 => 0 pairs (_) H3,H5: 3.. / H3 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) F1,G1: 4.. / F1 = 4 => 0 pairs (X) / G1 = 4 => 0 pairs (_) B4,G4: 4.. / B4 = 4 => 0 pairs (*) / G4 = 4 => 0 pairs (X) B8,F8: 4.. / B8 = 4 => 0 pairs (X) / F8 = 4 => 0 pairs (_) A6,A9: 4.. / A6 = 4 => 0 pairs (X) / A9 = 4 => 0 pairs (_) D3,D9: 4.. / D3 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) H3,H6: 4.. / H3 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) E4,F4: 7.. / E4 = 7 => 5 pairs (_) / F4 = 7 => 6 pairs (_) E4,F4: 8.. / E4 = 8 => 6 pairs (_) / F4 = 8 => 5 pairs (_) G5,G6: 8.. / G5 = 8 => 7 pairs (_) / G6 = 8 => 10 pairs (_) H7,H9: 9.. / H7 = 9 => 8 pairs (_) / H9 = 9 => 7 pairs (_) F9,H9: 9.. / F9 = 9 => 8 pairs (_) / H9 = 9 => 7 pairs (_) * DURATION: 0:00:27.985556 START: 19:00:06.843433 END: 19:00:34.828989 2017-05-04 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B4,D2,D7,E4,F4,G4) * .6.7...8..34...............5..9...2....541......623.........1.49..8.........5.3.8 * PAIR A1: 1,2 BLK 1 C1: 1,2,5,9 # reduction candidate for 1,2 C1: 1,2 # 15 pairs A2: 1,2,7,8 # reduction candidate for 1,2 A2: 1,2 => CTR * .6.7...8..34...............5..9...2....541.3....623...3..2..1.49..83.......15.3.8 A2: 7,8 # 8 pairs A3: 1,2,7,8 # reduction candidate for 1,2 A3: 1,2 # 10 pairs B3: 1,2,5,7,8,9 # reduction candidate for 1,2 B3: 1,2 # 17 pairs C3: 1,2,5,7,8,9 # reduction candidate for 1,2 C3: 1,2 # 14 pairs * PAIR A1: 1,2 ROW 1 I1: 1,2,3,5,9 # reduction candidate for 1,2 I1: 1,2 => SOLVED * 169735482834296715257418936541987623326541879798623541685372194913864257472159368 I1: 3,5,9 # 7 pairs * PAIR A1: 1,2 COL A A9: 1,2,4,6,7 # reduction candidate for 1,2 A9: 1,2 => CTR * .6.7...8..34.............4.51.9..42....541.3.4..623...3..2..1.49..83........5.3.8 A9: 4,6,7 # 7 pairs * PAIR D2: 1,2 BLK 2 D3: 1,2,3,4 # reduction candidate for 1,2 D3: 1,2 => CTR * .6.7...8..34...............5..9...233..541...4..623......3..1.494381.......45.3.8 D3: 3,4 # 8 pairs * PAIR D2: 1,2 ROW 2 A2: 1,2,7,8 # reduction candidate for 1,2 A2: 1,2 => CTR * .6.7...8..34...............5..9...2....541.3....623...3..2..1.49..83.......15.3.8 A2: 7,8 # 8 pairs I2: 1,2,5,6,7,9 # reduction candidate for 1,2 I2: 1,2 => CTR * .6.7...8..34...............5..9...2....541.3....623...3..2..1.49..83.......15.3.8 I2: 5,6,7,9 # 7 pairs * PAIR D2: 1,2 COL D D9: 1,2,4 # reduction candidate for 1,2 D9: 1,2 => SOLVED * 169735482834296715257418936541987623326541879798623541685372194913864257472159368 D9: 4 => CTR * .6.7...8..34.............4.5169..4233..541...4..623.........1.494381.......45.3.8 * PAIR B4: 1,4 BLK 4 A6: 1,4,7,8 # reduction candidate for 1,4 A6: 1,4 # 9 pairs B6: 1,4,7,8,9 # reduction candidate for 1,4 B6: 1,4 => CTR * .6.7..48..34.........4.....54.9..621...541....1.623.4....3..1.49.38.4...4...5.3.8 B6: 7,8,9 # 7 pairs * PAIR B4: 1,4 COL B B8: 1,4,5,7 # reduction candidate for 1,4 B8: 1,4 # 9 pairs B9: 1,4,2,7 # reduction candidate for 1,4 B9: 1,4 => CTR * .6.7..48..341........4...1.5419..6233.6541.79...623.416..3..1.49.3814...417256398 B9: 2,7 # 8 pairs * PAIR G4: 4,6 COL G G3: 4,6,2,5,7,9 # reduction candidate for 4,6 G3: 4,6 => CTR * .6.7.4.8..34............64.51.9..42....541.3.4..623...3..2..1.494.81.......45.3.8 G3: 2,5,7,9 # 7 pairs * PAIR D7: 2,3 ROW 7 A7: 2,3,6,7,8 # reduction candidate for 2,3 A7: 2,3 # 8 pairs C7: 2,3,5,6,7,8 # reduction candidate for 2,3 C7: 2,3 => CTR * .6.73..8..34....1....41..3.5419..6233.6541.79...6235416823..1.49.38.....4...5.3.8 C7: 5,6,7,8 # 7 pairs * PAIR D7: 2,3 COL D D3: 2,3,1,4 # reduction candidate for 2,3 D3: 2,3 => CTR * .6.7...8..341............4.51.9..42....541.3.4..623.1.3..2..1.494.81.......45.3.8 D3: 1,4 => SOLVED * 169735482834296715257418936541987623326541879798623541685372194913864257472159368 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-477-base-pr-000.dot * REASONING * DIS # A2: 1,2 => CTR => A2: 7,8 * PRF # I1: 1,2 => SOL * DIS # A9: 1,2 => CTR => A9: 4,6,7 * DIS # D3: 1,2 => CTR => D3: 3,4 * DIS # A2: 1,2 => CTR => A2: 7,8 * DIS # I2: 1,2 => CTR => I2: 5,6,7,9 * PRF # D9: 1,2 => SOL * DIS # D9: 4 => CTR => D9: 1,2 * DIS # B6: 1,4 => CTR => B6: 7,8,9 * DIS # B9: 1,4 => CTR => B9: 2,7 * DIS # G3: 4,6 => CTR => G3: 2,5,7,9 * DIS # C7: 2,3 => CTR => C7: 5,6,7,8 * DIS # D3: 2,3 => CTR => D3: 1,4 * PRF # D3: 1,4 => SOL * CNT 14 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B4,D2,D7,E4,F4,G4) * .6.7...8..34...............5..9...2....541......623.........1.49..8.........5.3.8 * PAIR A1: 1,2 BLK 1 C1: 1,2,5,9 # reduction candidate for 1,2 C1: 1,2 # 15 pairs A2: 1,2,7,8 # reduction candidate for 1,2 A2: 1,2 => CTR * .6.7...8..34...............5..9...2....541.3....623...3..2..1.49..83.......15.3.8 A3: 1,2,7,8 # reduction candidate for 1,2 A3: 1,2 # 10 pairs B3: 1,2,5,7,8,9 # reduction candidate for 1,2 B3: 1,2 # 17 pairs C3: 1,2,5,7,8,9 # reduction candidate for 1,2 C3: 1,2 # 14 pairs * PAIR A1: 1,2 ROW 1 I1: 1,2,3,5,9 # reduction candidate for 1,2 I1: 1,2 => SOLVED * 169735482834296715257418936541987623326541879798623541685372194913864257472159368 * DURATION: 0:00:06.032121 START: 19:00:56.508659 END: 19:01:02.540780 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-477-base-pr-001.dot * REASONING * DIS # A2: 1,2 => CTR => A2: 7,8 * PRF A2: 7,8 # I1: 1,2 => SOL * STA A2: 7,8 + I1: 1,2 * CNT 2 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 477 solution: 169735482834296715257418936541987623326541879798623541685372194913864257472159368 info: 95757 FNBHWYK S8.f 21582 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 169735482834296715257418936541987623326541879798623541685372194913864257472159368 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 # C1: 1,2 => UNS * DIS # A2: 1,2 => CTR => A2: 7,8 * INC # A2: 7,8 => UNS * INC # A3: 1,2 => UNS * INC # B3: 1,2 => UNS * INC # C3: 1,2 => UNS * PRF # I1: 1,2 => SOL * INC # I1: 3,5,9 => UNS * DIS # A9: 1,2 => CTR => A9: 4,6,7 * INC # A9: 4,6,7 => UNS * DIS # D3: 1,2 => CTR => D3: 3,4 * INC # D3: 3,4 => UNS * DIS # A2: 1,2 => CTR => A2: 7,8 * INC # A2: 7,8 => UNS * DIS # I2: 1,2 => CTR => I2: 5,6,7,9 * INC # I2: 5,6,7,9 => UNS * PRF # D9: 1,2 => SOL * DIS # D9: 4 => CTR => D9: 1,2 * INC # A6: 1,4 => UNS * DIS # B6: 1,4 => CTR => B6: 7,8,9 * INC # B6: 7,8,9 => UNS * INC # B8: 1,4 => UNS * DIS # B9: 1,4 => CTR => B9: 2,7 * INC # B9: 2,7 => UNS * DIS # G3: 4,6 => CTR => G3: 2,5,7,9 * INC # G3: 2,5,7,9 => UNS * INC # A7: 2,3 => UNS * DIS # C7: 2,3 => CTR => C7: 5,6,7,8 * INC # C7: 5,6,7,8 => UNS * DIS # D3: 2,3 => CTR => D3: 1,4 * PRF # D3: 1,4 => SOL * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 1,2 => UNS * DIS # A2: 1,2 => CTR => A2: 7,8 * INC A2: 7,8 # A3: 1,2 => UNS * INC A2: 7,8 # B3: 1,2 => UNS * INC A2: 7,8 # C3: 1,2 => UNS * PRF A2: 7,8 # I1: 1,2 => SOL * STA A2: 7,8 + I1: 1,2 * CNT 6 HDP CHAINS / 6 HYP OPENED