Analysis of xx-top500-335-base.sdk
Contents
Original Sudoku
level: medium
position: ...5..1..7...3....9.........5.2..6..3......9....1.....4...9..7..8....2...1....... initial
Autosolve
position: 2385.71.97.193....9.5.1.3.7154279638372.8..918961.37..423.91.7..897..213.1732.9.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 4,6 => CTR => F2: 2,8 * PRF # H2: 4,6 => SOL * DIS # I2: 4,6 => CTR => I2: 2,5 * PRF # D3: 4,6 => SOL * DIS # D3: 8 => CTR => D3: 4,6 * DIS # F3: 4,6 => CTR => F3: 2,8 * DIS # H3: 4,6 => CTR => H3: 2,8 * DIS # F2: 4,6 => CTR => F2: 2,8 * PRF # D3: 4,6 => SOL * DIS # D3: 8 => CTR => D3: 4,6 * DIS # F3: 4,6 => CTR => F3: 2,8 * DIS # E8: 4,6 => CTR => E8: 5 * PRF # E8: 5 => SOL * PRF # H2: 4,6 => SOL * DIS # I2: 4,6 => CTR => I2: 2,5 * DIS # H3: 4,6 => CTR => H3: 2,8 * DIS # H9: 4,6 => CTR => H9: 8 * PRF # H9: 8 => SOL * DIS # F5: 4,6 => CTR => F5: 5 * PRF # F5: 5 => SOL * PRF # D3: 4,6 => SOL * DIS # D3: 8 => CTR => D3: 4,6 * PRF # F5: 4,5 => SOL * DIS # F5: 6 => CTR => F5: 4,5 * PRF # E8: 4,5 => SOL * DIS # E8: 6 => CTR => E8: 4,5 * PRF # F5: 4,5 => SOL * DIS # F5: 6 => CTR => F5: 4,5 * DIS # G2: 4,5 => CTR => G2: 8 * PRF # G2: 8 => SOL * DIS # F8: 5,6 => CTR => F8: 4 * PRF # F9: 5,6 => SOL * DIS # F9: 8 => CTR => F9: 5,6 * PRF # F9: 6,8 => SOL * DIS # F9: 5 => CTR => F9: 6,8 * DIS # D3: 6,8 => CTR => D3: 4 * PRF # D3: 4 => SOL * PRF # G2: 5,8 => SOL * DIS # G2: 4 => CTR => G2: 5,8 * DIS # H9: 4,6 => CTR => H9: 8 * PRF # H9: 8 => SOL * DIS # I2: 4,6 => CTR => I2: 2,5 * CNT 42 HDP CHAINS / 61 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 4,6 => CTR => F2: 2,8 * PRF F2: 2,8 # H2: 4,6 => SOL * STA F2: 2,8 + H2: 4,6 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...5..1..7...3....9.........5.2..6..3......9....1.....4...9..7..8....2...1....... | initial |
| 2385.71.97.193....9.5.1.3.7154279638372.8..918961.37..423.91.7..897..213.1732.9.. | autosolve |
| 238567149741932865965418327154279638372685491896143752423891576689754213517326984 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B2: 4,6 B3: 4,6 E1: 4,6 H1: 4,6 D5: 4,6 E6: 4,5 G5: 4,5 A8: 5,6 A9: 5,6 D7: 6,8 G7: 5,8 I7: 5,6 I9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,F3: 2.. / F2 = 2 => 14 pairs (_) / F3 = 2 => 15 pairs (_) H6,I6: 2.. / H6 = 2 => 16 pairs (_) / I6 = 2 => 14 pairs (_) F3,H3: 2.. / F3 = 2 => 15 pairs (_) / H3 = 2 => 14 pairs (_) I2,I6: 2.. / I2 = 2 => 16 pairs (_) / I6 = 2 => 14 pairs (_) B2,B3: 4.. / B2 = 4 => 0 pairs (*) / B3 = 4 => 0 pairs (X) E8,F8: 4.. / E8 = 4 => 0 pairs (X) / F8 = 4 => 15 pairs (_) H9,I9: 4.. / H9 = 4 => 0 pairs (X) / I9 = 4 => 14 pairs (_) E1,H1: 4.. / E1 = 4 => 0 pairs (X) / H1 = 4 => 0 pairs (_) D3,D5: 4.. / D3 = 4 => 0 pairs (*) / D5 = 4 => 0 pairs (X) G2,G5: 4.. / G2 = 4 => 0 pairs (X) / G5 = 4 => 0 pairs (_) F5,E6: 5.. / F5 = 5 => 0 pairs (*) / E6 = 5 => 0 pairs (X) A8,A9: 5.. / A8 = 5 => 0 pairs (X) / A9 = 5 => 0 pairs (_) G7,I7: 5.. / G7 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) F5,G5: 5.. / F5 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) A9,F9: 5.. / A9 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) E6,E8: 5.. / E6 = 5 => 0 pairs (X) / E8 = 5 => 0 pairs (_) H2,H6: 5.. / H2 = 5 => 15 pairs (_) / H6 = 5 => 0 pairs (*) B2,B3: 6.. / B2 = 6 => 0 pairs (X) / B3 = 6 => 0 pairs (_) D5,F5: 6.. / D5 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) A8,A9: 6.. / A8 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) E1,H1: 6.. / E1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) D7,I7: 6.. / D7 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) E1,E8: 6.. / E1 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) D7,F9: 8.. / D7 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) G7,H9: 8.. / G7 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) D7,G7: 8.. / D7 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) F9,H9: 8.. / F9 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) D3,D7: 8.. / D3 = 8 => 0 pairs (X) / D7 = 8 => 0 pairs (_) G2,G7: 8.. / G2 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) * DURATION: 0:00:46.715761 START: 14:12:32.536426 END: 14:13:19.252187 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B2,B3,D5,D7,E1,E6,G5,G7,H1,I7,I9) * 2385.71.97.193....9.5.1.3.7154279638372.8..918961.37..423.91.7..897..213.1732.9.. * PAIR B2: 4,6 ROW 2 F2: 4,6,2,8 # reduction candidate for 4,6 F2: 4,6 => CTR * 2385.71.97.193....9.58123.71542796383724865918961537..4236918756897452135173289.. F2: 2,8 # 14 pairs H2: 4,6,2,5,8 # reduction candidate for 4,6 H2: 4,6 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 H2: 2,5,8 # 13 pairs I2: 4,6,2,5 # reduction candidate for 4,6 I2: 4,6 => CTR * 2385671497.193.5869658143.7154279638372.8..918961.37.24236918756897..2135173289.. I2: 2,5 # 15 pairs * PAIR B3: 4,6 ROW 3 D3: 4,6,8 # reduction candidate for 4,6 D3: 4,6 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 D3: 8 => CTR * 2385.71.97.193....9.581.3.71542796383724865918961537..4236918756897452135173289.. F3: 4,6,2,8 # reduction candidate for 4,6 F3: 4,6 => CTR * 2385.71.97.1932...9.581.32715427963837248659189615374242369187568974.213.1732.9.. F3: 2,8 # 14 pairs H3: 4,6,2,8 # reduction candidate for 4,6 H3: 4,6 => CTR * 2385.71.97.193....9.58123.71542796383724865918961537..4236918756897452135173289.. H3: 2,8 # 14 pairs * PAIR E1: 4,6 BLK 2 F2: 4,6,2,8 # reduction candidate for 4,6 F2: 4,6 => CTR * 2385.71.97.193....9.58123.71542796383724865918961537..4236918756897452135173289.. F2: 2,8 # 14 pairs D3: 4,6,8 # reduction candidate for 4,6 D3: 4,6 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 D3: 8 => CTR * 2385.71.97.193....9.581.3.71542796383724865918961537..4236918756897452135173289.. F3: 4,6,2,8 # reduction candidate for 4,6 F3: 4,6 => CTR * 2385.71.97.1932...9.581.32715427963837248659189615374242369187568974.213.1732.9.. F3: 2,8 # 14 pairs * PAIR E1: 4,6 COL E E8: 4,6,5 # reduction candidate for 4,6 E8: 4,6 => CTR * 2385.71.97.193..5.9.5.1.3.7154279638372.8.5918961537..423.91875.897..213.173289.. E8: 5 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 * PAIR H1: 4,6 BLK 3 H2: 4,6,2,5,8 # reduction candidate for 4,6 H2: 4,6 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 H2: 2,5,8 # 13 pairs I2: 4,6,2,5 # reduction candidate for 4,6 I2: 4,6 => CTR * 2385671497.193.5869658143.7154279638372.8..918961.37.24236918756897..2135173289.. I2: 2,5 # 15 pairs H3: 4,6,2,8 # reduction candidate for 4,6 H3: 4,6 => CTR * 2385.71.97.193....9.58123.71542796383724865918961537..4236918756897452135173289.. H3: 2,8 # 14 pairs * PAIR H1: 4,6 COL H H9: 4,6,8 # reduction candidate for 4,6 H9: 4,6 => CTR * 2385.71.97.193..8.9.581.3.71542796383724865918961.37..423.91875.897..213.173289.. H9: 8 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 * PAIR D5: 4,6 BLK 5 F5: 4,6,5 # reduction candidate for 4,6 F5: 4,6 => CTR * 2385.71.97.193....9.5.1.3.7154279638372.8.5918961537..423.91875.897..213.173289.. F5: 5 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 * PAIR D5: 4,6 COL D D3: 4,6,8 # reduction candidate for 4,6 D3: 4,6 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 D3: 8 => CTR * 2385.71.97.193....9.581.3.71542796383724865918961537..4236918756897452135173289.. * PAIR E6: 4,5 BLK 5 F5: 4,5,6 # reduction candidate for 4,5 F5: 4,5 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 F5: 6 => CTR * 2385.71.97.193....9.5.1.3.7154279638372.865918961537..423.91875.897..213.173289.. * PAIR E6: 4,5 ROW 6 H6: 4,5,2 # reduction candidate for 4,5 H6: 4,5 # 14 pairs I6: 4,5,2 # reduction candidate for 4,5 I6: 4,5 # 16 pairs * PAIR E6: 4,5 COL E E8: 4,5,6 # reduction candidate for 4,5 E8: 4,5 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 E8: 6 => CTR * 2385471697.193.8529.5.1.3.7154279638372.8..918961537..423.91.7..89764213617325984 * PAIR G5: 4,5 BLK 6 H6: 4,5,2 # reduction candidate for 4,5 H6: 4,5 # 14 pairs I6: 4,5,2 # reduction candidate for 4,5 I6: 4,5 # 16 pairs * PAIR G5: 4,5 ROW 5 F5: 4,5,6 # reduction candidate for 4,5 F5: 4,5 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 F5: 6 => CTR * 2385.71.97.193....9.5.1.3.7154279638372.865918961537..423.91875.897..213.173289.. * PAIR G5: 4,5 COL G G2: 4,5,8 # reduction candidate for 4,5 G2: 4,5 => CTR * 2385.71.97.193..8.9.581.3.71542796383724865918961.37..423.91875.897..213.173289.. G2: 8 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 * PAIR A8: 5,6 ROW 8 E8: 5,6,4 # reduction candidate for 5,6 E8: 5,6 # 15 pairs F8: 5,6,4 # reduction candidate for 5,6 F8: 5,6 => CTR * 2385671497.193....9.5.1.3.7154279638372.8.49189615372.423.91.7..8974.213.1732.9.. F8: 4 # 15 pairs * PAIR A9: 5,6 ROW 9 F9: 5,6,8 # reduction candidate for 5,6 F9: 5,6 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 F9: 8 => CTR * 2385.71.97.193....9.581.3.71542796383724865918961537..4236918756897452135173289.. * PAIR D7: 6,8 BLK 8 F9: 6,8,5 # reduction candidate for 6,8 F9: 6,8 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 F9: 5 => CTR * 2385.71.97.193....9.5.1.3.7154279638372.8..918961.37..423891576.897..213617325984 * PAIR D7: 6,8 COL D D3: 6,8,4 # reduction candidate for 6,8 D3: 6,8 => CTR * 2385.71.97.193....9.5.1.3.71542796383724865918961537..423.91875.897..213.173289.. D3: 4 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 * PAIR G7: 5,8 COL G G2: 5,8,4 # reduction candidate for 5,8 G2: 5,8 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 G2: 4 => CTR * 2385.71.97.193.4..945.1.3.71542796383724865918961537..423.91875.897.4213.1732.9.. * PAIR I7: 5,6 COL I I2: 5,6,2,4 # reduction candidate for 5,6 I2: 5,6 # 15 pairs I2: 2,4 # 15 pairs * PAIR I9: 4,6 BLK 9 H9: 4,6,8 # reduction candidate for 4,6 H9: 4,6 => CTR * 2385.71.97.193..8.9.581.3.71542796383724865918961.37..423.91875.897..213.173289.. H9: 8 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 * PAIR I9: 4,6 COL I I2: 4,6,2,5 # reduction candidate for 4,6 I2: 4,6 => CTR * 2385671497.193.5869658143.7154279638372.8..918961.37.24236918756897..2135173289.. I2: 2,5 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-335-base-pr-000.dot * REASONING * DIS # F2: 4,6 => CTR => F2: 2,8 * PRF # H2: 4,6 => SOL * DIS # I2: 4,6 => CTR => I2: 2,5 * PRF # D3: 4,6 => SOL * DIS # D3: 8 => CTR => D3: 4,6 * DIS # F3: 4,6 => CTR => F3: 2,8 * DIS # H3: 4,6 => CTR => H3: 2,8 * DIS # F2: 4,6 => CTR => F2: 2,8 * PRF # D3: 4,6 => SOL * DIS # D3: 8 => CTR => D3: 4,6 * DIS # F3: 4,6 => CTR => F3: 2,8 * DIS # E8: 4,6 => CTR => E8: 5 * PRF # E8: 5 => SOL * PRF # H2: 4,6 => SOL * DIS # I2: 4,6 => CTR => I2: 2,5 * DIS # H3: 4,6 => CTR => H3: 2,8 * DIS # H9: 4,6 => CTR => H9: 8 * PRF # H9: 8 => SOL * DIS # F5: 4,6 => CTR => F5: 5 * PRF # F5: 5 => SOL * PRF # D3: 4,6 => SOL * DIS # D3: 8 => CTR => D3: 4,6 * PRF # F5: 4,5 => SOL * DIS # F5: 6 => CTR => F5: 4,5 * PRF # E8: 4,5 => SOL * DIS # E8: 6 => CTR => E8: 4,5 * PRF # F5: 4,5 => SOL * DIS # F5: 6 => CTR => F5: 4,5 * DIS # G2: 4,5 => CTR => G2: 8 * PRF # G2: 8 => SOL * DIS # F8: 5,6 => CTR => F8: 4 * PRF # F9: 5,6 => SOL * DIS # F9: 8 => CTR => F9: 5,6 * PRF # F9: 6,8 => SOL * DIS # F9: 5 => CTR => F9: 6,8 * DIS # D3: 6,8 => CTR => D3: 4 * PRF # D3: 4 => SOL * PRF # G2: 5,8 => SOL * DIS # G2: 4 => CTR => G2: 5,8 * DIS # H9: 4,6 => CTR => H9: 8 * PRF # H9: 8 => SOL * DIS # I2: 4,6 => CTR => I2: 2,5 * CNT 42 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B2,B3,D5,D7,E1,E6,G5,G7,H1,I7,I9) * 2385.71.97.193....9.5.1.3.7154279638372.8..918961.37..423.91.7..897..213.1732.9.. * PAIR B2: 4,6 ROW 2 F2: 4,6,2,8 # reduction candidate for 4,6 F2: 4,6 => CTR * 2385.71.97.193....9.58123.71542796383724865918961537..4236918756897452135173289.. H2: 4,6,2,5,8 # reduction candidate for 4,6 H2: 4,6 => SOLVED * 238567149741932865965418327154279638372685491896143752423891576689754213517326984 * DURATION: 0:00:03.061930 START: 14:14:20.416121 END: 14:14:23.478051 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-335-base-pr-001.dot * REASONING * DIS # F2: 4,6 => CTR => F2: 2,8 * PRF F2: 2,8 # H2: 4,6 => SOL * STA F2: 2,8 + H2: 4,6 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 335 solution: 238567149741932865965418327154279638372685491896143752423891576689754213517326984 info: 3094 FNBWXY S8.f 9733 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 238567149741932865965418327154279638372685491896143752423891576689754213517326984 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:
* DIS # F2: 4,6 => CTR => F2: 2,8 * INC # F2: 2,8 => UNS * PRF # H2: 4,6 => SOL * INC # H2: 2,5,8 => UNS * DIS # I2: 4,6 => CTR => I2: 2,5 * INC # I2: 2,5 => UNS * PRF # D3: 4,6 => SOL * DIS # D3: 8 => CTR => D3: 4,6 * DIS # F3: 4,6 => CTR => F3: 2,8 * INC # F3: 2,8 => UNS * DIS # H3: 4,6 => CTR => H3: 2,8 * INC # H3: 2,8 => UNS * DIS # F2: 4,6 => CTR => F2: 2,8 * INC # F2: 2,8 => UNS * PRF # D3: 4,6 => SOL * DIS # D3: 8 => CTR => D3: 4,6 * DIS # F3: 4,6 => CTR => F3: 2,8 * INC # F3: 2,8 => UNS * DIS # E8: 4,6 => CTR => E8: 5 * PRF # E8: 5 => SOL * PRF # H2: 4,6 => SOL * INC # H2: 2,5,8 => UNS * DIS # I2: 4,6 => CTR => I2: 2,5 * INC # I2: 2,5 => UNS * DIS # H3: 4,6 => CTR => H3: 2,8 * INC # H3: 2,8 => UNS * DIS # H9: 4,6 => CTR => H9: 8 * PRF # H9: 8 => SOL * DIS # F5: 4,6 => CTR => F5: 5 * PRF # F5: 5 => SOL * PRF # D3: 4,6 => SOL * DIS # D3: 8 => CTR => D3: 4,6 * PRF # F5: 4,5 => SOL * DIS # F5: 6 => CTR => F5: 4,5 * INC # H6: 4,5 => UNS * INC # I6: 4,5 => UNS * PRF # E8: 4,5 => SOL * DIS # E8: 6 => CTR => E8: 4,5 * INC # H6: 4,5 => UNS * INC # I6: 4,5 => UNS * PRF # F5: 4,5 => SOL * DIS # F5: 6 => CTR => F5: 4,5 * DIS # G2: 4,5 => CTR => G2: 8 * PRF # G2: 8 => SOL * INC # E8: 5,6 => UNS * DIS # F8: 5,6 => CTR => F8: 4 * INC # F8: 4 => UNS * PRF # F9: 5,6 => SOL * DIS # F9: 8 => CTR => F9: 5,6 * PRF # F9: 6,8 => SOL * DIS # F9: 5 => CTR => F9: 6,8 * DIS # D3: 6,8 => CTR => D3: 4 * PRF # D3: 4 => SOL * PRF # G2: 5,8 => SOL * DIS # G2: 4 => CTR => G2: 5,8 * INC # I2: 5,6 => UNS * INC # I2: 2,4 => UNS * DIS # H9: 4,6 => CTR => H9: 8 * PRF # H9: 8 => SOL * DIS # I2: 4,6 => CTR => I2: 2,5 * INC # I2: 2,5 => UNS * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F2: 4,6 => CTR => F2: 2,8 * PRF F2: 2,8 # H2: 4,6 => SOL * STA F2: 2,8 + H2: 4,6 * CNT 2 HDP CHAINS / 2 HYP OPENED