Analysis of xx-top500-199-base.sdk
Contents
Original Sudoku
level: medium
position: ...17....4.......8....3....23.............6.7.......1..5.6..2....7....3...3..8... initial
Autosolve
position: 38917..62471.623.856283.7.1236.1798.81.3..62779.286.131586.327...7..183...37.81.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D8: 5,9 => SOL * DIS # D8: 4 => CTR => D8: 5,9 * DIS # E5: 4,5 => CTR => E5: 9 * PRF # E5: 9 => SOL * DIS # E5: 4,5 => CTR => E5: 9 * PRF # E5: 9 => SOL * DIS # D8: 4,5 => CTR => D8: 9 * PRF # D8: 9 => SOL * PRF # E5: 5,9 => SOL * DIS # E5: 4 => CTR => E5: 5,9 * PRF # I8: 4,5 => SOL * DIS # I8: 6,9 => CTR => I8: 4,5 * DIS # I9: 4,5 => CTR => I9: 6,9 * DIS # I8: 6,9 => CTR => I8: 4,5 * PRF # I8: 4,5 => SOL * DIS # E8: 2,4 => CTR => E8: 5,9 * PRF # E8: 5,9 => SOL * DIS # I9: 4,5 => CTR => I9: 6,9 * PRF # E9: 2,4 => SOL * DIS # E9: 5,9 => CTR => E9: 2,4 * DIS # E8: 4,9 => CTR => E8: 2,5 * DIS # E9: 4,9 => CTR => E9: 2,5 * DIS # E5: 5 => CTR => E5: 4,9 * PRF # I8: 4,9 => SOL * DIS # I9: 4,9 => CTR => I9: 5,6 * PRF # I8: 4,5 => SOL * DIS # I8: 6,9 => CTR => I8: 4,5 * DIS # I9: 4,5 => CTR => I9: 6,9 * DIS # E9: 4,5 => CTR => E9: 2,9 * CNT 29 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D8: 5,9 => SOL * STA D8: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...17....4.......8....3....23.............6.7.......1..5.6..2....7....3...3..8... | initial |
| 38917..62471.623.856283.7.1236.1798.81.3..62779.286.131586.327...7..183...37.81.. | autosolve |
| 389174562471562398562839741236417985814395627795286413158643279627951834943728156 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) F1: 4,5 D2: 5,9 F3: 4,9 G1: 4,5 H2: 5,9 H3: 4,9 C5: 4,5 C6: 4,5 D4: 4,5 F5: 5,9 I4: 4,5 G6: 4,5 A8: 6,9 B8: 2,4 A9: 6,9 B9: 2,4 E7: 4,9 I7: 4,9 H9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B8,B9: 2.. / B8 = 2 => 0 pairs (*) / B9 = 2 => 0 pairs (X) E8,E9: 2.. / E8 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) B8,E8: 2.. / B8 = 2 => 0 pairs (*) / E8 = 2 => 0 pairs (X) B9,E9: 2.. / B9 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) F1,F3: 4.. / F1 = 4 => 0 pairs (*) / F3 = 4 => 0 pairs (X) G1,H3: 4.. / G1 = 4 => 0 pairs (X) / H3 = 4 => 0 pairs (_) C5,C6: 4.. / C5 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) D4,E5: 4.. / D4 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) I4,G6: 4.. / I4 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) B8,B9: 4.. / B8 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) F1,G1: 4.. / F1 = 4 => 0 pairs (*) / G1 = 4 => 0 pairs (X) F3,H3: 4.. / F3 = 4 => 0 pairs (X) / H3 = 4 => 0 pairs (_) D4,I4: 4.. / D4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) C5,E5: 4.. / C5 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) C6,G6: 4.. / C6 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) E7,I7: 4.. / E7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) D4,D8: 4.. / D4 = 4 => 0 pairs (*) / D8 = 4 => 0 pairs (X) G1,G6: 4.. / G1 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) H3,H9: 4.. / H3 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) F1,D2: 5.. / F1 = 5 => 0 pairs (X) / D2 = 5 => 0 pairs (_) G1,H2: 5.. / G1 = 5 => 0 pairs (*) / H2 = 5 => 0 pairs (X) C5,C6: 5.. / C5 = 5 => 0 pairs (X) / C6 = 5 => 0 pairs (_) I4,G6: 5.. / I4 = 5 => 0 pairs (*) / G6 = 5 => 0 pairs (X) F1,G1: 5.. / F1 = 5 => 0 pairs (X) / G1 = 5 => 0 pairs (_) D2,H2: 5.. / D2 = 5 => 0 pairs (*) / H2 = 5 => 0 pairs (X) D4,I4: 5.. / D4 = 5 => 0 pairs (X) / I4 = 5 => 0 pairs (_) C6,G6: 5.. / C6 = 5 => 0 pairs (*) / G6 = 5 => 0 pairs (X) F1,F5: 5.. / F1 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) G1,G6: 5.. / G1 = 5 => 0 pairs (*) / G6 = 5 => 0 pairs (X) H2,H9: 5.. / H2 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) A8,A9: 6.. / A8 = 6 => 17 pairs (_) / A9 = 6 => 0 pairs (X) I8,I9: 6.. / I8 = 6 => 0 pairs (X) / I9 = 6 => 17 pairs (_) A8,I8: 6.. / A8 = 6 => 17 pairs (_) / I8 = 6 => 0 pairs (X) A9,I9: 6.. / A9 = 6 => 0 pairs (X) / I9 = 6 => 17 pairs (_) D2,F3: 9.. / D2 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) H2,H3: 9.. / H2 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) E5,F5: 9.. / E5 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) A8,A9: 9.. / A8 = 9 => 0 pairs (X) / A9 = 9 => 17 pairs (_) D2,H2: 9.. / D2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) F3,H3: 9.. / F3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) E7,I7: 9.. / E7 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) D2,D8: 9.. / D2 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) F3,F5: 9.. / F3 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) * DURATION: 0:01:10.231686 START: 09:32:13.308500 END: 09:33:23.540186 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B8,B9,C5,C6,D2,D4,E7,F1,F3,F5,G1,G6,H2,H3,H9,I4,I7) * 38917..62471.623.856283.7.1236.1798.81.3..62779.286.131586.327...7..183...37.81.. * PAIR D2: 5,9 COL D D8: 5,9,4 # reduction candidate for 5,9 D8: 5,9 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 D8: 4 => CTR * 38917..6247196235856283479123651798481534962779428651315869327...7..183...37.81.. * PAIR C5: 4,5 ROW 5 E5: 4,5,9 # reduction candidate for 4,5 E5: 4,5 => CTR * 389175462471962358562834791236.1798481.34962779428651315869327...7..183...37.81.. E5: 9 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 * PAIR D4: 4,5 BLK 5 E5: 4,5,9 # reduction candidate for 4,5 E5: 4,5 => CTR * 389175462471962358562834791236.1798481.34962779428651315869327...7..183...37.81.. E5: 9 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 * PAIR D4: 4,5 COL D D8: 4,5,9 # reduction candidate for 4,5 D8: 4,5 => CTR * 38917546247196235856283479123651798481534962779428651315869327...7..183...37.814. D8: 9 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 * PAIR F5: 5,9 BLK 5 E5: 5,9,4 # reduction candidate for 5,9 E5: 5,9 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 E5: 4 => CTR * 38917..62471.623.856283.7.1236.1798.81.349627794286513158693274..7..183...37.81.. * PAIR I4: 4,5 COL I I8: 4,5,6,9 # reduction candidate for 4,5 I8: 4,5 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 I8: 6,9 => CTR * 389175462471962358562834791236.1798481.34962779428651315869327...7..183...37.81.. I9: 4,5,6,9 # reduction candidate for 4,5 I9: 4,5 => CTR * 38917..62471962358562834791236.1798.81.3.962779.2865131586432799475.18366.37981.. I9: 6,9 # 20 pairs * PAIR A8: 6,9 ROW 8 I8: 6,9,4,5 # reduction candidate for 6,9 I8: 6,9 => CTR * 389175462471962358562834791236.1798481.34962779428651315869327...7..183...37.81.. I8: 4,5 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 * PAIR B8: 2,4 ROW 8 E8: 2,4,5,9 # reduction candidate for 2,4 E8: 2,4 => CTR * 38917..62471.623.856283.7.12364179858143..6277952864131586.327...75.183...37.815. E8: 5,9 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 * PAIR A9: 6,9 ROW 9 I9: 6,9,4,5 # reduction candidate for 6,9 I9: 4,5 => CTR * 38917..62471962358562834791236.1798.81.3.962779.2865131586432799475.18366.37981.. I9: 6,9 # 20 pairs * PAIR B9: 2,4 ROW 9 E9: 2,4,5,9 # reduction candidate for 2,4 E9: 2,4 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 E9: 5,9 => CTR * 38917..62471.623.856283.7.12364179858143..627795286413158643279.47521836623798154 * PAIR E7: 4,9 BLK 8 D8: 4,9,5 # reduction candidate for 4,9 D8: 4,9 # 24 pairs E8: 4,9,2,5 # reduction candidate for 4,9 E8: 4,9 => CTR * 38917.56247156239856283974123641798.81.3..62779.286.131586.327..27..183..4372815. E8: 2,5 # 20 pairs E9: 4,9,2,5 # reduction candidate for 4,9 E9: 4,9 => CTR * 38917..62471.623.856283.7.1236.1798.81.3596277952864131586.327..4752183..237.81.. E9: 2,5 # 21 pairs * PAIR E7: 4,9 COL E E5: 4,9,5 # reduction candidate for 4,9 E5: 5 => CTR * 38917..62471.623.856283.7.12364179858143596277952864131586.327...75.183...37.815. E5: 4,9 # 24 pairs * PAIR I7: 4,9 BLK 9 I8: 4,9,5,6 # reduction candidate for 4,9 I8: 4,9 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 I8: 5,6 # 20 pairs I9: 4,9,5,6 # reduction candidate for 4,9 I9: 4,9 => CTR * 38917.562471562398562839741236417985814395627795286413158643279..7..18366.37.815. I9: 5,6 # 20 pairs * PAIR H9: 4,5 BLK 9 I8: 4,5,6,9 # reduction candidate for 4,5 I8: 4,5 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 I8: 6,9 => CTR * 389175462471962358562834791236.1798481.34962779428651315869327...7..183...37.81.. I9: 4,5,6,9 # reduction candidate for 4,5 I9: 4,5 => CTR * 38917..62471962358562834791236.1798.81.3.962779.2865131586432799475.18366.37981.. I9: 6,9 # 20 pairs * PAIR H9: 4,5 ROW 9 E9: 4,5,2,9 # reduction candidate for 4,5 E9: 4,5 => CTR * 38917..62471.623.856283.7.12364179858143..6277952864131586.327..4752183..2374815. E9: 2,9 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-199-base-pr-000.dot * REASONING * PRF # D8: 5,9 => SOL * DIS # D8: 4 => CTR => D8: 5,9 * DIS # E5: 4,5 => CTR => E5: 9 * PRF # E5: 9 => SOL * DIS # E5: 4,5 => CTR => E5: 9 * PRF # E5: 9 => SOL * DIS # D8: 4,5 => CTR => D8: 9 * PRF # D8: 9 => SOL * PRF # E5: 5,9 => SOL * DIS # E5: 4 => CTR => E5: 5,9 * PRF # I8: 4,5 => SOL * DIS # I8: 6,9 => CTR => I8: 4,5 * DIS # I9: 4,5 => CTR => I9: 6,9 * DIS # I8: 6,9 => CTR => I8: 4,5 * PRF # I8: 4,5 => SOL * DIS # E8: 2,4 => CTR => E8: 5,9 * PRF # E8: 5,9 => SOL * DIS # I9: 4,5 => CTR => I9: 6,9 * PRF # E9: 2,4 => SOL * DIS # E9: 5,9 => CTR => E9: 2,4 * DIS # E8: 4,9 => CTR => E8: 2,5 * DIS # E9: 4,9 => CTR => E9: 2,5 * DIS # E5: 5 => CTR => E5: 4,9 * PRF # I8: 4,9 => SOL * DIS # I9: 4,9 => CTR => I9: 5,6 * PRF # I8: 4,5 => SOL * DIS # I8: 6,9 => CTR => I8: 4,5 * DIS # I9: 4,5 => CTR => I9: 6,9 * DIS # E9: 4,5 => CTR => E9: 2,9 * CNT 29 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B8,B9,C5,C6,D2,D4,E7,F1,F3,F5,G1,G6,H2,H3,H9,I4,I7) * 38917..62471.623.856283.7.1236.1798.81.3..62779.286.131586.327...7..183...37.81.. * PAIR D2: 5,9 COL D D8: 5,9,4 # reduction candidate for 5,9 D8: 5,9 => SOLVED * 389174562471562398562839741236417985814395627795286413158643279627951834943728156 * DURATION: 0:00:01.921929 START: 09:34:04.979948 END: 09:34:06.901877 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-199-base-pr-001.dot * REASONING * PRF # D8: 5,9 => SOL * STA D8: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 199 solution: 389174562471562398562839741236417985814395627795286413158643279627951834943728156 info: 1887 FNBTHWX S8.f 7342 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 389174562471562398562839741236417985814395627795286413158643279627951834943728156 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:
* PRF # D8: 5,9 => SOL * DIS # D8: 4 => CTR => D8: 5,9 * DIS # E5: 4,5 => CTR => E5: 9 * PRF # E5: 9 => SOL * DIS # E5: 4,5 => CTR => E5: 9 * PRF # E5: 9 => SOL * DIS # D8: 4,5 => CTR => D8: 9 * PRF # D8: 9 => SOL * PRF # E5: 5,9 => SOL * DIS # E5: 4 => CTR => E5: 5,9 * PRF # I8: 4,5 => SOL * DIS # I8: 6,9 => CTR => I8: 4,5 * DIS # I9: 4,5 => CTR => I9: 6,9 * INC # I9: 6,9 => UNS * DIS # I8: 6,9 => CTR => I8: 4,5 * PRF # I8: 4,5 => SOL * DIS # E8: 2,4 => CTR => E8: 5,9 * PRF # E8: 5,9 => SOL * INC # I9: 6,9 => UNS * DIS # I9: 4,5 => CTR => I9: 6,9 * PRF # E9: 2,4 => SOL * DIS # E9: 5,9 => CTR => E9: 2,4 * INC # D8: 4,9 => UNS * DIS # E8: 4,9 => CTR => E8: 2,5 * INC # E8: 2,5 => UNS * DIS # E9: 4,9 => CTR => E9: 2,5 * INC # E9: 2,5 => UNS * INC # E5: 4,9 => UNS * DIS # E5: 5 => CTR => E5: 4,9 * PRF # I8: 4,9 => SOL * INC # I8: 5,6 => UNS * DIS # I9: 4,9 => CTR => I9: 5,6 * INC # I9: 5,6 => UNS * PRF # I8: 4,5 => SOL * DIS # I8: 6,9 => CTR => I8: 4,5 * DIS # I9: 4,5 => CTR => I9: 6,9 * INC # I9: 6,9 => UNS * DIS # E9: 4,5 => CTR => E9: 2,9 * INC # E9: 2,9 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D8: 5,9 => SOL * STA D8: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED