Analysis of xx-top500-164-base.sdk
Contents
Original Sudoku
level: medium
position: .74..........1.6......9....89....1.....4.2...5...........7...43...3...2.1........ initial
Autosolve
position: 6748..2193.92146.721.69743.8925..1.47314.2.9.5461.93.296.721.434.73..92112394.7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H9: 5,8 => SOL * DIS # H9: 6 => CTR => H9: 5,8 * PRF # I5: 5,8 => SOL * DIS # I5: 6 => CTR => I5: 5,8 * DIS # I9: 5,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * DIS # E4: 3,6 => CTR => E4: 7 * PRF # E4: 7 => SOL * PRF # I5: 6,8 => SOL * DIS # I5: 5 => CTR => I5: 6,8 * PRF # E4: 6,7 => SOL * DIS # E4: 3 => CTR => E4: 6,7 * PRF # I5: 5,8 => SOL * DIS # I5: 6 => CTR => I5: 5,8 * DIS # F8: 5,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # F8: 5,6 => SOL * DIS # F8: 8 => CTR => F8: 5,6 * DIS # F8: 5,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # H9: 5,8 => SOL * DIS # H9: 6 => CTR => H9: 5,8 * DIS # I9: 5,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * PRF # H9: 5,8 => SOL * DIS # H9: 6 => CTR => H9: 5,8 * DIS # I9: 5,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * CNT 28 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H9: 5,8 => SOL * STA H9: 5,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .74..........1.6......9....89....1.....4.2...5...........7...43...3...2.1........ | initial |
| 6748..2193.92146.721.69743.8925..1.47314.2.9.5461.93.296.721.434.73..92112394.7.. | autosolve |
| 674835219359214687218697435892573164731462598546189372965721843487356921123948756 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B2: 5,8 C3: 5,8 E1: 3,5 F1: 3,5 H2: 5,8 I3: 5,8 F4: 3,6 E5: 6,8 E6: 7,8 H4: 6,7 G5: 5,8 H6: 7,8 C7: 5,8 B8: 5,8 E8: 5,6 F9: 5,8 G7: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 3.. / E1 = 3 => 0 pairs (*) / F1 = 3 => 0 pairs (X) E4,F4: 3.. / E4 = 3 => 0 pairs (X) / F4 = 3 => 0 pairs (_) E1,E4: 3.. / E1 = 3 => 0 pairs (*) / E4 = 3 => 0 pairs (X) F1,F4: 3.. / F1 = 3 => 0 pairs (X) / F4 = 3 => 0 pairs (_) B2,C3: 5.. / B2 = 5 => 0 pairs (*) / C3 = 5 => 0 pairs (X) E1,F1: 5.. / E1 = 5 => 0 pairs (X) / F1 = 5 => 0 pairs (_) H2,I3: 5.. / H2 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) G5,I5: 5.. / G5 = 5 => 0 pairs (*) / I5 = 5 => 0 pairs (X) C7,B8: 5.. / C7 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) B2,H2: 5.. / B2 = 5 => 0 pairs (*) / H2 = 5 => 0 pairs (X) C3,I3: 5.. / C3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) C7,G7: 5.. / C7 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) B2,B8: 5.. / B2 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) C3,C7: 5.. / C3 = 5 => 0 pairs (X) / C7 = 5 => 0 pairs (_) E1,E8: 5.. / E1 = 5 => 0 pairs (X) / E8 = 5 => 0 pairs (_) G5,G7: 5.. / G5 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) H2,H9: 5.. / H2 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) H4,I5: 6.. / H4 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) E8,F8: 6.. / E8 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) H9,I9: 6.. / H9 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) E5,I5: 6.. / E5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) F4,F8: 6.. / F4 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) H4,H9: 6.. / H4 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) I5,I9: 6.. / I5 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) E4,E6: 7.. / E4 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) H4,H6: 7.. / H4 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) E4,H4: 7.. / E4 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) E6,H6: 7.. / E6 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) B2,C3: 8.. / B2 = 8 => 0 pairs (X) / C3 = 8 => 0 pairs (_) H2,I3: 8.. / H2 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) E5,E6: 8.. / E5 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) C7,B8: 8.. / C7 = 8 => 0 pairs (X) / B8 = 8 => 0 pairs (_) F8,F9: 8.. / F8 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) B2,H2: 8.. / B2 = 8 => 0 pairs (X) / H2 = 8 => 0 pairs (_) C3,I3: 8.. / C3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) E6,H6: 8.. / E6 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) C7,G7: 8.. / C7 = 8 => 0 pairs (X) / G7 = 8 => 0 pairs (_) B8,F8: 8.. / B8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) B2,B8: 8.. / B2 = 8 => 0 pairs (X) / B8 = 8 => 0 pairs (_) C3,C7: 8.. / C3 = 8 => 0 pairs (*) / C7 = 8 => 0 pairs (X) G5,G7: 8.. / G5 = 8 => 0 pairs (X) / G7 = 8 => 0 pairs (_) * DURATION: 0:01:15.515170 START: 08:21:09.240422 END: 08:22:24.755592 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B8,C3,C7,E1,E5,E6,E8,F1,F4,F9,G5,G7,H2,H4,H6,I3) * 6748..2193.92146.721.69743.8925..1.47314.2.9.5461.93.296.721.434.73..92112394.7.. * PAIR H2: 5,8 COL H H9: 5,8,6 # reduction candidate for 5,8 H9: 5,8 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 H9: 6 => CTR * 6748..2193.92146572156974388925..1.47314.2.9.5461.9382968721.434.73..92112394.7.. * PAIR I3: 5,8 COL I I5: 5,8,6 # reduction candidate for 5,8 I5: 5,8 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 I5: 6 => CTR * 6748..2193.92146.721.69743.8925..1.47314.25965461.93829657218434873..92112394.7.. I9: 5,8,6 # reduction candidate for 5,8 I9: 5,8 => CTR * 6748..2193.92146572156974388925..1747314825965461.93.296.721.434.73..92112394.76. I9: 6 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 * PAIR F4: 3,6 BLK 5 E4: 3,6,7 # reduction candidate for 3,6 E4: 3,6 => CTR * 6748..2193.92146.721.69743.8925..1747314.2.9654617938296.7218434873..921123948765 E4: 7 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 * PAIR E5: 6,8 ROW 5 I5: 6,8,5 # reduction candidate for 6,8 I5: 6,8 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 I5: 5 => CTR * 6748..2193.92146.721.69743.8925..1647314628955461893729687215434573..92112394.7.. * PAIR H4: 6,7 ROW 4 E4: 6,7,3 # reduction candidate for 6,7 E4: 6,7 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 E4: 3 => CTR * 6748..2193.92146.721.69743.8925361747314825965461793829657218434873..92112394.7.. * PAIR G5: 5,8 BLK 6 I5: 5,8,6 # reduction candidate for 5,8 I5: 5,8 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 I5: 6 => CTR * 6748..2193.92146.721.69743.8925..1.47314.25965461.93829657218434873..92112394.7.. * PAIR B8: 5,8 ROW 8 F8: 5,8,6 # reduction candidate for 5,8 F8: 5,8 => CTR * 6748..2193.92146.721.69743.8925.61747314825965461793829657218434873..92112394.7.. F8: 6 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 * PAIR E8: 5,6 BLK 8 F8: 5,6,8 # reduction candidate for 5,6 F8: 5,6 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 F8: 8 => CTR * 6748..2193.92146.721.69743.8925.61747314825965461793829657218434873..92112394.7.. * PAIR F9: 5,8 BLK 8 F8: 5,8,6 # reduction candidate for 5,8 F8: 5,8 => CTR * 6748..2193.92146.721.69743.8925.61747314825965461793829657218434873..92112394.7.. F8: 6 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 * PAIR F9: 5,8 ROW 9 H9: 5,8,6 # reduction candidate for 5,8 H9: 5,8 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 H9: 6 => CTR * 6748..2193.92146572156974388925..1.47314.2.9.5461.9382968721.434.73..92112394.7.. I9: 5,8,6 # reduction candidate for 5,8 I9: 5,8 => CTR * 6748..2193.92146572156974388925..1747314825965461.93.296.721.434.73..92112394.76. I9: 6 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 * PAIR G7: 5,8 BLK 9 H9: 5,8,6 # reduction candidate for 5,8 H9: 5,8 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 H9: 6 => CTR * 6748..2193.92146572156974388925..1.47314.2.9.5461.9382968721.434.73..92112394.7.. I9: 5,8,6 # reduction candidate for 5,8 I9: 5,8 => CTR * 6748..2193.92146572156974388925..1747314825965461.93.296.721.434.73..92112394.76. I9: 6 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-164-base-pr-000.dot * REASONING * PRF # H9: 5,8 => SOL * DIS # H9: 6 => CTR => H9: 5,8 * PRF # I5: 5,8 => SOL * DIS # I5: 6 => CTR => I5: 5,8 * DIS # I9: 5,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * DIS # E4: 3,6 => CTR => E4: 7 * PRF # E4: 7 => SOL * PRF # I5: 6,8 => SOL * DIS # I5: 5 => CTR => I5: 6,8 * PRF # E4: 6,7 => SOL * DIS # E4: 3 => CTR => E4: 6,7 * PRF # I5: 5,8 => SOL * DIS # I5: 6 => CTR => I5: 5,8 * DIS # F8: 5,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # F8: 5,6 => SOL * DIS # F8: 8 => CTR => F8: 5,6 * DIS # F8: 5,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # H9: 5,8 => SOL * DIS # H9: 6 => CTR => H9: 5,8 * DIS # I9: 5,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * PRF # H9: 5,8 => SOL * DIS # H9: 6 => CTR => H9: 5,8 * DIS # I9: 5,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * CNT 28 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B8,C3,C7,E1,E5,E6,E8,F1,F4,F9,G5,G7,H2,H4,H6,I3) * 6748..2193.92146.721.69743.8925..1.47314.2.9.5461.93.296.721.434.73..92112394.7.. * PAIR H2: 5,8 COL H H9: 5,8,6 # reduction candidate for 5,8 H9: 5,8 => SOLVED * 674835219359214687218697435892573164731462598546189372965721843487356921123948756 * DURATION: 0:00:02.088696 START: 08:22:59.206772 END: 08:23:01.295468 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-164-base-pr-001.dot * REASONING * PRF # H9: 5,8 => SOL * STA H9: 5,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 164 solution: 674835219359214687218697435892573164731462598546189372965721843487356921123948756 info: 1822 FNBWX S8.f 23080 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 674835219359214687218697435892573164731462598546189372965721843487356921123948756 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 # H9: 5,8 => SOL * DIS # H9: 6 => CTR => H9: 5,8 * PRF # I5: 5,8 => SOL * DIS # I5: 6 => CTR => I5: 5,8 * DIS # I9: 5,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * DIS # E4: 3,6 => CTR => E4: 7 * PRF # E4: 7 => SOL * PRF # I5: 6,8 => SOL * DIS # I5: 5 => CTR => I5: 6,8 * PRF # E4: 6,7 => SOL * DIS # E4: 3 => CTR => E4: 6,7 * PRF # I5: 5,8 => SOL * DIS # I5: 6 => CTR => I5: 5,8 * DIS # F8: 5,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # F8: 5,6 => SOL * DIS # F8: 8 => CTR => F8: 5,6 * DIS # F8: 5,8 => CTR => F8: 6 * PRF # F8: 6 => SOL * PRF # H9: 5,8 => SOL * DIS # H9: 6 => CTR => H9: 5,8 * DIS # I9: 5,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * PRF # H9: 5,8 => SOL * DIS # H9: 6 => CTR => H9: 5,8 * DIS # I9: 5,8 => CTR => I9: 6 * PRF # I9: 6 => SOL * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # H9: 5,8 => SOL * STA H9: 5,8 * CNT 1 HDP CHAINS / 1 HYP OPENED