Analysis of xx-top500-487-base.sdk
Contents
Original Sudoku
level: medium
position: ....7.81..42...............8......6....4.2......5....1...36.4...25......1........ initial
Autosolve
position: 5..674812.42158......923...85.7.926.3..4.2...2..5.6..19..3614254258971361..245... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G2: 6,7 => SOL * DIS # G2: 3,9 => CTR => G2: 6,7 * DIS # G3: 6,7 => CTR => G3: 5 * PRF # G3: 5 => SOL * DIS # G2: 7,9 => CTR => G2: 3,6 * DIS # I2: 7,9 => CTR => I2: 3 * PRF # I2: 3 => SOL * DIS # H5: 7,9 => CTR => H5: 5,8 * PRF # H6: 7,9 => SOL * PRF # H3: 4,7 => SOL * DIS # H3: 5 => CTR => H3: 4,7 * PRF # B5: 7,9 => SOL * DIS # C5: 7,9 => CTR => C5: 1,6 * DIS # C6: 7,9 => CTR => C6: 4 * PRF # C6: 4 => SOL * DIS # G6: 7,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # H6: 7,9 => SOL * PRF # I9: 7,9 => SOL * DIS # G2: 7,9 => CTR => G2: 3,6 * PRF # G5: 7,9 => SOL * DIS # G5: 5 => CTR => G5: 7,9 * DIS # G6: 7,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * CNT 24 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G2: 6,7 => SOL * STA G2: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....7.81..42...............8......6....4.2......5....1...36.4...25......1........ | initial |
| 5..674812.42158......923...85.7.926.3..4.2...2..5.6..19..3614254258971361..245... | autosolve |
| 539674812742158693618923547851739264376412958294586371987361425425897136163245789 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B1: 3,9 C1: 3,9 A2: 6,7 A3: 6,7 B3: 1,8 C3: 1,8 H2: 7,9 I3: 4,7 C4: 1,4 B6: 7,9 E4: 1,3 E5: 1,8 E6: 3,8 I4: 3,4 B7: 7,8 C7: 7,8 B9: 3,6 C9: 3,6 G9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 1.. / B3 = 1 => 16 pairs (_) / C3 = 1 => 0 pairs (X) E4,E5: 1.. / E4 = 1 => 0 pairs (X) / E5 = 1 => 0 pairs (_) C4,E4: 1.. / C4 = 1 => 0 pairs (*) / E4 = 1 => 0 pairs (X) B3,B5: 1.. / B3 = 1 => 16 pairs (_) / B5 = 1 => 0 pairs (X) B1,C1: 3.. / B1 = 3 => 16 pairs (_) / C1 = 3 => 13 pairs (_) G2,I2: 3.. / G2 = 3 => 0 pairs (X) / I2 = 3 => 0 pairs (_) E4,E6: 3.. / E4 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) I4,G6: 3.. / I4 = 3 => 0 pairs (X) / G6 = 3 => 0 pairs (_) B9,C9: 3.. / B9 = 3 => 13 pairs (_) / C9 = 3 => 16 pairs (_) E4,I4: 3.. / E4 = 3 => 0 pairs (*) / I4 = 3 => 0 pairs (X) E6,G6: 3.. / E6 = 3 => 0 pairs (X) / G6 = 3 => 0 pairs (_) B1,B9: 3.. / B1 = 3 => 16 pairs (_) / B9 = 3 => 13 pairs (_) C1,C9: 3.. / C1 = 3 => 13 pairs (_) / C9 = 3 => 16 pairs (_) G2,G6: 3.. / G2 = 3 => 0 pairs (X) / G6 = 3 => 0 pairs (_) I2,I4: 3.. / I2 = 3 => 0 pairs (*) / I4 = 3 => 0 pairs (X) H3,I3: 4.. / H3 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) C4,C6: 4.. / C4 = 4 => 0 pairs (X) / C6 = 4 => 0 pairs (_) I4,H6: 4.. / I4 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) C4,I4: 4.. / C4 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) C6,H6: 4.. / C6 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) H3,H6: 4.. / H3 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) I3,I4: 4.. / I3 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) G3,H3: 5.. / G3 = 5 => 0 pairs (*) / H3 = 5 => 0 pairs (X) G5,H5: 5.. / G5 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) G3,G5: 5.. / G3 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) H3,H5: 5.. / H3 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 0 pairs (_) G2,G3: 6.. / G2 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) B5,C5: 6.. / B5 = 6 => 13 pairs (_) / C5 = 6 => 16 pairs (_) B9,C9: 6.. / B9 = 6 => 16 pairs (_) / C9 = 6 => 13 pairs (_) A2,G2: 6.. / A2 = 6 => 0 pairs (X) / G2 = 6 => 0 pairs (_) A3,G3: 6.. / A3 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) B5,B9: 6.. / B5 = 6 => 13 pairs (_) / B9 = 6 => 16 pairs (_) C5,C9: 6.. / C5 = 6 => 16 pairs (_) / C9 = 6 => 13 pairs (_) A2,A3: 7.. / A2 = 7 => 0 pairs (*) / A3 = 7 => 0 pairs (X) B7,C7: 7.. / B7 = 7 => 0 pairs (X) / C7 = 7 => 16 pairs (_) B3,C3: 8.. / B3 = 8 => 0 pairs (X) / C3 = 8 => 16 pairs (_) E5,E6: 8.. / E5 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) B7,C7: 8.. / B7 = 8 => 16 pairs (_) / C7 = 8 => 0 pairs (X) H9,I9: 8.. / H9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) E6,H6: 8.. / E6 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) B3,B7: 8.. / B3 = 8 => 0 pairs (X) / B7 = 8 => 16 pairs (_) C3,C7: 8.. / C3 = 8 => 16 pairs (_) / C7 = 8 => 0 pairs (X) I5,I9: 8.. / I5 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) B1,C1: 9.. / B1 = 9 => 13 pairs (_) / C1 = 9 => 16 pairs (_) * DURATION: 0:01:50.637565 START: 19:16:41.555573 END: 19:18:32.193138 2017-05-04 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B1,B3,B6,B7,B9,C1,C3,C4,C7,C9,E4,E5,E6,G9,H2,I3,I4) * 5..674812.42158......923...85.7.926.3..4.2...2..5.6..19..3614254258971361..245... * PAIR A2: 6,7 ROW 2 G2: 6,7,3,9 # reduction candidate for 6,7 G2: 6,7 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 G2: 3,9 => CTR * 5..674812642158...7..9236548547192633..4825..2..5.6..19..3614254258971361..245... * PAIR A3: 6,7 ROW 3 G3: 6,7,5 # reduction candidate for 6,7 G3: 6,7 => CTR * 5..674812.42158......923.548547192633..4825..2..5.6..19..3614254258971361..245... G3: 5 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 * PAIR H2: 7,9 BLK 3 G2: 7,9,3,6 # reduction candidate for 7,9 G2: 7,9 => CTR * 5..674812642158..37..92365485.7.926.3..4.2...2..5.6..19..3614254258971361..245... G2: 3,6 # 20 pairs I2: 7,9,3 # reduction candidate for 7,9 I2: 7,9 => CTR * 5..674812.421583.....9236548547192633..4825..2..5.6..19..3614254258971361..245... I2: 3 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 * PAIR H2: 7,9 COL H H5: 7,9,5,8 # reduction candidate for 7,9 H5: 7,9 => CTR * 5..674812.42158......923.548547192633..4825..2..5.6..19..3614254258971361..245... H5: 5,8 # 20 pairs H6: 7,9,4,8 # reduction candidate for 7,9 H6: 7,9 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 H6: 4,8 # 20 pairs H9: 7,9,8 # reduction candidate for 7,9 H9: 7,9 # 24 pairs * PAIR I3: 4,7 BLK 3 H3: 4,7,5 # reduction candidate for 4,7 H3: 4,7 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 H3: 5 => CTR * 5..674812.42158......923.548547192633..4825..2..5.6..19..3614254258971361..245... * PAIR B6: 7,9 BLK 4 B5: 7,9,1,6 # reduction candidate for 7,9 B5: 7,9 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 B5: 1,6 # 20 pairs C5: 7,9,1,6 # reduction candidate for 7,9 C5: 7,9 => CTR * 593674812.42158..3.18923...85173926436.412...274586391987361425425897136136245..9 C5: 1,6 # 20 pairs C6: 7,9,4 # reduction candidate for 7,9 C6: 7,9 => CTR * 5..674812.42158......923...8547192633..482...2..536..19..3614254258971361..245... C6: 4 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 * PAIR B6: 7,9 ROW 6 G6: 7,9,3 # reduction candidate for 7,9 G6: 7,9 => CTR * 5..674812.421583.....9236548547192633..4825..2..5.6..19..3614254258971361..245... G6: 3 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 H6: 7,9,4,8 # reduction candidate for 7,9 H6: 7,9 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 H6: 4,8 # 20 pairs * PAIR G9: 7,9 BLK 9 H9: 7,9,8 # reduction candidate for 7,9 H9: 7,9 # 24 pairs I9: 7,9,8 # reduction candidate for 7,9 I9: 7,9 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 I9: 8 # 24 pairs * PAIR G9: 7,9 COL G G2: 7,9,3,6 # reduction candidate for 7,9 G2: 7,9 => CTR * 5..674812642158..37..92365485.7.926.3..4.2...2..5.6..19..3614254258971361..245... G2: 3,6 # 20 pairs G5: 7,9,5 # reduction candidate for 7,9 G5: 7,9 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 G5: 5 => CTR * 5..674812.42158......923.548547192633..4825..2..536..19..3614254258971361..245... G6: 7,9,3 # reduction candidate for 7,9 G6: 7,9 => CTR * 5..674812.421583.....9236548547192633..4825..2..5.6..19..3614254258971361..245... G6: 3 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-487-base-pr-000.dot * REASONING * PRF # G2: 6,7 => SOL * DIS # G2: 3,9 => CTR => G2: 6,7 * DIS # G3: 6,7 => CTR => G3: 5 * PRF # G3: 5 => SOL * DIS # G2: 7,9 => CTR => G2: 3,6 * DIS # I2: 7,9 => CTR => I2: 3 * PRF # I2: 3 => SOL * DIS # H5: 7,9 => CTR => H5: 5,8 * PRF # H6: 7,9 => SOL * PRF # H3: 4,7 => SOL * DIS # H3: 5 => CTR => H3: 4,7 * PRF # B5: 7,9 => SOL * DIS # C5: 7,9 => CTR => C5: 1,6 * DIS # C6: 7,9 => CTR => C6: 4 * PRF # C6: 4 => SOL * DIS # G6: 7,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # H6: 7,9 => SOL * PRF # I9: 7,9 => SOL * DIS # G2: 7,9 => CTR => G2: 3,6 * PRF # G5: 7,9 => SOL * DIS # G5: 5 => CTR => G5: 7,9 * DIS # G6: 7,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * CNT 24 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B1,B3,B6,B7,B9,C1,C3,C4,C7,C9,E4,E5,E6,G9,H2,I3,I4) * 5..674812.42158......923...85.7.926.3..4.2...2..5.6..19..3614254258971361..245... * PAIR A2: 6,7 ROW 2 G2: 6,7,3,9 # reduction candidate for 6,7 G2: 6,7 => SOLVED * 539674812742158693618923547851739264376412958294586371987361425425897136163245789 * DURATION: 0:00:02.734341 START: 19:19:24.639073 END: 19:19:27.373414 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-487-base-pr-001.dot * REASONING * PRF # G2: 6,7 => SOL * STA G2: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 487 solution: 539674812742158693618923547851739264376412958294586371987361425425897136163245789 info: 96136 FNBYK S8.f 42986 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 539674812742158693618923547851739264376412958294586371987361425425897136163245789 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 # G2: 6,7 => SOL * DIS # G2: 3,9 => CTR => G2: 6,7 * DIS # G3: 6,7 => CTR => G3: 5 * PRF # G3: 5 => SOL * DIS # G2: 7,9 => CTR => G2: 3,6 * INC # G2: 3,6 => UNS * DIS # I2: 7,9 => CTR => I2: 3 * PRF # I2: 3 => SOL * DIS # H5: 7,9 => CTR => H5: 5,8 * INC # H5: 5,8 => UNS * PRF # H6: 7,9 => SOL * INC # H6: 4,8 => UNS * INC # H9: 7,9 => UNS * PRF # H3: 4,7 => SOL * DIS # H3: 5 => CTR => H3: 4,7 * PRF # B5: 7,9 => SOL * INC # B5: 1,6 => UNS * DIS # C5: 7,9 => CTR => C5: 1,6 * INC # C5: 1,6 => UNS * DIS # C6: 7,9 => CTR => C6: 4 * PRF # C6: 4 => SOL * DIS # G6: 7,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # H6: 7,9 => SOL * INC # H6: 4,8 => UNS * INC # H9: 7,9 => UNS * PRF # I9: 7,9 => SOL * INC # I9: 8 => UNS * DIS # G2: 7,9 => CTR => G2: 3,6 * INC # G2: 3,6 => UNS * PRF # G5: 7,9 => SOL * DIS # G5: 5 => CTR => G5: 7,9 * DIS # G6: 7,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # G2: 6,7 => SOL * STA G2: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED