Analysis of xx-top500-242-base.sdk
Contents
Original Sudoku
level: medium
position: 8......13...674............3..5..1........7.6....8.......2...8..41.......7....... initial
Autosolve
position: 867925413.136748..4..81367.3.45671.818.43.7.67.618..3463.241.87.417.836..783.6.41 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 5,9 => CTR => C3: 2 * PRF # I2: 5,9 => SOL * PRF # A8: 5,9 => SOL * PRF # I2: 5,9 => SOL * DIS # C3: 5,9 => CTR => C3: 2 * PRF # I8: 2 => SOL * DIS # B6: 2,9 => CTR => B6: 5 * DIS # B3: 5 => CTR => B3: 2,9 * DIS # H5: 2,9 => CTR => H5: 5 * DIS # B6: 2,9 => CTR => B6: 5 * DIS # H5: 2,9 => CTR => H5: 5 * DIS # H2: 5 => CTR => H2: 2,9 * PRF # A8: 5,9 => SOL * DIS # C3: 5,9 => CTR => C3: 2 * PRF # A8: 5,9 => SOL * PRF # G9: 5,9 => SOL * PRF # G9: 5,9 => SOL * PRF # G6: 2 => SOL * CNT 18 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 5,9 => CTR => C3: 2 * PRF C3: 2 # I2: 5,9 => SOL * STA C3: 2 + I2: 5,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8......13...674............3..5..1........7.6....8.......2...8..41.......7....... | initial |
| 867925413.136748..4..81367.3.45671.818.43.7.67.618..3463.241.87.417.836..783.6.41 | autosolve |
| 867925413513674829492813675324567198189432756756189234635241987941758362278396541 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A2: 5,9 I3: 5,9 B4: 2,9 F5: 2,9 F6: 2,9 H4: 2,9 C7: 5,9 E8: 5,9 E9: 5,9 G7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 2.. / B3 = 2 => 0 pairs (X) / C3 = 2 => 12 pairs (_) H2,I2: 2.. / H2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) F5,F6: 2.. / F5 = 2 => 15 pairs (_) / F6 = 2 => 16 pairs (_) A8,A9: 2.. / A8 = 2 => 14 pairs (_) / A9 = 2 => 0 pairs (*) I8,G9: 2.. / I8 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) B4,H4: 2.. / B4 = 2 => 15 pairs (_) / H4 = 2 => 16 pairs (_) A8,I8: 2.. / A8 = 2 => 14 pairs (_) / I8 = 2 => 0 pairs (*) A9,G9: 2.. / A9 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) C3,C5: 2.. / C3 = 2 => 12 pairs (_) / C5 = 2 => 0 pairs (X) G6,G9: 2.. / G6 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) I2,I8: 2.. / I2 = 2 => 14 pairs (_) / I8 = 2 => 0 pairs (*) C5,B6: 5.. / C5 = 5 => 0 pairs (X) / B6 = 5 => 15 pairs (_) H5,G6: 5.. / H5 = 5 => 15 pairs (_) / G6 = 5 => 0 pairs (X) E8,E9: 5.. / E8 = 5 => 16 pairs (_) / E9 = 5 => 14 pairs (_) C5,H5: 5.. / C5 = 5 => 0 pairs (X) / H5 = 5 => 15 pairs (_) B6,G6: 5.. / B6 = 5 => 15 pairs (_) / G6 = 5 => 0 pairs (X) C7,G7: 5.. / C7 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) B3,B6: 5.. / B3 = 5 => 0 pairs (X) / B6 = 5 => 15 pairs (_) H2,H5: 5.. / H2 = 5 => 0 pairs (X) / H5 = 5 => 15 pairs (_) F5,F6: 9.. / F5 = 9 => 16 pairs (_) / F6 = 9 => 15 pairs (_) E8,E9: 9.. / E8 = 9 => 14 pairs (_) / E9 = 9 => 16 pairs (_) B4,H4: 9.. / B4 = 9 => 16 pairs (_) / H4 = 9 => 15 pairs (_) C7,G7: 9.. / C7 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) * DURATION: 0:00:39.915415 START: 11:04:28.328554 END: 11:05:08.243969 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B4,C7,E8,E9,F5,F6,G7,H4,I3) * 867925413.136748..4..81367.3.45671.818.43.7.67.618..3463.241.87.417.836..783.6.41 * PAIR A2: 5,9 BLK 1 B3: 5,9,2 # reduction candidate for 5,9 B3: 5,9 # 12 pairs C3: 5,9,2 # reduction candidate for 5,9 C3: 5,9 => CTR * 867925413.136748..42.81367.394567128182439756756182934639241587.417.8369.78396241 C3: 2 # 12 pairs * PAIR A2: 5,9 ROW 2 H2: 5,9,2 # reduction candidate for 5,9 H2: 5,9 # 14 pairs I2: 5,9,2 # reduction candidate for 5,9 I2: 5,9 => SOLVED * 867925413513674829492813675324567198189432756756189234635241987941758362278396541 I2: 2 # 14 pairs * PAIR A2: 5,9 COL A A8: 5,9,2 # reduction candidate for 5,9 A8: 5,9 => SOLVED * 867925413513674829492813675324567198189432756756189234635241987941758362278396541 A8: 2 # 14 pairs A9: 5,9,2 # reduction candidate for 5,9 A9: 5,9 # 14 pairs * PAIR I3: 5,9 BLK 3 H2: 5,9,2 # reduction candidate for 5,9 H2: 5,9 # 14 pairs I2: 5,9,2 # reduction candidate for 5,9 I2: 5,9 => SOLVED * 867925413513674829492813675324567198189432756756189234635241987941758362278396541 I2: 2 # 14 pairs * PAIR I3: 5,9 ROW 3 B3: 5,9,2 # reduction candidate for 5,9 B3: 5,9 # 12 pairs C3: 5,9,2 # reduction candidate for 5,9 C3: 5,9 => CTR * 867925413.136748..42.81367.394567128182439756756182934639241587.417.8369.78396241 C3: 2 # 12 pairs * PAIR I3: 5,9 COL I I8: 5,9,2 # reduction candidate for 5,9 I8: 2 => SOLVED * 867925413513674829492813675324567198189432756756189234635241987941758362278396541 I8: 5,9 # 14 pairs * PAIR B4: 2,9 BLK 4 C5: 2,9,5 # reduction candidate for 2,9 C5: 2,9 # 15 pairs B6: 2,9,5 # reduction candidate for 2,9 B6: 2,9 => CTR * 867925413.136748..4528136793.45671.818543.7.67.618.534639241.87.417.836..783.6.41 B6: 5 # 15 pairs * PAIR B4: 2,9 COL B B3: 2,9,5 # reduction candidate for 2,9 B3: 5 => CTR * 867925413.136748..4528136793.45671.818543.7.67.618.534639241.87.417.836..783.6.41 B3: 2,9 # 15 pairs * PAIR F5: 2,9 ROW 5 C5: 2,9,5 # reduction candidate for 2,9 C5: 2,9 # 15 pairs H5: 2,9,5 # reduction candidate for 2,9 H5: 2,9 => CTR * 867925413.136748524..8136793.45671.818543.7.67.618.534639241.87.417.836..783.6.41 H5: 5 # 15 pairs * PAIR F6: 2,9 ROW 6 B6: 2,9,5 # reduction candidate for 2,9 B6: 2,9 => CTR * 867925413.136748..4528136793.45671.818543.7.67.618.534639241.87.417.836..783.6.41 B6: 5 # 15 pairs G6: 2,9,5 # reduction candidate for 2,9 G6: 2,9 # 15 pairs * PAIR H4: 2,9 BLK 6 H5: 2,9,5 # reduction candidate for 2,9 H5: 2,9 => CTR * 867925413.136748524..8136793.45671.818543.7.67.618.534639241.87.417.836..783.6.41 H5: 5 # 15 pairs G6: 2,9,5 # reduction candidate for 2,9 G6: 2,9 # 15 pairs * PAIR H4: 2,9 COL H H2: 2,9,5 # reduction candidate for 2,9 H2: 5 => CTR * 867925413.136748524..8136793.45671.818543.7.67.618.534639241.87.417.836..783.6.41 H2: 2,9 # 15 pairs * PAIR C7: 5,9 BLK 7 A8: 5,9,2 # reduction candidate for 5,9 A8: 5,9 => SOLVED * 867925413513674829492813675324567198189432756756189234635241987941758362278396541 A8: 2 # 14 pairs A9: 5,9,2 # reduction candidate for 5,9 A9: 5,9 # 14 pairs * PAIR C7: 5,9 COL C C3: 5,9,2 # reduction candidate for 5,9 C3: 5,9 => CTR * 867925413.136748..42.81367.394567128182439756756182934639241587.417.8369.78396241 C3: 2 # 12 pairs C5: 5,9,2 # reduction candidate for 5,9 C5: 5,9 # 12 pairs * PAIR E8: 5,9 ROW 8 A8: 5,9,2 # reduction candidate for 5,9 A8: 5,9 => SOLVED * 867925413513674829492813675324567198189432756756189234635241987941758362278396541 A8: 2 # 14 pairs I8: 5,9,2 # reduction candidate for 5,9 I8: 5,9 # 14 pairs * PAIR E9: 5,9 ROW 9 A9: 5,9,2 # reduction candidate for 5,9 A9: 5,9 # 14 pairs G9: 5,9,2 # reduction candidate for 5,9 G9: 5,9 => SOLVED * 867925413513674829492813675324567198189432756756189234635241987941758362278396541 G9: 2 # 14 pairs * PAIR G7: 5,9 BLK 9 I8: 5,9,2 # reduction candidate for 5,9 I8: 5,9 # 14 pairs G9: 5,9,2 # reduction candidate for 5,9 G9: 5,9 => SOLVED * 867925413513674829492813675324567198189432756756189234635241987941758362278396541 G9: 2 # 14 pairs * PAIR G7: 5,9 COL G G6: 5,9,2 # reduction candidate for 5,9 G6: 2 => SOLVED * 867925413513674829492813675324567198189432756756189234635241987941758362278396541 G6: 5,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-242-base-pr-000.dot * REASONING * DIS # C3: 5,9 => CTR => C3: 2 * PRF # I2: 5,9 => SOL * PRF # A8: 5,9 => SOL * PRF # I2: 5,9 => SOL * DIS # C3: 5,9 => CTR => C3: 2 * PRF # I8: 2 => SOL * DIS # B6: 2,9 => CTR => B6: 5 * DIS # B3: 5 => CTR => B3: 2,9 * DIS # H5: 2,9 => CTR => H5: 5 * DIS # B6: 2,9 => CTR => B6: 5 * DIS # H5: 2,9 => CTR => H5: 5 * DIS # H2: 5 => CTR => H2: 2,9 * PRF # A8: 5,9 => SOL * DIS # C3: 5,9 => CTR => C3: 2 * PRF # A8: 5,9 => SOL * PRF # G9: 5,9 => SOL * PRF # G9: 5,9 => SOL * PRF # G6: 2 => SOL * CNT 18 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B4,C7,E8,E9,F5,F6,G7,H4,I3) * 867925413.136748..4..81367.3.45671.818.43.7.67.618..3463.241.87.417.836..783.6.41 * PAIR A2: 5,9 BLK 1 B3: 5,9,2 # reduction candidate for 5,9 B3: 5,9 # 12 pairs C3: 5,9,2 # reduction candidate for 5,9 C3: 5,9 => CTR * 867925413.136748..42.81367.394567128182439756756182934639241587.417.8369.78396241 * RESTART * PAIR A2: 5,9 ROW 2 H2: 5,9,2 # reduction candidate for 5,9 H2: 5,9 # 16 pairs I2: 5,9,2 # reduction candidate for 5,9 I2: 5,9 => SOLVED * 867925413513674829492813675324567198189432756756189234635241987941758362278396541 * DURATION: 0:00:04.907793 START: 11:05:58.791854 END: 11:06:03.699647 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-242-base-pr-001.dot * REASONING * DIS # C3: 5,9 => CTR => C3: 2 * PRF C3: 2 # I2: 5,9 => SOL * STA C3: 2 + I2: 5,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 242 solution: 867925413513674829492813675324567198189432756756189234635241987941758362278396541 info: 2069 FNBWX S8.f 37857 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 867925413513674829492813675324567198189432756756189234635241987941758362278396541 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 # B3: 5,9 => UNS * DIS # C3: 5,9 => CTR => C3: 2 * INC # C3: 2 => UNS * INC # H2: 5,9 => UNS * PRF # I2: 5,9 => SOL * INC # I2: 2 => UNS * PRF # A8: 5,9 => SOL * INC # A8: 2 => UNS * INC # A9: 5,9 => UNS * INC # H2: 5,9 => UNS * PRF # I2: 5,9 => SOL * INC # I2: 2 => UNS * INC # B3: 5,9 => UNS * DIS # C3: 5,9 => CTR => C3: 2 * INC # C3: 2 => UNS * INC # I8: 5,9 => UNS * PRF # I8: 2 => SOL * INC # C5: 2,9 => UNS * DIS # B6: 2,9 => CTR => B6: 5 * INC # B6: 5 => UNS * INC # B3: 2,9 => UNS * DIS # B3: 5 => CTR => B3: 2,9 * INC # C5: 2,9 => UNS * DIS # H5: 2,9 => CTR => H5: 5 * INC # H5: 5 => UNS * DIS # B6: 2,9 => CTR => B6: 5 * INC # B6: 5 => UNS * INC # G6: 2,9 => UNS * DIS # H5: 2,9 => CTR => H5: 5 * INC # H5: 5 => UNS * INC # G6: 2,9 => UNS * INC # H2: 2,9 => UNS * DIS # H2: 5 => CTR => H2: 2,9 * PRF # A8: 5,9 => SOL * INC # A8: 2 => UNS * INC # A9: 5,9 => UNS * DIS # C3: 5,9 => CTR => C3: 2 * INC # C3: 2 => UNS * INC # C5: 5,9 => UNS * PRF # A8: 5,9 => SOL * INC # A8: 2 => UNS * INC # I8: 5,9 => UNS * INC # A9: 5,9 => UNS * PRF # G9: 5,9 => SOL * INC # G9: 2 => UNS * INC # I8: 5,9 => UNS * PRF # G9: 5,9 => SOL * INC # G9: 2 => UNS * INC # G6: 5,9 => UNS * PRF # G6: 2 => SOL * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 5,9 => UNS * DIS # C3: 5,9 => CTR => C3: 2 * INC C3: 2 # H2: 5,9 => UNS * PRF C3: 2 # I2: 5,9 => SOL * STA C3: 2 + I2: 5,9 * CNT 4 HDP CHAINS / 4 HYP OPENED