Analysis of xx-top500-037-base.sdk
Contents
Original Sudoku
level: medium
position: ...2..6..3.4.......1......82.....7......8..4......1......76.5...6.3............1. initial
Autosolve
position: ...2486313841.6...612...4.82416..78...6.8.14.8..4.1.6.1.876.5...6.31.8.....8...16 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E3: 5,9 => CTR => E3: 3,7 * DIS # F3: 5,9 => CTR => F3: 3,7 * DIS # H3: 7 => CTR => H3: 5,9 * DIS # I2: 2,9 => CTR => I2: 7 * DIS # G6: 2,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # G9: 2,9 => SOL * DIS # G9: 3 => CTR => G9: 2,9 * PRF # F4: 5,9 => SOL * DIS # B5: 5,9 => CTR => B5: 3,7 * DIS # I5: 5,9 => CTR => I5: 2,3 * DIS # I5: 5,9 => CTR => I5: 2,3 * PRF # F4: 5,9 => SOL * DIS # A9: 5,9 => CTR => A9: 4,7 * DIS # B9: 5,9 => CTR => B9: 2,3,7 * DIS # C9: 5,9 => CTR => C9: 3,7 * DIS # F8: 5,9 => CTR => F8: 2,4 * DIS # C6: 5,9 => CTR => C6: 3,7 * DIS # I7: 2,9 => CTR => I7: 3,4 * DIS # H8: 2,9 => CTR => H8: 7 * DIS # I8: 2,9 => CTR => I8: 4,7 * PRF # G9: 2,9 => SOL * DIS # G9: 3 => CTR => G9: 2,9 * PRF # B7: 2,9 => SOL * DIS # B7: 3 => CTR => B7: 2,9 * DIS # F7: 2,9 => CTR => F7: 4 * PRF # F7: 4 => SOL * CNT 27 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E3: 5,9 => CTR => E3: 3,7 * DIS E3: 3,7 # F3: 5,9 => CTR => F3: 3,7 * DIS E3: 3,7 + F3: 3,7 # I2: 2,9 => CTR => I2: 7 * DIS E3: 3,7 + F3: 3,7 + I2: 7 # H2: 5 => CTR => H2: 2,9 * DIS E3: 3,7 + F3: 3,7 + I2: 7 + H2: 2,9 # G6: 2,9 => CTR => G6: 3 * PRF E3: 3,7 + F3: 3,7 + I2: 7 + H2: 2,9 + G6: 3 => SOL * STA E3: 3,7 + F3: 3,7 + I2: 7 + H2: 2,9 + G6: 3 * CNT 6 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2..6..3.4.......1......82.....7......8..4......1......76.5...6.3............1. | initial |
| ...2486313841.6...612...4.82416..78...6.8.14.8..4.1.6.1.876.5...6.31.8.....8...16 | autosolve |
| 795248631384156927612973458241639785936587142857421369128764593569312874473895216 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) D3: 5,9 G2: 2,9 D5: 5,9 F5: 2,7 E6: 2,7 I4: 5,9 C8: 5,9 H7: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F5,E6: 2.. / F5 = 2 => 0 pairs (X) / E6 = 2 => 0 pairs (_) B7,B9: 2.. / B7 = 2 => 0 pairs (*) / B9 = 2 => 0 pairs (X) F5,I5: 2.. / F5 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) E6,E9: 2.. / E6 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) E3,F3: 3.. / E3 = 3 => 9 pairs (_) / F3 = 3 => 0 pairs (*) E4,F4: 3.. / E4 = 3 => 0 pairs (*) / F4 = 3 => 0 pairs (X) I7,G9: 3.. / I7 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) B5,I5: 3.. / B5 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) B7,I7: 3.. / B7 = 3 => 0 pairs (X) / I7 = 3 => 0 pairs (_) C6,C9: 3.. / C6 = 3 => 0 pairs (X) / C9 = 3 => 0 pairs (_) E3,E4: 3.. / E3 = 3 => 9 pairs (_) / E4 = 3 => 0 pairs (*) F3,F4: 3.. / F3 = 3 => 0 pairs (*) / F4 = 3 => 0 pairs (X) G6,G9: 3.. / G6 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) A8,A9: 4.. / A8 = 4 => 0 pairs (X) / A9 = 4 => 13 pairs (_) I7,I8: 4.. / I7 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) F7,I7: 4.. / F7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) A9,F9: 4.. / A9 = 4 => 13 pairs (_) / F9 = 4 => 0 pairs (X) H2,H3: 5.. / H2 = 5 => 11 pairs (_) / H3 = 5 => 11 pairs (_) E2,H2: 5.. / E2 = 5 => 11 pairs (_) / H2 = 5 => 11 pairs (_) D3,D5: 5.. / D3 = 5 => 15 pairs (_) / D5 = 5 => 10 pairs (_) F5,E6: 7.. / F5 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) H8,I8: 7.. / H8 = 7 => 12 pairs (_) / I8 = 7 => 0 pairs (X) F3,F5: 7.. / F3 = 7 => 0 pairs (X) / F5 = 7 => 0 pairs (_) I2,I8: 7.. / I2 = 7 => 12 pairs (_) / I8 = 7 => 0 pairs (X) D3,D5: 9.. / D3 = 9 => 10 pairs (_) / D5 = 9 => 15 pairs (_) * DURATION: 0:00:41.616835 START: 03:56:07.548075 END: 03:56:49.164910 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D3,D5,E6,F5,G2,H7,I4) * ...2486313841.6...612...4.82416..78...6.8.14.8..4.1.6.1.876.5...6.31.8.....8...16 * PAIR D3: 5,9 BLK 2 E2: 5,9,7 # reduction candidate for 5,9 E2: 5,9 # 12 pairs E3: 5,9,3,7 # reduction candidate for 5,9 E3: 5,9 => CTR * ...248631384176.59612..3478241639785.365871428..4219631.876.5...6.31.8.7...8...16 E3: 3,7 # 9 pairs F3: 5,9,3,7 # reduction candidate for 5,9 F3: 5,9 => CTR * ...248631384176.59612.3.478241693785.365871428..4219631.876.5...6.31.8.7...8...16 F3: 3,7 # 9 pairs * PAIR D3: 5,9 ROW 3 H3: 5,9,7 # reduction candidate for 5,9 H3: 7 => CTR * ...248631384176259612...4782416..785.365871428..4219631.876.5...6.31.8.7...8...16 H3: 5,9 # 12 pairs * PAIR G2: 2,9 BLK 3 H2: 2,9,5,7 # reduction candidate for 2,9 H2: 2,9 # 12 pairs I2: 2,9,7 # reduction candidate for 2,9 I2: 2,9 => CTR * ...2486313841.6...612...4.82416..78...6.8.1438.342196513876.5.4.6.31.8.7.2.8..316 I2: 7 # 12 pairs * PAIR G2: 2,9 COL G G6: 2,9,3 # reduction candidate for 2,9 G6: 2,9 => CTR * ...2486313841.6...612...4.82416..78...6.8.1438.342196513876.5...6.31.8...2.8..316 G6: 3 => SOLVED * 795248631384156927612973458241639785936587142857421369128764593569312874473895216 G9: 2,9,3 # reduction candidate for 2,9 G9: 2,9 => SOLVED * 795248631384156927612973458241639785936587142857421369128764593569312874473895216 G9: 3 => CTR * ...2486313841.6...612...4.82416..78...6.8.1438.342196513876.5...6.31.8...2.8..316 * PAIR D5: 5,9 BLK 5 E4: 5,9,3 # reduction candidate for 5,9 E4: 5,9 # 9 pairs F4: 5,9,3 # reduction candidate for 5,9 F4: 5,9 => SOLVED * 795248631384156927612973458241639785936587142857421369128764593569312874473895216 F4: 3 # 9 pairs * PAIR D5: 5,9 ROW 5 A5: 5,9,7 # reduction candidate for 5,9 A5: 5,9 # 11 pairs B5: 5,9,3,7 # reduction candidate for 5,9 B5: 5,9 => CTR * ...2486313841.6...612...4.82416..78...6.821438.3471.6.13876.5...6.31.8...2.8..316 B5: 3,7 # 9 pairs I5: 5,9,2,3 # reduction candidate for 5,9 I5: 5,9 => CTR * ...2486313841.6...612...4.82416..78..36.8214.8..471.6.1.876.5.3.6.31.8.44.382.916 I5: 2,3 # 9 pairs * PAIR I4: 5,9 BLK 6 I5: 5,9,2,3 # reduction candidate for 5,9 I5: 5,9 => CTR * ...2486313841.6...612...4.82416..78..36.8214.8..471.6.1.876.5.3.6.31.8.44.382.916 I5: 2,3 # 9 pairs I6: 5,9,2,3 # reduction candidate for 5,9 I6: 5,9 # 12 pairs * PAIR I4: 5,9 ROW 4 E4: 5,9,3 # reduction candidate for 5,9 E4: 5,9 # 9 pairs F4: 5,9,3 # reduction candidate for 5,9 F4: 5,9 => SOLVED * 795248631384156927612973458241639785936587142857421369128764593569312874473895216 F4: 3 # 9 pairs * PAIR C8: 5,9 BLK 7 A8: 5,9,4 # reduction candidate for 5,9 A8: 5,9 # 13 pairs A9: 5,9,4,7 # reduction candidate for 5,9 A9: 5,9 => CTR * ...2486313841.6...612...4.82416..78...6.8.1438.342196513876.5.446.31.8...278.4316 A9: 4,7 # 9 pairs B9: 5,9,2,3,7 # reduction candidate for 5,9 B9: 5,9 => CTR * ...2486313841.6...612...4.82416..78...6.8.14.8..4.1.6.12876.593.6.31.8.44..8...16 B9: 2,3,7 # 8 pairs C9: 5,9,3,7 # reduction candidate for 5,9 C9: 5,9 => CTR * ..72486313841.6...612...4.82416..78...6.821438.3471.6.13876.5...6.31.8..72.8.4316 C9: 3,7 # 9 pairs * PAIR C8: 5,9 ROW 8 F8: 5,9,2,4 # reduction candidate for 5,9 F8: 5,9 => CTR * ...2486313841.6...612...4.82416..78...6.8.14.8.34.1.6.138762594.6.31.8.....8..316 F8: 2,4 # 9 pairs * PAIR C8: 5,9 COL C C1: 5,9,7 # reduction candidate for 5,9 C1: 5,9 # 11 pairs C6: 5,9,3,7 # reduction candidate for 5,9 C6: 5,9 => CTR * ..72486313841.6..7612...4.82416..78.736.8214.8..471362128764593.6.31.8.44738...16 C6: 3,7 # 9 pairs * PAIR H7: 2,9 BLK 9 I7: 2,9,3,4 # reduction candidate for 2,9 I7: 2,9 => CTR * ...2486313841.6..7612...4.82416..78...6.8.1438.34219651387645...6.31.8.44278..316 I7: 3,4 # 9 pairs H8: 2,9,7 # reduction candidate for 2,9 H8: 2,9 => CTR * ...2486313841.6...612...4.82416..78...6.8.1438.342196513876.5.4.6.31.8.7.2.8..316 H8: 7 # 12 pairs I8: 2,9,4,7 # reduction candidate for 2,9 I8: 2,9 => CTR * ...2486313841.6..7612...4.82416..78...6.8.1438.342196513876.5.4.6.31.87..2.8..316 I8: 4,7 # 9 pairs G9: 2,9,3 # reduction candidate for 2,9 G9: 2,9 => SOLVED * 795248631384156927612973458241639785936587142857421369128764593569312874473895216 G9: 3 => CTR * ...2486313841.6...612...4.82416..78...6.8.1438.342196513876.5...6.31.8...2.8..316 * PAIR H7: 2,9 ROW 7 B7: 2,9,3 # reduction candidate for 2,9 B7: 2,9 => SOLVED * 795248631384156927612973458241639785936587142857421369128764593569312874473895216 B7: 3 => CTR * ...2486313841.6...612...4.82416..78...6.8.1438.342196513876.5...6.31.8...2.8..316 F7: 2,9,4 # reduction candidate for 2,9 F7: 2,9 => CTR * ...2486313841.6...612...4.82416..78...6.8.1438.342196513876.5.4.6.31.8...2.8..316 F7: 4 => SOLVED * 795248631384156927612973458241639785936587142857421369128764593569312874473895216 * PAIR H7: 2,9 COL H H2: 2,9,5,7 # reduction candidate for 2,9 H2: 2,9 # 12 pairs H2: 5,7 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-037-base-pr-000.dot * REASONING * DIS # E3: 5,9 => CTR => E3: 3,7 * DIS # F3: 5,9 => CTR => F3: 3,7 * DIS # H3: 7 => CTR => H3: 5,9 * DIS # I2: 2,9 => CTR => I2: 7 * DIS # G6: 2,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # G9: 2,9 => SOL * DIS # G9: 3 => CTR => G9: 2,9 * PRF # F4: 5,9 => SOL * DIS # B5: 5,9 => CTR => B5: 3,7 * DIS # I5: 5,9 => CTR => I5: 2,3 * DIS # I5: 5,9 => CTR => I5: 2,3 * PRF # F4: 5,9 => SOL * DIS # A9: 5,9 => CTR => A9: 4,7 * DIS # B9: 5,9 => CTR => B9: 2,3,7 * DIS # C9: 5,9 => CTR => C9: 3,7 * DIS # F8: 5,9 => CTR => F8: 2,4 * DIS # C6: 5,9 => CTR => C6: 3,7 * DIS # I7: 2,9 => CTR => I7: 3,4 * DIS # H8: 2,9 => CTR => H8: 7 * DIS # I8: 2,9 => CTR => I8: 4,7 * PRF # G9: 2,9 => SOL * DIS # G9: 3 => CTR => G9: 2,9 * PRF # B7: 2,9 => SOL * DIS # B7: 3 => CTR => B7: 2,9 * DIS # F7: 2,9 => CTR => F7: 4 * PRF # F7: 4 => SOL * CNT 27 HDP CHAINS / 54 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D3,D5,E6,F5,G2,H7,I4) * ...2486313841.6...612...4.82416..78...6.8.14.8..4.1.6.1.876.5...6.31.8.....8...16 * PAIR D3: 5,9 BLK 2 E2: 5,9,7 # reduction candidate for 5,9 E2: 5,9 # 12 pairs E3: 5,9,3,7 # reduction candidate for 5,9 E3: 5,9 => CTR * ...248631384176.59612..3478241639785.365871428..4219631.876.5...6.31.8.7...8...16 F3: 5,9,3,7 # reduction candidate for 5,9 F3: 5,9 => CTR * ...248631384176.59612.3.478241693785.365871428..4219631.876.5...6.31.8.7...8...16 * RESTART * PAIR G2: 2,9 BLK 3 H2: 2,9,5,7 # reduction candidate for 2,9 H2: 2,9 # 12 pairs I2: 2,9,7 # reduction candidate for 2,9 I2: 2,9 => CTR * ...248631384156.7.6129..458241639785..658.1438534.1.6.13876.5.4.6.31.8.7.2.89.316 * RESTART * PAIR G2: 2,9 BLK 3 H2: 2,9,5 # reduction candidate for 2,9 H2: 5 => CTR * ...2486313841962576125..4982416..789..69871428..4213651.876.523.6.31287442.8...16 * PAIR G2: 2,9 COL G G6: 2,9,3 # reduction candidate for 2,9 G6: 2,9 => CTR * ...248631384156..76129..458241639785..658.1438534.1.6.13876.5...6.31.87..2.89.316 G6: 3 => SOLVED * 795248631384156927612973458241639785936587142857421369128764593569312874473895216 * DURATION: 0:00:09.110727 START: 03:57:37.419951 END: 03:57:46.530678 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-037-base-pr-001.dot * REASONING * DIS # E3: 5,9 => CTR => E3: 3,7 * DIS E3: 3,7 # F3: 5,9 => CTR => F3: 3,7 * DIS E3: 3,7 + F3: 3,7 # I2: 2,9 => CTR => I2: 7 * DIS E3: 3,7 + F3: 3,7 + I2: 7 # H2: 5 => CTR => H2: 2,9 * DIS E3: 3,7 + F3: 3,7 + I2: 7 + H2: 2,9 # G6: 2,9 => CTR => G6: 3 * PRF E3: 3,7 + F3: 3,7 + I2: 7 + H2: 2,9 + G6: 3 => SOL * STA E3: 3,7 + F3: 3,7 + I2: 7 + H2: 2,9 + G6: 3 * CNT 6 HDP CHAINS / 8 HYP OPENED
Header Info
Top 500 Minimum 17 037 solution: 795248631384156927612973458241639785936587142857421369128764593569312874473895216 info: 1368 FNBHWXY S8.f 7698 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 795248631384156927612973458241639785936587142857421369128764593569312874473895216 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 # E2: 5,9 => UNS * DIS # E3: 5,9 => CTR => E3: 3,7 * INC # E3: 3,7 => UNS * DIS # F3: 5,9 => CTR => F3: 3,7 * INC # F3: 3,7 => UNS * INC # H3: 5,9 => UNS * DIS # H3: 7 => CTR => H3: 5,9 * INC # H2: 2,9 => UNS * DIS # I2: 2,9 => CTR => I2: 7 * INC # I2: 7 => UNS * DIS # G6: 2,9 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # G9: 2,9 => SOL * DIS # G9: 3 => CTR => G9: 2,9 * INC # E4: 5,9 => UNS * PRF # F4: 5,9 => SOL * INC # F4: 3 => UNS * INC # A5: 5,9 => UNS * DIS # B5: 5,9 => CTR => B5: 3,7 * INC # B5: 3,7 => UNS * DIS # I5: 5,9 => CTR => I5: 2,3 * INC # I5: 2,3 => UNS * DIS # I5: 5,9 => CTR => I5: 2,3 * INC # I5: 2,3 => UNS * INC # I6: 5,9 => UNS * INC # E4: 5,9 => UNS * PRF # F4: 5,9 => SOL * INC # F4: 3 => UNS * INC # A8: 5,9 => UNS * DIS # A9: 5,9 => CTR => A9: 4,7 * INC # A9: 4,7 => UNS * DIS # B9: 5,9 => CTR => B9: 2,3,7 * INC # B9: 2,3,7 => UNS * DIS # C9: 5,9 => CTR => C9: 3,7 * INC # C9: 3,7 => UNS * DIS # F8: 5,9 => CTR => F8: 2,4 * INC # F8: 2,4 => UNS * INC # C1: 5,9 => UNS * DIS # C6: 5,9 => CTR => C6: 3,7 * INC # C6: 3,7 => UNS * DIS # I7: 2,9 => CTR => I7: 3,4 * INC # I7: 3,4 => UNS * DIS # H8: 2,9 => CTR => H8: 7 * INC # H8: 7 => UNS * DIS # I8: 2,9 => CTR => I8: 4,7 * INC # I8: 4,7 => UNS * PRF # G9: 2,9 => SOL * DIS # G9: 3 => CTR => G9: 2,9 * PRF # B7: 2,9 => SOL * DIS # B7: 3 => CTR => B7: 2,9 * DIS # F7: 2,9 => CTR => F7: 4 * PRF # F7: 4 => SOL * INC # H2: 2,9 => UNS * INC # H2: 5,7 => UNS * CNT 54 HDP CHAINS / 54 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 5,9 => UNS * DIS # E3: 5,9 => CTR => E3: 3,7 * DIS E3: 3,7 # F3: 5,9 => CTR => F3: 3,7 * INC E3: 3,7 + F3: 3,7 # H2: 2,9 => UNS * DIS E3: 3,7 + F3: 3,7 # I2: 2,9 => CTR => I2: 7 * INC E3: 3,7 + F3: 3,7 + I2: 7 # H2: 2,9 => UNS * DIS E3: 3,7 + F3: 3,7 + I2: 7 # H2: 5 => CTR => H2: 2,9 * DIS E3: 3,7 + F3: 3,7 + I2: 7 + H2: 2,9 # G6: 2,9 => CTR => G6: 3 * PRF E3: 3,7 + F3: 3,7 + I2: 7 + H2: 2,9 + G6: 3 => SOL * STA E3: 3,7 + F3: 3,7 + I2: 7 + H2: 2,9 + G6: 3 * CNT 9 HDP CHAINS / 8 HYP OPENED