Analysis of xx-top500-233-base.sdk
Contents
Original Sudoku
level: medium
position: 725.6..........31...........4....8.....5.2......1.......1.....23..8.........3.4.. initial
Autosolve
position: 7253619488.4.2531..134..25.14...3825.3.5.21.425.14...3481.5..323.28145.95..23.481 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B9: 6,9 => CTR => B9: 7 * PRF # B9: 7 => SOL * DIS # D4: 7,9 => CTR => D4: 6 * DIS # C5: 6,9 => CTR => C5: 7,8 * DIS # H5: 7 => CTR => H5: 6,9 * DIS # D4: 7,9 => CTR => D4: 6 * DIS # C4: 6 => CTR => C4: 7,9 * DIS # H6: 6,7 => CTR => H6: 9 * DIS # B9: 9 => CTR => B9: 6,7 * DIS # B9: 6,9 => CTR => B9: 7 * PRF # B9: 7 => SOL * DIS # C5: 6,9 => CTR => C5: 7,8 * PRF # F7: 6,7 => SOL * DIS # B9: 9 => CTR => B9: 6,7 * PRF # F7: 6,7 => SOL * DIS # H6: 6,7 => CTR => H6: 9 * CNT 16 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B9: 6,9 => CTR => B9: 7 * PRF B9: 7 => SOL * STA B9: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 725.6..........31...........4....8.....5.2......1.......1.....23..8.........3.4.. | initial |
| 7253619488.4.2531..134..25.14...3825.3.5.21.425.14...3481.5..323.28145.95..23.481 | autosolve |
| 725361948894725316613489257147693825938572164256148793481957632362814579579236481 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B2: 6,9 A3: 6,9 D2: 7,9 I2: 6,7 I3: 6,7 A5: 6,9 E4: 7,9 G6: 6,7 B8: 6,7 C9: 6,9 F9: 6,7 G7: 6,7 H8: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,A3: 6.. / B2 = 6 => 0 pairs (X) / A3 = 6 => 15 pairs (_) I2,I3: 6.. / I2 = 6 => 15 pairs (_) / I3 = 6 => 0 pairs (X) D4,F6: 6.. / D4 = 6 => 15 pairs (_) / F6 = 6 => 0 pairs (X) G7,H8: 6.. / G7 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) B2,I2: 6.. / B2 = 6 => 0 pairs (X) / I2 = 6 => 15 pairs (_) A3,I3: 6.. / A3 = 6 => 15 pairs (_) / I3 = 6 => 0 pairs (X) C4,D4: 6.. / C4 = 6 => 0 pairs (X) / D4 = 6 => 15 pairs (_) B8,H8: 6.. / B8 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) A3,A5: 6.. / A3 = 6 => 15 pairs (_) / A5 = 6 => 0 pairs (X) D4,D7: 6.. / D4 = 6 => 15 pairs (_) / D7 = 6 => 0 pairs (X) G6,G7: 6.. / G6 = 6 => 0 pairs (X) / G7 = 6 => 0 pairs (_) I2,I3: 7.. / I2 = 7 => 0 pairs (X) / I3 = 7 => 15 pairs (_) B8,B9: 7.. / B8 = 7 => 0 pairs (X) / B9 = 7 => 0 pairs (_) G7,H8: 7.. / G7 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) D2,I2: 7.. / D2 = 7 => 15 pairs (_) / I2 = 7 => 0 pairs (X) B8,H8: 7.. / B8 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) B9,F9: 7.. / B9 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) G6,G7: 7.. / G6 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) E3,F3: 8.. / E3 = 8 => 17 pairs (_) / F3 = 8 => 14 pairs (_) C5,C6: 8.. / C5 = 8 => 17 pairs (_) / C6 = 8 => 14 pairs (_) E5,F6: 8.. / E5 = 8 => 14 pairs (_) / F6 = 8 => 17 pairs (_) C5,E5: 8.. / C5 = 8 => 17 pairs (_) / E5 = 8 => 14 pairs (_) C6,F6: 8.. / C6 = 8 => 14 pairs (_) / F6 = 8 => 17 pairs (_) E3,E5: 8.. / E3 = 8 => 17 pairs (_) / E5 = 8 => 14 pairs (_) F3,F6: 8.. / F3 = 8 => 14 pairs (_) / F6 = 8 => 17 pairs (_) B2,A3: 9.. / B2 = 9 => 15 pairs (_) / A3 = 9 => 0 pairs (X) H5,H6: 9.. / H5 = 9 => 0 pairs (X) / H6 = 9 => 14 pairs (_) B9,C9: 9.. / B9 = 9 => 0 pairs (X) / C9 = 9 => 15 pairs (_) D7,F7: 9.. / D7 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) B2,D2: 9.. / B2 = 9 => 15 pairs (_) / D2 = 9 => 0 pairs (X) A3,A5: 9.. / A3 = 9 => 0 pairs (X) / A5 = 9 => 15 pairs (_) B2,B9: 9.. / B2 = 9 => 15 pairs (_) / B9 = 9 => 0 pairs (X) * DURATION: 0:00:55.977160 START: 10:47:49.398838 END: 10:48:45.375998 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B2,B8,C9,D2,E4,F9,G6,G7,H8,I2,I3) * 7253619488.4.2531..134..25.14...3825.3.5.21.425.14...3481.5..323.28145.95..23.481 * PAIR B2: 6,9 COL B B9: 6,9,7 # reduction candidate for 6,9 B9: 6,9 => CTR * 7253619488947253166134..25714.6.382593658217425.14.6.34819567323728145695..237481 B9: 7 => SOLVED * 725361948894725316613489257147693825938572164256148793481957632362814579579236481 * PAIR D2: 7,9 BLK 2 E3: 7,9,8 # reduction candidate for 7,9 E3: 7,9 # 14 pairs F3: 7,9,8 # reduction candidate for 7,9 F3: 7,9 # 17 pairs * PAIR D2: 7,9 COL D D4: 7,9,6 # reduction candidate for 7,9 D4: 7,9 => CTR * 7253619488.4.2531..134..25.146..382593.5.216425.14679348165..323.28145.95..23.481 D4: 6 # 15 pairs D7: 7,9,6 # reduction candidate for 7,9 D7: 7,9 # 15 pairs * PAIR A5: 6,9 BLK 4 C4: 6,9,7 # reduction candidate for 6,9 C4: 6,9 # 17 pairs C5: 6,9,7,8 # reduction candidate for 6,9 C5: 6,9 => CTR * 7253619488.4.2531..134..25.14...3825.3.58217425814769348175..323.28145.95..23.481 C5: 7,8 # 14 pairs C6: 6,9,7,8 # reduction candidate for 6,9 C6: 6,9 # 16 pairs * PAIR A5: 6,9 ROW 5 H5: 6,9,7 # reduction candidate for 6,9 H5: 7 => CTR * 7253619488947253166134..25.14.673825.3.5921742571486934819567323728145695..237481 H5: 6,9 # 16 pairs * PAIR E4: 7,9 BLK 5 D4: 7,9,6 # reduction candidate for 7,9 D4: 7,9 => CTR * 7253619488.4.2531..134..25.146..382593.5.216425.14679348165..323.28145.95..23.481 D4: 6 # 15 pairs E5: 7,9,8 # reduction candidate for 7,9 E5: 7,9 # 17 pairs F6: 7,9,6,8 # reduction candidate for 7,9 F6: 7,9 # 18 pairs * PAIR E4: 7,9 ROW 4 C4: 7,9,6 # reduction candidate for 7,9 C4: 6 => CTR * 7253619488.4.2531..134..25.146..382593.5.216425.14679348165..323.28145.95..23.481 C4: 7,9 # 15 pairs * PAIR E4: 7,9 COL E E3: 7,9,8 # reduction candidate for 7,9 E3: 8 # 17 pairs E3: 7,9 # 14 pairs * PAIR G6: 6,7 BLK 6 H5: 6,7,9 # reduction candidate for 6,7 H5: 6,7 # 14 pairs H6: 6,7,9 # reduction candidate for 6,7 H6: 6,7 => CTR * 7253619488.4.2531.9134..25614..9382563.5.2194259148..3481.59.323.28145.959623.481 H6: 9 # 14 pairs * PAIR G6: 6,7 ROW 6 C6: 6,7,8,9 # reduction candidate for 6,7 C6: 6,7 # 19 pairs F6: 6,7,8,9 # reduction candidate for 6,7 F6: 6,7 # 18 pairs * PAIR B8: 6,7 BLK 7 B9: 6,7,9 # reduction candidate for 6,7 B9: 9 => CTR * 72536194886492531791347825614...3825.3.5.21.425.14...3481.5..32372814569596237481 B9: 6,7 # 15 pairs * PAIR C9: 6,9 BLK 7 B9: 6,9,7 # reduction candidate for 6,9 B9: 6,9 => CTR * 7253619488947253166134..25714.6.382593658217425.14.6.34819567323728145695..237481 B9: 7 => SOLVED * 725361948894725316613489257147693825938572164256148793481957632362814579579236481 * PAIR C9: 6,9 COL C C4: 6,9,7 # reduction candidate for 6,9 C4: 6,9 # 17 pairs C5: 6,9,7,8 # reduction candidate for 6,9 C5: 6,9 => CTR * 7253619488.4.2531..134..25.14...3825.3.58217425814769348175..323.28145.95..23.481 C5: 7,8 # 14 pairs C6: 6,9,7,8 # reduction candidate for 6,9 C6: 6,9 # 16 pairs * PAIR F9: 6,7 BLK 8 D7: 6,7,9 # reduction candidate for 6,7 D7: 6,7 # 15 pairs F7: 6,7,9 # reduction candidate for 6,7 F7: 6,7 => SOLVED * 725361948894725316613489257147693825938572164256148793481957632362814579579236481 F7: 9 # 15 pairs * PAIR F9: 6,7 ROW 9 B9: 6,7,9 # reduction candidate for 6,7 B9: 9 => CTR * 72536194886492531791347825614...3825.3.5.21.425.14...3481.5..32372814569596237481 B9: 6,7 # 15 pairs * PAIR F9: 6,7 COL F F6: 6,7,8,9 # reduction candidate for 6,7 F6: 6,7 # 18 pairs F6: 8,9 # 17 pairs * PAIR G7: 6,7 ROW 7 D7: 6,7,9 # reduction candidate for 6,7 D7: 6,7 # 15 pairs F7: 6,7,9 # reduction candidate for 6,7 F7: 6,7 => SOLVED * 725361948894725316613489257147693825938572164256148793481957632362814579579236481 F7: 9 # 15 pairs * PAIR H8: 6,7 COL H H5: 6,7,9 # reduction candidate for 6,7 H5: 6,7 # 14 pairs H6: 6,7,9 # reduction candidate for 6,7 H6: 6,7 => CTR * 7253619488.4.2531.9134..25614..9382563.5.2194259148..3481.59.323.28145.959623.481 H6: 9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-233-base-pr-000.dot * REASONING * DIS # B9: 6,9 => CTR => B9: 7 * PRF # B9: 7 => SOL * DIS # D4: 7,9 => CTR => D4: 6 * DIS # C5: 6,9 => CTR => C5: 7,8 * DIS # H5: 7 => CTR => H5: 6,9 * DIS # D4: 7,9 => CTR => D4: 6 * DIS # C4: 6 => CTR => C4: 7,9 * DIS # H6: 6,7 => CTR => H6: 9 * DIS # B9: 9 => CTR => B9: 6,7 * DIS # B9: 6,9 => CTR => B9: 7 * PRF # B9: 7 => SOL * DIS # C5: 6,9 => CTR => C5: 7,8 * PRF # F7: 6,7 => SOL * DIS # B9: 9 => CTR => B9: 6,7 * PRF # F7: 6,7 => SOL * DIS # H6: 6,7 => CTR => H6: 9 * CNT 16 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B2,B8,C9,D2,E4,F9,G6,G7,H8,I2,I3) * 7253619488.4.2531..134..25.14...3825.3.5.21.425.14...3481.5..323.28145.95..23.481 * PAIR B2: 6,9 COL B B9: 6,9,7 # reduction candidate for 6,9 B9: 6,9 => CTR * 7253619488947253166134..25714.6.382593658217425.14.6.34819567323728145695..237481 B9: 7 => SOLVED * 725361948894725316613489257147693825938572164256148793481957632362814579579236481 * DURATION: 0:00:03.026159 START: 10:49:30.116277 END: 10:49:33.142436 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-233-base-pr-001.dot * REASONING * DIS # B9: 6,9 => CTR => B9: 7 * PRF B9: 7 => SOL * STA B9: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 233 solution: 725361948894725316613489257147693825938572164256148793481957632362814579579236481 info: 2067 FNBWXY S8.f 37570 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 725361948894725316613489257147693825938572164256148793481957632362814579579236481 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:
* DIS # B9: 6,9 => CTR => B9: 7 * PRF # B9: 7 => SOL * INC # E3: 7,9 => UNS * INC # F3: 7,9 => UNS * DIS # D4: 7,9 => CTR => D4: 6 * INC # D4: 6 => UNS * INC # D7: 7,9 => UNS * INC # C4: 6,9 => UNS * DIS # C5: 6,9 => CTR => C5: 7,8 * INC # C5: 7,8 => UNS * INC # C6: 6,9 => UNS * INC # H5: 6,9 => UNS * DIS # H5: 7 => CTR => H5: 6,9 * DIS # D4: 7,9 => CTR => D4: 6 * INC # D4: 6 => UNS * INC # E5: 7,9 => UNS * INC # F6: 7,9 => UNS * INC # C4: 7,9 => UNS * DIS # C4: 6 => CTR => C4: 7,9 * INC # E3: 7,9 => UNS * INC # E3: 8 => UNS * INC # H5: 6,7 => UNS * DIS # H6: 6,7 => CTR => H6: 9 * INC # H6: 9 => UNS * INC # C6: 6,7 => UNS * INC # F6: 6,7 => UNS * INC # B9: 6,7 => UNS * DIS # B9: 9 => CTR => B9: 6,7 * DIS # B9: 6,9 => CTR => B9: 7 * PRF # B9: 7 => SOL * INC # C4: 6,9 => UNS * DIS # C5: 6,9 => CTR => C5: 7,8 * INC # C5: 7,8 => UNS * INC # C6: 6,9 => UNS * INC # D7: 6,7 => UNS * PRF # F7: 6,7 => SOL * INC # F7: 9 => UNS * INC # B9: 6,7 => UNS * DIS # B9: 9 => CTR => B9: 6,7 * INC # F6: 6,7 => UNS * INC # F6: 8,9 => UNS * INC # D7: 6,7 => UNS * PRF # F7: 6,7 => SOL * INC # F7: 9 => UNS * INC # H5: 6,7 => UNS * DIS # H6: 6,7 => CTR => H6: 9 * INC # H6: 9 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B9: 6,9 => CTR => B9: 7 * PRF B9: 7 => SOL * STA B9: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED