Analysis of xx-top500-379-base.sdk
Contents
Original Sudoku
level: medium
position: 7.3....8.....12............5..7...3..1..5....4.6.......8....1.5......2.....3..... initial
Autosolve
position: 7235...81....1237.1...37.525927.183.817.53.2.43692851738.27.1.5.7.18.2.32.13..7.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 4 => CTR => I2: 6,9 * PRF # G3: 4,6 => SOL * PRF # G3: 4,6 => SOL * PRF # G5: 9 => SOL * PRF # I5: 4,6 => SOL * PRF # I5: 4,6 => SOL * PRF # I2: 9 => SOL * CNT 7 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I2: 4 => CTR => I2: 6,9 * DIS I2: 6,9 # D3: 4,6 => CTR => D3: 8 * PRF I2: 6,9 + D3: 8 => SOL * STA I2: 6,9 + D3: 8 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7.3....8.....12............5..7...3..1..5....4.6.......8....1.5......2.....3..... | initial |
| 7235...81....1237.1...37.525927.183.817.53.2.43692851738.27.1.5.7.18.2.32.13..7.8 | autosolve |
| 723569481658412379149837652592741836817653924436928517384276195975184263261395748 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A2: 6,9 B3: 4,6 G1: 4,6 E4: 4,6 D5: 4,6 I4: 4,6 C7: 4,9 A8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,D5: 4.. / E4 = 4 => 0 pairs (*) / D5 = 4 => 0 pairs (X) E4,I4: 4.. / E4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) B2,C2: 5.. / B2 = 5 => 9 pairs (_) / C2 = 5 => 12 pairs (_) C8,B9: 5.. / C8 = 5 => 9 pairs (_) / B9 = 5 => 12 pairs (_) F8,F9: 5.. / F8 = 5 => 12 pairs (_) / F9 = 5 => 9 pairs (_) C8,F8: 5.. / C8 = 5 => 9 pairs (_) / F8 = 5 => 12 pairs (_) B9,F9: 5.. / B9 = 5 => 12 pairs (_) / F9 = 5 => 9 pairs (_) B2,B9: 5.. / B2 = 5 => 9 pairs (_) / B9 = 5 => 12 pairs (_) C2,C8: 5.. / C2 = 5 => 12 pairs (_) / C8 = 5 => 9 pairs (_) E4,D5: 6.. / E4 = 6 => 0 pairs (X) / D5 = 6 => 0 pairs (_) A8,B9: 6.. / A8 = 6 => 11 pairs (_) / B9 = 6 => 18 pairs (_) E4,I4: 6.. / E4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) F7,H7: 6.. / F7 = 6 => 11 pairs (_) / H7 = 6 => 11 pairs (_) A2,A8: 6.. / A2 = 6 => 18 pairs (_) / A8 = 6 => 11 pairs (_) C2,C3: 8.. / C2 = 8 => 12 pairs (_) / C3 = 8 => 11 pairs (_) D2,D3: 8.. / D2 = 8 => 11 pairs (_) / D3 = 8 => 12 pairs (_) C2,D2: 8.. / C2 = 8 => 12 pairs (_) / D2 = 8 => 11 pairs (_) C3,D3: 8.. / C3 = 8 => 11 pairs (_) / D3 = 8 => 12 pairs (_) E1,F1: 9.. / E1 = 9 => 10 pairs (_) / F1 = 9 => 11 pairs (_) I2,G3: 9.. / I2 = 9 => 0 pairs (*) / G3 = 9 => 0 pairs (X) G5,I5: 9.. / G5 = 9 => 0 pairs (*) / I5 = 9 => 0 pairs (X) C3,G3: 9.. / C3 = 9 => 0 pairs (*) / G3 = 9 => 0 pairs (X) A2,A8: 9.. / A2 = 9 => 11 pairs (_) / A8 = 9 => 18 pairs (_) E1,E9: 9.. / E1 = 9 => 10 pairs (_) / E9 = 9 => 11 pairs (_) G3,G5: 9.. / G3 = 9 => 11 pairs (_) / G5 = 9 => 0 pairs (*) I2,I5: 9.. / I2 = 9 => 0 pairs (*) / I5 = 9 => 0 pairs (X) * DURATION: 0:00:43.098030 START: 15:50:14.534354 END: 15:50:57.632384 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B3,C7,D5,E4,G1,I4) * 7235...81....1237.1...37.525927.183.817.53.2.43692851738.27.1.5.7.18.2.32.13..7.8 * PAIR A2: 6,9 ROW 2 I2: 6,9,4 # reduction candidate for 6,9 I2: 4 => CTR * 7235.4681....123741...3795259274183681765342943692851738.27.1.5.7.18.2.32.13..7.8 I2: 6,9 # 12 pairs * PAIR B3: 4,6 BLK 1 B2: 4,6,5 # reduction candidate for 4,6 B2: 4,6 # 12 pairs B2: 5 # 9 pairs * PAIR B3: 4,6 ROW 3 D3: 4,6,8 # reduction candidate for 4,6 D3: 4,6 # 11 pairs G3: 4,6,9 # reduction candidate for 4,6 G3: 4,6 => SOLVED * 723569481658412379149837652592741836817653924436928517384276195975184263261395748 G3: 9 # 11 pairs * PAIR B3: 4,6 COL B B9: 4,6,5 # reduction candidate for 4,6 B9: 5 # 12 pairs B9: 4,6 # 9 pairs * PAIR G1: 4,6 BLK 3 I2: 4,6,9 # reduction candidate for 4,6 I2: 4,6 # 11 pairs G3: 4,6,9 # reduction candidate for 4,6 G3: 4,6 => SOLVED * 723569481658412379149837652592741836817653924436928517384276195975184263261395748 G3: 9 # 11 pairs * PAIR G1: 4,6 ROW 1 E1: 4,6,9 # reduction candidate for 4,6 E1: 4,6 # 11 pairs F1: 4,6,9 # reduction candidate for 4,6 F1: 4,6 # 10 pairs * PAIR G1: 4,6 COL G G5: 4,6,9 # reduction candidate for 4,6 G5: 9 => SOLVED * 723569481658412379149837652592741836817653924436928517384276195975184263261395748 G5: 4,6 # 11 pairs * PAIR E4: 4,6 COL E E1: 4,6,9 # reduction candidate for 4,6 E1: 4,6 # 11 pairs E9: 4,6,9 # reduction candidate for 4,6 E9: 4,6 # 10 pairs * PAIR D5: 4,6 ROW 5 G5: 4,6,9 # reduction candidate for 4,6 G5: 4,6 # 11 pairs I5: 4,6,9 # reduction candidate for 4,6 I5: 4,6 => SOLVED * 723569481658412379149837652592741836817653924436928517384276195975184263261395748 I5: 9 # 11 pairs * PAIR D5: 4,6 COL D D2: 4,6,8 # reduction candidate for 4,6 D2: 4,6 # 12 pairs D3: 4,6,8 # reduction candidate for 4,6 D3: 4,6 # 11 pairs * PAIR I4: 4,6 BLK 6 G5: 4,6,9 # reduction candidate for 4,6 G5: 4,6 # 11 pairs I5: 4,6,9 # reduction candidate for 4,6 I5: 4,6 => SOLVED * 723569481658412379149837652592741836817653924436928517384276195975184263261395748 I5: 9 # 11 pairs * PAIR I4: 4,6 COL I I2: 4,6,9 # reduction candidate for 4,6 I2: 9 => SOLVED * 723569481658412379149837652592741836817653924436928517384276195975184263261395748 I2: 4,6 # 11 pairs * PAIR C7: 4,9 BLK 7 C8: 4,9,5 # reduction candidate for 4,9 C8: 4,9 # 12 pairs C8: 5 # 9 pairs * PAIR C7: 4,9 ROW 7 F7: 4,9,6 # reduction candidate for 4,9 F7: 4,9 # 11 pairs H7: 4,9,6 # reduction candidate for 4,9 H7: 4,9 # 11 pairs * PAIR C7: 4,9 COL C C2: 4,9,5,8 # reduction candidate for 4,9 C2: 4,9 # 13 pairs C3: 4,9,8 # reduction candidate for 4,9 C3: 4,9 # 12 pairs * PAIR A8: 6,9 ROW 8 F8: 6,9,4,5 # reduction candidate for 6,9 F8: 6,9 # 12 pairs H8: 6,9,4 # reduction candidate for 6,9 H8: 6,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-379-base-pr-000.dot * REASONING * DIS # I2: 4 => CTR => I2: 6,9 * PRF # G3: 4,6 => SOL * PRF # G3: 4,6 => SOL * PRF # G5: 9 => SOL * PRF # I5: 4,6 => SOL * PRF # I5: 4,6 => SOL * PRF # I2: 9 => SOL * CNT 7 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B3,C7,D5,E4,G1,I4) * 7235...81....1237.1...37.525927.183.817.53.2.43692851738.27.1.5.7.18.2.32.13..7.8 * PAIR A2: 6,9 ROW 2 I2: 6,9,4 # reduction candidate for 6,9 I2: 4 => CTR * 7235.4681....123741...3795259274183681765342943692851738.27.1.5.7.18.2.32.13..7.8 * PAIR RESTART * PAIR B3: 4,6 ROW 3 D3: 4,6,8 # reduction candidate for 4,6 D3: 4,6 => CTR * 7235..4819..812376168.379525927.183.817.5362943692851738.27.1.5.7.18.2.32.13..7.8 D3: 8 => SOLVED * 723569481658412379149837652592741836817653924436928517384276195975184263261395748 * DURATION: 0:00:03.665051 START: 15:51:32.169113 END: 15:51:35.834164 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-379-base-pr-001.dot * REASONING * DIS # I2: 4 => CTR => I2: 6,9 * DIS I2: 6,9 # D3: 4,6 => CTR => D3: 8 * PRF I2: 6,9 + D3: 8 => SOL * STA I2: 6,9 + D3: 8 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 379 solution: 723569481658412379149837652592741836817653924436928517384276195975184263261395748 info: 32792 FNBO S8.f 37319 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 723569481658412379149837652592741836817653924436928517384276195975184263261395748 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 # I2: 6,9 => UNS * DIS # I2: 4 => CTR => I2: 6,9 * INC # B2: 4,6 => UNS * INC # B2: 5 => UNS * INC # D3: 4,6 => UNS * PRF # G3: 4,6 => SOL * INC # G3: 9 => UNS * INC # B9: 4,6 => UNS * INC # B9: 5 => UNS * INC # I2: 4,6 => UNS * PRF # G3: 4,6 => SOL * INC # G3: 9 => UNS * INC # E1: 4,6 => UNS * INC # F1: 4,6 => UNS * INC # G5: 4,6 => UNS * PRF # G5: 9 => SOL * INC # E1: 4,6 => UNS * INC # E9: 4,6 => UNS * INC # G5: 4,6 => UNS * PRF # I5: 4,6 => SOL * INC # I5: 9 => UNS * INC # D2: 4,6 => UNS * INC # D3: 4,6 => UNS * INC # G5: 4,6 => UNS * PRF # I5: 4,6 => SOL * INC # I5: 9 => UNS * INC # I2: 4,6 => UNS * PRF # I2: 9 => SOL * INC # C8: 4,9 => UNS * INC # C8: 5 => UNS * INC # F7: 4,9 => UNS * INC # H7: 4,9 => UNS * INC # C2: 4,9 => UNS * INC # C3: 4,9 => UNS * INC # F8: 6,9 => UNS * INC # H8: 6,9 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I2: 6,9 => UNS * DIS # I2: 4 => CTR => I2: 6,9 * DIS I2: 6,9 # D3: 4,6 => CTR => D3: 8 * PRF I2: 6,9 + D3: 8 => SOL * STA I2: 6,9 + D3: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED