Analysis of xx-top500-137-base.sdk
Contents
Original Sudoku
level: medium
position: ...8..4...67...................17.6.....6.5..4.........9.....718..4.5......2..... initial
Autosolve
position: 1..8.64.7.6714..58.4875.1.6.8..17.647...645824.6...71.5946..2718..4756..673291845 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F3: 2,3 => SOL * PRF # B1: 2,3 => SOL * DIS # B1: 5 => CTR => B1: 2,3 * DIS # H1: 2,3 => CTR => H1: 9 * PRF # H1: 9 => SOL * DIS # H3: 3,9 => CTR => H3: 2 * PRF # F2: 3,9 => SOL * DIS # D6: 3,5 => CTR => D6: 9 * PRF # D6: 9 => SOL * PRF # B1: 3,5 => SOL * DIS # B1: 2 => CTR => B1: 3,5 * DIS # D4: 3,9 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # D6: 3,9 => SOL * DIS # D6: 5 => CTR => D6: 3,9 * PRF # A4: 3,9 => SOL * DIS # A4: 2 => CTR => A4: 3,9 * DIS # D4: 3,9 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # D6: 3,9 => SOL * DIS # D6: 5 => CTR => D6: 3,9 * DIS # H3: 3,9 => CTR => H3: 2 * CNT 22 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F3: 2,3 => SOL * STA F3: 2,3 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8..4...67...................17.6.....6.5..4.........9.....718..4.5......2..... | initial |
| 1..8.64.7.6714..58.4875.1.6.8..17.647...645824.6...71.5946..2718..4756..673291845 | autosolve |
| 135826497267149358948753126382517964719364582456982713594638271821475639673291845 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) E1: 2,3 G2: 3,9 B5: 1,3 C5: 1,9 B6: 3,5 D5: 3,9 E6: 2,8 F6: 2,8 G4: 3,9 I6: 3,9 B8: 1,2 C8: 1,2 E7: 3,8 F7: 3,8 H8: 3,9 I8: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,C5: 1.. / B5 = 1 => 0 pairs (*) / C5 = 1 => 0 pairs (X) B8,C8: 1.. / B8 = 1 => 0 pairs (X) / C8 = 1 => 0 pairs (_) B5,B8: 1.. / B5 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) C5,C8: 1.. / C5 = 1 => 0 pairs (X) / C8 = 1 => 0 pairs (_) H1,H3: 2.. / H1 = 2 => 0 pairs (X) / H3 = 2 => 19 pairs (_) A4,C4: 2.. / A4 = 2 => 0 pairs (X) / C4 = 2 => 0 pairs (_) E6,F6: 2.. / E6 = 2 => 16 pairs (_) / F6 = 2 => 0 pairs (*) B8,C8: 2.. / B8 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) A2,F2: 2.. / A2 = 2 => 0 pairs (*) / F2 = 2 => 0 pairs (X) B1,B8: 2.. / B1 = 2 => 0 pairs (X) / B8 = 2 => 0 pairs (_) E1,E6: 2.. / E1 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) G4,I6: 3.. / G4 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) E7,F7: 3.. / E7 = 3 => 0 pairs (*) / F7 = 3 => 0 pairs (X) H8,I8: 3.. / H8 = 3 => 0 pairs (*) / I8 = 3 => 0 pairs (X) B5,D5: 3.. / B5 = 3 => 0 pairs (X) / D5 = 3 => 0 pairs (_) E1,E7: 3.. / E1 = 3 => 16 pairs (_) / E7 = 3 => 0 pairs (*) G2,G4: 3.. / G2 = 3 => 0 pairs (*) / G4 = 3 => 0 pairs (X) I6,I8: 3.. / I6 = 3 => 0 pairs (*) / I8 = 3 => 0 pairs (X) B1,C1: 5.. / B1 = 5 => 0 pairs (X) / C1 = 5 => 0 pairs (_) C4,B6: 5.. / C4 = 5 => 0 pairs (X) / B6 = 5 => 0 pairs (_) D4,D6: 5.. / D4 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) C4,D4: 5.. / C4 = 5 => 0 pairs (X) / D4 = 5 => 0 pairs (_) B6,D6: 5.. / B6 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) B1,B6: 5.. / B1 = 5 => 0 pairs (X) / B6 = 5 => 0 pairs (_) C1,C4: 5.. / C1 = 5 => 0 pairs (*) / C4 = 5 => 0 pairs (X) E6,F6: 8.. / E6 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) E7,F7: 8.. / E7 = 8 => 16 pairs (_) / F7 = 8 => 0 pairs (*) E6,E7: 8.. / E6 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) F6,F7: 8.. / F6 = 8 => 16 pairs (_) / F7 = 8 => 0 pairs (*) F2,F3: 9.. / F2 = 9 => 0 pairs (*) / F3 = 9 => 0 pairs (X) G4,I6: 9.. / G4 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) H8,I8: 9.. / H8 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) C1,H1: 9.. / C1 = 9 => 0 pairs (X) / H1 = 9 => 0 pairs (_) C5,D5: 9.. / C5 = 9 => 0 pairs (*) / D5 = 9 => 0 pairs (X) D6,I6: 9.. / D6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) G2,G4: 9.. / G2 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) I6,I8: 9.. / I6 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) * DURATION: 0:01:01.380716 START: 07:25:19.188939 END: 07:26:20.569655 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B6,B8,C5,C8,D5,E1,E6,E7,F6,F7,G2,G4,H8,I6,I8) * 1..8.64.7.6714..58.4875.1.6.8..17.647...645824.6...71.5946..2718..4756..673291845 * PAIR E1: 2,3 BLK 2 F2: 2,3,9 # reduction candidate for 2,3 F2: 2,3 # 19 pairs F3: 2,3,9 # reduction candidate for 2,3 F3: 2,3 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 F3: 9 # 19 pairs * PAIR E1: 2,3 ROW 1 B1: 2,3,5 # reduction candidate for 2,3 B1: 2,3 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 B1: 5 => CTR * 15.8.64.7.6714..58.4875.1.6.85.17.647...645824365..7195946..271821475693673291845 H1: 2,3,9 # reduction candidate for 2,3 H1: 2,3 => CTR * 1.98.64.7.6714..58.4875.1.698..17.647...645824.6...71.5946..2718..4756..673291845 H1: 9 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 * PAIR G2: 3,9 BLK 3 H1: 3,9,2 # reduction candidate for 3,9 H1: 3,9 # 19 pairs H3: 3,9,2 # reduction candidate for 3,9 H3: 3,9 => CTR * 1.98.6427.6714..58.4875.1.6.8..17.647...645824.6.2871.5946832718214756..673291845 H3: 2 # 19 pairs * PAIR G2: 3,9 ROW 2 A2: 3,9,2 # reduction candidate for 3,9 A2: 3,9 # 17 pairs F2: 3,9,2 # reduction candidate for 3,9 F2: 3,9 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 F2: 2 # 17 pairs * PAIR B6: 3,5 ROW 6 D6: 3,5,9 # reduction candidate for 3,5 D6: 3,5 => CTR * 1.98.64.7.6714.958.487591.698..17.647...645824.6...7195946..2718..475693673291845 D6: 9 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 * PAIR B6: 3,5 COL B B1: 3,5,2 # reduction candidate for 3,5 B1: 3,5 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 B1: 2 => CTR * 125836497.6714235834875912628..17.647...645824.6...71.5946..2718..4756..673291845 * PAIR D5: 3,9 BLK 5 D4: 3,9,5 # reduction candidate for 3,9 D4: 3,9 => CTR * 1598.64.7.6714.958.487591.6.85.17.647...645824365..7195946..2718..475693673291845 D4: 5 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 D6: 3,9,5 # reduction candidate for 3,9 D6: 3,9 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 D6: 5 => CTR * 1598.64.7.6714.958.487591.698..17.647...645824.65..7195946..2718..475693673291845 * PAIR G4: 3,9 ROW 4 A4: 3,9,2 # reduction candidate for 3,9 A4: 3,9 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 A4: 2 => CTR * 1..83649796714235834875912628.31796473..645824.6.2871.5946832718..4756..673291845 D4: 3,9,5 # reduction candidate for 3,9 D4: 3,9 => CTR * 1598.64.7.6714.958.487591.6.85.17.647...645824365..7195946..2718..475693673291845 D4: 5 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 * PAIR I6: 3,9 ROW 6 D6: 3,9,5 # reduction candidate for 3,9 D6: 3,9 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 D6: 5 => CTR * 1598.64.7.6714.958.487591.698..17.647...645824.65..7195946..2718..475693673291845 * PAIR H8: 3,9 COL H H1: 3,9,2 # reduction candidate for 3,9 H1: 3,9 # 19 pairs H3: 3,9,2 # reduction candidate for 3,9 H3: 3,9 => CTR * 1.98.6427.6714..58.4875.1.6.8..17.647...645824.6.2871.5946832718214756..673291845 H3: 2 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-137-base-pr-000.dot * REASONING * PRF # F3: 2,3 => SOL * PRF # B1: 2,3 => SOL * DIS # B1: 5 => CTR => B1: 2,3 * DIS # H1: 2,3 => CTR => H1: 9 * PRF # H1: 9 => SOL * DIS # H3: 3,9 => CTR => H3: 2 * PRF # F2: 3,9 => SOL * DIS # D6: 3,5 => CTR => D6: 9 * PRF # D6: 9 => SOL * PRF # B1: 3,5 => SOL * DIS # B1: 2 => CTR => B1: 3,5 * DIS # D4: 3,9 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # D6: 3,9 => SOL * DIS # D6: 5 => CTR => D6: 3,9 * PRF # A4: 3,9 => SOL * DIS # A4: 2 => CTR => A4: 3,9 * DIS # D4: 3,9 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # D6: 3,9 => SOL * DIS # D6: 5 => CTR => D6: 3,9 * DIS # H3: 3,9 => CTR => H3: 2 * CNT 22 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B6,B8,C5,C8,D5,E1,E6,E7,F6,F7,G2,G4,H8,I6,I8) * 1..8.64.7.6714..58.4875.1.6.8..17.647...645824.6...71.5946..2718..4756..673291845 * PAIR E1: 2,3 BLK 2 F2: 2,3,9 # reduction candidate for 2,3 F2: 2,3 # 19 pairs F3: 2,3,9 # reduction candidate for 2,3 F3: 2,3 => SOLVED * 135826497267149358948753126382517964719364582456982713594638271821475639673291845 * DURATION: 0:00:02.823219 START: 07:26:52.450636 END: 07:26:55.273855 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-137-base-pr-001.dot * REASONING * PRF # F3: 2,3 => SOL * STA F3: 2,3 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 137 solution: 135826497267149358948753126382517964719364582456982713594638271821475639673291845 info: 1813 FNBWY S8.f 12183 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 135826497267149358948753126382517964719364582456982713594638271821475639673291845 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 # F2: 2,3 => UNS * PRF # F3: 2,3 => SOL * INC # F3: 9 => UNS * PRF # B1: 2,3 => SOL * DIS # B1: 5 => CTR => B1: 2,3 * DIS # H1: 2,3 => CTR => H1: 9 * PRF # H1: 9 => SOL * INC # H1: 3,9 => UNS * DIS # H3: 3,9 => CTR => H3: 2 * INC # H3: 2 => UNS * INC # A2: 3,9 => UNS * PRF # F2: 3,9 => SOL * INC # F2: 2 => UNS * DIS # D6: 3,5 => CTR => D6: 9 * PRF # D6: 9 => SOL * PRF # B1: 3,5 => SOL * DIS # B1: 2 => CTR => B1: 3,5 * DIS # D4: 3,9 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # D6: 3,9 => SOL * DIS # D6: 5 => CTR => D6: 3,9 * PRF # A4: 3,9 => SOL * DIS # A4: 2 => CTR => A4: 3,9 * DIS # D4: 3,9 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # D6: 3,9 => SOL * DIS # D6: 5 => CTR => D6: 3,9 * INC # H1: 3,9 => UNS * DIS # H3: 3,9 => CTR => H3: 2 * INC # H3: 2 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F2: 2,3 => UNS * PRF # F3: 2,3 => SOL * STA F3: 2,3 * CNT 2 HDP CHAINS / 2 HYP OPENED