Analysis of xx-top500-151-base.sdk
Contents
Original Sudoku
level: medium
position: 4.73...........1..6........21....5.....48.......7..........2.47.5..6...........3. initial
Autosolve
position: 4.7316.5.....47163631.5.7.4214693578.7.48.3..3..72.4..1..532.47753.64....4217.635 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D3: 8,9 => SOL * PRF # H3: 2 => SOL * DIS # G1: 2,9 => CTR => G1: 8 * PRF # G1: 8 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 8 => CTR => H3: 2,9 * PRF # B1: 2,9 => SOL * DIS # B1: 8 => CTR => B1: 2,9 * DIS # I8: 2,9 => CTR => I8: 1 * PRF # C6: 5,9 => SOL * DIS # A2: 5,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * DIS # H8: 1,9 => CTR => H8: 2,8 * DIS # A2: 5 => CTR => A2: 8,9 * DIS # G8: 8,9 => CTR => G8: 2 * PRF # D3: 8,9 => SOL * DIS # G8: 8,9 => CTR => G8: 2 * DIS # G1: 2 => CTR => G1: 8,9 * CNT 18 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D3: 8,9 => SOL * STA D3: 8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.73...........1..6........21....5.....48.......7..........2.47.5..6...........3. | initial |
| 4.7316.5.....47163631.5.7.4214693578.7.48.3..3..72.4..1..532.47753.64....4217.635 | autosolve |
| 427316859895247163631859724214693578576481392389725416168532947753964281942178635 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) F3: 8,9 I1: 2,9 A5: 5,9 F5: 1,5 F6: 1,5 H6: 1,9 A9: 8,9 D8: 8,9 F9: 8,9 G7: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F5,F6: 1.. / F5 = 1 => 9 pairs (_) / F6 = 1 => 0 pairs (X) H8,I8: 1.. / H8 = 1 => 0 pairs (X) / I8 = 1 => 11 pairs (_) B1,B2: 2.. / B1 = 2 => 0 pairs (*) / B2 = 2 => 0 pairs (X) D2,D3: 2.. / D2 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) H5,I5: 2.. / H5 = 2 => 13 pairs (_) / I5 = 2 => 17 pairs (_) B2,D2: 2.. / B2 = 2 => 13 pairs (_) / D2 = 2 => 0 pairs (*) D3,H3: 2.. / D3 = 2 => 13 pairs (_) / H3 = 2 => 0 pairs (*) G1,G8: 2.. / G1 = 2 => 0 pairs (X) / G8 = 2 => 12 pairs (_) A2,C2: 5.. / A2 = 5 => 0 pairs (X) / C2 = 5 => 10 pairs (_) F5,F6: 5.. / F5 = 5 => 0 pairs (X) / F6 = 5 => 9 pairs (_) C6,F6: 5.. / C6 = 5 => 0 pairs (X) / F6 = 5 => 9 pairs (_) A2,A5: 5.. / A2 = 5 => 0 pairs (X) / A5 = 5 => 10 pairs (_) I5,I6: 6.. / I5 = 6 => 15 pairs (_) / I6 = 6 => 12 pairs (_) B7,C7: 6.. / B7 = 6 => 12 pairs (_) / C7 = 6 => 15 pairs (_) C5,I5: 6.. / C5 = 6 => 12 pairs (_) / I5 = 6 => 15 pairs (_) B6,B7: 6.. / B6 = 6 => 15 pairs (_) / B7 = 6 => 12 pairs (_) G1,H3: 8.. / G1 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) B6,C6: 8.. / B6 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) D8,F9: 8.. / D8 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) B1,G1: 8.. / B1 = 8 => 0 pairs (X) / G1 = 8 => 0 pairs (_) A9,F9: 8.. / A9 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) A2,A9: 8.. / A2 = 8 => 0 pairs (*) / A9 = 8 => 0 pairs (X) F3,F9: 8.. / F3 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) H3,H8: 8.. / H3 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) D8,F9: 9.. / D8 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) A9,F9: 9.. / A9 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) F3,F9: 9.. / F3 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) * DURATION: 0:00:47.129618 START: 07:55:01.661312 END: 07:55:48.790930 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,D8,F3,F5,F6,F9,G7,H6,I1) * 4.7316.5.....47163631.5.7.4214693578.7.48.3..3..72.4..1..532.47753.64....4217.635 * PAIR F3: 8,9 BLK 2 D2: 8,9,2 # reduction candidate for 8,9 D2: 8,9 # 13 pairs D3: 8,9,2 # reduction candidate for 8,9 D3: 8,9 => SOLVED * 427316859895247163631859724214693578576481392389725416168532947753964281942178635 D3: 2 # 13 pairs * PAIR F3: 8,9 ROW 3 H3: 8,9,2 # reduction candidate for 8,9 H3: 2 => SOLVED * 427316859895247163631859724214693578576481392389725416168532947753964281942178635 H3: 8,9 # 13 pairs * PAIR I1: 2,9 BLK 3 G1: 2,9,8 # reduction candidate for 2,9 G1: 2,9 => CTR * 487316.5..2.847163631259784214693578.7.48.3..3.87254..1..53284775396421..4217.635 G1: 8 => SOLVED * 427316859895247163631859724214693578576481392389725416168532947753964281942178635 H3: 2,9,8 # reduction candidate for 2,9 H3: 2,9 => SOLVED * 427316859895247163631859724214693578576481392389725416168532947753964281942178635 H3: 8 => CTR * 4873162595...47163631259784214693578.7.48.3..3..72.4..1..532.477539648..942178635 * PAIR I1: 2,9 ROW 1 B1: 2,9,8 # reduction candidate for 2,9 B1: 2,9 => SOLVED * 427316859895247163631859724214693578576481392389725416168532947753964281942178635 B1: 8 => CTR * 487316.5..2.847163631259784214693578.7.48.3..3.87254..1..53284775396421..4217.635 * PAIR I1: 2,9 COL I I5: 2,9,1,6 # reduction candidate for 2,9 I5: 2,9 # 13 pairs I8: 2,9,1 # reduction candidate for 2,9 I8: 2,9 => CTR * 487316.5..2.847163631259784214693578.7.48.32.36872.49.1..532.47753.64.1..42178635 I8: 1 # 11 pairs * PAIR A5: 5,9 BLK 4 C5: 5,9,6 # reduction candidate for 5,9 C5: 5,9 # 15 pairs C6: 5,9,6,8 # reduction candidate for 5,9 C6: 5,9 => SOLVED * 427316859895247163631859724214693578576481392389725416168532947753964281942178635 C6: 6,8 # 10 pairs * PAIR A5: 5,9 COL A A2: 5,9,8 # reduction candidate for 5,9 A2: 5,9 => CTR * 4.7316.5.....47163631.587.4214693578.7.48.3..3..72.4..1..532847753864...842179635 A2: 8 => SOLVED * 427316859895247163631859724214693578576481392389725416168532947753964281942178635 * PAIR H6: 1,9 BLK 6 H5: 1,9,2 # reduction candidate for 1,9 H5: 1,9 # 17 pairs I5: 1,9,2,6 # reduction candidate for 1,9 I5: 1,9 # 16 pairs I6: 1,9,6 # reduction candidate for 1,9 I6: 1,9 # 15 pairs * PAIR H6: 1,9 COL H H8: 1,9,2,8 # reduction candidate for 1,9 H8: 1,9 => CTR * 487316.5..2.847163631259784214693578.7.48.32.3.87254..1..53284775396421..42178635 H8: 2,8 # 13 pairs * PAIR A9: 8,9 BLK 7 B7: 8,9,6 # reduction candidate for 8,9 B7: 8,9 # 15 pairs C7: 8,9,6 # reduction candidate for 8,9 C7: 8,9 # 12 pairs * PAIR A9: 8,9 COL A A2: 8,9,5 # reduction candidate for 8,9 A2: 5 => CTR * 4.7316.5.5...47163631.587.421469357897.48.3..3..72.4..1..532847753864...842179635 A2: 8,9 # 10 pairs * PAIR D8: 8,9 ROW 8 G8: 8,9,2 # reduction candidate for 8,9 G8: 8,9 => CTR * 48731625952..47163631259784214693578.7.48.3..3..72.4..1..532.477539648..942178635 G8: 2 # 12 pairs H8: 8,9,1,2 # reduction candidate for 8,9 H8: 8,9 # 13 pairs * PAIR D8: 8,9 COL D D2: 8,9,2 # reduction candidate for 8,9 D2: 8,9 # 13 pairs D3: 8,9,2 # reduction candidate for 8,9 D3: 8,9 => SOLVED * 427316859895247163631859724214693578576481392389725416168532947753964281942178635 D3: 2 # 13 pairs * PAIR G7: 8,9 BLK 9 G8: 8,9,2 # reduction candidate for 8,9 G8: 8,9 => CTR * 48731625952..47163631259784214693578.7.48.3..3..72.4..1..532.477539648..942178635 G8: 2 # 12 pairs H8: 8,9,1,2 # reduction candidate for 8,9 H8: 8,9 # 13 pairs * PAIR G7: 8,9 ROW 7 B7: 8,9,6 # reduction candidate for 8,9 B7: 8,9 # 15 pairs C7: 8,9,6 # reduction candidate for 8,9 C7: 8,9 # 12 pairs * PAIR G7: 8,9 COL G G1: 8,9,2 # reduction candidate for 8,9 G1: 2 => CTR * 487316259.2.847163631259784214693578.7.48.3..3.87254..1..532847753964....4217.635 G1: 8,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-151-base-pr-000.dot * REASONING * PRF # D3: 8,9 => SOL * PRF # H3: 2 => SOL * DIS # G1: 2,9 => CTR => G1: 8 * PRF # G1: 8 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 8 => CTR => H3: 2,9 * PRF # B1: 2,9 => SOL * DIS # B1: 8 => CTR => B1: 2,9 * DIS # I8: 2,9 => CTR => I8: 1 * PRF # C6: 5,9 => SOL * DIS # A2: 5,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * DIS # H8: 1,9 => CTR => H8: 2,8 * DIS # A2: 5 => CTR => A2: 8,9 * DIS # G8: 8,9 => CTR => G8: 2 * PRF # D3: 8,9 => SOL * DIS # G8: 8,9 => CTR => G8: 2 * DIS # G1: 2 => CTR => G1: 8,9 * CNT 18 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,D8,F3,F5,F6,F9,G7,H6,I1) * 4.7316.5.....47163631.5.7.4214693578.7.48.3..3..72.4..1..532.47753.64....4217.635 * PAIR F3: 8,9 BLK 2 D2: 8,9,2 # reduction candidate for 8,9 D2: 8,9 # 13 pairs D3: 8,9,2 # reduction candidate for 8,9 D3: 8,9 => SOLVED * 427316859895247163631859724214693578576481392389725416168532947753964281942178635 * DURATION: 0:00:02.985276 START: 07:56:32.988977 END: 07:56:35.974253 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-151-base-pr-001.dot * REASONING * PRF # D3: 8,9 => SOL * STA D3: 8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 151 solution: 427316859895247163631859724214693578576481392389725416168532947753964281942178635 info: 1816 FNBWX S8.f 39334 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 427316859895247163631859724214693578576481392389725416168532947753964281942178635 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 # D2: 8,9 => UNS * PRF # D3: 8,9 => SOL * INC # D3: 2 => UNS * INC # H3: 8,9 => UNS * PRF # H3: 2 => SOL * DIS # G1: 2,9 => CTR => G1: 8 * PRF # G1: 8 => SOL * PRF # H3: 2,9 => SOL * DIS # H3: 8 => CTR => H3: 2,9 * PRF # B1: 2,9 => SOL * DIS # B1: 8 => CTR => B1: 2,9 * INC # I5: 2,9 => UNS * DIS # I8: 2,9 => CTR => I8: 1 * INC # I8: 1 => UNS * INC # C5: 5,9 => UNS * PRF # C6: 5,9 => SOL * INC # C6: 6,8 => UNS * DIS # A2: 5,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * INC # H5: 1,9 => UNS * INC # I5: 1,9 => UNS * INC # I6: 1,9 => UNS * DIS # H8: 1,9 => CTR => H8: 2,8 * INC # H8: 2,8 => UNS * INC # B7: 8,9 => UNS * INC # C7: 8,9 => UNS * INC # A2: 8,9 => UNS * DIS # A2: 5 => CTR => A2: 8,9 * DIS # G8: 8,9 => CTR => G8: 2 * INC # G8: 2 => UNS * INC # H8: 8,9 => UNS * INC # D2: 8,9 => UNS * PRF # D3: 8,9 => SOL * INC # D3: 2 => UNS * DIS # G8: 8,9 => CTR => G8: 2 * INC # G8: 2 => UNS * INC # H8: 8,9 => UNS * INC # B7: 8,9 => UNS * INC # C7: 8,9 => UNS * INC # G1: 8,9 => UNS * DIS # G1: 2 => CTR => G1: 8,9 * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 8,9 => UNS * PRF # D3: 8,9 => SOL * STA D3: 8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED