Analysis of xx-top500-494-base.sdk
Contents
Original Sudoku
level: medium
position: .6.41..7.......3.....6.....2...53....7.....6.........13.5...2..8..7.............. initial
Autosolve
position: 963412875.825..3.675.638..22.6.537...7.2...63.3.....213.5...2.78..7.563.6.73...5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H3: 1,4 => CTR => H3: 9 * PRF # C8: 9 => SOL * DIS # H3: 1,4 => CTR => H3: 9 * PRF # G6: 9 => SOL * DIS # B4: 4 => CTR => B4: 1,9 * PRF # C6: 4 => SOL * DIS # D7: 1 => CTR => D7: 8,9 * DIS # G6: 4 => CTR => G6: 5,9 * DIS # B8: 4,9 => CTR => B8: 1,2 * DIS # B9: 4,9 => CTR => B9: 2 * DIS # B4: 1 => CTR => B4: 4,9 * DIS # G9: 4,9 => CTR => G9: 1 * DIS # B8: 4,9 => CTR => B8: 1,2 * DIS # E8: 4,9 => CTR => E8: 2 * CNT 14 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 # H3: 1,4 => CTR => H3: 9 * PRF H3: 9 # C8: 9 => SOL * STA H3: 9 + C8: 9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.41..7.......3.....6.....2...53....7.....6.........13.5...2..8..7.............. | initial |
| 963412875.825..3.675.638..22.6.537...7.2...63.3.....213.5...2.78..7.563.6.73...5. | autosolve |
| 963412875482597316751638492296153748178249563534876921345961287819725634627384159 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A2: 1,4 C3: 1,4 E2: 7,9 F2: 7,9 H2: 1,4 A5: 1,5 A6: 4,5 D4: 1,9 D6: 8,9 E6: 6,7 F6: 6,7 G5: 5,9 B7: 4,9 I8: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,C3: 1.. / A2 = 1 => 0 pairs (X) / C3 = 1 => 15 pairs (_) D4,F5: 1.. / D4 = 1 => 17 pairs (_) / F5 = 1 => 0 pairs (X) B8,C8: 1.. / B8 = 1 => 17 pairs (_) / C8 = 1 => 0 pairs (X) H7,G9: 1.. / H7 = 1 => 0 pairs (X) / G9 = 1 => 16 pairs (_) A2,H2: 1.. / A2 = 1 => 0 pairs (X) / H2 = 1 => 15 pairs (_) B4,D4: 1.. / B4 = 1 => 0 pairs (X) / D4 = 1 => 17 pairs (_) F9,G9: 1.. / F9 = 1 => 0 pairs (X) / G9 = 1 => 16 pairs (_) A2,A5: 1.. / A2 = 1 => 0 pairs (X) / A5 = 1 => 15 pairs (_) B4,B8: 1.. / B4 = 1 => 0 pairs (X) / B8 = 1 => 17 pairs (_) D4,D7: 1.. / D4 = 1 => 17 pairs (_) / D7 = 1 => 0 pairs (X) G3,G9: 1.. / G3 = 1 => 0 pairs (X) / G9 = 1 => 16 pairs (_) B8,B9: 2.. / B8 = 2 => 0 pairs (X) / B9 = 2 => 14 pairs (_) E8,E9: 2.. / E8 = 2 => 14 pairs (_) / E9 = 2 => 0 pairs (X) B8,E8: 2.. / B8 = 2 => 0 pairs (X) / E8 = 2 => 14 pairs (_) B9,E9: 2.. / B9 = 2 => 14 pairs (_) / E9 = 2 => 0 pairs (X) A2,C3: 4.. / A2 = 4 => 15 pairs (_) / C3 = 4 => 0 pairs (X) E5,F5: 4.. / E5 = 4 => 17 pairs (_) / F5 = 4 => 18 pairs (_) A2,H2: 4.. / A2 = 4 => 15 pairs (_) / H2 = 4 => 0 pairs (X) A2,A6: 4.. / A2 = 4 => 15 pairs (_) / A6 = 4 => 0 pairs (X) A5,A6: 5.. / A5 = 5 => 0 pairs (X) / A6 = 5 => 15 pairs (_) G5,G6: 5.. / G5 = 5 => 15 pairs (_) / G6 = 5 => 0 pairs (X) A5,G5: 5.. / A5 = 5 => 0 pairs (X) / G5 = 5 => 15 pairs (_) A6,G6: 5.. / A6 = 5 => 15 pairs (_) / G6 = 5 => 0 pairs (X) E6,F6: 6.. / E6 = 6 => 12 pairs (_) / F6 = 6 => 12 pairs (_) E7,F7: 6.. / E7 = 6 => 12 pairs (_) / F7 = 6 => 12 pairs (_) E6,E7: 6.. / E6 = 6 => 12 pairs (_) / E7 = 6 => 12 pairs (_) F6,F7: 6.. / F6 = 6 => 12 pairs (_) / F7 = 6 => 12 pairs (_) E2,F2: 7.. / E2 = 7 => 12 pairs (_) / F2 = 7 => 12 pairs (_) E6,F6: 7.. / E6 = 7 => 12 pairs (_) / F6 = 7 => 12 pairs (_) E2,E6: 7.. / E2 = 7 => 12 pairs (_) / E6 = 7 => 12 pairs (_) F2,F6: 7.. / F2 = 7 => 12 pairs (_) / F6 = 7 => 12 pairs (_) C5,C6: 8.. / C5 = 8 => 16 pairs (_) / C6 = 8 => 19 pairs (_) E5,D6: 8.. / E5 = 8 => 19 pairs (_) / D6 = 8 => 16 pairs (_) H4,I4: 8.. / H4 = 8 => 15 pairs (_) / I4 = 8 => 20 pairs (_) H7,I9: 8.. / H7 = 8 => 20 pairs (_) / I9 = 8 => 15 pairs (_) C5,E5: 8.. / C5 = 8 => 16 pairs (_) / E5 = 8 => 19 pairs (_) C6,D6: 8.. / C6 = 8 => 19 pairs (_) / D6 = 8 => 16 pairs (_) E9,I9: 8.. / E9 = 8 => 20 pairs (_) / I9 = 8 => 15 pairs (_) D6,D7: 8.. / D6 = 8 => 16 pairs (_) / D7 = 8 => 19 pairs (_) H4,H7: 8.. / H4 = 8 => 15 pairs (_) / H7 = 8 => 20 pairs (_) I4,I9: 8.. / I4 = 8 => 20 pairs (_) / I9 = 8 => 15 pairs (_) E2,F2: 9.. / E2 = 9 => 12 pairs (_) / F2 = 9 => 12 pairs (_) G3,H3: 9.. / G3 = 9 => 0 pairs (X) / H3 = 9 => 16 pairs (_) * DURATION: 0:01:19.059883 START: 19:32:42.104480 END: 19:34:01.164363 2017-05-04 * CP COUNT: (43) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A6,B7,C3,D4,D6,E2,E6,F2,F6,G5,H2,I8) * 963412875.825..3.675.638..22.6.537...7.2...63.3.....213.5...2.78..7.563.6.73...5. * PAIR C3: 1,4 ROW 3 G3: 1,4,9 # reduction candidate for 1,4 G3: 1,4 # 16 pairs H3: 1,4,9 # reduction candidate for 1,4 H3: 1,4 => CTR * 9634128754825..3167516389422461537..17.2..56353....4213958..2.78..7.563.6.73..15. H3: 9 # 16 pairs * PAIR C3: 1,4 COL C C8: 1,4,9 # reduction candidate for 1,4 C8: 9 => SOLVED * 963412875482597316751638492296153748178249563534876921345961287819725634627384159 C8: 1,4 # 19 pairs * PAIR H2: 1,4 BLK 3 G3: 1,4,9 # reduction candidate for 1,4 G3: 1,4 # 16 pairs H3: 1,4,9 # reduction candidate for 1,4 H3: 1,4 => CTR * 9634128754825..3167516389422461537..17.2..56353....4213958..2.78..7.563.6.73..15. H3: 9 # 16 pairs * PAIR H2: 1,4 COL H H7: 1,4,8,9 # reduction candidate for 1,4 H7: 8,9 # 18 pairs H7: 1,4 # 17 pairs * PAIR A6: 4,5 ROW 6 G6: 4,5,9 # reduction candidate for 4,5 G6: 9 => SOLVED * 963412875482597316751638492296153748178249563534876921345961287819725634627384159 G6: 4,5 # 16 pairs * PAIR D4: 1,9 BLK 5 F5: 1,9,4 # reduction candidate for 1,9 F5: 4 # 18 pairs F5: 1,9 # 17 pairs * PAIR D4: 1,9 ROW 4 B4: 1,9,4 # reduction candidate for 1,9 B4: 4 => CTR * 963412875.825..3.675.638..22461537...7.2...6353....4213958..2.78147256396.73...5. B4: 1,9 # 21 pairs * PAIR D4: 1,9 COL D D7: 1,9,8 # reduction candidate for 1,9 D7: 8 # 19 pairs D7: 1,9 # 16 pairs * PAIR D6: 8,9 BLK 5 E5: 8,9,4 # reduction candidate for 8,9 E5: 8,9 # 18 pairs E5: 4 # 17 pairs * PAIR D6: 8,9 ROW 6 C6: 8,9,4 # reduction candidate for 8,9 C6: 4 => SOLVED * 963412875482597316751638492296153748178249563534876921345961287819725634627384159 C6: 8,9 # 16 pairs * PAIR D6: 8,9 COL D D7: 8,9,1 # reduction candidate for 8,9 D7: 1 => CTR * 963412875.825..3.675.638..22169537..5782419634398..5213.51..2.78.17.563.6.73..15. D7: 8,9 # 17 pairs * PAIR G5: 5,9 BLK 6 G6: 5,9,4 # reduction candidate for 5,9 G6: 4 => CTR * 9634128754825..3167516389422461537..17.2..56353....4213958..2.78..7.563.6.73...5. G6: 5,9 # 21 pairs * PAIR B7: 4,9 BLK 7 B8: 4,9,1,2 # reduction candidate for 4,9 B8: 4,9 => CTR * 963412875.825..3.675.638..22169537..57.2.19634398..5213.51..2.78.172563.6273..15. B8: 1,2 # 15 pairs C8: 4,9,1 # reduction candidate for 4,9 C8: 4,9 # 17 pairs B9: 4,9,2 # reduction candidate for 4,9 B9: 4,9 => CTR * 9634128751825..346754638..221695378457.2.1963.3.....213.5...2.78217.563.6.732..58 B9: 2 # 14 pairs * PAIR B7: 4,9 ROW 7 E7: 4,9,6,8 # reduction candidate for 4,9 E7: 4,9 # 16 pairs F7: 4,9,1,6 # reduction candidate for 4,9 F7: 4,9 # 16 pairs H7: 4,9,1,8 # reduction candidate for 4,9 H7: 4,9 # 23 pairs * PAIR B7: 4,9 COL B B4: 4,9,1 # reduction candidate for 4,9 B4: 1 => CTR * 963412875.825..3.675.638..22169537..57.2.19634398..5213.51..2.78.17.563.6.73..15. B4: 4,9 # 17 pairs * PAIR I8: 4,9 BLK 9 H7: 4,9,1,8 # reduction candidate for 4,9 H7: 4,9 # 23 pairs G9: 4,9,1 # reduction candidate for 4,9 G9: 4,9 => CTR * 9634128751825..3467546381922.615378.5712849634389..5213.58..2178197256346.73.1.58 G9: 1 # 16 pairs I9: 4,9,8 # reduction candidate for 4,9 I9: 4,9 # 20 pairs * PAIR I8: 4,9 ROW 8 B8: 4,9,1,2 # reduction candidate for 4,9 B8: 4,9 => CTR * 963412875.825..3.675.638..22169537..57.2.19634398..5213.51..2.78.172563.6273..15. B8: 1,2 # 15 pairs C8: 4,9,1 # reduction candidate for 4,9 C8: 4,9 # 17 pairs E8: 4,9,2 # reduction candidate for 4,9 E8: 4,9 => CTR * 9634128751825..346754638..221695378457.2.1963.3.....213.5...2.78217.563.6.732..58 E8: 2 # 14 pairs * PAIR I8: 4,9 COL I I4: 4,9,8 # reduction candidate for 4,9 I4: 8 # 20 pairs I4: 4,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-494-base-pr-000.dot * REASONING * DIS # H3: 1,4 => CTR => H3: 9 * PRF # C8: 9 => SOL * DIS # H3: 1,4 => CTR => H3: 9 * PRF # G6: 9 => SOL * DIS # B4: 4 => CTR => B4: 1,9 * PRF # C6: 4 => SOL * DIS # D7: 1 => CTR => D7: 8,9 * DIS # G6: 4 => CTR => G6: 5,9 * DIS # B8: 4,9 => CTR => B8: 1,2 * DIS # B9: 4,9 => CTR => B9: 2 * DIS # B4: 1 => CTR => B4: 4,9 * DIS # G9: 4,9 => CTR => G9: 1 * DIS # B8: 4,9 => CTR => B8: 1,2 * DIS # E8: 4,9 => CTR => E8: 2 * CNT 14 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A6,B7,C3,D4,D6,E2,E6,F2,F6,G5,H2,I8) * 963412875.825..3.675.638..22.6.537...7.2...63.3.....213.5...2.78..7.563.6.73...5. * PAIR C3: 1,4 ROW 3 G3: 1,4,9 # reduction candidate for 1,4 G3: 1,4 # 16 pairs H3: 1,4,9 # reduction candidate for 1,4 H3: 1,4 => CTR * 9634128754825..3167516389422461537..17.2..56353....4213958..2.78..7.563.6.73..15. * RESTART * PAIR C3: 1,4 COL C C8: 1,4,9 # reduction candidate for 1,4 C8: 9 => SOLVED * 963412875482597316751638492296153748178249563534876921345961287819725634627384159 * DURATION: 0:00:05.216425 START: 19:34:47.777368 END: 19:34:52.993793 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-494-base-pr-001.dot * REASONING * DIS # H3: 1,4 => CTR => H3: 9 * PRF H3: 9 # C8: 9 => SOL * STA H3: 9 + C8: 9 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 494 solution: 963412875482597316751638492296153748178249563534876921345961287819725634627384159 info: 96272 FNBHYK S8.f 21504 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 963412875482597316751638492296153748178249563534876921345961287819725634627384159 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 # G3: 1,4 => UNS * DIS # H3: 1,4 => CTR => H3: 9 * INC # H3: 9 => UNS * INC # C8: 1,4 => UNS * PRF # C8: 9 => SOL * INC # G3: 1,4 => UNS * DIS # H3: 1,4 => CTR => H3: 9 * INC # H3: 9 => UNS * INC # H7: 1,4 => UNS * INC # H7: 8,9 => UNS * INC # G6: 4,5 => UNS * PRF # G6: 9 => SOL * INC # F5: 1,9 => UNS * INC # F5: 4 => UNS * INC # B4: 1,9 => UNS * DIS # B4: 4 => CTR => B4: 1,9 * INC # D7: 1,9 => UNS * INC # D7: 8 => UNS * INC # E5: 8,9 => UNS * INC # E5: 4 => UNS * INC # C6: 8,9 => UNS * PRF # C6: 4 => SOL * INC # D7: 8,9 => UNS * DIS # D7: 1 => CTR => D7: 8,9 * INC # G6: 5,9 => UNS * DIS # G6: 4 => CTR => G6: 5,9 * DIS # B8: 4,9 => CTR => B8: 1,2 * INC # B8: 1,2 => UNS * INC # C8: 4,9 => UNS * DIS # B9: 4,9 => CTR => B9: 2 * INC # B9: 2 => UNS * INC # E7: 4,9 => UNS * INC # F7: 4,9 => UNS * INC # H7: 4,9 => UNS * INC # B4: 4,9 => UNS * DIS # B4: 1 => CTR => B4: 4,9 * INC # H7: 4,9 => UNS * DIS # G9: 4,9 => CTR => G9: 1 * INC # G9: 1 => UNS * INC # I9: 4,9 => UNS * DIS # B8: 4,9 => CTR => B8: 1,2 * INC # B8: 1,2 => UNS * INC # C8: 4,9 => UNS * DIS # E8: 4,9 => CTR => E8: 2 * INC # E8: 2 => UNS * INC # I4: 4,9 => UNS * INC # I4: 8 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 1,4 => UNS * DIS # H3: 1,4 => CTR => H3: 9 * INC H3: 9 # C8: 1,4 => UNS * PRF H3: 9 # C8: 9 => SOL * STA H3: 9 + C8: 9 * CNT 4 HDP CHAINS / 4 HYP OPENED