Analysis of xx-top500-094-base.sdk
Contents
Original Sudoku
level: medium
position: .81.........4...5.....2.........18..5......2....3.....64....3..2...5.........7..1 initial
Autosolve
position: .81.........41..5.....2..1......18..5.....12.1..3.....64.1..3..21..5....8....7..1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D8: 8,9 => CTR => D8: 6 * DIS # H7: 8,9 => CTR => H7: 7 * CNT 2 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D8: 8,9 => CTR => D8: 6 * DIS D8: 6 # F7: 2 => CTR => F7: 8,9 * DIS D8: 6 + F7: 8,9 # E5: 8,9 => CTR => E5: 6,7 * DIS D8: 6 + F7: 8,9 + E5: 6,7 # E6: 7 => CTR => E6: 8,9 * PRF D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 # D3: 7,9 => SOL * STA D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 + D3: 7,9 * CNT 5 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .81.........4...5.....2.........18..5......2....3.....64....3..2...5.........7..1 | initial |
| .81.........41..5.....2..1......18..5.....12.1..3.....64.1..3..21..5....8....7..1 | autosolve |
| 481735296392416758756928413924561837563874129178392645645189372217653984839247561 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) D4: 2,5 F6: 2,5 E7: 8,9 F8: 3,4 E9: 3,4 I7: 2,5 G9: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 2.. / B2 = 2 => 7 pairs (_) / C2 = 2 => 7 pairs (_) G1,I1: 2.. / G1 = 2 => 15 pairs (_) / I1 = 2 => 0 pairs (X) D4,F6: 2.. / D4 = 2 => 0 pairs (X) / F6 = 2 => 15 pairs (_) F7,D9: 2.. / F7 = 2 => 0 pairs (X) / D9 = 2 => 15 pairs (_) I7,G9: 2.. / I7 = 2 => 15 pairs (_) / G9 = 2 => 0 pairs (X) F7,I7: 2.. / F7 = 2 => 0 pairs (X) / I7 = 2 => 15 pairs (_) D9,G9: 2.. / D9 = 2 => 15 pairs (_) / G9 = 2 => 0 pairs (X) D4,D9: 2.. / D4 = 2 => 0 pairs (X) / D9 = 2 => 15 pairs (_) F6,F7: 2.. / F6 = 2 => 15 pairs (_) / F7 = 2 => 0 pairs (X) G1,G9: 2.. / G1 = 2 => 15 pairs (_) / G9 = 2 => 0 pairs (X) I1,I7: 2.. / I1 = 2 => 0 pairs (X) / I7 = 2 => 15 pairs (_) F8,E9: 3.. / F8 = 3 => 10 pairs (_) / E9 = 3 => 0 pairs (X) C8,F8: 3.. / C8 = 3 => 0 pairs (X) / F8 = 3 => 10 pairs (_) E1,E9: 3.. / E1 = 3 => 10 pairs (_) / E9 = 3 => 0 pairs (X) H1,H4: 3.. / H1 = 3 => 0 pairs (X) / H4 = 3 => 7 pairs (_) F8,E9: 4.. / F8 = 4 => 0 pairs (X) / E9 = 4 => 10 pairs (_) E9,H9: 4.. / E9 = 4 => 10 pairs (_) / H9 = 4 => 0 pairs (X) F5,F8: 4.. / F5 = 4 => 10 pairs (_) / F8 = 4 => 0 pairs (X) B3,C3: 5.. / B3 = 5 => 8 pairs (_) / C3 = 5 => 0 pairs (X) D1,F1: 5.. / D1 = 5 => 0 pairs (X) / F1 = 5 => 15 pairs (_) D4,F6: 5.. / D4 = 5 => 15 pairs (_) / F6 = 5 => 0 pairs (X) I7,G9: 5.. / I7 = 5 => 0 pairs (X) / G9 = 5 => 15 pairs (_) D4,I4: 5.. / D4 = 5 => 15 pairs (_) / I4 = 5 => 0 pairs (X) C7,I7: 5.. / C7 = 5 => 15 pairs (_) / I7 = 5 => 0 pairs (X) B3,B9: 5.. / B3 = 5 => 8 pairs (_) / B9 = 5 => 0 pairs (X) D1,D4: 5.. / D1 = 5 => 0 pairs (X) / D4 = 5 => 15 pairs (_) F1,F6: 5.. / F1 = 5 => 15 pairs (_) / F6 = 5 => 0 pairs (X) G6,G9: 5.. / G6 = 5 => 0 pairs (X) / G9 = 5 => 15 pairs (_) D8,D9: 6.. / D8 = 6 => 11 pairs (_) / D9 = 6 => 0 pairs (X) D9,H9: 6.. / D9 = 6 => 0 pairs (X) / H9 = 6 => 11 pairs (_) C7,C8: 7.. / C7 = 7 => 0 pairs (X) / C8 = 7 => 11 pairs (_) C7,H7: 7.. / C7 = 7 => 0 pairs (X) / H7 = 7 => 11 pairs (_) I2,I3: 8.. / I2 = 8 => 7 pairs (_) / I3 = 8 => 9 pairs (_) C5,C6: 8.. / C5 = 8 => 12 pairs (_) / C6 = 8 => 7 pairs (_) H7,H8: 8.. / H7 = 8 => 0 pairs (X) / H8 = 8 => 9 pairs (_) F2,I2: 8.. / F2 = 8 => 9 pairs (_) / I2 = 8 => 7 pairs (_) C6,E6: 8.. / C6 = 8 => 7 pairs (_) / E6 = 8 => 12 pairs (_) D8,H8: 8.. / D8 = 8 => 0 pairs (X) / H8 = 8 => 9 pairs (_) * DURATION: 0:00:57.521279 START: 05:59:49.621148 END: 06:00:47.142427 2017-05-04 * CP COUNT: (38) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E7,E9,F6,F8,G9,I7) * .81.........41..5.....2..1......18..5.....12.1..3.....64.1..3..21..5....8....7..1 * PAIR E7: 8,9 BLK 8 F7: 8,9,2 # reduction candidate for 8,9 F7: 8,9 # 15 pairs D8: 8,9,6 # reduction candidate for 8,9 D8: 8,9 => CTR * .81.....2...41..5.....2..1....2.18.55.....12.1..3.....64.1..3..21..5....8..6.72.1 D8: 6 # 11 pairs * PAIR E7: 8,9 ROW 7 H7: 8,9,7 # reduction candidate for 8,9 H7: 8,9 => CTR * .81.........41..5.....2..1......18..5.....12.1..3.....6471..3.521..5....8....72.1 H7: 7 # 11 pairs * PAIR E7: 8,9 COL E E5: 8,9,4,6,7 # reduction candidate for 8,9 E5: 8,9 # 8 pairs E6: 8,9,4,6,7 # reduction candidate for 8,9 E6: 8,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-094-base-pr-000.dot * REASONING * DIS # D8: 8,9 => CTR => D8: 6 * DIS # H7: 8,9 => CTR => H7: 7 * CNT 2 HDP CHAINS / 7 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E7,E9,F6,F8,G9,I7) * .81.........41..5.....2..1......18..5.....12.1..3.....64.1..3..21..5....8....7..1 * PAIR E7: 8,9 BLK 8 F7: 8,9,2 # reduction candidate for 8,9 F7: 8,9 # 15 pairs D8: 8,9,6 # reduction candidate for 8,9 D8: 8,9 => CTR * .81.....2...41..5.....2..1....2.18.55.....12.1..3.....64.1..3..21..5....8..6.72.1 * RESTART * PAIR E7: 8,9 BLK 8 F7: 8,9,2 # reduction candidate for 8,9 F7: 2 => CTR * .81.3.......41..5.....2..1......183.5....412.1..3.....64.1823.521.653.8.8..947.61 * PAIR E7: 8,9 COL E E5: 8,9,6,7 # reduction candidate for 8,9 E5: 8,9 => CTR * 481735296...41.75.75..2..1....56183.5....412.1983726456451..372217653.84839247561 E6: 8,9,7 # reduction candidate for 8,9 E6: 8,9 # 18 pairs * RESTART * PAIR E7: 8,9 COL E E6: 8,9,7 # reduction candidate for 8,9 E6: 7 => CTR * 481735296...41.75.75.92.4139..5.183.5..8.412.1.8372645645189372217653.848..247561 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,B9,C9,D1,D5,E4,E5,E6,E7,F7,G2,G8,H1,H6,I2,I3,I5,I8) * .81.352.6...41..5..5..2..1....5.183.5....412.17.3.26.56451..372217653.8.8..247561 * PAIR D1: 7,9 BLK 2 D3: 7,9,8 # reduction candidate for 7,9 D3: 7,9 => SOLVED * 481735296392416758756928413924561837563874129178392645645189372217653984839247561 * DURATION: 0:00:12.552672 START: 06:00:53.684394 END: 06:01:06.237066 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-094-base-pr-001.dot * REASONING * DIS # D8: 8,9 => CTR => D8: 6 * DIS D8: 6 # F7: 2 => CTR => F7: 8,9 * DIS D8: 6 + F7: 8,9 # E5: 8,9 => CTR => E5: 6,7 * DIS D8: 6 + F7: 8,9 + E5: 6,7 # E6: 7 => CTR => E6: 8,9 * PRF D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 # D3: 7,9 => SOL * STA D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 + D3: 7,9 * CNT 5 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 094 solution: 481735296392416758756928413924561837563874129178392645645189372217653984839247561 info: 1572 FNBTHXY S8.f 39264 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 481735296392416758756928413924561837563874129178392645645189372217653984839247561 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 # F7: 8,9 => UNS * DIS # D8: 8,9 => CTR => D8: 6 * INC # D8: 6 => UNS * DIS # H7: 8,9 => CTR => H7: 7 * INC # H7: 7 => UNS * INC # E5: 8,9 => UNS * INC # E6: 8,9 => UNS * CNT 7 HDP CHAINS / 7 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F7: 8,9 => UNS * DIS # D8: 8,9 => CTR => D8: 6 * INC D8: 6 # F7: 8,9 => UNS * DIS D8: 6 # F7: 2 => CTR => F7: 8,9 * DIS D8: 6 + F7: 8,9 # E5: 8,9 => CTR => E5: 6,7 * INC D8: 6 + F7: 8,9 + E5: 6,7 # E6: 8,9 => UNS * INC D8: 6 + F7: 8,9 + E5: 6,7 # E6: 8,9 => UNS * DIS D8: 6 + F7: 8,9 + E5: 6,7 # E6: 7 => CTR => E6: 8,9 * PRF D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 # D3: 7,9 => SOL * STA D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 + D3: 7,9 * CNT 9 HDP CHAINS / 9 HYP OPENED