Analysis of xx-top500-289-base.sdk
Contents
Original Sudoku
level: medium
position: 6..2.8.3...7...1.4........5..5.1........4...........2.28.3...........7...3....... initial
Autosolve
position: 6..258937527.3.184398.7.265..5.123....2.43.....3.8..2.28.397....5682.793739.658.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B6: 1,4 => CTR => B6: 6,7 * DIS # D5: 6,9 => CTR => D5: 5,7 * DIS # D6: 6,9 => CTR => D6: 5,7 * DIS # D5: 6,9 => CTR => D5: 5,7 * DIS # D6: 6,9 => CTR => D6: 5,7 * DIS # G6: 5,6 => CTR => G6: 4 * DIS # G7: 4 => CTR => G7: 5,6 * PRF # H7: 1,4 => SOL * DIS # I5: 1,6 => CTR => I5: 8,9 * PRF # H7: 1,4 => SOL * CNT 10 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B6: 1,4 => CTR => B6: 6,7 * DIS B6: 6,7 # D5: 6,9 => CTR => D5: 5,7 * DIS B6: 6,7 + D5: 5,7 # D6: 6,9 => CTR => D6: 5,7 * DIS B6: 6,7 + D5: 5,7 + D6: 5,7 # I6: 6,9 => CTR => I6: 1 * PRF B6: 6,7 + D5: 5,7 + D6: 5,7 + I6: 1 => SOL * STA B6: 6,7 + D5: 5,7 + D6: 5,7 + I6: 1 * CNT 5 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6..2.8.3...7...1.4........5..5.1........4...........2.28.3...........7...3....... | initial |
| 6..258937527.3.184398.7.265..5.123....2.43.....3.8..2.28.397....5682.793739.658.2 | autosolve |
| 641258937527639184398471265465912378812743659973586421284397516156824793739165842 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B1: 1,4 C1: 1,4 D2: 6,9 F2: 6,9 D3: 1,4 F3: 1,4 F6: 6,9 H4: 4,7 G5: 5,6 C7: 1,4 A8: 1,4 F8: 1,4 D9: 1,4 I7: 1,6 H9: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,C1: 1.. / B1 = 1 => 0 pairs (X) / C1 = 1 => 0 pairs (_) D3,F3: 1.. / D3 = 1 => 0 pairs (X) / F3 = 1 => 0 pairs (_) C7,A8: 1.. / C7 = 1 => 0 pairs (X) / A8 = 1 => 0 pairs (_) F8,D9: 1.. / F8 = 1 => 0 pairs (X) / D9 = 1 => 0 pairs (_) A8,F8: 1.. / A8 = 1 => 0 pairs (*) / F8 = 1 => 0 pairs (X) D9,H9: 1.. / D9 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) C1,C7: 1.. / C1 = 1 => 0 pairs (*) / C7 = 1 => 0 pairs (X) D3,D9: 1.. / D3 = 1 => 0 pairs (X) / D9 = 1 => 0 pairs (_) F3,F8: 1.. / F3 = 1 => 0 pairs (*) / F8 = 1 => 0 pairs (X) B1,C1: 4.. / B1 = 4 => 0 pairs (*) / C1 = 4 => 0 pairs (X) D3,F3: 4.. / D3 = 4 => 0 pairs (*) / F3 = 4 => 0 pairs (X) H4,G6: 4.. / H4 = 4 => 0 pairs (X) / G6 = 4 => 22 pairs (_) C7,A8: 4.. / C7 = 4 => 0 pairs (*) / A8 = 4 => 0 pairs (X) F8,D9: 4.. / F8 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) A8,F8: 4.. / A8 = 4 => 0 pairs (X) / F8 = 4 => 0 pairs (_) D9,H9: 4.. / D9 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) C1,C7: 4.. / C1 = 4 => 0 pairs (X) / C7 = 4 => 0 pairs (_) D3,D9: 4.. / D3 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) F3,F8: 4.. / F3 = 4 => 0 pairs (X) / F8 = 4 => 0 pairs (_) G6,G7: 4.. / G6 = 4 => 22 pairs (_) / G7 = 4 => 0 pairs (X) D5,D6: 5.. / D5 = 5 => 0 pairs (X) / D6 = 5 => 18 pairs (_) G7,H7: 5.. / G7 = 5 => 0 pairs (*) / H7 = 5 => 0 pairs (X) D6,G6: 5.. / D6 = 5 => 18 pairs (_) / G6 = 5 => 0 pairs (X) H5,H7: 5.. / H5 = 5 => 0 pairs (*) / H7 = 5 => 0 pairs (X) D2,F2: 6.. / D2 = 6 => 15 pairs (_) / F2 = 6 => 19 pairs (_) G7,I7: 6.. / G7 = 6 => 0 pairs (X) / I7 = 6 => 18 pairs (_) F2,F6: 6.. / F2 = 6 => 19 pairs (_) / F6 = 6 => 15 pairs (_) H4,H5: 7.. / H4 = 7 => 22 pairs (_) / H5 = 7 => 0 pairs (X) B6,D6: 7.. / B6 = 7 => 17 pairs (_) / D6 = 7 => 0 pairs (X) A4,A5: 8.. / A4 = 8 => 17 pairs (_) / A5 = 8 => 16 pairs (_) I4,I5: 8.. / I4 = 8 => 16 pairs (_) / I5 = 8 => 17 pairs (_) A4,I4: 8.. / A4 = 8 => 17 pairs (_) / I4 = 8 => 16 pairs (_) A5,I5: 8.. / A5 = 8 => 16 pairs (_) / I5 = 8 => 17 pairs (_) D2,F2: 9.. / D2 = 9 => 19 pairs (_) / F2 = 9 => 15 pairs (_) F2,F6: 9.. / F2 = 9 => 15 pairs (_) / F6 = 9 => 19 pairs (_) * DURATION: 0:01:05.821048 START: 12:49:37.607350 END: 12:50:43.428398 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,C1,C7,D2,D3,D9,F2,F3,F6,F8,G5,H4,H9,I7) * 6..258937527.3.184398.7.265..5.123....2.43.....3.8..2.28.397....5682.793739.658.2 * PAIR B1: 1,4 COL B B6: 1,4,6,7 # reduction candidate for 1,4 B6: 1,4 => CTR * 6.4258937527.3.184398174265..5.1234...254367..4378.52.28.397456456821793739465812 B6: 6,7 # 16 pairs * PAIR D2: 6,9 COL D D4: 6,9,7 # reduction candidate for 6,9 D4: 6,9 # 20 pairs D5: 6,9,5,7 # reduction candidate for 6,9 D5: 6,9 => CTR * 6..258937527.3.184398.7.265..571234...2.43.7..7358.62.28.397456456821793739465812 D5: 5,7 # 18 pairs D6: 6,9,5,7 # reduction candidate for 6,9 D6: 6,9 => CTR * 6..258937527.3.184398.7.265..5.123....25436...73.8.52.28.397456456821793739465812 D6: 5,7 # 16 pairs * PAIR F6: 6,9 BLK 5 D4: 6,9,7 # reduction candidate for 6,9 D4: 6,9 # 20 pairs D5: 6,9,5,7 # reduction candidate for 6,9 D5: 6,9 => CTR * 6..258937527.3.184398.7.265..571234...2.43.7..7358.62.28.397456456821793739465812 D5: 5,7 # 18 pairs D6: 6,9,5,7 # reduction candidate for 6,9 D6: 6,9 => CTR * 6..258937527.3.184398.7.265..5.123....25436...73.8.52.28.397456456821793739465812 D6: 5,7 # 16 pairs * PAIR F6: 6,9 ROW 6 I6: 6,9,1 # reduction candidate for 6,9 I6: 6,9 # 22 pairs I6: 1 # 19 pairs * PAIR H4: 4,7 ROW 4 B4: 4,7,6 # reduction candidate for 4,7 B4: 4,7 # 23 pairs B4: 6 # 18 pairs * PAIR G5: 5,6 BLK 6 G6: 5,6,4 # reduction candidate for 5,6 G6: 5,6 => CTR * 614258937527.3.184398174265.7561234..62.43.7..4378.52.281397456456821793739465812 G6: 4 # 22 pairs * PAIR G5: 5,6 ROW 5 D5: 5,6,7,9 # reduction candidate for 5,6 D5: 5,6 # 21 pairs D5: 7,9 # 19 pairs * PAIR G5: 5,6 COL G G7: 5,6,4 # reduction candidate for 5,6 G7: 4 => CTR * 614258937527.3.184398174265.7561234..62.43.7..4378.52.281397456456821793739465812 G7: 5,6 # 22 pairs * PAIR C7: 1,4 ROW 7 H7: 1,4,5 # reduction candidate for 1,4 H7: 1,4 => SOLVED * 641258937527639184398471265465912378812743659973586421284397516156824793739165842 H7: 5 # 17 pairs * PAIR A8: 1,4 COL A A6: 1,4,9 # reduction candidate for 1,4 A6: 9 # 21 pairs A6: 1,4 # 18 pairs * PAIR I7: 1,6 COL I I5: 1,6,8,9 # reduction candidate for 1,6 I5: 1,6 => CTR * 6..258937527.3.184398.7.265..5.123.88.2943.....358642928.397....5682.793739.658.2 I5: 8,9 # 16 pairs I6: 1,6,9 # reduction candidate for 1,6 I6: 1,6 # 18 pairs * PAIR H9: 1,4 BLK 9 H7: 1,4,5 # reduction candidate for 1,4 H7: 1,4 => SOLVED * 641258937527639184398471265465912378812743659973586421284397516156824793739165842 H7: 5 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-289-base-pr-000.dot * REASONING * DIS # B6: 1,4 => CTR => B6: 6,7 * DIS # D5: 6,9 => CTR => D5: 5,7 * DIS # D6: 6,9 => CTR => D6: 5,7 * DIS # D5: 6,9 => CTR => D5: 5,7 * DIS # D6: 6,9 => CTR => D6: 5,7 * DIS # G6: 5,6 => CTR => G6: 4 * DIS # G7: 4 => CTR => G7: 5,6 * PRF # H7: 1,4 => SOL * DIS # I5: 1,6 => CTR => I5: 8,9 * PRF # H7: 1,4 => SOL * CNT 10 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,C1,C7,D2,D3,D9,F2,F3,F6,F8,G5,H4,H9,I7) * 6..258937527.3.184398.7.265..5.123....2.43.....3.8..2.28.397....5682.793739.658.2 * PAIR B1: 1,4 COL B B6: 1,4,6,7 # reduction candidate for 1,4 B6: 1,4 => CTR * 6.4258937527.3.184398174265..5.1234...254367..4378.52.28.397456456821793739465812 * PAIR RESTART * PAIR D2: 6,9 COL D D4: 6,9,7 # reduction candidate for 6,9 D4: 6,9 # 21 pairs D5: 6,9,5,7 # reduction candidate for 6,9 D5: 6,9 => CTR * 6..258937527.3.184398.7.265..571234...2.43.7.47358.6212843975...5682.793739.658.2 D6: 6,9,5,7 # reduction candidate for 6,9 D6: 6,9 => CTR * 6..258937527.3.184398.7.265..5.123....25436...73.8.52.28.397456456821793739465812 * RESTART * PAIR RESTART * PAIR F6: 6,9 ROW 6 I6: 6,9,1 # reduction candidate for 6,9 I6: 6,9 => CTR * 6..258937527.3.184398.7.265..5.123....2.43.1.1.3.8.42.281397....5682.793739.658.2 I6: 1 => SOLVED * 641258937527639184398471265465912378812743659973586421284397516156824793739165842 * DURATION: 0:00:08.900672 START: 12:51:15.341815 END: 12:51:24.242487 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-289-base-pr-001.dot * REASONING * DIS # B6: 1,4 => CTR => B6: 6,7 * DIS B6: 6,7 # D5: 6,9 => CTR => D5: 5,7 * DIS B6: 6,7 + D5: 5,7 # D6: 6,9 => CTR => D6: 5,7 * DIS B6: 6,7 + D5: 5,7 + D6: 5,7 # I6: 6,9 => CTR => I6: 1 * PRF B6: 6,7 + D5: 5,7 + D6: 5,7 + I6: 1 => SOL * STA B6: 6,7 + D5: 5,7 + D6: 5,7 + I6: 1 * CNT 5 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 289 solution: 641258937527639184398471265465912378812743659973586421284397516156824793739165842 info: 2370 FNBTWXY S8.f 34957 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 641258937527639184398471265465912378812743659973586421284397516156824793739165842 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:
* DIS # B6: 1,4 => CTR => B6: 6,7 * INC # B6: 6,7 => UNS * INC # D4: 6,9 => UNS * DIS # D5: 6,9 => CTR => D5: 5,7 * INC # D5: 5,7 => UNS * DIS # D6: 6,9 => CTR => D6: 5,7 * INC # D6: 5,7 => UNS * INC # D4: 6,9 => UNS * DIS # D5: 6,9 => CTR => D5: 5,7 * INC # D5: 5,7 => UNS * DIS # D6: 6,9 => CTR => D6: 5,7 * INC # D6: 5,7 => UNS * INC # I6: 6,9 => UNS * INC # I6: 1 => UNS * INC # B4: 4,7 => UNS * INC # B4: 6 => UNS * DIS # G6: 5,6 => CTR => G6: 4 * INC # G6: 4 => UNS * INC # D5: 5,6 => UNS * INC # D5: 7,9 => UNS * INC # G7: 5,6 => UNS * DIS # G7: 4 => CTR => G7: 5,6 * PRF # H7: 1,4 => SOL * INC # H7: 5 => UNS * INC # A6: 1,4 => UNS * INC # A6: 9 => UNS * DIS # I5: 1,6 => CTR => I5: 8,9 * INC # I5: 8,9 => UNS * INC # I6: 1,6 => UNS * PRF # H7: 1,4 => SOL * INC # H7: 5 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B6: 1,4 => CTR => B6: 6,7 * INC B6: 6,7 # D4: 6,9 => UNS * DIS B6: 6,7 # D5: 6,9 => CTR => D5: 5,7 * DIS B6: 6,7 + D5: 5,7 # D6: 6,9 => CTR => D6: 5,7 * DIS B6: 6,7 + D5: 5,7 + D6: 5,7 # I6: 6,9 => CTR => I6: 1 * PRF B6: 6,7 + D5: 5,7 + D6: 5,7 + I6: 1 => SOL * STA B6: 6,7 + D5: 5,7 + D6: 5,7 + I6: 1 * CNT 6 HDP CHAINS / 5 HYP OPENED