Analysis of xx-top500-419-base.sdk
Contents
Original Sudoku
level: medium
position: .543.........6..7..........76..2.......5..3.81..........24..........35.........6. initial
Autosolve
position: .543.7.......6..7..76.4....763.2......9576318185934.2.6.245......76.35.25..7.2.6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 2,8 => CTR => A2: 3,9 * DIS # G1: 8,9 => CTR => G1: 1,2,6 * DIS # H3: 8,9 => CTR => H3: 3,5 * DIS # A1: 8,9 => CTR => A1: 2 * DIS # F3: 1,8 => CTR => F3: 5,9 * PRF # G9: 4,9 => SOL * DIS # E9: 1,8 => CTR => E9: 9 * CNT 7 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 2,8 => CTR => A2: 3,9 * DIS A2: 3,9 # G1: 8,9 => CTR => G1: 1,2,6 * DIS A2: 3,9 + G1: 1,2,6 # H3: 8,9 => CTR => H3: 3,5 * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 # A1: 8,9 => CTR => A1: 2 * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 # E1: 1 => CTR => E1: 8,9 * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 # G3: 8,9 => CTR => G3: 2 * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 # G2: 4 => CTR => G2: 8,9 * PRF A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 + G2: 8,9 # H8: 8,9 => SOL * STA A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 + G2: 8,9 + H8: 8,9 * CNT 8 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .543.........6..7..........76..2.......5..3.81..........24..........35.........6. | initial |
| .543.7.......6..7..76.4....763.2......9576318185934.2.6.245......76.35.25..7.2.6. | autosolve |
| 254387196391265874876149253763821945429576318185934627612458739947613582538792461 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) C2: 1,8 D2: 2,8 H1: 8,9 A5: 2,4 B5: 2,4 D4: 1,8 F4: 1,8 G4: 4,9 G6: 6,7 I6: 6,7 C9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 1.. / B2 = 1 => 0 pairs (X) / C2 = 1 => 12 pairs (_) D4,F4: 1.. / D4 = 1 => 14 pairs (_) / F4 = 1 => 12 pairs (_) B8,E8: 1.. / B8 = 1 => 14 pairs (_) / E8 = 1 => 17 pairs (_) C2,C9: 1.. / C2 = 1 => 12 pairs (_) / C9 = 1 => 0 pairs (X) D3,D4: 1.. / D3 = 1 => 12 pairs (_) / D4 = 1 => 14 pairs (_) D2,D3: 2.. / D2 = 2 => 11 pairs (_) / D3 = 2 => 14 pairs (_) A5,B5: 2.. / A5 = 2 => 0 pairs (X) / B5 = 2 => 11 pairs (_) A1,G1: 2.. / A1 = 2 => 11 pairs (_) / G1 = 2 => 0 pairs (X) B2,B5: 2.. / B2 = 2 => 0 pairs (X) / B5 = 2 => 11 pairs (_) A2,A3: 3.. / A2 = 3 => 11 pairs (_) / A3 = 3 => 0 pairs (X) B7,B9: 3.. / B7 = 3 => 15 pairs (_) / B9 = 3 => 12 pairs (_) A2,I2: 3.. / A2 = 3 => 11 pairs (_) / I2 = 3 => 0 pairs (X) B9,I9: 3.. / B9 = 3 => 12 pairs (_) / I9 = 3 => 15 pairs (_) H3,H7: 3.. / H3 = 3 => 15 pairs (_) / H7 = 3 => 12 pairs (_) G2,I2: 4.. / G2 = 4 => 20 pairs (_) / I2 = 4 => 14 pairs (_) A5,B5: 4.. / A5 = 4 => 11 pairs (_) / B5 = 4 => 0 pairs (X) A5,A8: 4.. / A5 = 4 => 11 pairs (_) / A8 = 4 => 0 pairs (X) H4,H8: 4.. / H4 = 4 => 12 pairs (_) / H8 = 4 => 15 pairs (_) F2,F3: 5.. / F2 = 5 => 11 pairs (_) / F3 = 5 => 0 pairs (X) H4,I4: 5.. / H4 = 5 => 15 pairs (_) / I4 = 5 => 12 pairs (_) F2,I2: 5.. / F2 = 5 => 11 pairs (_) / I2 = 5 => 0 pairs (X) H3,H4: 5.. / H3 = 5 => 12 pairs (_) / H4 = 5 => 15 pairs (_) G1,I1: 6.. / G1 = 6 => 10 pairs (_) / I1 = 6 => 9 pairs (_) G6,I6: 6.. / G6 = 6 => 9 pairs (_) / I6 = 6 => 10 pairs (_) G1,G6: 6.. / G1 = 6 => 10 pairs (_) / G6 = 6 => 9 pairs (_) I1,I6: 6.. / I1 = 6 => 9 pairs (_) / I6 = 6 => 10 pairs (_) G6,I6: 7.. / G6 = 7 => 10 pairs (_) / I6 = 7 => 9 pairs (_) G7,I7: 7.. / G7 = 7 => 9 pairs (_) / I7 = 7 => 10 pairs (_) G6,G7: 7.. / G6 = 7 => 10 pairs (_) / G7 = 7 => 9 pairs (_) I6,I7: 7.. / I6 = 7 => 9 pairs (_) / I7 = 7 => 10 pairs (_) D4,F4: 8.. / D4 = 8 => 12 pairs (_) / F4 = 8 => 14 pairs (_) A8,C9: 8.. / A8 = 8 => 0 pairs (X) / C9 = 8 => 12 pairs (_) C2,C9: 8.. / C2 = 8 => 0 pairs (X) / C9 = 8 => 12 pairs (_) * DURATION: 0:00:51.230713 START: 17:08:52.822707 END: 17:09:44.053420 2017-05-04 * CP COUNT: (33) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B5,C2,C9,D2,D4,F4,G4,G6,H1,I6) * .543.7.......6..7..76.4....763.2......9576318185934.2.6.245......76.35.25..7.2.6. * PAIR D2: 2,8 BLK 2 D3: 2,8,1 # reduction candidate for 2,8 D3: 2,8 # 14 pairs D3: 1 # 12 pairs * PAIR D2: 2,8 ROW 2 A2: 2,8,3,9 # reduction candidate for 2,8 A2: 2,8 => CTR * .54387.91.91.65473376.4....763.2.945.29576318185934.2.61245..3.947613582538792164 A2: 3,9 # 12 pairs G2: 2,8,4,9 # reduction candidate for 2,8 G2: 2,8 # 18 pairs * PAIR H1: 8,9 BLK 3 G1: 8,9,1,2,6 # reduction candidate for 8,9 G1: 8,9 => CTR * 25431789639186527..76.4....763128...4295763181859346276.245178..176.3542548792163 G1: 1,2,6 # 11 pairs G2: 8,9,2,4 # reduction candidate for 8,9 G2: 8,9 # 17 pairs G3: 8,9,1,2 # reduction candidate for 8,9 G3: 8,9 # 15 pairs H3: 8,9,3,5 # reduction candidate for 8,9 H3: 8,9 => CTR * .543.7.......6..7..76.4....763.2..5...9576318185934.2.6.245..3...76.35425..7.2.6. H3: 3,5 # 12 pairs * PAIR H1: 8,9 ROW 1 A1: 8,9,2 # reduction candidate for 8,9 A1: 8,9 => CTR * 854317296391265.7..76.4..3.763128954..95763181859346276.2451789917683542548792163 A1: 2 # 11 pairs E1: 8,9,1 # reduction candidate for 8,9 E1: 8,9 # 15 pairs * PAIR H1: 8,9 COL H H7: 8,9,3 # reduction candidate for 8,9 H7: 8,9 # 15 pairs H8: 8,9,4 # reduction candidate for 8,9 H8: 8,9 # 12 pairs * PAIR D4: 1,8 COL D D3: 1,8,2 # reduction candidate for 1,8 D3: 2 # 14 pairs D3: 1,8 # 11 pairs * PAIR F4: 1,8 COL F F3: 1,8,5,9 # reduction candidate for 1,8 F3: 1,8 => CTR * 254397.8.....65.7..76.4....763.2....429576318185934726612459837.4761359253.7.2.6. F3: 5,9 # 12 pairs F7: 1,8,9 # reduction candidate for 1,8 F7: 1,8 # 15 pairs * PAIR G4: 4,9 BLK 6 H4: 4,9,5 # reduction candidate for 4,9 H4: 4,9 # 12 pairs I4: 4,9,5 # reduction candidate for 4,9 I4: 4,9 # 15 pairs * PAIR G4: 4,9 COL G G2: 4,9,2,8 # reduction candidate for 4,9 G2: 4,9 # 20 pairs G9: 4,9,1,8 # reduction candidate for 4,9 G9: 4,9 => SOLVED * 254387196391265874876149253763821945429576318185934627612458739947613582538792461 G9: 1,8 # 19 pairs * PAIR C9: 1,8 ROW 9 E9: 1,8,9 # reduction candidate for 1,8 E9: 1,8 => CTR * .54397.8.391865274876241...763.2.....29576318185934.2.6.245....9.76.35.25.8712.6. E9: 9 # 16 pairs G9: 1,8,4,9 # reduction candidate for 1,8 G9: 1,8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-419-base-pr-000.dot * REASONING * DIS # A2: 2,8 => CTR => A2: 3,9 * DIS # G1: 8,9 => CTR => G1: 1,2,6 * DIS # H3: 8,9 => CTR => H3: 3,5 * DIS # A1: 8,9 => CTR => A1: 2 * DIS # F3: 1,8 => CTR => F3: 5,9 * PRF # G9: 4,9 => SOL * DIS # E9: 1,8 => CTR => E9: 9 * CNT 7 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B5,C2,C9,D2,D4,F4,G4,G6,H1,I6) * .543.7.......6..7..76.4....763.2......9576318185934.2.6.245......76.35.25..7.2.6. * PAIR D2: 2,8 BLK 2 D3: 2,8,1 # reduction candidate for 2,8 D3: 2,8 # 14 pairs D3: 1 # 12 pairs * PAIR D2: 2,8 ROW 2 A2: 2,8,3,9 # reduction candidate for 2,8 A2: 2,8 => CTR * .54387.91.91.65473376.4....763.2.945.29576318185934.2.61245..3.947613582538792164 G2: 2,8,4,9 # reduction candidate for 2,8 G2: 2,8 # 18 pairs * RESTART * PAIR D2: 2,8 ROW 2 G2: 2,8,4,9 # reduction candidate for 2,8 G2: 4,9 # 23 pairs G2: 2,8 # 18 pairs * PAIR RESTART * PAIR D2: 2,8 BLK 2 D3: 2,8,1 # reduction candidate for 2,8 D3: 2,8 # 15 pairs D3: 1 # 13 pairs * PAIR D2: 2,8 ROW 2 G2: 2,8,4,9 # reduction candidate for 2,8 G2: 4,9 # 23 pairs G2: 2,8 # 18 pairs * PAIR H1: 8,9 BLK 3 G1: 8,9,1,2,6 # reduction candidate for 8,9 G1: 8,9 => CTR * 25431789639186527..76.4....763128...4295763181859346276.245178..176.3542548792163 G2: 8,9,2,4 # reduction candidate for 8,9 G2: 8,9 # 17 pairs G3: 8,9,1,2 # reduction candidate for 8,9 G3: 8,9 # 16 pairs H3: 8,9,3,5 # reduction candidate for 8,9 H3: 8,9 => CTR * .543.7.......6..7..76.4....763.2..5...9576318185934.2.6.245..3...76.35425..7.2.6. * PAIR H1: 8,9 ROW 1 A1: 8,9,2 # reduction candidate for 8,9 A1: 8,9 => CTR * 854317296391265.7..76.4..3.763128954..95763181859346276.2451789917683542548792163 E1: 8,9,1 # reduction candidate for 8,9 E1: 8,9 # 17 pairs * RESTART * PAIR H1: 8,9 ROW 1 E1: 8,9,1 # reduction candidate for 8,9 E1: 1 => CTR * 25431768939186527..76.4....763128...4295763181859347266.24518.7.176.3542548792163 * PAIR H1: 8,9 COL H H7: 8,9,3 # reduction candidate for 8,9 H7: 8,9 # 24 pairs H8: 8,9,4 # reduction candidate for 8,9 H8: 8,9 # 20 pairs * PAIR RESTART * PAIR H1: 8,9 BLK 3 G2: 8,9,2,4 # reduction candidate for 8,9 G2: 8,9 # 20 pairs G3: 8,9,2 # reduction candidate for 8,9 G3: 8,9 => CTR * 254397.8.3918652748762419..7631284..429576318185934.2.6.24598379.76.35.25..7.2.6. * RESTART * PAIR H1: 8,9 BLK 3 G2: 8,9,4 # reduction candidate for 8,9 G2: 4 => CTR * 254397.8....26.47..76.4.2..763.2.9..429576318185934.2.6.2459837..76.35925..7.2.6. * PAIR H1: 8,9 COL H H7: 8,9,3 # reduction candidate for 8,9 H7: 8,9 # 22 pairs H8: 8,9,4 # reduction candidate for 8,9 H8: 8,9 => SOLVED * 254387196391265874876149253763821945429576318185934627612458739947613582538792461 * DURATION: 0:00:27.483975 START: 17:10:09.955865 END: 17:10:37.439840 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-419-base-pr-001.dot * REASONING * DIS # A2: 2,8 => CTR => A2: 3,9 * DIS A2: 3,9 # G1: 8,9 => CTR => G1: 1,2,6 * DIS A2: 3,9 + G1: 1,2,6 # H3: 8,9 => CTR => H3: 3,5 * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 # A1: 8,9 => CTR => A1: 2 * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 # E1: 1 => CTR => E1: 8,9 * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 # G3: 8,9 => CTR => G3: 2 * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 # G2: 4 => CTR => G2: 8,9 * PRF A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 + G2: 8,9 # H8: 8,9 => SOL * STA A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 + G2: 8,9 + H8: 8,9 * CNT 8 HDP CHAINS / 26 HYP OPENED
Header Info
Top 500 Minimum 17 419 solution: 254387196391265874876149253763821945429576318185934627612458739947613582538792461 info: 95092 FNBHXYK S8.f 40995 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 254387196391265874876149253763821945429576318185934627612458739947613582538792461 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 # D3: 2,8 => UNS * INC # D3: 1 => UNS * DIS # A2: 2,8 => CTR => A2: 3,9 * INC # A2: 3,9 => UNS * INC # G2: 2,8 => UNS * DIS # G1: 8,9 => CTR => G1: 1,2,6 * INC # G1: 1,2,6 => UNS * INC # G2: 8,9 => UNS * INC # G3: 8,9 => UNS * DIS # H3: 8,9 => CTR => H3: 3,5 * INC # H3: 3,5 => UNS * DIS # A1: 8,9 => CTR => A1: 2 * INC # A1: 2 => UNS * INC # E1: 8,9 => UNS * INC # H7: 8,9 => UNS * INC # H8: 8,9 => UNS * INC # D3: 1,8 => UNS * INC # D3: 2 => UNS * DIS # F3: 1,8 => CTR => F3: 5,9 * INC # F3: 5,9 => UNS * INC # F7: 1,8 => UNS * INC # H4: 4,9 => UNS * INC # I4: 4,9 => UNS * INC # G2: 4,9 => UNS * PRF # G9: 4,9 => SOL * INC # G9: 1,8 => UNS * DIS # E9: 1,8 => CTR => E9: 9 * INC # E9: 9 => UNS * INC # G9: 1,8 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 2,8 => UNS * INC # D3: 1 => UNS * DIS # A2: 2,8 => CTR => A2: 3,9 * INC A2: 3,9 # G2: 2,8 => UNS * INC A2: 3,9 # G2: 2,8 => UNS * INC A2: 3,9 # G2: 4,9 => UNS * INC A2: 3,9 # D3: 2,8 => UNS * INC A2: 3,9 # D3: 1 => UNS * INC A2: 3,9 # G2: 2,8 => UNS * INC A2: 3,9 # G2: 4,9 => UNS * DIS A2: 3,9 # G1: 8,9 => CTR => G1: 1,2,6 * INC A2: 3,9 + G1: 1,2,6 # G2: 8,9 => UNS * INC A2: 3,9 + G1: 1,2,6 # G3: 8,9 => UNS * DIS A2: 3,9 + G1: 1,2,6 # H3: 8,9 => CTR => H3: 3,5 * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 # A1: 8,9 => CTR => A1: 2 * INC A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 # E1: 8,9 => UNS * INC A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 # E1: 8,9 => UNS * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 # E1: 1 => CTR => E1: 8,9 * INC A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 # H7: 8,9 => UNS * INC A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 # H8: 8,9 => UNS * INC A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 # G2: 8,9 => UNS * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 # G3: 8,9 => CTR => G3: 2 * INC A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 # G2: 8,9 => UNS * DIS A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 # G2: 4 => CTR => G2: 8,9 * INC A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 + G2: 8,9 # H7: 8,9 => UNS * PRF A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 + G2: 8,9 # H8: 8,9 => SOL * STA A2: 3,9 + G1: 1,2,6 + H3: 3,5 + A1: 2 + E1: 8,9 + G3: 2 + G2: 8,9 + H8: 8,9 * CNT 26 HDP CHAINS / 26 HYP OPENED