Analysis of xx-top500-056-base.sdk
Contents
Original Sudoku
level: medium
position: 1.......2....8..7.....1....4..3..6..5.8...1.....7......7...2......6...3.......4.. initial
Autosolve
position: 1...67..2....8..717...1..644273.168.538.261.7...7.82.3.74832.1....6..73....17.42. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 2,3 => CTR => C2: 5,6,9 * DIS # C3: 2,3 => CTR => C3: 5,9 * DIS # F2: 3,9 => CTR => F2: 4 * PRF # F2: 4 => SOL * PRF # G3: 3,9 => SOL * DIS # G1: 5,9 => CTR => G1: 3,8 * PRF # G3: 5,9 => SOL * DIS # B1: 5,9 => CTR => B1: 4,8 * DIS # C1: 5,9 => CTR => C1: 3 * PRF # C1: 3 => SOL * PRF # D1: 5,9 => SOL * DIS # D1: 4 => CTR => D1: 5,9 * DIS # C6: 6,9 => CTR => C6: 1 * DIS # D2: 4,9 => CTR => D2: 2,5 * DIS # I7: 5,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * PRF # C9: 6,9 => SOL * PRF # I7: 6,9 => SOL * DIS # I7: 5 => CTR => I7: 6,9 * DIS # F8: 4,9 => CTR => F8: 5 * PRF # F8: 5 => SOL * PRF # F8: 5,9 => SOL * DIS # F8: 4 => CTR => F8: 5,9 * DIS # C9: 5,9 => CTR => C9: 3,6 * DIS # I7: 5,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * DIS # G1: 5,9 => CTR => G1: 3,8 * PRF # G3: 5,9 => SOL * PRF # I9: 8,9 => SOL * DIS # I9: 6 => CTR => I9: 8,9 * CNT 30 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 2,3 => CTR => C2: 5,6,9 * DIS C2: 5,6,9 # C3: 2,3 => CTR => C3: 5,9 * PRF C2: 5,6,9 + C3: 5,9 => SOL * STA C2: 5,6,9 + C3: 5,9 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.......2....8..7.....1....4..3..6..5.8...1.....7......7...2......6...3.......4.. | initial |
| 1...67..2....8..717...1..644273.168.538.261.7...7.82.3.74832.1....6..73....17.42. | autosolve |
| 143967852269584371785213964427391685538426197691758243974832516812645739356179428 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A2: 2,3 F3: 3,9 H1: 5,9 A6: 6,9 E4: 5,9 D5: 4,9 E6: 4,5 I4: 5,9 H5: 4,9 H6: 4,5 A7: 6,9 A8: 2,8 A9: 3,8 E8: 4,9 F9: 5,9 G7: 5,9 I8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B6,C6: 1.. / B6 = 1 => 0 pairs (X) / C6 = 1 => 18 pairs (_) B8,C8: 1.. / B8 = 1 => 18 pairs (_) / C8 = 1 => 0 pairs (X) B6,B8: 1.. / B6 = 1 => 0 pairs (X) / B8 = 1 => 18 pairs (_) C6,C8: 1.. / C6 = 1 => 18 pairs (_) / C8 = 1 => 0 pairs (X) D2,D3: 2.. / D2 = 2 => 0 pairs (X) / D3 = 2 => 17 pairs (_) A8,C8: 2.. / A8 = 2 => 0 pairs (X) / C8 = 2 => 0 pairs (_) C3,D3: 2.. / C3 = 2 => 0 pairs (X) / D3 = 2 => 17 pairs (_) A2,A8: 2.. / A2 = 2 => 0 pairs (*) / A8 = 2 => 0 pairs (X) F2,F3: 3.. / F2 = 3 => 0 pairs (X) / F3 = 3 => 17 pairs (_) A9,C9: 3.. / A9 = 3 => 0 pairs (*) / C9 = 3 => 0 pairs (X) C1,G1: 3.. / C1 = 3 => 0 pairs (*) / G1 = 3 => 0 pairs (X) A2,A9: 3.. / A2 = 3 => 0 pairs (X) / A9 = 3 => 0 pairs (_) B1,B2: 4.. / B1 = 4 => 0 pairs (*) / B2 = 4 => 0 pairs (X) D5,E6: 4.. / D5 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) H5,H6: 4.. / H5 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) E8,F8: 4.. / E8 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) B1,D1: 4.. / B1 = 4 => 0 pairs (*) / D1 = 4 => 0 pairs (X) D5,H5: 4.. / D5 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) E6,H6: 4.. / E6 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) E6,E8: 4.. / E6 = 4 => 0 pairs (X) / E8 = 4 => 0 pairs (_) F2,F8: 4.. / F2 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) E4,E6: 5.. / E4 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) I4,H6: 5.. / I4 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) F8,F9: 5.. / F8 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) G7,I7: 5.. / G7 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) E4,I4: 5.. / E4 = 5 => 0 pairs (X) / I4 = 5 => 0 pairs (_) E6,H6: 5.. / E6 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) H1,H6: 5.. / H1 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) I4,I7: 5.. / I4 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) B2,C2: 6.. / B2 = 6 => 0 pairs (*) / C2 = 6 => 0 pairs (X) I7,I9: 6.. / I7 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) A7,I7: 6.. / A7 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) A6,A7: 6.. / A6 = 6 => 0 pairs (*) / A7 = 6 => 0 pairs (X) B1,B3: 8.. / B1 = 8 => 0 pairs (X) / B3 = 8 => 0 pairs (_) G1,G3: 8.. / G1 = 8 => 0 pairs (*) / G3 = 8 => 0 pairs (X) A8,A9: 8.. / A8 = 8 => 0 pairs (*) / A9 = 8 => 0 pairs (X) I8,I9: 8.. / I8 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) B1,G1: 8.. / B1 = 8 => 0 pairs (X) / G1 = 8 => 0 pairs (_) B3,G3: 8.. / B3 = 8 => 0 pairs (*) / G3 = 8 => 0 pairs (X) A8,I8: 8.. / A8 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) A9,I9: 8.. / A9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) E4,D5: 9.. / E4 = 9 => 0 pairs (*) / D5 = 9 => 0 pairs (X) I4,H5: 9.. / I4 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) E4,I4: 9.. / E4 = 9 => 0 pairs (*) / I4 = 9 => 0 pairs (X) D5,H5: 9.. / D5 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) A6,A7: 9.. / A6 = 9 => 0 pairs (X) / A7 = 9 => 0 pairs (_) E4,E8: 9.. / E4 = 9 => 0 pairs (*) / E8 = 9 => 0 pairs (X) H1,H5: 9.. / H1 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) * DURATION: 0:01:27.415908 START: 04:35:27.747877 END: 04:36:55.163785 2017-05-04 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,A8,A9,D5,E4,E6,E8,F3,F9,G7,H1,H5,H6,I4,I8) * 1...67..2....8..717...1..644273.168.538.261.7...7.82.3.74832.1....6..73....17.42. * PAIR A2: 2,3 BLK 1 C2: 2,3,5,6,9 # reduction candidate for 2,3 C2: 2,3 => CTR * 143.678.226..8..7178..1..644273.168.538.261.7...7.82.3.74832.1....6..73....17.42. C2: 5,6,9 # 17 pairs C3: 2,3,5,9 # reduction candidate for 2,3 C3: 2,3 => CTR * 18546739234628957179..1.8644273.168.538926147...748253.74832.15...6947388.3175426 C3: 5,9 # 18 pairs * PAIR F3: 3,9 BLK 2 F2: 3,9,4 # reduction candidate for 3,9 F2: 3,9 => CTR * 1...673923...895717...13864427351689538926147...7482536748329152..694738893175426 F2: 4 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 * PAIR F3: 3,9 ROW 3 C3: 3,9,2,5 # reduction candidate for 3,9 C3: 3,9 # 20 pairs G3: 3,9,5,8 # reduction candidate for 3,9 G3: 3,9 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 G3: 5,8 # 18 pairs * PAIR H1: 5,9 BLK 3 G1: 5,9,3,8 # reduction candidate for 5,9 G1: 5,9 => CTR * 183467..2246.8..717..21.8644273.168.538926147...748253.74832.158.269.73....17.42. G1: 3,8 # 18 pairs G2: 5,9,3 # reduction candidate for 5,9 G2: 5,9 # 20 pairs G3: 5,9,3,8 # reduction candidate for 5,9 G3: 5,9 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 G3: 3,8 # 18 pairs * PAIR H1: 5,9 ROW 1 B1: 5,9,4,8 # reduction candidate for 5,9 B1: 5,9 => CTR * 1..4678.2.46.8..7178..1..644273.168.538926147...748253.74832.15...6947388.3175426 B1: 4,8 # 18 pairs C1: 5,9,3 # reduction candidate for 5,9 C1: 5,9 => CTR * 18546739234628957179..1.8644273.168.538926147...748253.74832.15...6947388.3175426 C1: 3 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 D1: 5,9,4 # reduction candidate for 5,9 D1: 5,9 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 D1: 4 => CTR * 1..4673923462895717.2513864427351689538926147.6.748253.74832.15...6947388.3175426 * PAIR A6: 6,9 BLK 4 B6: 6,9,1 # reduction candidate for 6,9 B6: 6,9 # 18 pairs C6: 6,9,1 # reduction candidate for 6,9 C6: 6,9 => CTR * 18.4673.23462895717.25138644273.168.538926147619748253974832.1.2.16..7388.317.42. C6: 1 # 18 pairs * PAIR D5: 4,9 COL D D1: 4,9,5 # reduction candidate for 4,9 D1: 4,9 # 20 pairs D2: 4,9,2,5 # reduction candidate for 4,9 D2: 4,9 => CTR * 1..567.92....8..717..21..644273.1689538926147...748253.74832915...6947388.317.42. D2: 2,5 # 18 pairs * PAIR I4: 5,9 COL I I7: 5,9,6 # reduction candidate for 5,9 I7: 5,9 => CTR * 18.4673.23462895717.25138644273.168.53892614796174825367483291521.6947388.317.426 I7: 6 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 * PAIR A7: 6,9 BLK 7 B9: 6,9,5 # reduction candidate for 6,9 B9: 6,9 # 20 pairs C9: 6,9,3,5 # reduction candidate for 6,9 C9: 6,9 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 C9: 3,5 # 18 pairs * PAIR A7: 6,9 ROW 7 I7: 6,9,5 # reduction candidate for 6,9 I7: 6,9 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 I7: 5 => CTR * 1...673923...8.5717...138644273516895389261479..7482536748329152..694738893175426 * PAIR E8: 4,9 BLK 8 F8: 4,9,5 # reduction candidate for 4,9 F8: 4,9 => CTR * 18.4673.23462895717.25138644273.168.538926147...748253.7483291525169473889317542. F8: 5 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 * PAIR F9: 5,9 BLK 8 F8: 5,9,4 # reduction candidate for 5,9 F8: 5,9 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 F8: 4 => CTR * 1...673923...895717...13864427351689538926147...7482536748329152..694738893175426 * PAIR F9: 5,9 ROW 9 B9: 5,9,6 # reduction candidate for 5,9 B9: 5,9 # 20 pairs C9: 5,9,3,6 # reduction candidate for 5,9 C9: 5,9 => CTR * 143.67..22.6.8..717..213.644273916855384261976.1758243974832516812645739365179428 C9: 3,6 # 18 pairs * PAIR G7: 5,9 BLK 9 I7: 5,9,6 # reduction candidate for 5,9 I7: 5,9 => CTR * 18.4673.23462895717.25138644273.168.53892614796174825367483291521.6947388.317.426 I7: 6 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 * PAIR G7: 5,9 COL G G1: 5,9,3,8 # reduction candidate for 5,9 G1: 5,9 => CTR * 183467..2246.8..717..21.8644273.168.538926147...748253.74832.158.269.73....17.42. G1: 3,8 # 18 pairs G2: 5,9,3 # reduction candidate for 5,9 G2: 5,9 # 20 pairs G3: 5,9,3,8 # reduction candidate for 5,9 G3: 5,9 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 G3: 3,8 # 18 pairs * PAIR I8: 8,9 BLK 9 I9: 8,9,6 # reduction candidate for 8,9 I9: 8,9 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 I9: 6 => CTR * 18.4673.23462895717.25138644273.168.53892614796174825367483291521.6947388.317.426 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-056-base-pr-000.dot * REASONING * DIS # C2: 2,3 => CTR => C2: 5,6,9 * DIS # C3: 2,3 => CTR => C3: 5,9 * DIS # F2: 3,9 => CTR => F2: 4 * PRF # F2: 4 => SOL * PRF # G3: 3,9 => SOL * DIS # G1: 5,9 => CTR => G1: 3,8 * PRF # G3: 5,9 => SOL * DIS # B1: 5,9 => CTR => B1: 4,8 * DIS # C1: 5,9 => CTR => C1: 3 * PRF # C1: 3 => SOL * PRF # D1: 5,9 => SOL * DIS # D1: 4 => CTR => D1: 5,9 * DIS # C6: 6,9 => CTR => C6: 1 * DIS # D2: 4,9 => CTR => D2: 2,5 * DIS # I7: 5,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * PRF # C9: 6,9 => SOL * PRF # I7: 6,9 => SOL * DIS # I7: 5 => CTR => I7: 6,9 * DIS # F8: 4,9 => CTR => F8: 5 * PRF # F8: 5 => SOL * PRF # F8: 5,9 => SOL * DIS # F8: 4 => CTR => F8: 5,9 * DIS # C9: 5,9 => CTR => C9: 3,6 * DIS # I7: 5,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * DIS # G1: 5,9 => CTR => G1: 3,8 * PRF # G3: 5,9 => SOL * PRF # I9: 8,9 => SOL * DIS # I9: 6 => CTR => I9: 8,9 * CNT 30 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,A8,A9,D5,E4,E6,E8,F3,F9,G7,H1,H5,H6,I4,I8) * 1...67..2....8..717...1..644273.168.538.261.7...7.82.3.74832.1....6..73....17.42. * PAIR A2: 2,3 BLK 1 C2: 2,3,5,6,9 # reduction candidate for 2,3 C2: 2,3 => CTR * 143.678.226..8..7178..1..644273.168.538.261.7...7.82.3.74832.1....6..73....17.42. C3: 2,3,5,9 # reduction candidate for 2,3 C3: 2,3 => CTR * 18546739234628957179..1.8644273.168.538926147...748253.74832.15...6947388.3175426 C3: 5,9 => SOLVED * 143967852269584371785213964427391685538426197691758243974832516812645739356179428 * DURATION: 0:00:02.959184 START: 04:37:48.467626 END: 04:37:51.426810 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-056-base-pr-001.dot * REASONING * DIS # C2: 2,3 => CTR => C2: 5,6,9 * DIS C2: 5,6,9 # C3: 2,3 => CTR => C3: 5,9 * PRF C2: 5,6,9 + C3: 5,9 => SOL * STA C2: 5,6,9 + C3: 5,9 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 056 solution: 143967852269584371785213964427391685538426197691758243974832516812645739356179428 info: 1420 FNBTHWY S8.f 46656 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 143967852269584371785213964427391685538426197691758243974832516812645739356179428 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 # C2: 2,3 => CTR => C2: 5,6,9 * INC # C2: 5,6,9 => UNS * DIS # C3: 2,3 => CTR => C3: 5,9 * INC # C3: 5,9 => UNS * DIS # F2: 3,9 => CTR => F2: 4 * PRF # F2: 4 => SOL * INC # C3: 3,9 => UNS * PRF # G3: 3,9 => SOL * INC # G3: 5,8 => UNS * DIS # G1: 5,9 => CTR => G1: 3,8 * INC # G1: 3,8 => UNS * INC # G2: 5,9 => UNS * PRF # G3: 5,9 => SOL * INC # G3: 3,8 => UNS * DIS # B1: 5,9 => CTR => B1: 4,8 * INC # B1: 4,8 => UNS * DIS # C1: 5,9 => CTR => C1: 3 * PRF # C1: 3 => SOL * PRF # D1: 5,9 => SOL * DIS # D1: 4 => CTR => D1: 5,9 * INC # B6: 6,9 => UNS * DIS # C6: 6,9 => CTR => C6: 1 * INC # C6: 1 => UNS * INC # D1: 4,9 => UNS * DIS # D2: 4,9 => CTR => D2: 2,5 * INC # D2: 2,5 => UNS * DIS # I7: 5,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * INC # B9: 6,9 => UNS * PRF # C9: 6,9 => SOL * INC # C9: 3,5 => UNS * PRF # I7: 6,9 => SOL * DIS # I7: 5 => CTR => I7: 6,9 * DIS # F8: 4,9 => CTR => F8: 5 * PRF # F8: 5 => SOL * PRF # F8: 5,9 => SOL * DIS # F8: 4 => CTR => F8: 5,9 * INC # B9: 5,9 => UNS * DIS # C9: 5,9 => CTR => C9: 3,6 * INC # C9: 3,6 => UNS * DIS # I7: 5,9 => CTR => I7: 6 * PRF # I7: 6 => SOL * DIS # G1: 5,9 => CTR => G1: 3,8 * INC # G1: 3,8 => UNS * INC # G2: 5,9 => UNS * PRF # G3: 5,9 => SOL * INC # G3: 3,8 => UNS * PRF # I9: 8,9 => SOL * DIS # I9: 6 => CTR => I9: 8,9 * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 2,3 => CTR => C2: 5,6,9 * DIS C2: 5,6,9 # C3: 2,3 => CTR => C3: 5,9 * PRF C2: 5,6,9 + C3: 5,9 => SOL * STA C2: 5,6,9 + C3: 5,9 * CNT 3 HDP CHAINS / 2 HYP OPENED