Analysis of xx-top500-111-base.sdk
Contents
Original Sudoku
level: medium
position: .3..2.......5...7........1..4..3.6........2..1..........6...4.35..7.1......8..... initial
Autosolve
position: .3..2..6....5..37....3...1..4..3.69.3.....24.1.....73.716...483583741926...863157 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 5,7 => CTR => C1: 1,4,8 * PRF # C1: 1,4,8 => SOL * PRF # C3: 5,7 => SOL * DIS # C3: 2,4,8 => CTR => C3: 5,7 * DIS # B5: 6 => CTR => B5: 5,7 * DIS # C1: 5,8 => CTR => C1: 1,4,7 * DIS # A1: 4,9 => CTR => A1: 8 * PRF # A1: 8 => SOL * PRF # D1: 4,9 => SOL * DIS # D1: 1 => CTR => D1: 4,9 * DIS # F1: 4,9 => CTR => F1: 7,8 * PRF # C3: 5,8 => SOL * DIS # C4: 2,8 => CTR => C4: 5,7 * DIS # F4: 2,8 => CTR => F4: 5,7 * DIS # A2: 2,8 => CTR => A2: 4,6,9 * DIS # A3: 2,8 => CTR => A3: 4,6,9 * PRF # B5: 5,6 => SOL * DIS # B5: 7 => CTR => B5: 5,6 * PRF # I4: 5,8 => SOL * DIS # I4: 1 => CTR => I4: 5,8 * DIS # I5: 5,8 => CTR => I5: 1 * PRF # I5: 1 => SOL * DIS # C6: 5,8 => CTR => C6: 2,9 * DIS # F6: 5,8 => CTR => F6: 2,4,9 * DIS # A9: 4 => CTR => A9: 2,9 * PRF # C2: 2,4 => SOL * DIS # C3: 2,4 => CTR => C3: 5,7,8 * PRF # C3: 5,7,8 => SOL * DIS # F7: 5 => CTR => F7: 2,9 * PRF # D6: 2,9 => SOL * DIS # F7: 5,9 => CTR => F7: 2 * DIS # E5: 5,9 => CTR => E5: 1,7,8 * DIS # E6: 5,9 => CTR => E6: 8 * CNT 33 HDP CHAINS / 60 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 5,7 => CTR => C1: 1,4,8 * PRF C1: 1,4,8 => SOL * STA C1: 1,4,8 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3..2.......5...7........1..4..3.6........2..1..........6...4.35..7.1......8..... | initial |
| .3..2..6....5..37....3...1..4..3.69.3.....24.1.....73.716...483583741926...863157 | autosolve |
| 831427569692518374475396812247135698358679241169284735716952483583741926924863157 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B2: 2,9 B3: 5,7 G1: 5,8 I1: 4,9 G3: 5,8 A4: 2,8 B6: 5,6 D4: 1,2 I6: 5,8 B9: 2,9 C9: 2,4 D7: 2,9 E7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C2: 1.. / C1 = 1 => 0 pairs (*) / C2 = 1 => 0 pairs (X) D1,E2: 1.. / D1 = 1 => 0 pairs (X) / E2 = 1 => 0 pairs (_) I4,I5: 1.. / I4 = 1 => 0 pairs (X) / I5 = 1 => 0 pairs (_) C1,D1: 1.. / C1 = 1 => 0 pairs (*) / D1 = 1 => 0 pairs (X) C2,E2: 1.. / C2 = 1 => 0 pairs (X) / E2 = 1 => 0 pairs (_) D4,I4: 1.. / D4 = 1 => 0 pairs (*) / I4 = 1 => 0 pairs (X) E2,E5: 1.. / E2 = 1 => 0 pairs (*) / E5 = 1 => 0 pairs (X) I2,I3: 2.. / I2 = 2 => 16 pairs (_) / I3 = 2 => 14 pairs (_) D7,F7: 2.. / D7 = 2 => 0 pairs (X) / F7 = 2 => 14 pairs (_) B2,B9: 2.. / B2 = 2 => 13 pairs (_) / B9 = 2 => 13 pairs (_) D6,F6: 4.. / D6 = 4 => 14 pairs (_) / F6 = 4 => 0 pairs (*) A9,C9: 4.. / A9 = 4 => 0 pairs (X) / C9 = 4 => 13 pairs (_) D1,D6: 4.. / D1 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) G1,G3: 5.. / G1 = 5 => 12 pairs (_) / G3 = 5 => 0 pairs (X) E7,F7: 5.. / E7 = 5 => 14 pairs (_) / F7 = 5 => 0 pairs (X) C1,G1: 5.. / C1 = 5 => 0 pairs (X) / G1 = 5 => 12 pairs (_) A2,A3: 6.. / A2 = 6 => 13 pairs (_) / A3 = 6 => 13 pairs (_) F2,F3: 6.. / F2 = 6 => 13 pairs (_) / F3 = 6 => 13 pairs (_) B5,B6: 6.. / B5 = 6 => 0 pairs (X) / B6 = 6 => 13 pairs (_) D5,D6: 6.. / D5 = 6 => 13 pairs (_) / D6 = 6 => 0 pairs (X) A2,F2: 6.. / A2 = 6 => 13 pairs (_) / F2 = 6 => 13 pairs (_) A3,F3: 6.. / A3 = 6 => 13 pairs (_) / F3 = 6 => 13 pairs (_) B5,D5: 6.. / B5 = 6 => 0 pairs (X) / D5 = 6 => 13 pairs (_) B6,D6: 6.. / B6 = 6 => 13 pairs (_) / D6 = 6 => 0 pairs (X) C1,F1: 7.. / C1 = 7 => 0 pairs (X) / F1 = 7 => 0 pairs (_) C4,F4: 7.. / C4 = 7 => 0 pairs (*) / F4 = 7 => 0 pairs (X) B3,B5: 7.. / B3 = 7 => 0 pairs (*) / B5 = 7 => 0 pairs (X) E3,E5: 7.. / E3 = 7 => 0 pairs (X) / E5 = 7 => 0 pairs (_) G1,G3: 8.. / G1 = 8 => 0 pairs (X) / G3 = 8 => 12 pairs (_) C5,C6: 9.. / C5 = 9 => 14 pairs (_) / C6 = 9 => 0 pairs (*) A9,B9: 9.. / A9 = 9 => 13 pairs (_) / B9 = 9 => 13 pairs (_) B2,B9: 9.. / B2 = 9 => 13 pairs (_) / B9 = 9 => 13 pairs (_) * DURATION: 0:00:54.189283 START: 06:33:43.200678 END: 06:34:37.389961 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B2,B3,B6,B9,C9,D4,D7,E7,G1,G3,I1,I6) * .3..2..6....5..37....3...1..4..3.69.3.....24.1.....73.716...483583741926...863157 * PAIR B2: 2,9 BLK 1 A2: 2,9,4,6,8 # reduction candidate for 2,9 A2: 2,9 # 17 pairs A3: 2,9,4,6,8 # reduction candidate for 2,9 A3: 2,9 # 15 pairs * PAIR B2: 2,9 ROW 2 I2: 2,9,4 # reduction candidate for 2,9 I2: 2,9 # 15 pairs I2: 4 # 14 pairs * PAIR B3: 5,7 BLK 1 C1: 5,7,1,4,8 # reduction candidate for 5,7 C1: 5,7 => CTR * .3712.56...15..37..5837..1.84.23.69137961.24.1624..73.716952483583741926..4863157 C1: 1,4,8 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 C3: 5,7,2,4,8 # reduction candidate for 5,7 C3: 5,7 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 C3: 2,4,8 => CTR * .3.12..6...15..37...837.51..4.23.6913...1.24.1.24..73.716952483583741926..4863157 * PAIR B3: 5,7 COL B B5: 5,7,6 # reduction candidate for 5,7 B5: 6 => CTR * .3.427.69...51.37..7.38.51..47.3.69.36..7.24.15.6.4738716.5.483583741926...863157 B5: 5,7 # 13 pairs * PAIR G1: 5,8 ROW 1 C1: 5,8,1,4,7 # reduction candidate for 5,8 C1: 5,8 => CTR * .3.127.6...15..37....3...1..4723.69.3.....24.1.....73.716...483583741926...863157 C1: 1,4,7 # 12 pairs * PAIR I1: 4,9 BLK 3 I2: 4,9,2 # reduction candidate for 4,9 I2: 4,9 # 14 pairs I3: 4,9,2 # reduction candidate for 4,9 I3: 4,9 # 16 pairs * PAIR I1: 4,9 ROW 1 A1: 4,9,8 # reduction candidate for 4,9 A1: 4,9 => CTR * .3712856...159.37..5837..1.84.23.69137961.24.1624..73.716952483583741926..4863157 A1: 8 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 D1: 4,9,1 # reduction candidate for 4,9 D1: 4,9 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 D1: 1 => CTR * .3712.56...15..37..5837..1.84.23.69137961.24.1624..73.716952483583741926..4863157 F1: 4,9,7,8 # reduction candidate for 4,9 F1: 4,9 => CTR * .3712.56...15..37..5.3..81..4.23769137.61.24.1624..73.716952483583741926..4863157 F1: 7,8 # 14 pairs * PAIR G3: 5,8 ROW 3 C3: 5,8,2,4,7 # reduction candidate for 5,8 C3: 5,8 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 C3: 2,4,7 # 13 pairs * PAIR A4: 2,8 BLK 4 C4: 2,8,5,7 # reduction candidate for 2,8 C4: 2,8 => CTR * .3712.56...15..37..5.37.81..4.23769537.6..2411624..738716952483583741926..4863157 C4: 5,7 # 15 pairs C6: 2,8,5,9 # reduction candidate for 2,8 C6: 2,8 # 16 pairs * PAIR A4: 2,8 ROW 4 F4: 2,8,5,7 # reduction candidate for 2,8 F4: 2,8 => CTR * .31.2756....51.37..7538..1..4713.6953...7.2411.....738716...483583741926...863157 F4: 5,7 # 14 pairs * PAIR A4: 2,8 COL A A2: 2,8,4,6,9 # reduction candidate for 2,8 A2: 2,8 => CTR * .3.12..6...15.63746..3.4.12.4.23.6913...1.24.1.24..73.71695.483583741926...863157 A2: 4,6,9 # 13 pairs A3: 2,8,4,6,9 # reduction candidate for 2,8 A3: 2,8 => CTR * 43.12..6969158437....3.6.1..4.23.6913...1.24.1.24..73.716952483583741926.24863157 A3: 4,6,9 # 13 pairs * PAIR B6: 5,6 BLK 4 B5: 5,6,7 # reduction candidate for 5,6 B5: 5,6 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 B5: 7 => CTR * .3712.56...15..37..5.37.81..4.23769137.61.24.1624..73.716952483583741926..4863157 * PAIR I6: 5,8 BLK 6 I4: 5,8,1 # reduction candidate for 5,8 I4: 5,8 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 I4: 1 => CTR * .3.12..6...158.37....39..1.84.23.6913.9...24.1.2...73.716952483583741926..4863157 I5: 5,8,1 # reduction candidate for 5,8 I5: 5,8 => CTR * .3.12..6...158.37....39..1.84.23.6913.9...24.1.2...73.716952483583741926..4863157 I5: 1 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 * PAIR I6: 5,8 ROW 6 C6: 5,8,2,9 # reduction candidate for 5,8 C6: 5,8 => CTR * .31.2756....51.37....3..81..4713.69.359678241168...735716.5.483583741926...863157 C6: 2,9 # 14 pairs E6: 5,8,9 # reduction candidate for 5,8 E6: 5,8 # 15 pairs F6: 5,8,2,4,9 # reduction candidate for 5,8 F6: 5,8 => CTR * .3..2..6....5..37....3...1.84..3.69.3.96..24.16249.73.716.5.483583741926..4863157 F6: 2,4,9 # 13 pairs * PAIR B9: 2,9 BLK 7 A9: 2,9,4 # reduction candidate for 2,9 A9: 4 => CTR * 831.2756..245183799..3..81224713.69.3...7.2411...8.735716.5.483583741926492863157 A9: 2,9 # 13 pairs * PAIR C9: 2,4 BLK 7 A9: 2,4,9 # reduction candidate for 2,4 A9: 9 # 13 pairs A9: 2,4 # 13 pairs * PAIR C9: 2,4 COL C C2: 2,4,1,8 # reduction candidate for 2,4 C2: 2,4 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 C2: 1,8 # 14 pairs C3: 2,4,5,7,8 # reduction candidate for 2,4 C3: 2,4 => CTR * .3.12..6...15..37....3...1.24..3.69.3.....24.1.....73.716...483583741926...863157 C3: 5,7,8 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 * PAIR D7: 2,9 BLK 8 F7: 2,9,5 # reduction candidate for 2,9 F7: 5 => CTR * .31.2756....51.37....38..1..4.13.69.3.....2411.....73.716295483583741926...863157 F7: 2,9 # 14 pairs * PAIR D7: 2,9 COL D D6: 2,9,4,6 # reduction candidate for 2,9 D6: 2,9 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 D6: 4,6 # 14 pairs * PAIR E7: 5,9 BLK 8 F7: 5,9,2 # reduction candidate for 5,9 F7: 5,9 => CTR * 831.2756....51837..7539681.24713569.3...7.2411...8.735716259483583741926...863157 F7: 2 # 14 pairs * PAIR E7: 5,9 COL E E5: 5,9,1,7,8 # reduction candidate for 5,9 E5: 5,9 => CTR * .3..2..6....51.37....37..1..4..3.69.37.6..24116..8.735716...483583741926...863157 E5: 1,7,8 # 13 pairs E6: 5,9,8 # reduction candidate for 5,9 E6: 5,9 => CTR * .31.2756...85..37....3...1.24.13.69.3.....2411.....73.716...483583741926...863157 E6: 8 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-111-base-pr-000.dot * REASONING * DIS # C1: 5,7 => CTR => C1: 1,4,8 * PRF # C1: 1,4,8 => SOL * PRF # C3: 5,7 => SOL * DIS # C3: 2,4,8 => CTR => C3: 5,7 * DIS # B5: 6 => CTR => B5: 5,7 * DIS # C1: 5,8 => CTR => C1: 1,4,7 * DIS # A1: 4,9 => CTR => A1: 8 * PRF # A1: 8 => SOL * PRF # D1: 4,9 => SOL * DIS # D1: 1 => CTR => D1: 4,9 * DIS # F1: 4,9 => CTR => F1: 7,8 * PRF # C3: 5,8 => SOL * DIS # C4: 2,8 => CTR => C4: 5,7 * DIS # F4: 2,8 => CTR => F4: 5,7 * DIS # A2: 2,8 => CTR => A2: 4,6,9 * DIS # A3: 2,8 => CTR => A3: 4,6,9 * PRF # B5: 5,6 => SOL * DIS # B5: 7 => CTR => B5: 5,6 * PRF # I4: 5,8 => SOL * DIS # I4: 1 => CTR => I4: 5,8 * DIS # I5: 5,8 => CTR => I5: 1 * PRF # I5: 1 => SOL * DIS # C6: 5,8 => CTR => C6: 2,9 * DIS # F6: 5,8 => CTR => F6: 2,4,9 * DIS # A9: 4 => CTR => A9: 2,9 * PRF # C2: 2,4 => SOL * DIS # C3: 2,4 => CTR => C3: 5,7,8 * PRF # C3: 5,7,8 => SOL * DIS # F7: 5 => CTR => F7: 2,9 * PRF # D6: 2,9 => SOL * DIS # F7: 5,9 => CTR => F7: 2 * DIS # E5: 5,9 => CTR => E5: 1,7,8 * DIS # E6: 5,9 => CTR => E6: 8 * CNT 33 HDP CHAINS / 60 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B2,B3,B6,B9,C9,D4,D7,E7,G1,G3,I1,I6) * .3..2..6....5..37....3...1..4..3.69.3.....24.1.....73.716...483583741926...863157 * PAIR B2: 2,9 BLK 1 A2: 2,9,4,6,8 # reduction candidate for 2,9 A2: 2,9 # 17 pairs A3: 2,9,4,6,8 # reduction candidate for 2,9 A3: 2,9 # 15 pairs * PAIR B2: 2,9 ROW 2 I2: 2,9,4 # reduction candidate for 2,9 I2: 2,9 # 15 pairs I2: 4 # 14 pairs * PAIR B3: 5,7 BLK 1 C1: 5,7,1,4,8 # reduction candidate for 5,7 C1: 5,7 => CTR * .3712.56...15..37..5837..1.84.23.69137961.24.1624..73.716952483583741926..4863157 C1: 1,4,8 => SOLVED * 831427569692518374475396812247135698358679241169284735716952483583741926924863157 * DURATION: 0:00:05.483766 START: 06:35:37.455686 END: 06:35:42.939452 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-111-base-pr-001.dot * REASONING * DIS # C1: 5,7 => CTR => C1: 1,4,8 * PRF C1: 1,4,8 => SOL * STA C1: 1,4,8 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 111 solution: 831427569692518374475396812247135698358679241169284735716952483583741926924863157 info: 1646 FNBTHWY S8.f 17717 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 831427569692518374475396812247135698358679241169284735716952483583741926924863157 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 # A2: 2,9 => UNS * INC # A3: 2,9 => UNS * INC # I2: 2,9 => UNS * INC # I2: 4 => UNS * DIS # C1: 5,7 => CTR => C1: 1,4,8 * PRF # C1: 1,4,8 => SOL * PRF # C3: 5,7 => SOL * DIS # C3: 2,4,8 => CTR => C3: 5,7 * INC # B5: 5,7 => UNS * DIS # B5: 6 => CTR => B5: 5,7 * DIS # C1: 5,8 => CTR => C1: 1,4,7 * INC # C1: 1,4,7 => UNS * INC # I2: 4,9 => UNS * INC # I3: 4,9 => UNS * DIS # A1: 4,9 => CTR => A1: 8 * PRF # A1: 8 => SOL * PRF # D1: 4,9 => SOL * DIS # D1: 1 => CTR => D1: 4,9 * DIS # F1: 4,9 => CTR => F1: 7,8 * INC # F1: 7,8 => UNS * PRF # C3: 5,8 => SOL * INC # C3: 2,4,7 => UNS * DIS # C4: 2,8 => CTR => C4: 5,7 * INC # C4: 5,7 => UNS * INC # C6: 2,8 => UNS * DIS # F4: 2,8 => CTR => F4: 5,7 * INC # F4: 5,7 => UNS * DIS # A2: 2,8 => CTR => A2: 4,6,9 * INC # A2: 4,6,9 => UNS * DIS # A3: 2,8 => CTR => A3: 4,6,9 * INC # A3: 4,6,9 => UNS * PRF # B5: 5,6 => SOL * DIS # B5: 7 => CTR => B5: 5,6 * PRF # I4: 5,8 => SOL * DIS # I4: 1 => CTR => I4: 5,8 * DIS # I5: 5,8 => CTR => I5: 1 * PRF # I5: 1 => SOL * DIS # C6: 5,8 => CTR => C6: 2,9 * INC # C6: 2,9 => UNS * INC # E6: 5,8 => UNS * DIS # F6: 5,8 => CTR => F6: 2,4,9 * INC # F6: 2,4,9 => UNS * INC # A9: 2,9 => UNS * DIS # A9: 4 => CTR => A9: 2,9 * INC # A9: 2,4 => UNS * INC # A9: 9 => UNS * PRF # C2: 2,4 => SOL * INC # C2: 1,8 => UNS * DIS # C3: 2,4 => CTR => C3: 5,7,8 * PRF # C3: 5,7,8 => SOL * INC # F7: 2,9 => UNS * DIS # F7: 5 => CTR => F7: 2,9 * PRF # D6: 2,9 => SOL * INC # D6: 4,6 => UNS * DIS # F7: 5,9 => CTR => F7: 2 * INC # F7: 2 => UNS * DIS # E5: 5,9 => CTR => E5: 1,7,8 * INC # E5: 1,7,8 => UNS * DIS # E6: 5,9 => CTR => E6: 8 * INC # E6: 8 => UNS * CNT 60 HDP CHAINS / 60 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 2,9 => UNS * INC # A3: 2,9 => UNS * INC # I2: 2,9 => UNS * INC # I2: 4 => UNS * DIS # C1: 5,7 => CTR => C1: 1,4,8 * PRF C1: 1,4,8 => SOL * STA C1: 1,4,8 * CNT 6 HDP CHAINS / 5 HYP OPENED