Analysis of xx-top500-116-base.sdk
Contents
Original Sudoku
level: medium
position: ....236...1.....5..........3.2.7.......5...4.6...........1....8.5.4.....7.....3.. initial
Autosolve
position: 5...236...136...5..267...3.3.2.7.......5...436.53......3.1....8.5.43....76.2..3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 8,9 => CTR => B1: 7 * DIS # C1: 8,9 => CTR => C1: 4,7 * DIS # A5: 8,9 => CTR => A5: 1 * DIS # A8: 8,9 => CTR => A8: 1,2 * DIS # B1: 8,9 => CTR => B1: 7 * DIS # C1: 8,9 => CTR => C1: 4,7 * DIS # G6: 2,7 => CTR => G6: 1,8,9 * DIS # G8: 2,7 => CTR => G8: 1,9 * DIS # I8: 2,7 => CTR => I8: 1,6,9 * DIS # I1: 4,9 => CTR => I1: 1 * DIS # A3: 4,9 => CTR => A3: 8 * DIS # F4: 8,9 => CTR => F4: 1,4 * DIS # F5: 8,9 => CTR => F5: 2,6 * DIS # E6: 8,9 => CTR => E6: 1,4 * DIS # F6: 8,9 => CTR => F6: 1,2,4 * PRF # G4: 8,9 => SOL * DIS # H4: 8,9 => CTR => H4: 1,6 * DIS # C9: 4,9 => CTR => C9: 1,8 * DIS # C1: 7,8 => CTR => C1: 4,9 * DIS # H8: 1,9 => CTR => H8: 2,6,7 * DIS # I8: 1,9 => CTR => I8: 2,6,7 * PRF # C9: 1,9 => SOL * DIS # C9: 4,8 => CTR => C9: 1,9 * DIS # H1: 1,9 => CTR => H1: 8 * DIS # H4: 1,9 => CTR => H4: 6,8 * CNT 25 HDP CHAINS / 62 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 8,9 => CTR => B1: 7 * DIS B1: 7 # C1: 8,9 => CTR => C1: 4 * PRF B1: 7 + C1: 4 # F9: 8,9 => SOL * STA B1: 7 + C1: 4 + F9: 8,9 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....236...1.....5..........3.2.7.......5...4.6...........1....8.5.4.....7.....3.. | initial |
| 5...236...136...5..267...3.3.2.7.......5...436.53......3.1....8.5.43....76.2..3.. | autosolve |
| 574923681913684752826715439342871965187596243695342817439167528258439176761258394 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A2: 8,9 D1: 8,9 E3: 1,5 F3: 1,5 G2: 2,7 I2: 2,7 I3: 4,9 D4: 8,9 C7: 4,9 G7: 4,5 H9: 1,9 I9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 1.. / E3 = 1 => 11 pairs (_) / F3 = 1 => 15 pairs (_) H1,I1: 1.. / H1 = 1 => 0 pairs (X) / I1 = 1 => 16 pairs (_) A5,C5: 1.. / A5 = 1 => 12 pairs (_) / C5 = 1 => 0 pairs (X) C9,H9: 1.. / C9 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) A5,A8: 1.. / A5 = 1 => 12 pairs (_) / A8 = 1 => 0 pairs (X) E3,E6: 1.. / E3 = 1 => 11 pairs (_) / E6 = 1 => 15 pairs (_) G2,I2: 2.. / G2 = 2 => 0 pairs (X) / I2 = 2 => 10 pairs (_) F5,F6: 2.. / F5 = 2 => 0 pairs (X) / F6 = 2 => 14 pairs (_) A7,A8: 2.. / A7 = 2 => 0 pairs (X) / A8 = 2 => 16 pairs (_) F5,G5: 2.. / F5 = 2 => 0 pairs (X) / G5 = 2 => 14 pairs (_) A7,H7: 2.. / A7 = 2 => 0 pairs (X) / H7 = 2 => 16 pairs (_) C1,A3: 4.. / C1 = 4 => 16 pairs (_) / A3 = 4 => 0 pairs (X) E2,F2: 4.. / E2 = 4 => 13 pairs (_) / F2 = 4 => 12 pairs (_) B4,B6: 4.. / B4 = 4 => 12 pairs (_) / B6 = 4 => 16 pairs (_) G7,I9: 4.. / G7 = 4 => 0 pairs (X) / I9 = 4 => 16 pairs (_) C1,I1: 4.. / C1 = 4 => 16 pairs (_) / I1 = 4 => 0 pairs (X) B4,F4: 4.. / B4 = 4 => 12 pairs (_) / F4 = 4 => 16 pairs (_) C9,I9: 4.. / C9 = 4 => 0 pairs (X) / I9 = 4 => 16 pairs (_) A3,A7: 4.. / A3 = 4 => 0 pairs (X) / A7 = 4 => 16 pairs (_) E2,E6: 4.. / E2 = 4 => 13 pairs (_) / E6 = 4 => 12 pairs (_) G3,G7: 4.. / G3 = 4 => 16 pairs (_) / G7 = 4 => 0 pairs (X) E3,F3: 5.. / E3 = 5 => 15 pairs (_) / F3 = 5 => 11 pairs (_) G4,I4: 5.. / G4 = 5 => 0 pairs (X) / I4 = 5 => 16 pairs (_) G7,I9: 5.. / G7 = 5 => 16 pairs (_) / I9 = 5 => 0 pairs (X) G4,G7: 5.. / G4 = 5 => 0 pairs (X) / G7 = 5 => 16 pairs (_) I4,I9: 5.. / I4 = 5 => 16 pairs (_) / I9 = 5 => 0 pairs (X) E5,F5: 6.. / E5 = 6 => 0 pairs (X) / F5 = 6 => 16 pairs (_) H4,I4: 6.. / H4 = 6 => 13 pairs (_) / I4 = 6 => 0 pairs (X) E5,E7: 6.. / E5 = 6 => 0 pairs (X) / E7 = 6 => 16 pairs (_) I4,I8: 6.. / I4 = 6 => 0 pairs (X) / I8 = 6 => 13 pairs (_) B1,C1: 7.. / B1 = 7 => 13 pairs (_) / C1 = 7 => 0 pairs (X) G2,I2: 7.. / G2 = 7 => 10 pairs (_) / I2 = 7 => 0 pairs (X) F7,F8: 7.. / F7 = 7 => 12 pairs (_) / F8 = 7 => 0 pairs (X) F7,H7: 7.. / F7 = 7 => 12 pairs (_) / H7 = 7 => 0 pairs (X) C1,C5: 7.. / C1 = 7 => 0 pairs (X) / C5 = 7 => 13 pairs (_) H1,G3: 8.. / H1 = 8 => 16 pairs (_) / G3 = 8 => 0 pairs (X) A3,G3: 8.. / A3 = 8 => 16 pairs (_) / G3 = 8 => 0 pairs (X) D1,D4: 8.. / D1 = 8 => 0 pairs (X) / D4 = 8 => 19 pairs (_) D1,D4: 9.. / D1 = 9 => 19 pairs (_) / D4 = 9 => 0 pairs (X) * DURATION: 0:01:08.398208 START: 06:43:52.839729 END: 06:45:01.237937 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C7,D1,D4,E3,F3,G2,G7,H9,I2,I3,I9) * 5...236...136...5..267...3.3.2.7.......5...436.53......3.1....8.5.43....76.2..3.. * PAIR A2: 8,9 BLK 1 B1: 8,9,7 # reduction candidate for 8,9 B1: 8,9 => CTR * 5.7.236.4.136...5.4267..8393.2.7.......5...436.53......3.1..4.8.5.43....7642..31. B1: 7 # 13 pairs C1: 8,9,4,7 # reduction candidate for 8,9 C1: 8,9 => CTR * 57..236.4.136...5.4267..8393.2.7......75...436.53......3.1..4.8.5.43....7642..31. C1: 4,7 # 13 pairs A3: 8,9,4 # reduction candidate for 8,9 A3: 8,9 # 16 pairs * PAIR A2: 8,9 ROW 2 E2: 8,9,4 # reduction candidate for 8,9 E2: 8,9 # 12 pairs F2: 8,9,4 # reduction candidate for 8,9 F2: 8,9 # 13 pairs * PAIR A2: 8,9 COL A A5: 8,9,1 # reduction candidate for 8,9 A5: 8,9 => CTR * 5.7.236...136...5..267...3.3.2.7......15...436.53......3.1....815.43....76.2..31. A5: 1 # 12 pairs A8: 8,9,1,2 # reduction candidate for 8,9 A8: 8,9 => CTR * 5...236...136...5.4267..8393.2.7....1..5...436.53.....23.1..4.8.5.43....7642..31. A8: 1,2 # 13 pairs * PAIR D1: 8,9 BLK 2 E2: 8,9,4 # reduction candidate for 8,9 E2: 8,9 # 12 pairs F2: 8,9,4 # reduction candidate for 8,9 F2: 8,9 # 13 pairs * PAIR D1: 8,9 ROW 1 B1: 8,9,7 # reduction candidate for 8,9 B1: 8,9 => CTR * 5.7.236.4.136...5.4267..8393.2.7.......5...436.53......3.1..4.8.5.43....7642..31. B1: 7 # 13 pairs C1: 8,9,4,7 # reduction candidate for 8,9 C1: 8,9 => CTR * 57..236.4.136...5.4267..8393.2.7......75...436.53......3.1..4.8.5.43....7642..31. C1: 4,7 # 13 pairs H1: 8,9,1 # reduction candidate for 8,9 H1: 8,9 # 16 pairs * PAIR G2: 2,7 COL G G5: 2,7,8,9 # reduction candidate for 2,7 G5: 2,7 # 14 pairs G6: 2,7,1,8,9 # reduction candidate for 2,7 G6: 2,7 => CTR * 5...236...136...5.4267..8393.2.7.......5629436.53.....23.1..4.8.5.43.1..76.2..3.. G6: 1,8,9 # 12 pairs G8: 2,7,1,9 # reduction candidate for 2,7 G8: 2,7 => CTR * 5...236...136...5.4267..8393.2.7..86...5629436.53..1..23.1..4.8.5.43...176.2..3.. G8: 1,9 # 13 pairs * PAIR I2: 2,7 COL I I6: 2,7,1,9 # reduction candidate for 2,7 I6: 2,7 # 13 pairs I8: 2,7,1,6,9 # reduction candidate for 2,7 I8: 2,7 => CTR * 5...236...136...5..267...3.3.2.7.5.6...5...436.53......3.1..4.8.5.43....7642..315 I8: 1,6,9 # 13 pairs * PAIR I3: 4,9 BLK 3 I1: 4,9,1 # reduction candidate for 4,9 I1: 4,9 => CTR * 5...2361..136...5..267..83.3.2.7.......5...436.53......3.1..4.8.5.43....76.2..3.. I1: 1 # 16 pairs G3: 4,9,8 # reduction candidate for 4,9 G3: 4,9 # 16 pairs * PAIR I3: 4,9 ROW 3 A3: 4,9,8 # reduction candidate for 4,9 A3: 4,9 => CTR * 5...236...136...5..267..83.3.2.7.......5...436.53......3.1..4.8.5.43....7642..315 A3: 8 # 16 pairs * PAIR D4: 8,9 BLK 5 F4: 8,9,1,4 # reduction candidate for 8,9 F4: 8,9 => CTR * 5...236...136...5.4267..839342.7.......562.436.53...8.23.1..4.8.5.43..2.7642..3.. F4: 1,4 # 13 pairs E5: 8,9,6 # reduction candidate for 8,9 E5: 8,9 # 16 pairs F5: 8,9,2,6 # reduction candidate for 8,9 F5: 8,9 => CTR * 5...236...136..7524267..8393.2.7.......56.2436.53.2...23.1..4.8.5.43..2.7642..31. F5: 2,6 # 13 pairs E6: 8,9,1,4 # reduction candidate for 8,9 E6: 8,9 => CTR * 5...236...1364..5.4267158393.2.7.......562.436.53.....23.1..4.8.5.43....7642..31. E6: 1,4 # 13 pairs F6: 8,9,1,2,4 # reduction candidate for 8,9 F6: 8,9 => CTR * 5...236...136...5.4267..8393.2.7.......562.436.53.....23.1..4.8.5.43....7642..31. F6: 1,2,4 # 12 pairs * PAIR D4: 8,9 ROW 4 B4: 8,9,4 # reduction candidate for 8,9 B4: 8,9 # 16 pairs G4: 8,9,1,5 # reduction candidate for 8,9 G4: 8,9 => SOLVED * 574923681913684752826715439342871965187596243695342817439167528258439176761258394 G4: 1,5 # 13 pairs H4: 8,9,1,6 # reduction candidate for 8,9 H4: 8,9 => CTR * 5...236...136...5..267...3.3.2.7.5.6...5...436.53......3.1..4.8.5.43....7642..315 H4: 1,6 # 13 pairs * PAIR C7: 4,9 BLK 7 A7: 4,9,2 # reduction candidate for 4,9 A7: 4,9 # 16 pairs C9: 4,9,1,8 # reduction candidate for 4,9 C9: 4,9 => CTR * 5.4.236.1.136...5..267...3.3.2.7......75...436.53.....43.1....8.5.43....76.2..31. C9: 1,8 # 16 pairs * PAIR C7: 4,9 COL C C1: 4,9,7,8 # reduction candidate for 4,9 C1: 7,8 => CTR * 5...236.4.136...5.4267..8393.2.7.......5...436.53......3.1..4.8.5.43....7642..31. C1: 4,9 # 16 pairs * PAIR H9: 1,9 BLK 9 G8: 1,9,2,7 # reduction candidate for 1,9 G8: 1,9 # 13 pairs H8: 1,9,2,6,7 # reduction candidate for 1,9 H8: 1,9 => CTR * 5...23681.136...5.8267...3.3.287..6....5.2.436.53.....4391..52825.43.7.676.2..3.4 H8: 2,6,7 # 12 pairs I8: 1,9,2,6,7 # reduction candidate for 1,9 I8: 1,9 => CTR * 5...236...136...5..267...3.3.2.7.5.6...5...436.53......3.1..4.8.5.43....7642..315 I8: 2,6,7 # 12 pairs * PAIR H9: 1,9 ROW 9 C9: 1,9,4,8 # reduction candidate for 1,9 C9: 1,9 => SOLVED * 574923681913684752826715439342871965187596243695342817439167528258439176761258394 C9: 4,8 => CTR * 574923681913684.5.8267..43934287..651.7596243695342...439167528251438..67682..314 * PAIR H9: 1,9 COL H H1: 1,9,8 # reduction candidate for 1,9 H1: 1,9 => CTR * 5...236...136...5..267..83.3.2.7.......5...436.53......3.1..4.8.5.43....7642..315 H1: 8 # 16 pairs H4: 1,9,6,8 # reduction candidate for 1,9 H4: 1,9 => CTR * 5...236...136...5..267...3.3.2.7.5.6...5...436.53......3.1..4.8.5.43....7642..315 H4: 6,8 # 13 pairs H6: 1,9,2,7,8 # reduction candidate for 1,9 H6: 1,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-116-base-pr-000.dot * REASONING * DIS # B1: 8,9 => CTR => B1: 7 * DIS # C1: 8,9 => CTR => C1: 4,7 * DIS # A5: 8,9 => CTR => A5: 1 * DIS # A8: 8,9 => CTR => A8: 1,2 * DIS # B1: 8,9 => CTR => B1: 7 * DIS # C1: 8,9 => CTR => C1: 4,7 * DIS # G6: 2,7 => CTR => G6: 1,8,9 * DIS # G8: 2,7 => CTR => G8: 1,9 * DIS # I8: 2,7 => CTR => I8: 1,6,9 * DIS # I1: 4,9 => CTR => I1: 1 * DIS # A3: 4,9 => CTR => A3: 8 * DIS # F4: 8,9 => CTR => F4: 1,4 * DIS # F5: 8,9 => CTR => F5: 2,6 * DIS # E6: 8,9 => CTR => E6: 1,4 * DIS # F6: 8,9 => CTR => F6: 1,2,4 * PRF # G4: 8,9 => SOL * DIS # H4: 8,9 => CTR => H4: 1,6 * DIS # C9: 4,9 => CTR => C9: 1,8 * DIS # C1: 7,8 => CTR => C1: 4,9 * DIS # H8: 1,9 => CTR => H8: 2,6,7 * DIS # I8: 1,9 => CTR => I8: 2,6,7 * PRF # C9: 1,9 => SOL * DIS # C9: 4,8 => CTR => C9: 1,9 * DIS # H1: 1,9 => CTR => H1: 8 * DIS # H4: 1,9 => CTR => H4: 6,8 * CNT 25 HDP CHAINS / 62 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C7,D1,D4,E3,F3,G2,G7,H9,I2,I3,I9) * 5...236...136...5..267...3.3.2.7.......5...436.53......3.1....8.5.43....76.2..3.. * PAIR A2: 8,9 BLK 1 B1: 8,9,7 # reduction candidate for 8,9 B1: 8,9 => CTR * 5.7.236.4.136...5.4267..8393.2.7.......5...436.53......3.1..4.8.5.43....7642..31. C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 => CTR * 57..236.4.136...5.4267..8393.2.7....1.75...436.53......3.1..4.8.5.43....7642..31. * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B4,B6,C8,C9,E2,E3,E6,E9,F2,F3,F4,F8,G4,G8,H6,H9) * 5749236819136..7528267..4393.287..651875962436.53.28.743916752825.43..7676.2..3.4 * PAIR F8: 8,9 BLK 8 F9: 8,9,5 # reduction candidate for 8,9 F9: 8,9 => SOLVED * 574923681913684752826715439342871965187596243695342817439167528258439176761258394 * DURATION: 0:00:05.528666 START: 06:46:00.795536 END: 06:46:06.324202 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-116-base-pr-001.dot * REASONING * DIS # B1: 8,9 => CTR => B1: 7 * DIS B1: 7 # C1: 8,9 => CTR => C1: 4 * PRF B1: 7 + C1: 4 # F9: 8,9 => SOL * STA B1: 7 + C1: 4 + F9: 8,9 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 116 solution: 574923681913684752826715439342871965187596243695342817439167528258439176761258394 info: 1754 FNBHWXY S8.f 3556 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 574923681913684752826715439342871965187596243695342817439167528258439176761258394 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 # B1: 8,9 => CTR => B1: 7 * INC # B1: 7 => UNS * DIS # C1: 8,9 => CTR => C1: 4,7 * INC # C1: 4,7 => UNS * INC # A3: 8,9 => UNS * INC # E2: 8,9 => UNS * INC # F2: 8,9 => UNS * DIS # A5: 8,9 => CTR => A5: 1 * INC # A5: 1 => UNS * DIS # A8: 8,9 => CTR => A8: 1,2 * INC # A8: 1,2 => UNS * INC # E2: 8,9 => UNS * INC # F2: 8,9 => UNS * DIS # B1: 8,9 => CTR => B1: 7 * INC # B1: 7 => UNS * DIS # C1: 8,9 => CTR => C1: 4,7 * INC # C1: 4,7 => UNS * INC # H1: 8,9 => UNS * INC # G5: 2,7 => UNS * DIS # G6: 2,7 => CTR => G6: 1,8,9 * INC # G6: 1,8,9 => UNS * DIS # G8: 2,7 => CTR => G8: 1,9 * INC # G8: 1,9 => UNS * INC # I6: 2,7 => UNS * DIS # I8: 2,7 => CTR => I8: 1,6,9 * INC # I8: 1,6,9 => UNS * DIS # I1: 4,9 => CTR => I1: 1 * INC # I1: 1 => UNS * INC # G3: 4,9 => UNS * DIS # A3: 4,9 => CTR => A3: 8 * INC # A3: 8 => UNS * DIS # F4: 8,9 => CTR => F4: 1,4 * INC # F4: 1,4 => UNS * INC # E5: 8,9 => UNS * DIS # F5: 8,9 => CTR => F5: 2,6 * INC # F5: 2,6 => UNS * DIS # E6: 8,9 => CTR => E6: 1,4 * INC # E6: 1,4 => UNS * DIS # F6: 8,9 => CTR => F6: 1,2,4 * INC # F6: 1,2,4 => UNS * INC # B4: 8,9 => UNS * PRF # G4: 8,9 => SOL * INC # G4: 1,5 => UNS * DIS # H4: 8,9 => CTR => H4: 1,6 * INC # H4: 1,6 => UNS * INC # A7: 4,9 => UNS * DIS # C9: 4,9 => CTR => C9: 1,8 * INC # C9: 1,8 => UNS * INC # C1: 4,9 => UNS * DIS # C1: 7,8 => CTR => C1: 4,9 * INC # G8: 1,9 => UNS * DIS # H8: 1,9 => CTR => H8: 2,6,7 * INC # H8: 2,6,7 => UNS * DIS # I8: 1,9 => CTR => I8: 2,6,7 * INC # I8: 2,6,7 => UNS * PRF # C9: 1,9 => SOL * DIS # C9: 4,8 => CTR => C9: 1,9 * DIS # H1: 1,9 => CTR => H1: 8 * INC # H1: 8 => UNS * DIS # H4: 1,9 => CTR => H4: 6,8 * INC # H4: 6,8 => UNS * INC # H6: 1,9 => UNS * CNT 62 HDP CHAINS / 62 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 8,9 => CTR => B1: 7 * DIS B1: 7 # C1: 8,9 => CTR => C1: 4 * PRF B1: 7 + C1: 4 # F9: 8,9 => SOL * STA B1: 7 + C1: 4 + F9: 8,9 * CNT 3 HDP CHAINS / 3 HYP OPENED