Analysis of xx-top500-209-base.sdk
Contents
Original Sudoku
level: medium
position: ....7...5.6..4.....1.......5..6.3...7.......2...1..4..2..8...........63........1. initial
Autosolve
position: ....7...5.6..4.....1.......5..6.3...7.......2...1.74..2..81....1.....63.......21. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 3,9 => CTR => D2: 2,5 * DIS # D3: 3,9 => CTR => D3: 2,5 * DIS # G1: 3,9 => CTR => G1: 1,8 * DIS # D9: 4,5,7 => CTR => D9: 3,9 * DIS # I3: 4,7,9 => CTR => I3: 3,6 * DIS # D8: 5,9 => CTR => D8: 2,4,7 * DIS # F8: 5,9 => CTR => F8: 2,4 * DIS # D9: 5,9 => CTR => D9: 3,4,7 * CNT 8 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 3,9 => CTR => D2: 2,5 * DIS D2: 2,5 # D3: 3,9 => CTR => D3: 2,5 * DIS D2: 2,5 + D3: 2,5 # G1: 3,9 => CTR => G1: 1,8 * DIS D2: 2,5 + D3: 2,5 + G1: 1,8 # D9: 4,7 => CTR => D9: 3,9 * DIS D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 # I3: 4,7,9 => CTR => I3: 3,6 * PRF D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 + I3: 3,6 # F9: 5,9 => SOL * STA D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 + I3: 3,6 + F9: 5,9 * CNT 6 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....7...5.6..4.....1.......5..6.3...7.......2...1..4..2..8...........63........1. | initial |
| ....7...5.6..4.....1.......5..6.3...7.......2...1.74..2..81....1.....63.......21. | autosolve |
| 342976185867541923915238746594623871781459362623187459236814597158792634479365218 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) C2: 5,7 C3: 5,7 D1: 3,9 E3: 3,6 E8: 5,9 E9: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F2: 1.. / F1 = 1 => 0 pairs (X) / F2 = 1 => 0 pairs (_) C4,C5: 1.. / C4 = 1 => 0 pairs (X) / C5 = 1 => 0 pairs (_) F1,G1: 1.. / F1 = 1 => 0 pairs (X) / G1 = 1 => 0 pairs (_) C5,G5: 1.. / C5 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) I2,I4: 1.. / I2 = 1 => 0 pairs (X) / I4 = 1 => 0 pairs (_) B1,C1: 2.. / B1 = 2 => 6 pairs (_) / C1 = 2 => 6 pairs (_) H2,H3: 2.. / H2 = 2 => 6 pairs (_) / H3 = 2 => 8 pairs (_) E4,E6: 2.. / E4 = 2 => 6 pairs (_) / E6 = 2 => 0 pairs (X) D8,F8: 2.. / D8 = 2 => 0 pairs (X) / F8 = 2 => 6 pairs (_) G5,I6: 3.. / G5 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) B7,C7: 3.. / B7 = 3 => 0 pairs (*) / C7 = 3 => 0 pairs (X) D9,E9: 3.. / D9 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) E3,E9: 3.. / E3 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) B4,C4: 4.. / B4 = 4 => 6 pairs (_) / C4 = 4 => 0 pairs (*) D5,F5: 4.. / D5 = 4 => 7 pairs (_) / F5 = 4 => 0 pairs (X) C2,C3: 5.. / C2 = 5 => 4 pairs (_) / C3 = 5 => 4 pairs (_) B8,B9: 5.. / B8 = 5 => 13 pairs (_) / B9 = 5 => 6 pairs (_) G7,H7: 5.. / G7 = 5 => 6 pairs (_) / H7 = 5 => 0 pairs (X) E6,H6: 5.. / E6 = 5 => 0 pairs (X) / H6 = 5 => 6 pairs (_) G5,G7: 5.. / G5 = 5 => 0 pairs (X) / G7 = 5 => 6 pairs (_) F1,H1: 6.. / F1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) C5,H5: 6.. / C5 = 6 => 0 pairs (X) / H5 = 6 => 0 pairs (_) C7,F7: 6.. / C7 = 6 => 0 pairs (*) / F7 = 6 => 0 pairs (X) A6,A9: 6.. / A6 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) E3,E9: 6.. / E3 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) I3,I6: 6.. / I3 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) C2,C3: 7.. / C2 = 7 => 4 pairs (_) / C3 = 7 => 4 pairs (_) D8,D9: 7.. / D8 = 7 => 6 pairs (_) / D9 = 7 => 0 pairs (X) I8,I9: 8.. / I8 = 8 => 7 pairs (_) / I9 = 8 => 6 pairs (_) * DURATION: 0:00:47.677059 START: 09:58:36.289368 END: 09:59:23.966427 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C3,D1,E3,E8,E9) * ....7...5.6..4.....1.......5..6.3...7.......2...1.74..2..81....1.....63.......21. * PAIR D1: 3,9 BLK 2 D2: 3,9,2,5 # reduction candidate for 3,9 D2: 3,9 => CTR * ....7..65.6..4.....1..6....5..6.3...7.6...1.2...1.74..2..81....1.....63.......21. D2: 2,5 # 7 pairs D3: 3,9,2,5 # reduction candidate for 3,9 D3: 3,9 => CTR * ....7..65.6..4.....1..6....5..6.3...7.6...1.2...1.74..2..81....1.....63.......21. D3: 2,5 # 7 pairs * PAIR D1: 3,9 ROW 1 A1: 3,9,4,8 # reduction candidate for 3,9 A1: 3,9 # 9 pairs B1: 3,9,2,4,8 # reduction candidate for 3,9 B1: 3,9 # 10 pairs C1: 3,9,2,4,8 # reduction candidate for 3,9 C1: 3,9 # 10 pairs G1: 3,9,1,8 # reduction candidate for 3,9 G1: 3,9 => CTR * ....71.65.6..4.....1.......5..6.3...7.6...1.2...1.74..2..81....1.....63.......21. G1: 1,8 # 7 pairs * PAIR D1: 3,9 COL D D9: 3,9,4,5,7 # reduction candidate for 3,9 D9: 4,5,7 => CTR * ....7..65.6..4.....1..6....5..6.3...7.6.....2...1.74.62..81....1.....63.6...3.21. D9: 3,9 # 10 pairs * PAIR E3: 3,6 ROW 3 I3: 3,6,4,7,9 # reduction candidate for 3,6 I3: 4,7,9 => CTR * ....7...5.6..4...3.1..6....5..6.3..17.......2...1.74.62..81....1.....63.6...3.21. I3: 3,6 # 7 pairs * PAIR E8: 5,9 BLK 8 D8: 5,9,2,4,7 # reduction candidate for 5,9 D8: 5,9 => CTR * ....7..65.6..4.....1..6....5..6.3...7.64....2...1.74.62..81....1....263.6..73.21. D8: 2,4,7 # 6 pairs F8: 5,9,2,4 # reduction candidate for 5,9 F8: 5,9 => CTR * ....7..65.6..4.....1..6....5..6.3...7.64....2...1.74.62..81....1..2..63.6..73.21. F8: 2,4 # 7 pairs D9: 5,9,3,4,7 # reduction candidate for 5,9 D9: 5,9 => CTR * ....7..65.6..4.....1..6....5..6.3...7.64....2...1.74.62..81....1..7.263.6...3.21. D9: 3,4,7 # 6 pairs F9: 5,9,4,6 # reduction candidate for 5,9 F9: 5,9 # 9 pairs * PAIR E8: 5,9 ROW 8 B8: 5,9,4,7,8 # reduction candidate for 5,9 B8: 5,9 # 9 pairs B8: 4,7,8 # 6 pairs * PAIR E8: 5,9 COL E E5: 5,9,8 # reduction candidate for 5,9 E5: 5,9 # 11 pairs E6: 5,9,2,8 # reduction candidate for 5,9 E6: 5,9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-209-base-pr-000.dot * REASONING * DIS # D2: 3,9 => CTR => D2: 2,5 * DIS # D3: 3,9 => CTR => D3: 2,5 * DIS # G1: 3,9 => CTR => G1: 1,8 * DIS # D9: 4,5,7 => CTR => D9: 3,9 * DIS # I3: 4,7,9 => CTR => I3: 3,6 * DIS # D8: 5,9 => CTR => D8: 2,4,7 * DIS # F8: 5,9 => CTR => F8: 2,4 * DIS # D9: 5,9 => CTR => D9: 3,4,7 * CNT 8 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C3,D1,E3,E8,E9) * ....7...5.6..4.....1.......5..6.3...7.......2...1.74..2..81....1.....63.......21. * PAIR D1: 3,9 BLK 2 D2: 3,9,2,5 # reduction candidate for 3,9 D2: 3,9 => CTR * ....7..65.6..4.....1..6....5..6.3...7.6...1.2...1.74..2..81....1.....63.......21. D3: 3,9,2,5 # reduction candidate for 3,9 D3: 3,9 => CTR * ....7..65.6..4.....1..6....5..6.3...7.6...1.2...1.74..2..81....1.....63.......21. * RESTART * PAIR D1: 3,9 ROW 1 A1: 3,9,4,8 # reduction candidate for 3,9 A1: 3,9 # 12 pairs B1: 3,9,2,4,8 # reduction candidate for 3,9 B1: 3,9 # 13 pairs C1: 3,9,2,4,8 # reduction candidate for 3,9 C1: 3,9 # 13 pairs G1: 3,9,1,8 # reduction candidate for 3,9 G1: 3,9 => CTR * ....71.65.6..4.....1.......5..6.3...7.6...1.2...1.74..2..81....1....263.......21. * PAIR D1: 3,9 COL D D9: 3,9,4,7 # reduction candidate for 3,9 D9: 4,7 => CTR * ...37..65.6..4.....1..6....5..6.3...7.6.....2...1.74.62..81....1....263.6...3.21. * PAIR RESTART * PAIR D1: 3,9 ROW 1 A1: 3,9,4,8 # reduction candidate for 3,9 A1: 3,9 # 13 pairs B1: 3,9,2,4,8 # reduction candidate for 3,9 B1: 3,9 # 16 pairs C1: 3,9,2,4,8 # reduction candidate for 3,9 C1: 3,9 # 16 pairs * PAIR E3: 3,6 ROW 3 I3: 3,6,4,7,9 # reduction candidate for 3,6 I3: 4,7,9 => CTR * ...37...5.6..4...331..6....5..6.3..17..4....2...1.74.62..81....1..7.263.6...3.21. * PAIR RESTART * PAIR E8: 5,9 BLK 8 F9: 5,9,4,6 # reduction candidate for 5,9 F9: 5,9 => SOLVED * 342976185867541923915238746594623871781459362623187459236814597158792634479365218 * DURATION: 0:00:14.877870 START: 09:59:42.425878 END: 09:59:57.303748 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-209-base-pr-001.dot * REASONING * DIS # D2: 3,9 => CTR => D2: 2,5 * DIS D2: 2,5 # D3: 3,9 => CTR => D3: 2,5 * DIS D2: 2,5 + D3: 2,5 # G1: 3,9 => CTR => G1: 1,8 * DIS D2: 2,5 + D3: 2,5 + G1: 1,8 # D9: 4,7 => CTR => D9: 3,9 * DIS D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 # I3: 4,7,9 => CTR => I3: 3,6 * PRF D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 + I3: 3,6 # F9: 5,9 => SOL * STA D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 + I3: 3,6 + F9: 5,9 * CNT 6 HDP CHAINS / 14 HYP OPENED
Header Info
Top 500 Minimum 17 209 solution: 342976185867541923915238746594623871781459362623187459236814597158792634479365218 info: 1941 FNBHWY S8.f 5570 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 342976185867541923915238746594623871781459362623187459236814597158792634479365218 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 # D2: 3,9 => CTR => D2: 2,5 * INC # D2: 2,5 => UNS * DIS # D3: 3,9 => CTR => D3: 2,5 * INC # D3: 2,5 => UNS * INC # A1: 3,9 => UNS * INC # B1: 3,9 => UNS * INC # C1: 3,9 => UNS * DIS # G1: 3,9 => CTR => G1: 1,8 * INC # G1: 1,8 => UNS * INC # D9: 3,9 => UNS * DIS # D9: 4,5,7 => CTR => D9: 3,9 * INC # I3: 3,6 => UNS * DIS # I3: 4,7,9 => CTR => I3: 3,6 * DIS # D8: 5,9 => CTR => D8: 2,4,7 * INC # D8: 2,4,7 => UNS * DIS # F8: 5,9 => CTR => F8: 2,4 * INC # F8: 2,4 => UNS * DIS # D9: 5,9 => CTR => D9: 3,4,7 * INC # D9: 3,4,7 => UNS * INC # F9: 5,9 => UNS * INC # B8: 5,9 => UNS * INC # B8: 4,7,8 => UNS * INC # E5: 5,9 => UNS * INC # E6: 5,9 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D2: 3,9 => CTR => D2: 2,5 * DIS D2: 2,5 # D3: 3,9 => CTR => D3: 2,5 * INC D2: 2,5 + D3: 2,5 # A1: 3,9 => UNS * INC D2: 2,5 + D3: 2,5 # B1: 3,9 => UNS * INC D2: 2,5 + D3: 2,5 # C1: 3,9 => UNS * DIS D2: 2,5 + D3: 2,5 # G1: 3,9 => CTR => G1: 1,8 * INC D2: 2,5 + D3: 2,5 + G1: 1,8 # D9: 3,9 => UNS * DIS D2: 2,5 + D3: 2,5 + G1: 1,8 # D9: 4,7 => CTR => D9: 3,9 * INC D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 # A1: 3,9 => UNS * INC D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 # B1: 3,9 => UNS * INC D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 # C1: 3,9 => UNS * INC D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 # I3: 3,6 => UNS * DIS D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 # I3: 4,7,9 => CTR => I3: 3,6 * PRF D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 + I3: 3,6 # F9: 5,9 => SOL * STA D2: 2,5 + D3: 2,5 + G1: 1,8 + D9: 3,9 + I3: 3,6 + F9: 5,9 * CNT 14 HDP CHAINS / 14 HYP OPENED