Analysis of xx-top500-341-base.sdk
Contents
Original Sudoku
level: medium
position: ....175..6.......3....4....37.....6....2....8.15............71.8..3.............. initial
Autosolve
position: ....175..6.......3....43...378....6....2....8215......5.....71.8..3.............. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 4,9 => CTR => C2: 1,7 * DIS # C3: 1,7 => CTR => C3: 2,9 * DIS # I3: 2,6,9 => CTR => I3: 1,7 * DIS # D4: 5,9 => CTR => D4: 1,4 * DIS # F4: 5,9 => CTR => F4: 1,4 * DIS # E2: 5,9 => CTR => E2: 2,8 * DIS # E8: 5,9 => CTR => E8: 2,6,7 * PRF # E6: 3,7 => SOL * DIS # E6: 6,8 => CTR => E6: 3,7 * PRF # H5: 3,7 => SOL * DIS # H5: 5 => CTR => H5: 3,7 * DIS # F4: 1,5 => CTR => F4: 4,9 * DIS # F9: 1,5 => CTR => F9: 2,4,6,9 * DIS # E6: 7,8 => CTR => E6: 3,6 * DIS # E6: 6,8 => CTR => E6: 3,7 * PRF # E6: 3,7 => SOL * DIS # I4: 1,2 => CTR => I4: 5 * PRF # I4: 5 => SOL * DIS # G3: 1,2 => CTR => G3: 6,8,9 * DIS # C9: 1,7 => CTR => C9: 2,4,6,9 * DIS # D9: 4,5,9 => CTR => D9: 1,7 * CNT 21 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 4,9 => CTR => C2: 1,7 * DIS C2: 1,7 # I3: 2,6,9 => CTR => I3: 1,7 * DIS C2: 1,7 + I3: 1,7 # D4: 5,9 => CTR => D4: 1,4 * DIS C2: 1,7 + I3: 1,7 + D4: 1,4 # F4: 5,9 => CTR => F4: 1,4 * PRF C2: 1,7 + I3: 1,7 + D4: 1,4 + F4: 1,4 => SOL * STA C2: 1,7 + I3: 1,7 + D4: 1,4 + F4: 1,4 * CNT 5 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....175..6.......3....4....37.....6....2....8.15............71.8..3.............. | initial |
| ....175..6.......3....43...378....6....2....8215......5.....71.8..3.............. | autosolve |
| 483917526691582473752643891378194265964275138215836947539468712847321659126759384 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 4,9 A3: 1,7 A5: 4,9 E4: 5,9 E5: 3,7 F5: 1,5 D6: 7,8 F6: 6,8 G4: 1,2 G5: 1,3 A9: 1,7 G9: 3,8 H9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,G2: 1.. / C2 = 1 => 0 pairs (*) / G2 = 1 => 0 pairs (X) F5,G5: 1.. / F5 = 1 => 0 pairs (X) / G5 = 1 => 0 pairs (_) C8,F8: 1.. / C8 = 1 => 0 pairs (X) / F8 = 1 => 0 pairs (_) A3,A9: 1.. / A3 = 1 => 0 pairs (X) / A9 = 1 => 0 pairs (_) D4,D9: 1.. / D4 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) I3,I4: 1.. / I3 = 1 => 0 pairs (*) / I4 = 1 => 0 pairs (X) E2,F2: 2.. / E2 = 2 => 13 pairs (_) / F2 = 2 => 13 pairs (_) G4,I4: 2.. / G4 = 2 => 13 pairs (_) / I4 = 2 => 0 pairs (X) B1,C1: 3.. / B1 = 3 => 18 pairs (_) / C1 = 3 => 13 pairs (_) E5,E6: 3.. / E5 = 3 => 0 pairs (X) / E6 = 3 => 0 pairs (_) B7,C7: 3.. / B7 = 3 => 13 pairs (_) / C7 = 3 => 18 pairs (_) G9,H9: 3.. / G9 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) B1,B7: 3.. / B1 = 3 => 18 pairs (_) / B7 = 3 => 13 pairs (_) C1,C7: 3.. / C1 = 3 => 13 pairs (_) / C7 = 3 => 18 pairs (_) D4,F4: 4.. / D4 = 4 => 0 pairs (X) / F4 = 4 => 13 pairs (_) A1,A5: 4.. / A1 = 4 => 17 pairs (_) / A5 = 4 => 14 pairs (_) B2,B3: 5.. / B2 = 5 => 16 pairs (_) / B3 = 5 => 13 pairs (_) I4,H5: 5.. / I4 = 5 => 0 pairs (*) / H5 = 5 => 0 pairs (X) B3,D3: 5.. / B3 = 5 => 13 pairs (_) / D3 = 5 => 16 pairs (_) F5,H5: 5.. / F5 = 5 => 0 pairs (*) / H5 = 5 => 0 pairs (X) H5,H8: 5.. / H5 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) D1,D3: 6.. / D1 = 6 => 13 pairs (_) / D3 = 6 => 14 pairs (_) B5,C5: 6.. / B5 = 6 => 14 pairs (_) / C5 = 6 => 14 pairs (_) E6,F6: 6.. / E6 = 6 => 0 pairs (X) / F6 = 6 => 12 pairs (_) D1,I1: 6.. / D1 = 6 => 13 pairs (_) / I1 = 6 => 14 pairs (_) G3,G8: 6.. / G3 = 6 => 13 pairs (_) / G8 = 6 => 13 pairs (_) C2,H2: 7.. / C2 = 7 => 0 pairs (X) / H2 = 7 => 0 pairs (_) E5,H5: 7.. / E5 = 7 => 0 pairs (*) / H5 = 7 => 0 pairs (X) C8,E8: 7.. / C8 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) A3,A9: 7.. / A3 = 7 => 0 pairs (*) / A9 = 7 => 0 pairs (X) D6,D9: 7.. / D6 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) I3,I6: 7.. / I3 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) G9,H9: 8.. / G9 = 8 => 12 pairs (_) / H9 = 8 => 0 pairs (*) A1,A5: 9.. / A1 = 9 => 14 pairs (_) / A5 = 9 => 17 pairs (_) * DURATION: 0:01:00.868727 START: 14:23:21.148398 END: 14:24:22.017125 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A5,A9,D6,E4,E5,F5,F6,G4,G5,G9,H9) * ....175..6.......3....43...378....6....2....8215......5.....71.8..3.............. * PAIR A1: 4,9 BLK 1 B1: 4,9,2,3,8 # reduction candidate for 4,9 B1: 4,9 # 22 pairs C1: 4,9,2,3 # reduction candidate for 4,9 C1: 4,9 # 22 pairs B2: 4,9,5,8 # reduction candidate for 4,9 B2: 4,9 # 16 pairs C2: 4,9,1,7 # reduction candidate for 4,9 C2: 4,9 => CTR * ....175..6.....173....43...378...261...2713582158.....5.....71.8..3.............. C2: 1,7 # 15 pairs * PAIR A1: 4,9 ROW 1 H1: 4,9,2,8 # reduction candidate for 4,9 H1: 4,9 # 17 pairs I1: 4,9,2,6 # reduction candidate for 4,9 I1: 4,9 # 16 pairs * PAIR A3: 1,7 BLK 1 C2: 1,7,4,9 # reduction candidate for 1,7 C2: 1,7 # 15 pairs C3: 1,7,2,9 # reduction candidate for 1,7 C3: 1,7 => CTR * ....175..6.....173....43...378...261...2713582158.....5.....71.8..3.............. C3: 2,9 # 15 pairs * PAIR A3: 1,7 ROW 3 I3: 1,7,2,6,9 # reduction candidate for 1,7 I3: 2,6,9 => CTR * ....175..6.......3....43...378....61...2.1358215.36..75.....71.8.137............. I3: 1,7 # 16 pairs * PAIR A5: 4,9 BLK 4 B5: 4,9,6 # reduction candidate for 4,9 B5: 4,9 # 14 pairs C5: 4,9,6 # reduction candidate for 4,9 C5: 4,9 # 14 pairs * PAIR E4: 5,9 BLK 5 D4: 5,9,1,4 # reduction candidate for 5,9 D4: 5,9 => CTR * ....175..6.......3....43...378..4.6....2.1358215.36...5.....71.8.137............. D4: 1,4 # 14 pairs F4: 5,9,1,4 # reduction candidate for 5,9 F4: 5,9 => CTR * ....175..6.......3....43...3784...6....2.1358215.36...5.....71.8.137............. F4: 1,4 # 14 pairs * PAIR E4: 5,9 COL E E2: 5,9,2,8 # reduction candidate for 5,9 E2: 5,9 => CTR * ....175..6....2..3....43..7378....61...23...82157.....5.....71.8..3.............. E2: 2,8 # 14 pairs E8: 5,9,2,6,7 # reduction candidate for 5,9 E8: 5,9 => CTR * ....175..6......737...43...3781.4265...275138215836..75.....71.8.73.1.5.1..75.38. E8: 2,6,7 # 13 pairs E9: 5,9,2,6,7 # reduction candidate for 5,9 E9: 5,9 # 15 pairs * PAIR E5: 3,7 BLK 5 E6: 3,7,6,8 # reduction candidate for 3,7 E6: 3,7 => SOLVED * 483917526691582473752643891378194265964275138215836947539468712847321659126759384 E6: 6,8 => CTR * ....175..6.......3....43...378....6....23.1782157.....5.....71.8..3...5.......... * PAIR E5: 3,7 ROW 5 H5: 3,7,5 # reduction candidate for 3,7 H5: 3,7 => SOLVED * 483917526691582473752643891378194265964275138215836947539468712847321659126759384 H5: 5 => CTR * ....175..6.......3....43...378....6....27.358215836...5.....71.8.73.1............ * PAIR F5: 1,5 BLK 5 D4: 1,5,4,9 # reduction candidate for 1,5 D4: 1,5 # 13 pairs F4: 1,5,4,9 # reduction candidate for 1,5 F4: 1,5 => CTR * ....175..6.......31...43...37849..61...2.13582157.....5.....71.8..3........1..... F4: 4,9 # 14 pairs * PAIR F5: 1,5 COL F F8: 1,5,2,4,6,9 # reduction candidate for 1,5 F8: 1,5 # 15 pairs F9: 1,5,2,4,6,9 # reduction candidate for 1,5 F9: 1,5 => CTR * ....175..6.....1.31...43...378...261...23...8215......5.....71.8.137....7........ F9: 2,4,6,9 # 13 pairs * PAIR D6: 7,8 BLK 5 E6: 7,8,3,6 # reduction candidate for 7,8 E6: 7,8 => CTR * ....175..6.......3....43...378....6....23.178215..6...5.....71.8..3...5.......... E6: 3,6 # 14 pairs * PAIR F6: 6,8 BLK 5 E6: 6,8,3,7 # reduction candidate for 6,8 E6: 6,8 => CTR * ....175..6.......3....43...378....6....23.1782157.....5.....71.8..3...5.......... E6: 3,7 => SOLVED * 483917526691582473752643891378194265964275138215836947539468712847321659126759384 * PAIR F6: 6,8 COL F F7: 6,8,2,4,9 # reduction candidate for 6,8 F7: 6,8 # 14 pairs F7: 2,4,9 # 13 pairs * PAIR G4: 1,2 BLK 6 I4: 1,2,5 # reduction candidate for 1,2 I4: 1,2 => CTR * ....175..6.......3....43...378....6....2713582158.....5.....71.8..3.............. I4: 5 => SOLVED * 483917526691582473752643891378194265964275138215836947539468712847321659126759384 * PAIR G4: 1,2 COL G G3: 1,2,6,8,9 # reduction candidate for 1,2 G3: 1,2 => CTR * ....175..6.1....737...43...378....6....2713582158.....5.....71.8..3..6........... G3: 6,8,9 # 13 pairs * PAIR A9: 1,7 BLK 7 C8: 1,7,2,4,6,9 # reduction candidate for 1,7 C8: 1,7 # 14 pairs C9: 1,7,2,4,6,9 # reduction candidate for 1,7 C9: 1,7 => CTR * ....175..6.......3....43...3781.4265...2.51.82157.....5.....71.8..371.5.......... C9: 2,4,6,9 # 14 pairs * PAIR A9: 1,7 ROW 9 D9: 1,7,4,5,9 # reduction candidate for 1,7 D9: 4,5,9 => CTR * ....175..6.......3....43...3781.4265...2.51.82157.....5.....71.8..3...5.......... D9: 1,7 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-341-base-pr-000.dot * REASONING * DIS # C2: 4,9 => CTR => C2: 1,7 * DIS # C3: 1,7 => CTR => C3: 2,9 * DIS # I3: 2,6,9 => CTR => I3: 1,7 * DIS # D4: 5,9 => CTR => D4: 1,4 * DIS # F4: 5,9 => CTR => F4: 1,4 * DIS # E2: 5,9 => CTR => E2: 2,8 * DIS # E8: 5,9 => CTR => E8: 2,6,7 * PRF # E6: 3,7 => SOL * DIS # E6: 6,8 => CTR => E6: 3,7 * PRF # H5: 3,7 => SOL * DIS # H5: 5 => CTR => H5: 3,7 * DIS # F4: 1,5 => CTR => F4: 4,9 * DIS # F9: 1,5 => CTR => F9: 2,4,6,9 * DIS # E6: 7,8 => CTR => E6: 3,6 * DIS # E6: 6,8 => CTR => E6: 3,7 * PRF # E6: 3,7 => SOL * DIS # I4: 1,2 => CTR => I4: 5 * PRF # I4: 5 => SOL * DIS # G3: 1,2 => CTR => G3: 6,8,9 * DIS # C9: 1,7 => CTR => C9: 2,4,6,9 * DIS # D9: 4,5,9 => CTR => D9: 1,7 * CNT 21 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A5,A9,D6,E4,E5,F5,F6,G4,G5,G9,H9) * ....175..6.......3....43...378....6....2....8215......5.....71.8..3.............. * PAIR A1: 4,9 BLK 1 B1: 4,9,2,3,8 # reduction candidate for 4,9 B1: 4,9 # 22 pairs C1: 4,9,2,3 # reduction candidate for 4,9 C1: 4,9 # 22 pairs B2: 4,9,5,8 # reduction candidate for 4,9 B2: 4,9 # 16 pairs C2: 4,9,1,7 # reduction candidate for 4,9 C2: 4,9 => CTR * ....175..6.....173....43...378...261...2713582158.....5.....71.8..3.............. * PAIR A1: 4,9 ROW 1 H1: 4,9,2,8 # reduction candidate for 4,9 H1: 4,9 # 19 pairs I1: 4,9,2,6 # reduction candidate for 4,9 I1: 4,9 # 18 pairs * PAIR RESTART * PAIR A1: 4,9 BLK 1 B1: 4,9,2,3,8 # reduction candidate for 4,9 B1: 4,9 # 22 pairs C1: 4,9,2,3 # reduction candidate for 4,9 C1: 4,9 # 22 pairs B2: 4,9,5,8 # reduction candidate for 4,9 B2: 4,9 # 16 pairs * PAIR A1: 4,9 ROW 1 H1: 4,9,2,8 # reduction candidate for 4,9 H1: 4,9 # 19 pairs I1: 4,9,2,6 # reduction candidate for 4,9 I1: 4,9 # 18 pairs * PAIR A3: 1,7 ROW 3 I3: 1,7,2,6,9 # reduction candidate for 1,7 I3: 2,6,9 => CTR * ....175..6.......3....43...378....61...2.1358215.36..75.....71.8.137............. * PAIR RESTART * PAIR A5: 4,9 BLK 4 B5: 4,9,6 # reduction candidate for 4,9 B5: 4,9 # 17 pairs C5: 4,9,6 # reduction candidate for 4,9 C5: 4,9 # 17 pairs * PAIR E4: 5,9 BLK 5 D4: 5,9,1,4 # reduction candidate for 5,9 D4: 5,9 => CTR * ....175..6.......3....43...378..4.6....2.1358215.36...5.....71.8.137............. F4: 5,9,1,4 # reduction candidate for 5,9 F4: 5,9 => CTR * ....175..6.......3....43...3784...6....2.1358215.36...5.....71.8.137............. F4: 1,4 => SOLVED * 483917526691582473752643891378194265964275138215836947539468712847321659126759384 * DURATION: 0:00:16.413587 START: 14:25:05.434097 END: 14:25:21.847684 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-341-base-pr-001.dot * REASONING * DIS # C2: 4,9 => CTR => C2: 1,7 * DIS C2: 1,7 # I3: 2,6,9 => CTR => I3: 1,7 * DIS C2: 1,7 + I3: 1,7 # D4: 5,9 => CTR => D4: 1,4 * DIS C2: 1,7 + I3: 1,7 + D4: 1,4 # F4: 5,9 => CTR => F4: 1,4 * PRF C2: 1,7 + I3: 1,7 + D4: 1,4 + F4: 1,4 => SOL * STA C2: 1,7 + I3: 1,7 + D4: 1,4 + F4: 1,4 * CNT 5 HDP CHAINS / 17 HYP OPENED
Header Info
Top 500 Minimum 17 341 solution: 483917526691582473752643891378194265964275138215836947539468712847321659126759384 info: 3230 FNBTHWY S8.f 3129 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 483917526691582473752643891378194265964275138215836947539468712847321659126759384 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 # B1: 4,9 => UNS * INC # C1: 4,9 => UNS * INC # B2: 4,9 => UNS * DIS # C2: 4,9 => CTR => C2: 1,7 * INC # C2: 1,7 => UNS * INC # H1: 4,9 => UNS * INC # I1: 4,9 => UNS * INC # C2: 1,7 => UNS * DIS # C3: 1,7 => CTR => C3: 2,9 * INC # C3: 2,9 => UNS * INC # I3: 1,7 => UNS * DIS # I3: 2,6,9 => CTR => I3: 1,7 * INC # B5: 4,9 => UNS * INC # C5: 4,9 => UNS * DIS # D4: 5,9 => CTR => D4: 1,4 * INC # D4: 1,4 => UNS * DIS # F4: 5,9 => CTR => F4: 1,4 * INC # F4: 1,4 => UNS * DIS # E2: 5,9 => CTR => E2: 2,8 * INC # E2: 2,8 => UNS * DIS # E8: 5,9 => CTR => E8: 2,6,7 * INC # E8: 2,6,7 => UNS * INC # E9: 5,9 => UNS * PRF # E6: 3,7 => SOL * DIS # E6: 6,8 => CTR => E6: 3,7 * PRF # H5: 3,7 => SOL * DIS # H5: 5 => CTR => H5: 3,7 * INC # D4: 1,5 => UNS * DIS # F4: 1,5 => CTR => F4: 4,9 * INC # F4: 4,9 => UNS * INC # F8: 1,5 => UNS * DIS # F9: 1,5 => CTR => F9: 2,4,6,9 * INC # F9: 2,4,6,9 => UNS * DIS # E6: 7,8 => CTR => E6: 3,6 * INC # E6: 3,6 => UNS * DIS # E6: 6,8 => CTR => E6: 3,7 * PRF # E6: 3,7 => SOL * INC # F7: 6,8 => UNS * INC # F7: 2,4,9 => UNS * DIS # I4: 1,2 => CTR => I4: 5 * PRF # I4: 5 => SOL * DIS # G3: 1,2 => CTR => G3: 6,8,9 * INC # G3: 6,8,9 => UNS * INC # C8: 1,7 => UNS * DIS # C9: 1,7 => CTR => C9: 2,4,6,9 * INC # C9: 2,4,6,9 => UNS * INC # D9: 1,7 => UNS * DIS # D9: 4,5,9 => CTR => D9: 1,7 * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 4,9 => UNS * INC # C1: 4,9 => UNS * INC # B2: 4,9 => UNS * DIS # C2: 4,9 => CTR => C2: 1,7 * INC C2: 1,7 # H1: 4,9 => UNS * INC C2: 1,7 # I1: 4,9 => UNS * INC C2: 1,7 # B1: 4,9 => UNS * INC C2: 1,7 # C1: 4,9 => UNS * INC C2: 1,7 # B2: 4,9 => UNS * INC C2: 1,7 # H1: 4,9 => UNS * INC C2: 1,7 # I1: 4,9 => UNS * INC C2: 1,7 # I3: 1,7 => UNS * DIS C2: 1,7 # I3: 2,6,9 => CTR => I3: 1,7 * INC C2: 1,7 + I3: 1,7 # B5: 4,9 => UNS * INC C2: 1,7 + I3: 1,7 # C5: 4,9 => UNS * DIS C2: 1,7 + I3: 1,7 # D4: 5,9 => CTR => D4: 1,4 * DIS C2: 1,7 + I3: 1,7 + D4: 1,4 # F4: 5,9 => CTR => F4: 1,4 * PRF C2: 1,7 + I3: 1,7 + D4: 1,4 + F4: 1,4 => SOL * STA C2: 1,7 + I3: 1,7 + D4: 1,4 + F4: 1,4 * CNT 18 HDP CHAINS / 17 HYP OPENED