Analysis of xx-top500-496-base.sdk
Contents
Original Sudoku
level: medium
position: ...2..5..1..7......3....8...5..3.4.....6....2.8.......2......1.6.7..........5.... initial
Autosolve
position: 76.2.35.112.7.56..53....82795.13.4...716.8.52.8.5..1..2.5....1.6.7.....5813.5.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H8: 4,9 => CTR => H8: 3,8 * DIS # F7: 4,9 => CTR => F7: 6 * DIS # H4: 7 => CTR => H4: 6,8 * DIS # H6: 3,9 => CTR => H6: 6,7 * DIS # G8: 3,9 => CTR => G8: 2 * DIS # F7: 4,9 => CTR => F7: 6 * PRF # I7: 4,9 => SOL * DIS # H8: 4,9 => CTR => H8: 3,8 * PRF # I7: 4,9 => SOL * DIS # H8: 4,9 => CTR => H8: 3,8 * DIS # F7: 4,9 => CTR => F7: 6 * CNT 11 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H8: 4,9 => CTR => H8: 3,8 * DIS H8: 3,8 # F7: 4,9 => CTR => F7: 6 * PRF H8: 3,8 + F7: 6 # I7: 4,9 => SOL * STA H8: 3,8 + F7: 6 + I7: 4,9 * CNT 3 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2..5..1..7......3....8...5..3.4.....6....2.8.......2......1.6.7..........5.... | initial |
| 76.2.35.112.7.56..53....82795.13.4...716.8.52.8.5..1..2.5....1.6.7.....5813.5.... | autosolve |
| 764283591128795634539461827952137468371648952486529173245876319697314285813952746 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (24) C3: 4,9 D3: 4,9 E3: 1,6 F3: 1,6 H1: 4,9 C4: 2,6 A5: 3,4 A6: 3,4 C6: 2,6 F4: 2,7 E5: 4,9 E6: 2,7 F6: 4,9 I4: 6,8 G5: 3,9 B7: 4,9 B8: 4,9 D7: 3,8 E7: 6,7 D8: 3,8 E8: 1,2 D9: 4,9 F9: 2,7 G9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 1.. / E3 = 1 => 0 pairs (X) / F3 = 1 => 19 pairs (_) E8,F8: 1.. / E8 = 1 => 19 pairs (_) / F8 = 1 => 0 pairs (X) E3,E8: 1.. / E3 = 1 => 0 pairs (X) / E8 = 1 => 19 pairs (_) F3,F8: 1.. / F3 = 1 => 19 pairs (_) / F8 = 1 => 0 pairs (X) C4,C6: 2.. / C4 = 2 => 19 pairs (_) / C6 = 2 => 0 pairs (X) F4,E6: 2.. / F4 = 2 => 0 pairs (X) / E6 = 2 => 19 pairs (_) E8,F9: 2.. / E8 = 2 => 0 pairs (X) / F9 = 2 => 19 pairs (_) G8,G9: 2.. / G8 = 2 => 19 pairs (_) / G9 = 2 => 0 pairs (X) C4,F4: 2.. / C4 = 2 => 19 pairs (_) / F4 = 2 => 0 pairs (X) C6,E6: 2.. / C6 = 2 => 0 pairs (X) / E6 = 2 => 19 pairs (_) E8,G8: 2.. / E8 = 2 => 0 pairs (X) / G8 = 2 => 19 pairs (_) F9,G9: 2.. / F9 = 2 => 19 pairs (_) / G9 = 2 => 0 pairs (X) E6,E8: 2.. / E6 = 2 => 19 pairs (_) / E8 = 2 => 0 pairs (X) F4,F9: 2.. / F4 = 2 => 0 pairs (X) / F9 = 2 => 19 pairs (_) H2,I2: 3.. / H2 = 3 => 25 pairs (_) / I2 = 3 => 31 pairs (_) A5,A6: 3.. / A5 = 3 => 29 pairs (_) / A6 = 3 => 0 pairs (X) D7,D8: 3.. / D7 = 3 => 0 pairs (X) / D8 = 3 => 23 pairs (_) A5,G5: 3.. / A5 = 3 => 29 pairs (_) / G5 = 3 => 0 pairs (X) A5,A6: 4.. / A5 = 4 => 0 pairs (X) / A6 = 4 => 29 pairs (_) E5,F6: 4.. / E5 = 4 => 29 pairs (_) / F6 = 4 => 0 pairs (X) B7,B8: 4.. / B7 = 4 => 25 pairs (_) / B8 = 4 => 25 pairs (_) C3,D3: 4.. / C3 = 4 => 0 pairs (X) / D3 = 4 => 29 pairs (_) A5,E5: 4.. / A5 = 4 => 0 pairs (X) / E5 = 4 => 29 pairs (_) A6,F6: 4.. / A6 = 4 => 29 pairs (_) / F6 = 4 => 0 pairs (X) D3,D9: 4.. / D3 = 4 => 29 pairs (_) / D9 = 4 => 0 pairs (X) E3,F3: 6.. / E3 = 6 => 19 pairs (_) / F3 = 6 => 0 pairs (X) C4,C6: 6.. / C4 = 6 => 0 pairs (X) / C6 = 6 => 19 pairs (_) E7,F7: 6.. / E7 = 6 => 0 pairs (X) / F7 = 6 => 19 pairs (_) H9,I9: 6.. / H9 = 6 => 26 pairs (_) / I9 = 6 => 27 pairs (_) E3,E7: 6.. / E3 = 6 => 19 pairs (_) / E7 = 6 => 0 pairs (X) F3,F7: 6.. / F3 = 6 => 0 pairs (X) / F7 = 6 => 19 pairs (_) F4,E6: 7.. / F4 = 7 => 19 pairs (_) / E6 = 7 => 0 pairs (X) H4,H6: 7.. / H4 = 7 => 0 pairs (X) / H6 = 7 => 19 pairs (_) E7,F9: 7.. / E7 = 7 => 19 pairs (_) / F9 = 7 => 0 pairs (X) G7,G9: 7.. / G7 = 7 => 0 pairs (X) / G9 = 7 => 19 pairs (_) F4,H4: 7.. / F4 = 7 => 19 pairs (_) / H4 = 7 => 0 pairs (X) E6,H6: 7.. / E6 = 7 => 0 pairs (X) / H6 = 7 => 19 pairs (_) E7,G7: 7.. / E7 = 7 => 19 pairs (_) / G7 = 7 => 0 pairs (X) F9,G9: 7.. / F9 = 7 => 0 pairs (X) / G9 = 7 => 19 pairs (_) E6,E7: 7.. / E6 = 7 => 0 pairs (X) / E7 = 7 => 19 pairs (_) F4,F9: 7.. / F4 = 7 => 19 pairs (_) / F9 = 7 => 0 pairs (X) C1,C2: 8.. / C1 = 8 => 26 pairs (_) / C2 = 8 => 26 pairs (_) E1,E2: 8.. / E1 = 8 => 26 pairs (_) / E2 = 8 => 26 pairs (_) H4,I4: 8.. / H4 = 8 => 0 pairs (X) / I4 = 8 => 23 pairs (_) D7,D8: 8.. / D7 = 8 => 23 pairs (_) / D8 = 8 => 0 pairs (X) I7,H8: 8.. / I7 = 8 => 0 pairs (X) / H8 = 8 => 23 pairs (_) C1,E1: 8.. / C1 = 8 => 26 pairs (_) / E1 = 8 => 26 pairs (_) C2,E2: 8.. / C2 = 8 => 26 pairs (_) / E2 = 8 => 26 pairs (_) D7,I7: 8.. / D7 = 8 => 23 pairs (_) / I7 = 8 => 0 pairs (X) D8,H8: 8.. / D8 = 8 => 0 pairs (X) / H8 = 8 => 23 pairs (_) H4,H8: 8.. / H4 = 8 => 0 pairs (X) / H8 = 8 => 23 pairs (_) I4,I7: 8.. / I4 = 8 => 23 pairs (_) / I7 = 8 => 0 pairs (X) E5,F6: 9.. / E5 = 9 => 0 pairs (X) / F6 = 9 => 29 pairs (_) B7,B8: 9.. / B7 = 9 => 25 pairs (_) / B8 = 9 => 25 pairs (_) C3,D3: 9.. / C3 = 9 => 29 pairs (_) / D3 = 9 => 0 pairs (X) E5,G5: 9.. / E5 = 9 => 0 pairs (X) / G5 = 9 => 29 pairs (_) D3,D9: 9.. / D3 = 9 => 0 pairs (X) / D9 = 9 => 29 pairs (_) * DURATION: 0:02:13.429696 START: 19:37:24.189233 END: 19:39:37.618929 2017-05-04 * CP COUNT: (57) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B7,B8,C3,C4,C6,D3,D7,D8,D9,E3,E5,E6,E7,E8,F3,F4,F6,F9,G5,G9,H1,I4) * 76.2.35.112.7.56..53....82795.13.4...716.8.52.8.5..1..2.5....1.6.7.....5813.5.... * PAIR C3: 4,9 BLK 1 C1: 4,9,8 # reduction candidate for 4,9 C1: 4,9 # 26 pairs C2: 4,9,8 # reduction candidate for 4,9 C2: 4,9 # 26 pairs * PAIR D3: 4,9 BLK 2 E1: 4,9,8 # reduction candidate for 4,9 E1: 4,9 # 26 pairs E2: 4,9,8 # reduction candidate for 4,9 E2: 4,9 # 26 pairs * PAIR H1: 4,9 BLK 3 H2: 4,9,3 # reduction candidate for 4,9 H2: 4,9 # 31 pairs I2: 4,9,3 # reduction candidate for 4,9 I2: 4,9 # 25 pairs * PAIR H1: 4,9 ROW 1 C1: 4,9,8 # reduction candidate for 4,9 C1: 4,9 # 26 pairs E1: 4,9,8 # reduction candidate for 4,9 E1: 4,9 # 26 pairs * PAIR H1: 4,9 COL H H8: 4,9,3,8 # reduction candidate for 4,9 H8: 4,9 => CTR * 76.2.35.112.7.56..53....82795.13.486.716.8.52.8652.17.2.5.76.186.781...5813.5.... H8: 3,8 # 26 pairs H9: 4,9,6 # reduction candidate for 4,9 H9: 4,9 # 27 pairs * PAIR E5: 4,9 COL E E1: 4,9,8 # reduction candidate for 4,9 E1: 4,9 # 26 pairs E2: 4,9,8 # reduction candidate for 4,9 E2: 4,9 # 26 pairs * PAIR F6: 4,9 COL F F7: 4,9,6 # reduction candidate for 4,9 F7: 4,9 => CTR * 76.2.35.112.7.563.539416827956132478.716.8.52.8257.1..2.586.7136.73219858139572.. F7: 6 # 19 pairs F8: 4,9,1 # reduction candidate for 4,9 F8: 4,9 # 19 pairs * PAIR I4: 6,8 BLK 6 H4: 6,8,7 # reduction candidate for 6,8 H4: 7 => CTR * 76.2.35.112.7.563.53941.82795.13.478.716.8.52.8.57.1..2.586.7136.73219858139572.. H4: 6,8 # 19 pairs * PAIR G5: 3,9 BLK 6 H6: 3,9,6,7 # reduction candidate for 3,9 H6: 3,9 => CTR * 76.2.35.112.7.563953941.82795.13.478.716.8.52.8.57.1.62.586.7136.7321985813957264 H6: 6,7 # 26 pairs I6: 3,9,6 # reduction candidate for 3,9 I6: 3,9 # 26 pairs * PAIR G5: 3,9 COL G G7: 3,9,7 # reduction candidate for 3,9 G7: 3,9 # 19 pairs G8: 3,9,2 # reduction candidate for 3,9 G8: 3,9 => CTR * 76.2.35.112.7.563.539416827956132478.716.8.52.8257.1..2.586.7136.73219858139572.. G8: 2 # 19 pairs * PAIR B7: 4,9 ROW 7 F7: 4,9,6 # reduction candidate for 4,9 F7: 4,9 => CTR * 76.2.35.112.7.563.539416827956132478.716.8.52.8257.1..2.586.7136.73219858139572.. F7: 6 # 19 pairs I7: 4,9,3,8 # reduction candidate for 4,9 I7: 4,9 => SOLVED * 764283591128795634539461827952137468371648952486529173245876319697314285813952746 I7: 3,8 # 26 pairs * PAIR B8: 4,9 ROW 8 F8: 4,9,1 # reduction candidate for 4,9 F8: 4,9 # 19 pairs H8: 4,9,3,8 # reduction candidate for 4,9 H8: 4,9 => CTR * 76.2.35.112.7.56..53....82795.13.486.716.8.52.8652.17.2.5.76.186.781...5813.5.... H8: 3,8 # 26 pairs * PAIR D7: 3,8 ROW 7 I7: 3,8,4,9 # reduction candidate for 3,8 I7: 4,9 => SOLVED * 764283591128795634539461827952137468371648952486529173245876319697314285813952746 I7: 3,8 # 26 pairs * PAIR D8: 3,8 ROW 8 H8: 3,8,4,9 # reduction candidate for 3,8 H8: 4,9 => CTR * 76.2.35.112.7.56..53....82795.13.486.716.8.52.8652.17.2.5.76.186.781...5813.5.... H8: 3,8 # 26 pairs * PAIR D9: 4,9 BLK 8 F7: 4,9,6 # reduction candidate for 4,9 F7: 4,9 => CTR * 76.2.35.112.7.563.539416827956132478.716.8.52.8257.1..2.586.7136.73219858139572.. F7: 6 # 19 pairs F8: 4,9,1 # reduction candidate for 4,9 F8: 4,9 # 19 pairs * PAIR D9: 4,9 ROW 9 H9: 4,9,6 # reduction candidate for 4,9 H9: 4,9 # 27 pairs I9: 4,9,6 # reduction candidate for 4,9 I9: 4,9 # 26 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-496-base-pr-000.dot * REASONING * DIS # H8: 4,9 => CTR => H8: 3,8 * DIS # F7: 4,9 => CTR => F7: 6 * DIS # H4: 7 => CTR => H4: 6,8 * DIS # H6: 3,9 => CTR => H6: 6,7 * DIS # G8: 3,9 => CTR => G8: 2 * DIS # F7: 4,9 => CTR => F7: 6 * PRF # I7: 4,9 => SOL * DIS # H8: 4,9 => CTR => H8: 3,8 * PRF # I7: 4,9 => SOL * DIS # H8: 4,9 => CTR => H8: 3,8 * DIS # F7: 4,9 => CTR => F7: 6 * CNT 11 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B7,B8,C3,C4,C6,D3,D7,D8,D9,E3,E5,E6,E7,E8,F3,F4,F6,F9,G5,G9,H1,I4) * 76.2.35.112.7.56..53....82795.13.4...716.8.52.8.5..1..2.5....1.6.7.....5813.5.... * PAIR C3: 4,9 BLK 1 C1: 4,9,8 # reduction candidate for 4,9 C1: 4,9 # 26 pairs C2: 4,9,8 # reduction candidate for 4,9 C2: 4,9 # 26 pairs * PAIR D3: 4,9 BLK 2 E1: 4,9,8 # reduction candidate for 4,9 E1: 4,9 # 26 pairs E2: 4,9,8 # reduction candidate for 4,9 E2: 4,9 # 26 pairs * PAIR H1: 4,9 BLK 3 H2: 4,9,3 # reduction candidate for 4,9 H2: 4,9 # 31 pairs I2: 4,9,3 # reduction candidate for 4,9 I2: 4,9 # 25 pairs * PAIR H1: 4,9 ROW 1 C1: 4,9,8 # reduction candidate for 4,9 C1: 4,9 # 26 pairs E1: 4,9,8 # reduction candidate for 4,9 E1: 4,9 # 26 pairs * PAIR H1: 4,9 COL H H8: 4,9,3,8 # reduction candidate for 4,9 H8: 4,9 => CTR * 76.2.35.112.7.56..53....82795.13.486.716.8.52.8652.17.2.5.76.186.781...5813.5.... H9: 4,9,6 # reduction candidate for 4,9 H9: 4,9 # 27 pairs * RESTART * PAIR H1: 4,9 COL H H9: 4,9,6 # reduction candidate for 4,9 H9: 6 # 29 pairs H9: 4,9 # 27 pairs * PAIR RESTART * PAIR H1: 4,9 BLK 3 H2: 4,9,3 # reduction candidate for 4,9 H2: 4,9 # 31 pairs I2: 4,9,3 # reduction candidate for 4,9 I2: 4,9 # 24 pairs * PAIR H1: 4,9 ROW 1 C1: 4,9,8 # reduction candidate for 4,9 C1: 4,9 # 28 pairs E1: 4,9,8 # reduction candidate for 4,9 E1: 4,9 # 28 pairs * PAIR H1: 4,9 COL H H9: 4,9,6 # reduction candidate for 4,9 H9: 6 # 29 pairs H9: 4,9 # 27 pairs * PAIR E5: 4,9 COL E E1: 4,9,8 # reduction candidate for 4,9 E1: 4,9 # 28 pairs E2: 4,9,8 # reduction candidate for 4,9 E2: 4,9 # 28 pairs * PAIR F6: 4,9 COL F F7: 4,9,6 # reduction candidate for 4,9 F7: 4,9 => CTR * 76.2.35.112.7.56..53..1682795.132478.716.83523825741..2.58697136.7..1..5813.572.. * RESTART * PAIR RESTART * PAIR B7: 4,9 ROW 7 I7: 4,9,3,8 # reduction candidate for 4,9 I7: 4,9 => SOLVED * 764283591128795634539461827952137468371648952486529173245876319697314285813952746 * DURATION: 0:00:27.337969 START: 19:40:26.220146 END: 19:40:53.558115 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-496-base-pr-001.dot * REASONING * DIS # H8: 4,9 => CTR => H8: 3,8 * DIS H8: 3,8 # F7: 4,9 => CTR => F7: 6 * PRF H8: 3,8 + F7: 6 # I7: 4,9 => SOL * STA H8: 3,8 + F7: 6 + I7: 4,9 * CNT 3 HDP CHAINS / 22 HYP OPENED
Header Info
Top 500 Minimum 17 496 solution: 764283591128795634539461827952137468371648952486529173245876319697314285813952746 info: 96455 FNBTHXK S8.f 7669 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 764283591128795634539461827952137468371648952486529173245876319697314285813952746 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 # C1: 4,9 => UNS * INC # C2: 4,9 => UNS * INC # E1: 4,9 => UNS * INC # E2: 4,9 => UNS * INC # H2: 4,9 => UNS * INC # I2: 4,9 => UNS * INC # C1: 4,9 => UNS * INC # E1: 4,9 => UNS * DIS # H8: 4,9 => CTR => H8: 3,8 * INC # H8: 3,8 => UNS * INC # H9: 4,9 => UNS * INC # E1: 4,9 => UNS * INC # E2: 4,9 => UNS * DIS # F7: 4,9 => CTR => F7: 6 * INC # F7: 6 => UNS * INC # F8: 4,9 => UNS * INC # H4: 6,8 => UNS * DIS # H4: 7 => CTR => H4: 6,8 * DIS # H6: 3,9 => CTR => H6: 6,7 * INC # H6: 6,7 => UNS * INC # I6: 3,9 => UNS * INC # G7: 3,9 => UNS * DIS # G8: 3,9 => CTR => G8: 2 * INC # G8: 2 => UNS * DIS # F7: 4,9 => CTR => F7: 6 * INC # F7: 6 => UNS * PRF # I7: 4,9 => SOL * INC # I7: 3,8 => UNS * INC # F8: 4,9 => UNS * DIS # H8: 4,9 => CTR => H8: 3,8 * INC # H8: 3,8 => UNS * INC # I7: 3,8 => UNS * PRF # I7: 4,9 => SOL * INC # H8: 3,8 => UNS * DIS # H8: 4,9 => CTR => H8: 3,8 * DIS # F7: 4,9 => CTR => F7: 6 * INC # F7: 6 => UNS * INC # F8: 4,9 => UNS * INC # H9: 4,9 => UNS * INC # I9: 4,9 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 4,9 => UNS * INC # C2: 4,9 => UNS * INC # E1: 4,9 => UNS * INC # E2: 4,9 => UNS * INC # H2: 4,9 => UNS * INC # I2: 4,9 => UNS * INC # C1: 4,9 => UNS * INC # E1: 4,9 => UNS * DIS # H8: 4,9 => CTR => H8: 3,8 * INC H8: 3,8 # H9: 4,9 => UNS * INC H8: 3,8 # H9: 4,9 => UNS * INC H8: 3,8 # H9: 6 => UNS * INC H8: 3,8 # H2: 4,9 => UNS * INC H8: 3,8 # I2: 4,9 => UNS * INC H8: 3,8 # C1: 4,9 => UNS * INC H8: 3,8 # E1: 4,9 => UNS * INC H8: 3,8 # H9: 4,9 => UNS * INC H8: 3,8 # H9: 6 => UNS * INC H8: 3,8 # E1: 4,9 => UNS * INC H8: 3,8 # E2: 4,9 => UNS * DIS H8: 3,8 # F7: 4,9 => CTR => F7: 6 * PRF H8: 3,8 + F7: 6 # I7: 4,9 => SOL * STA H8: 3,8 + F7: 6 + I7: 4,9 * CNT 22 HDP CHAINS / 22 HYP OPENED