Analysis of xx-top500-308-base.sdk
Contents
Original Sudoku
level: medium
position: ....2...18.4......3...........6.8.4..2....7.....3.....6..4...8..7..1.5........... initial
Autosolve
position: ....2...18.4....2.3.2.........6.8.4..2....7.....3.2...6..4...8..7..1.5........... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H8: 3,6 => CTR => H8: 9 * DIS # H9: 3,6 => CTR => H9: 1,7,9 * CNT 2 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H8: 3,6 => CTR => H8: 9 * DIS H8: 9 # H9: 3,6 => CTR => H9: 1,7 * DIS H8: 9 + H9: 1,7 # H1: 5 => CTR => H1: 3,6 * DIS H8: 9 + H9: 1,7 + H1: 3,6 # G1: 3,6 => CTR => G1: 4,8,9 * DIS H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 # F1: 3,6 => CTR => F1: 4,5,9 * DIS H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 # A6: 1,5 => CTR => A6: 4,7,9 * DIS H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 + A6: 4,7,9 # A9: 1,5,9 => CTR => A9: 2,4 * PRF H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 + A6: 4,7,9 + A9: 2,4 # C1: 5,7 => SOL * STA H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 + A6: 4,7,9 + A9: 2,4 + C1: 5,7 * CNT 8 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....2...18.4......3...........6.8.4..2....7.....3.....6..4...8..7..1.5........... | initial |
| ....2...18.4....2.3.2.........6.8.4..2....7.....3.2...6..4...8..7..1.5........... | autosolve |
| 765924831814763925392581476137658249528149763946372158651497382273816594489235617 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) B6: 4,8 H5: 3,6 B9: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 1.. / B2 = 1 => 3 pairs (_) / B3 = 1 => 3 pairs (_) D5,F5: 1.. / D5 = 1 => 3 pairs (_) / F5 = 1 => 4 pairs (_) C7,G7: 1.. / C7 = 1 => 3 pairs (_) / G7 = 1 => 3 pairs (_) H6,H9: 1.. / H6 = 1 => 3 pairs (_) / H9 = 1 => 3 pairs (_) G4,I4: 2.. / G4 = 2 => 3 pairs (_) / I4 = 2 => 3 pairs (_) A8,A9: 2.. / A8 = 2 => 4 pairs (_) / A9 = 2 => 0 pairs (X) D8,D9: 2.. / D8 = 2 => 0 pairs (X) / D9 = 2 => 4 pairs (_) G7,I7: 2.. / G7 = 2 => 3 pairs (_) / I7 = 2 => 3 pairs (_) A8,D8: 2.. / A8 = 2 => 4 pairs (_) / D8 = 2 => 0 pairs (X) A9,D9: 2.. / A9 = 2 => 0 pairs (X) / D9 = 2 => 4 pairs (_) G4,G7: 2.. / G4 = 2 => 3 pairs (_) / G7 = 2 => 3 pairs (_) I4,I7: 2.. / I4 = 2 => 3 pairs (_) / I7 = 2 => 3 pairs (_) B4,B7: 3.. / B4 = 3 => 5 pairs (_) / B7 = 3 => 8 pairs (_) F1,G1: 4.. / F1 = 4 => 4 pairs (_) / G1 = 4 => 0 pairs (X) A8,I8: 4.. / A8 = 4 => 0 pairs (X) / I8 = 4 => 4 pairs (_) B6,B9: 4.. / B6 = 4 => 12 pairs (_) / B9 = 4 => 5 pairs (_) C5,C6: 6.. / C5 = 6 => 0 pairs (X) / C6 = 6 => 4 pairs (_) A1,C1: 7.. / A1 = 7 => 4 pairs (_) / C1 = 7 => 4 pairs (_) E4,E6: 7.. / E4 = 7 => 3 pairs (_) / E6 = 7 => 5 pairs (_) F7,I7: 7.. / F7 = 7 => 3 pairs (_) / I7 = 7 => 3 pairs (_) H3,H9: 7.. / H3 = 7 => 3 pairs (_) / H9 = 7 => 3 pairs (_) D1,G1: 8.. / D1 = 8 => 0 pairs (X) / G1 = 8 => 14 pairs (_) C5,I5: 8.. / C5 = 8 => 12 pairs (_) / I5 = 8 => 4 pairs (_) C8,D8: 8.. / C8 = 8 => 0 pairs (X) / D8 = 8 => 12 pairs (_) B6,B9: 8.. / B6 = 8 => 5 pairs (_) / B9 = 8 => 12 pairs (_) E3,E9: 8.. / E3 = 8 => 15 pairs (_) / E9 = 8 => 0 pairs (X) * DURATION: 0:00:39.355567 START: 13:30:17.483770 END: 13:30:56.839337 2017-05-04 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B9,H5) * ....2...18.4....2.3.2.........6.8.4..2....7.....3.2...6..4...8..7..1.5........... * PAIR H5: 3,6 BLK 6 I5: 3,6,8 # reduction candidate for 3,6 I5: 3,6 # 12 pairs I5: 8 # 4 pairs * PAIR H5: 3,6 ROW 5 C5: 3,6,8 # reduction candidate for 3,6 C5: 8 # 12 pairs C5: 3,6 # 4 pairs * PAIR H5: 3,6 COL H H1: 3,6,5,9 # reduction candidate for 3,6 H1: 3,6 # 11 pairs H8: 3,6,9 # reduction candidate for 3,6 H8: 3,6 => CTR * .6.8234.18.4....2.3.2...8.....6.8.4..2....7.8.8.3.2...6..43..8..78.1.534.43.8.... H8: 9 # 7 pairs H9: 3,6,1,7,9 # reduction candidate for 3,6 H9: 3,6 => CTR * .6.82..518.4....2.3.2....7....6.8.4..2....7.....3.2.1.6..4...8..7821.59.24....... H9: 1,7,9 # 3 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-308-base-pr-000.dot * REASONING * DIS # H8: 3,6 => CTR => H8: 9 * DIS # H9: 3,6 => CTR => H9: 1,7,9 * CNT 2 HDP CHAINS / 9 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B9,H5) * ....2...18.4....2.3.2.........6.8.4..2....7.....3.2...6..4...8..7..1.5........... * PAIR H5: 3,6 BLK 6 I5: 3,6,8 # reduction candidate for 3,6 I5: 3,6 # 12 pairs I5: 8 # 4 pairs * PAIR H5: 3,6 ROW 5 C5: 3,6,8 # reduction candidate for 3,6 C5: 8 # 12 pairs C5: 3,6 # 4 pairs * PAIR H5: 3,6 COL H H1: 3,6,5,9 # reduction candidate for 3,6 H1: 3,6 # 11 pairs H8: 3,6,9 # reduction candidate for 3,6 H8: 3,6 => CTR * .6.8234.18.4....2.3.2...8.....6.8.4..2....7.8.8.3.2...6..43..8..78.1.534.43.8.... H9: 3,6,1,7 # reduction candidate for 3,6 H9: 3,6 => CTR * .6.82..518.4....2.3.2....7....6.8.4..2....7.....3.2.1.6..4...8..7821.59.24....... * RESTART * PAIR H5: 3,6 COL H H1: 3,6,5 # reduction candidate for 3,6 H1: 5 => CTR * .6.82..518.4....2.3.2.........6.8.4..2....73....3.2...6..4...8..7821.59.24....... * PAIR RESTART * PAIR H5: 3,6 BLK 6 I5: 3,6,8 # reduction candidate for 3,6 I5: 8 # 12 pairs I5: 3,6 # 12 pairs * PAIR H5: 3,6 ROW 5 C5: 3,6,8 # reduction candidate for 3,6 C5: 8 # 12 pairs C5: 3,6 # 12 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A8,B6,B9,C8,D8,F8,H1,H3,H5,H6,H9) * ....2...18.4....2.3.2.........6.8.4..2....7.....3.2...6..4...8..7..1.59.......... * PAIR H1: 3,6 BLK 3 G1: 3,6,4,8,9 # reduction candidate for 3,6 G1: 3,6 => CTR * ...824..18.4....2.3.2.........6.8.4..2....7.....3.2...6..4...8..7821.59.24....... G2: 3,6,9 # reduction candidate for 3,6 G2: 3,6 # 12 pairs I2: 3,6,5,7,9 # reduction candidate for 3,6 I2: 3,6 # 16 pairs * PAIR H1: 3,6 ROW 1 F1: 3,6,4,5,9 # reduction candidate for 3,6 F1: 3,6 => CTR * ...82.4.18.4....2.3.2.........6.8.4..2....7.....3.2...6..4...8..7821.59.24....... * PAIR RESTART * PAIR H3: 5,7 BLK 3 I2: 5,7,6,9 # reduction candidate for 5,7 I2: 5,7 # 13 pairs I3: 5,7,4,6,8,9 # reduction candidate for 5,7 I3: 5,7 # 22 pairs * PAIR H3: 5,7 ROW 3 D3: 5,7,1,8,9 # reduction candidate for 5,7 D3: 5,7 # 15 pairs F3: 5,7,1,4,6,9 # reduction candidate for 5,7 F3: 5,7 # 15 pairs * PAIR H6: 1,5 ROW 6 A6: 1,5,4,7,9 # reduction candidate for 1,5 A6: 1,5 => CTR * .6..2.8318.4.6392.3.2.8.4.6.3.6.8.49928.4.763.463721586..4...8..7381659448.2..... * PAIR RESTART * PAIR A8: 2,4 BLK 7 A9: 2,4,1,5,9 # reduction candidate for 2,4 A9: 1,5,9 => CTR * .6..2..318.4....2.3.2.........6.8.4..2....76...63.2...6..4...8.27.81.594......... * LEVEL 0 PASS 1 ROUND 3 (AUTO SOLVE) (A1,A5,A6,B3,B7,C4,C9,D1,E4,E6,E7,F9) * .6..248318147639253.2.8.47613.6.8249.28.4.763.463.21586.14.738227381659448.23.617 * PAIR A1: 5,7 BLK 1 C1: 5,7,9 # reduction candidate for 5,7 C1: 5,7 => SOLVED * 765924831814763925392581476137658249528149763946372158651497382273816594489235617 * DURATION: 0:00:28.735858 START: 13:31:05.294403 END: 13:31:34.030261 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-308-base-pr-001.dot * REASONING * DIS # H8: 3,6 => CTR => H8: 9 * DIS H8: 9 # H9: 3,6 => CTR => H9: 1,7 * DIS H8: 9 + H9: 1,7 # H1: 5 => CTR => H1: 3,6 * DIS H8: 9 + H9: 1,7 + H1: 3,6 # G1: 3,6 => CTR => G1: 4,8,9 * DIS H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 # F1: 3,6 => CTR => F1: 4,5,9 * DIS H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 # A6: 1,5 => CTR => A6: 4,7,9 * DIS H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 + A6: 4,7,9 # A9: 1,5,9 => CTR => A9: 2,4 * PRF H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 + A6: 4,7,9 + A9: 2,4 # C1: 5,7 => SOL * STA H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 + A6: 4,7,9 + A9: 2,4 + C1: 5,7 * CNT 8 HDP CHAINS / 25 HYP OPENED
Header Info
Top 500 Minimum 17 308 solution: 765924831814763925392581476137658249528149763946372158651497382273816594489235617 info: 2717 FNBHXYK S8.f 40423 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 765924831814763925392581476137658249528149763946372158651497382273816594489235617 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 # I5: 3,6 => UNS * INC # I5: 8 => UNS * INC # C5: 3,6 => UNS * INC # C5: 8 => UNS * INC # H1: 3,6 => UNS * DIS # H8: 3,6 => CTR => H8: 9 * INC # H8: 9 => UNS * DIS # H9: 3,6 => CTR => H9: 1,7,9 * INC # H9: 1,7,9 => UNS * CNT 9 HDP CHAINS / 9 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I5: 3,6 => UNS * INC # I5: 8 => UNS * INC # C5: 3,6 => UNS * INC # C5: 8 => UNS * INC # H1: 3,6 => UNS * DIS # H8: 3,6 => CTR => H8: 9 * DIS H8: 9 # H9: 3,6 => CTR => H9: 1,7 * INC H8: 9 + H9: 1,7 # H1: 3,6 => UNS * DIS H8: 9 + H9: 1,7 # H1: 5 => CTR => H1: 3,6 * INC H8: 9 + H9: 1,7 + H1: 3,6 # I5: 3,6 => UNS * INC H8: 9 + H9: 1,7 + H1: 3,6 # I5: 8 => UNS * INC H8: 9 + H9: 1,7 + H1: 3,6 # C5: 3,6 => UNS * INC H8: 9 + H9: 1,7 + H1: 3,6 # C5: 8 => UNS * DIS H8: 9 + H9: 1,7 + H1: 3,6 # G1: 3,6 => CTR => G1: 4,8,9 * INC H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 # G2: 3,6 => UNS * INC H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 # I2: 3,6 => UNS * DIS H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 # F1: 3,6 => CTR => F1: 4,5,9 * INC H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 # I2: 5,7 => UNS * INC H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 # I3: 5,7 => UNS * INC H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 # D3: 5,7 => UNS * INC H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 # F3: 5,7 => UNS * DIS H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 # A6: 1,5 => CTR => A6: 4,7,9 * INC H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 + A6: 4,7,9 # A9: 2,4 => UNS * DIS H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 + A6: 4,7,9 # A9: 1,5,9 => CTR => A9: 2,4 * PRF H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 + A6: 4,7,9 + A9: 2,4 # C1: 5,7 => SOL * STA H8: 9 + H9: 1,7 + H1: 3,6 + G1: 4,8,9 + F1: 4,5,9 + A6: 4,7,9 + A9: 2,4 + C1: 5,7 * CNT 25 HDP CHAINS / 25 HYP OPENED