Analysis of xx-top500-133-base.sdk
Contents
Original Sudoku
level: medium
position: 65....3.72..8........1....4...2...4...1.......3.......4...5........3.1.........8. initial
Autosolve
position: 658942317214873...3..1658248..217.43.413962.8.32584..148..51.32.2.4381..1.3.29485 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C7: 7,9 => SOL * DIS # C7: 6 => CTR => C7: 7,9 * DIS # C8: 7,9 => CTR => C8: 5,6 * PRF # C8: 5,6 => SOL * DIS # G2: 6,9 => CTR => G2: 5 * PRF # G2: 5 => SOL * PRF # H2: 6,9 => SOL * DIS # H2: 5 => CTR => H2: 6,9 * DIS # C4: 6,9 => CTR => C4: 5 * PRF # C4: 5 => SOL * PRF # G6: 7,9 => SOL * DIS # G6: 6 => CTR => G6: 7,9 * DIS # H6: 7,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * PRF # C4: 5,9 => SOL * DIS # C4: 6 => CTR => C4: 5,9 * PRF # G2: 5,9 => SOL * DIS # G2: 6 => CTR => G2: 5,9 * DIS # C8: 5,9 => CTR => C8: 6,7 * PRF # C8: 6,7 => SOL * DIS # C7: 6,7 => CTR => C7: 9 * PRF # C7: 9 => SOL * PRF # C8: 6,7 => SOL * DIS # C8: 5,9 => CTR => C8: 6,7 * DIS # C7: 6,7 => CTR => C7: 9 * PRF # C7: 9 => SOL * PRF # G7: 6,7 => SOL * DIS # G7: 9 => CTR => G7: 6,7 * PRF # G7: 6,9 => SOL * DIS # G7: 7 => CTR => G7: 6,9 * DIS # H8: 6,9 => CTR => H8: 7 * PRF # H8: 7 => SOL * PRF # C8: 6,9 => SOL * CNT 33 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C7: 7,9 => SOL * STA C7: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 65....3.72..8........1....4...2...4...1.......3.......4...5........3.1.........8. | initial |
| 658942317214873...3..1658248..217.43.413962.8.32584..148..51.32.2.4381..1.3.29485 | autosolve |
| 658942317214873596397165824865217943741396258932584761489751632526438179173629485 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B3: 7,9 C3: 7,9 I2: 6,9 B4: 6,9 A5: 5,7 A6: 7,9 G4: 5,9 H5: 5,7 A8: 5,9 B9: 6,7 D7: 6,7 D9: 6,7 I8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,H2: 5.. / G2 = 5 => 0 pairs (*) / H2 = 5 => 0 pairs (X) C4,A5: 5.. / C4 = 5 => 0 pairs (*) / A5 = 5 => 0 pairs (X) G4,H5: 5.. / G4 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) A8,C8: 5.. / A8 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) C4,G4: 5.. / C4 = 5 => 0 pairs (*) / G4 = 5 => 0 pairs (X) A5,H5: 5.. / A5 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) A5,A8: 5.. / A5 = 5 => 0 pairs (X) / A8 = 5 => 0 pairs (_) C4,C8: 5.. / C4 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) G2,G4: 5.. / G2 = 5 => 0 pairs (*) / G4 = 5 => 0 pairs (X) H2,H5: 5.. / H2 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) B4,C4: 6.. / B4 = 6 => 0 pairs (*) / C4 = 6 => 0 pairs (X) G6,H6: 6.. / G6 = 6 => 0 pairs (X) / H6 = 6 => 0 pairs (_) D7,D9: 6.. / D7 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) B9,D9: 6.. / B9 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) B4,B9: 6.. / B4 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) I2,I8: 6.. / I2 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) B3,C3: 7.. / B3 = 7 => 0 pairs (X) / C3 = 7 => 0 pairs (_) A5,A6: 7.. / A5 = 7 => 0 pairs (*) / A6 = 7 => 0 pairs (X) D7,D9: 7.. / D7 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) G7,H8: 7.. / G7 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) A5,H5: 7.. / A5 = 7 => 0 pairs (*) / H5 = 7 => 0 pairs (X) C8,H8: 7.. / C8 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) B9,D9: 7.. / B9 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) B3,B9: 7.. / B3 = 7 => 0 pairs (X) / B9 = 7 => 0 pairs (_) G6,G7: 7.. / G6 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) B3,C3: 9.. / B3 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) C7,G7: 9.. / C7 = 9 => 0 pairs (*) / G7 = 9 => 0 pairs (X) A6,A8: 9.. / A6 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) B3,B4: 9.. / B3 = 9 => 0 pairs (*) / B4 = 9 => 0 pairs (X) I2,I8: 9.. / I2 = 9 => 15 pairs (_) / I8 = 9 => 0 pairs (*) * DURATION: 0:00:46.790959 START: 07:17:55.262143 END: 07:18:42.053102 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A8,B3,B4,B9,C3,D7,D9,G4,H5,I2,I8) * 658942317214873...3..1658248..217.43.413962.8.32584..148..51.32.2.4381..1.3.29485 * PAIR C3: 7,9 COL C C7: 7,9,6 # reduction candidate for 7,9 C7: 7,9 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 C7: 6 => CTR * 658942317214873...3..1658248..217.43.413962.8.32584..1486751932.2.438176173629485 C8: 7,9,5,6 # reduction candidate for 7,9 C8: 7,9 => CTR * 658942317214873...3..1658248.5217943741396258932584..148..51.32.2.4381..1.3.29485 C8: 5,6 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 * PAIR I2: 6,9 BLK 3 G2: 6,9,5 # reduction candidate for 6,9 G2: 6,9 => CTR * 658942317214873.5.3..1658248..217543541396278732584..148..5173292.4381..1.3.29485 G2: 5 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 H2: 6,9,5 # reduction candidate for 6,9 H2: 6,9 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 H2: 5 => CTR * 658942317214873.5.3..1658248..217543541396278732584..148..5173292.4381..1.3.29485 * PAIR B4: 6,9 BLK 4 C4: 6,9,5 # reduction candidate for 6,9 C4: 6,9 => CTR * 658942317214873...3..1658248..217543541396278732584..148..5173292.4381..1.3.29485 C4: 5 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 * PAIR A6: 7,9 ROW 6 G6: 7,9,6 # reduction candidate for 7,9 G6: 7,9 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 G6: 6 => CTR * 658942317214873...3..1658248..217.43.413962.8.325846.148..51732.274381..163729485 H6: 7,9,6 # reduction candidate for 7,9 H6: 7,9 => CTR * 658942317214873...3..1658248..217.43.413962.8.325846.148..51732.274381..163729485 H6: 6 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 * PAIR G4: 5,9 ROW 4 C4: 5,9,6 # reduction candidate for 5,9 C4: 5,9 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 C4: 6 => CTR * 658942317214873...3..1658248.6217543541396278732584..148..5173292.4381..1.3.29485 * PAIR G4: 5,9 COL G G2: 5,9,6 # reduction candidate for 5,9 G2: 5,9 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 G2: 6 => CTR * 6589423172148736593..1658248..217543541396278732584961489.51.32.2.4381..1.3.29485 * PAIR A8: 5,9 BLK 7 C8: 5,9,6,7 # reduction candidate for 5,9 C8: 5,9 => CTR * 658942317214873..93..1658248..217.4374139625893258476148..51.32.2.4381761.3.29485 C8: 6,7 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 * PAIR B9: 6,7 BLK 7 C7: 6,7,9 # reduction candidate for 6,7 C7: 6,7 => CTR * 658942317214873...3..1658248..217.43.413962.8.32584..148..51932.2.4381761.3.29485 C7: 9 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 C8: 6,7,5,9 # reduction candidate for 6,7 C8: 6,7 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 C8: 5,9 => CTR * 658942317214873..93..1658248..217.4374139625893258476148..51.32.2.4381761.3.29485 * PAIR D7: 6,7 ROW 7 C7: 6,7,9 # reduction candidate for 6,7 C7: 6,7 => CTR * 658942317214873...3..1658248..217.43.413962.8.32584..148..51932.2.4381761.3.29485 C7: 9 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 G7: 6,7,9 # reduction candidate for 6,7 G7: 6,7 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 G7: 9 => CTR * 658942317214873...3..1658248..217.43.413962.8.3258476148..51932.2.4381761.3.29485 * PAIR I8: 6,9 BLK 9 G7: 6,9,7 # reduction candidate for 6,9 G7: 6,9 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 G7: 7 => CTR * 658942317214873...3..1658248..217.43.413962.8.32584..14896517325274381..1.3.29485 H8: 6,9,7 # reduction candidate for 6,9 H8: 6,9 => CTR * 658942317214873...3..1658248..217.43.413962.8.32584..148..51732.274381..163729485 H8: 7 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 * PAIR I8: 6,9 ROW 8 C8: 6,9,5,7 # reduction candidate for 6,9 C8: 6,9 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 C8: 5,7 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-133-base-pr-000.dot * REASONING * PRF # C7: 7,9 => SOL * DIS # C7: 6 => CTR => C7: 7,9 * DIS # C8: 7,9 => CTR => C8: 5,6 * PRF # C8: 5,6 => SOL * DIS # G2: 6,9 => CTR => G2: 5 * PRF # G2: 5 => SOL * PRF # H2: 6,9 => SOL * DIS # H2: 5 => CTR => H2: 6,9 * DIS # C4: 6,9 => CTR => C4: 5 * PRF # C4: 5 => SOL * PRF # G6: 7,9 => SOL * DIS # G6: 6 => CTR => G6: 7,9 * DIS # H6: 7,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * PRF # C4: 5,9 => SOL * DIS # C4: 6 => CTR => C4: 5,9 * PRF # G2: 5,9 => SOL * DIS # G2: 6 => CTR => G2: 5,9 * DIS # C8: 5,9 => CTR => C8: 6,7 * PRF # C8: 6,7 => SOL * DIS # C7: 6,7 => CTR => C7: 9 * PRF # C7: 9 => SOL * PRF # C8: 6,7 => SOL * DIS # C8: 5,9 => CTR => C8: 6,7 * DIS # C7: 6,7 => CTR => C7: 9 * PRF # C7: 9 => SOL * PRF # G7: 6,7 => SOL * DIS # G7: 9 => CTR => G7: 6,7 * PRF # G7: 6,9 => SOL * DIS # G7: 7 => CTR => G7: 6,9 * DIS # H8: 6,9 => CTR => H8: 7 * PRF # H8: 7 => SOL * PRF # C8: 6,9 => SOL * CNT 33 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A8,B3,B4,B9,C3,D7,D9,G4,H5,I2,I8) * 658942317214873...3..1658248..217.43.413962.8.32584..148..51.32.2.4381..1.3.29485 * PAIR C3: 7,9 COL C C7: 7,9,6 # reduction candidate for 7,9 C7: 7,9 => SOLVED * 658942317214873596397165824865217943741396258932584761489751632526438179173629485 * DURATION: 0:00:01.997137 START: 07:19:20.159052 END: 07:19:22.156189 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-133-base-pr-001.dot * REASONING * PRF # C7: 7,9 => SOL * STA C7: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 133 solution: 658942317214873596397165824865217943741396258932584761489751632526438179173629485 info: 1811 FNBWY S8.f 35977 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 658942317214873596397165824865217943741396258932584761489751632526438179173629485 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:
* PRF # C7: 7,9 => SOL * DIS # C7: 6 => CTR => C7: 7,9 * DIS # C8: 7,9 => CTR => C8: 5,6 * PRF # C8: 5,6 => SOL * DIS # G2: 6,9 => CTR => G2: 5 * PRF # G2: 5 => SOL * PRF # H2: 6,9 => SOL * DIS # H2: 5 => CTR => H2: 6,9 * DIS # C4: 6,9 => CTR => C4: 5 * PRF # C4: 5 => SOL * PRF # G6: 7,9 => SOL * DIS # G6: 6 => CTR => G6: 7,9 * DIS # H6: 7,9 => CTR => H6: 6 * PRF # H6: 6 => SOL * PRF # C4: 5,9 => SOL * DIS # C4: 6 => CTR => C4: 5,9 * PRF # G2: 5,9 => SOL * DIS # G2: 6 => CTR => G2: 5,9 * DIS # C8: 5,9 => CTR => C8: 6,7 * PRF # C8: 6,7 => SOL * DIS # C7: 6,7 => CTR => C7: 9 * PRF # C7: 9 => SOL * PRF # C8: 6,7 => SOL * DIS # C8: 5,9 => CTR => C8: 6,7 * DIS # C7: 6,7 => CTR => C7: 9 * PRF # C7: 9 => SOL * PRF # G7: 6,7 => SOL * DIS # G7: 9 => CTR => G7: 6,7 * PRF # G7: 6,9 => SOL * DIS # G7: 7 => CTR => G7: 6,9 * DIS # H8: 6,9 => CTR => H8: 7 * PRF # H8: 7 => SOL * PRF # C8: 6,9 => SOL * INC # C8: 5,7 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C7: 7,9 => SOL * STA C7: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED