Analysis of xx-top500-185-base.sdk
Contents
Original Sudoku
level: medium
position: ...62..3..71...............9...4..5.2...1..........8.....7..1.235.8.............. initial
Autosolve
position: 5..624731.7158392..231795.891.34.25.2.591...373425681984.7351.23528.1...1.74.2385 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I8: 4,6 => CTR => I8: 7 * PRF # I8: 7 => SOL * DIS # H5: 4,6 => CTR => H5: 7 * PRF # H5: 7 => SOL * PRF # H8: 4,6 => SOL * PRF # H5: 6,7 => SOL * DIS # H5: 4 => CTR => H5: 6,7 * PRF # I8: 6,7 => SOL * DIS # I8: 4 => CTR => I8: 6,7 * DIS # H5: 4,6 => CTR => H5: 7 * PRF # H5: 7 => SOL * DIS # H8: 6,9 => CTR => H8: 4,7 * PRF # H8: 4,7 => SOL * DIS # H8: 6,9 => CTR => H8: 4,7 * PRF # H8: 4,7 => SOL * PRF # H8: 4,6 => SOL * DIS # I8: 4,6 => CTR => I8: 7 * PRF # I8: 7 => SOL * CNT 18 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I8: 4,6 => CTR => I8: 7 * PRF I8: 7 => SOL * STA I8: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...62..3..71...............9...4..5.2...1..........8.....7..1.235.8.............. | initial |
| 5..624731.7158392..231795.891.34.25.2.591...373425681984.7351.23528.1...1.74.2385 | autosolve |
| 589624731671583924423179568918347256265918473734256819846735192352891647197462385 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B1: 8,9 C1: 8,9 A2: 4,6 A3: 4,6 I2: 4,6 H3: 4,6 C4: 6,8 B5: 6,8 F4: 7,8 F5: 7,8 I4: 6,7 G5: 4,6 C7: 6,9 B9: 6,9 E8: 6,9 E9: 6,9 H7: 6,9 G8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 4.. / A2 = 4 => 0 pairs (X) / A3 = 4 => 0 pairs (_) I2,H3: 4.. / I2 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) G5,H5: 4.. / G5 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) A2,I2: 4.. / A2 = 4 => 0 pairs (X) / I2 = 4 => 0 pairs (_) A3,H3: 4.. / A3 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) G5,G8: 4.. / G5 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) I2,I8: 4.. / I2 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) A2,A3: 6.. / A2 = 6 => 0 pairs (*) / A3 = 6 => 0 pairs (X) I2,H3: 6.. / I2 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) C4,B5: 6.. / C4 = 6 => 0 pairs (X) / B5 = 6 => 0 pairs (_) C7,B9: 6.. / C7 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) E8,E9: 6.. / E8 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) A2,I2: 6.. / A2 = 6 => 0 pairs (*) / I2 = 6 => 0 pairs (X) A3,H3: 6.. / A3 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) C4,I4: 6.. / C4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) C7,H7: 6.. / C7 = 6 => 0 pairs (*) / H7 = 6 => 0 pairs (X) B9,E9: 6.. / B9 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) B5,B9: 6.. / B5 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) C4,C7: 6.. / C4 = 6 => 0 pairs (X) / C7 = 6 => 0 pairs (_) G5,G8: 6.. / G5 = 6 => 0 pairs (X) / G8 = 6 => 0 pairs (_) F4,F5: 7.. / F4 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) I4,H5: 7.. / I4 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) H8,I8: 7.. / H8 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) F4,I4: 7.. / F4 = 7 => 0 pairs (*) / I4 = 7 => 0 pairs (X) F5,H5: 7.. / F5 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) H5,H8: 7.. / H5 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) I4,I8: 7.. / I4 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) B1,C1: 8.. / B1 = 8 => 0 pairs (*) / C1 = 8 => 0 pairs (X) C4,B5: 8.. / C4 = 8 => 0 pairs (*) / B5 = 8 => 0 pairs (X) F4,F5: 8.. / F4 = 8 => 0 pairs (X) / F5 = 8 => 0 pairs (_) C4,F4: 8.. / C4 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) B5,F5: 8.. / B5 = 8 => 0 pairs (X) / F5 = 8 => 0 pairs (_) B1,B5: 8.. / B1 = 8 => 0 pairs (*) / B5 = 8 => 0 pairs (X) C1,C4: 8.. / C1 = 8 => 0 pairs (X) / C4 = 8 => 0 pairs (_) B1,C1: 9.. / B1 = 9 => 0 pairs (X) / C1 = 9 => 0 pairs (_) C7,B9: 9.. / C7 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) E8,E9: 9.. / E8 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) H7,H8: 9.. / H7 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) C7,H7: 9.. / C7 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) E8,H8: 9.. / E8 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) B9,E9: 9.. / B9 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) B1,B9: 9.. / B1 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) C1,C7: 9.. / C1 = 9 => 0 pairs (*) / C7 = 9 => 0 pairs (X) * DURATION: 0:01:17.650648 START: 09:00:40.609714 END: 09:01:58.260362 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B1,B5,B9,C1,C4,C7,E8,E9,F4,F5,G5,G8,H3,H7,I2,I4) * 5..624731.7158392..231795.891.34.25.2.591...373425681984.7351.23528.1...1.74.2385 * PAIR I2: 4,6 COL I I8: 4,6,7 # reduction candidate for 4,6 I8: 4,6 => CTR * 5..624731.7158392..231795.8916348257285917..37342568198497351.23528.1.7.1.74.2385 I8: 7 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 * PAIR H3: 4,6 COL H H5: 4,6,7 # reduction candidate for 4,6 H5: 4,6 => CTR * 5..624731.7158392..231795.8916348257285917..37342568198497351.23528.1.7.1.74.2385 H5: 7 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 H8: 4,6,7,9 # reduction candidate for 4,6 H8: 4,6 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 H8: 7,9 # 19 pairs * PAIR I4: 6,7 BLK 6 H5: 6,7,4 # reduction candidate for 6,7 H5: 6,7 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 H5: 4 => CTR * 5..624731.7158392..231795.891.34.2572.591764373425681984.7351.23528.1476167492385 * PAIR I4: 6,7 COL I I8: 6,7,4 # reduction candidate for 6,7 I8: 6,7 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 I8: 4 => CTR * 5..62473147158392662317954891634825728591746373425681984.7351.23528.1.741.74.2385 * PAIR G5: 4,6 BLK 6 H5: 4,6,7 # reduction candidate for 4,6 H5: 4,6 => CTR * 5..624731.7158392..231795.8916348257285917..37342568198497351.23528.1.7.1.74.2385 H5: 7 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 * PAIR E8: 6,9 ROW 8 H8: 6,9,4,7 # reduction candidate for 6,9 H8: 6,9 => CTR * 5..624731.7158392442317956891.34725626591847373425681984.7351.23528.1..71.74.2385 H8: 4,7 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 * PAIR H7: 6,9 BLK 9 H8: 6,9,4,7 # reduction candidate for 6,9 H8: 6,9 => CTR * 5..624731.7158392442317956891.34725626591847373425681984.7351.23528.1..71.74.2385 H8: 4,7 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 * PAIR G8: 4,6 BLK 9 H8: 4,6,7,9 # reduction candidate for 4,6 H8: 4,6 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 H8: 7,9 # 19 pairs I8: 4,6,7 # reduction candidate for 4,6 I8: 4,6 => CTR * 5..624731.7158392..231795.8916348257285917..37342568198497351.23528.1.7.1.74.2385 I8: 7 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-185-base-pr-000.dot * REASONING * DIS # I8: 4,6 => CTR => I8: 7 * PRF # I8: 7 => SOL * DIS # H5: 4,6 => CTR => H5: 7 * PRF # H5: 7 => SOL * PRF # H8: 4,6 => SOL * PRF # H5: 6,7 => SOL * DIS # H5: 4 => CTR => H5: 6,7 * PRF # I8: 6,7 => SOL * DIS # I8: 4 => CTR => I8: 6,7 * DIS # H5: 4,6 => CTR => H5: 7 * PRF # H5: 7 => SOL * DIS # H8: 6,9 => CTR => H8: 4,7 * PRF # H8: 4,7 => SOL * DIS # H8: 6,9 => CTR => H8: 4,7 * PRF # H8: 4,7 => SOL * PRF # H8: 4,6 => SOL * DIS # I8: 4,6 => CTR => I8: 7 * PRF # I8: 7 => SOL * CNT 18 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B1,B5,B9,C1,C4,C7,E8,E9,F4,F5,G5,G8,H3,H7,I2,I4) * 5..624731.7158392..231795.891.34.25.2.591...373425681984.7351.23528.1...1.74.2385 * PAIR I2: 4,6 COL I I8: 4,6,7 # reduction candidate for 4,6 I8: 4,6 => CTR * 5..624731.7158392..231795.8916348257285917..37342568198497351.23528.1.7.1.74.2385 I8: 7 => SOLVED * 589624731671583924423179568918347256265918473734256819846735192352891647197462385 * DURATION: 0:00:03.176299 START: 09:02:24.152564 END: 09:02:27.328863 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-185-base-pr-001.dot * REASONING * DIS # I8: 4,6 => CTR => I8: 7 * PRF I8: 7 => SOL * STA I8: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 185 solution: 589624731671583924423179568918347256265918473734256819846735192352891647197462385 info: 1830 FNBTWY S8.f 42754 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 589624731671583924423179568918347256265918473734256819846735192352891647197462385 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 # I8: 4,6 => CTR => I8: 7 * PRF # I8: 7 => SOL * DIS # H5: 4,6 => CTR => H5: 7 * PRF # H5: 7 => SOL * PRF # H8: 4,6 => SOL * INC # H8: 7,9 => UNS * PRF # H5: 6,7 => SOL * DIS # H5: 4 => CTR => H5: 6,7 * PRF # I8: 6,7 => SOL * DIS # I8: 4 => CTR => I8: 6,7 * DIS # H5: 4,6 => CTR => H5: 7 * PRF # H5: 7 => SOL * DIS # H8: 6,9 => CTR => H8: 4,7 * PRF # H8: 4,7 => SOL * DIS # H8: 6,9 => CTR => H8: 4,7 * PRF # H8: 4,7 => SOL * PRF # H8: 4,6 => SOL * INC # H8: 7,9 => UNS * DIS # I8: 4,6 => CTR => I8: 7 * PRF # I8: 7 => SOL * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I8: 4,6 => CTR => I8: 7 * PRF I8: 7 => SOL * STA I8: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED