Analysis of xx-top500-433-base.sdk
Contents
Original Sudoku
level: medium
position: 9.24........6....1.........76.............54.......2..83..9...7....2..8......5... initial
Autosolve
position: 952431768...6.2951...5.9432764253819...71.54.5..94.27.835194627...327185...865394 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 7,8 => CTR => C3: 1,6 * DIS # B2: 7,8 => CTR => B2: 4 * PRF # B2: 4 => SOL * PRF # C2: 7,8 => SOL * DIS # C2: 3 => CTR => C2: 7,8 * DIS # C3: 7,8 => CTR => C3: 1,6 * PRF # C6: 3 => SOL * DIS # B9: 7 => CTR => B9: 1,2 * DIS # B9: 1,7 => CTR => B9: 2 * PRF # B9: 2 => SOL * PRF # C3: 1,7 => SOL * CNT 11 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 7,8 => CTR => C3: 1,6 * DIS C3: 1,6 # B2: 7,8 => CTR => B2: 4 * PRF C3: 1,6 + B2: 4 => SOL * STA C3: 1,6 + B2: 4 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9.24........6....1.........76.............54.......2..83..9...7....2..8......5... | initial |
| 952431768...6.2951...5.9432764253819...71.54.5..94.27.835194627...327185...865394 | autosolve |
| 952431768348672951671589432764253819289716543513948276835194627496327185127865394 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A2: 3,4 A3: 1,6 E2: 7,8 E3: 7,8 A5: 2,3 B6: 1,8 F5: 6,8 F6: 6,8 I5: 3,6 I6: 3,6 A8: 4,6 B8: 4,9 C8: 6,9 A9: 1,2 C9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B6,C6: 1.. / B6 = 1 => 18 pairs (_) / C6 = 1 => 16 pairs (_) A3,A9: 1.. / A3 = 1 => 0 pairs (X) / A9 = 1 => 0 pairs (_) A5,B5: 2.. / A5 = 2 => 0 pairs (*) / B5 = 2 => 0 pairs (X) A9,B9: 2.. / A9 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) A5,A9: 2.. / A5 = 2 => 0 pairs (*) / A9 = 2 => 0 pairs (X) B5,B9: 2.. / B5 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) A2,C2: 3.. / A2 = 3 => 0 pairs (*) / C2 = 3 => 0 pairs (X) I5,I6: 3.. / I5 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) C6,I6: 3.. / C6 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) A2,A5: 3.. / A2 = 3 => 0 pairs (*) / A5 = 3 => 0 pairs (X) A2,B2: 4.. / A2 = 4 => 0 pairs (X) / B2 = 4 => 0 pairs (_) A8,B8: 4.. / A8 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) A2,A8: 4.. / A2 = 4 => 0 pairs (X) / A8 = 4 => 0 pairs (_) B2,B8: 4.. / B2 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) A3,C3: 6.. / A3 = 6 => 0 pairs (*) / C3 = 6 => 0 pairs (X) F5,F6: 6.. / F5 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) I5,I6: 6.. / I5 = 6 => 14 pairs (_) / I6 = 6 => 0 pairs (*) A8,C8: 6.. / A8 = 6 => 0 pairs (X) / C8 = 6 => 0 pairs (_) F5,I5: 6.. / F5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) F6,I6: 6.. / F6 = 6 => 14 pairs (_) / I6 = 6 => 0 pairs (*) A3,A8: 6.. / A3 = 6 => 0 pairs (*) / A8 = 6 => 0 pairs (X) C3,C8: 6.. / C3 = 6 => 0 pairs (X) / C8 = 6 => 0 pairs (_) E2,E3: 7.. / E2 = 7 => 16 pairs (_) / E3 = 7 => 18 pairs (_) B9,C9: 7.. / B9 = 7 => 0 pairs (X) / C9 = 7 => 16 pairs (_) E2,E3: 8.. / E2 = 8 => 18 pairs (_) / E3 = 8 => 16 pairs (_) F5,F6: 8.. / F5 = 8 => 14 pairs (_) / F6 = 8 => 0 pairs (*) B5,C5: 9.. / B5 = 9 => 0 pairs (X) / C5 = 9 => 0 pairs (_) B8,C8: 9.. / B8 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) B5,B8: 9.. / B5 = 9 => 0 pairs (X) / B8 = 9 => 0 pairs (_) C5,C8: 9.. / C5 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) * DURATION: 0:00:53.576106 START: 17:33:30.200715 END: 17:34:23.776821 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A5,A8,A9,B6,B8,C8,C9,E2,E3,F5,F6,I5,I6) * 952431768...6.2951...5.9432764253819...71.54.5..94.27.835194627...327185...865394 * PAIR A3: 1,6 BLK 1 C3: 1,6,7,8 # reduction candidate for 1,6 C3: 7,8 => CTR * 952431768...6.295161.5.9432764253819...71.54.58194627383519462749632718512.865394 C3: 1,6 # 17 pairs * PAIR E2: 7,8 ROW 2 B2: 7,8,4 # reduction candidate for 7,8 B2: 7,8 => CTR * 9524317684.36.2951...5.94327642538193297185465..9462738351946276..327185...865394 B2: 4 => SOLVED * 952431768348672951671589432764253819289716543513948276835194627496327185127865394 C2: 7,8,3 # reduction candidate for 7,8 C2: 7,8 => SOLVED * 952431768348672951671589432764253819289716543513948276835194627496327185127865394 C2: 3 => CTR * 952431768..36.2951...5.94327642538193297185465..946273835194627.963271852..865394 * PAIR E3: 7,8 ROW 3 B3: 7,8,1 # reduction candidate for 7,8 B3: 7,8 # 17 pairs C3: 7,8,1,6 # reduction candidate for 7,8 C3: 7,8 => CTR * 952431768...6.295161.5.9432764253819...71.54.58194627383519462749632718512.865394 C3: 1,6 # 17 pairs * PAIR B6: 1,8 BLK 4 C6: 1,8,3 # reduction candidate for 1,8 C6: 3 => SOLVED * 952431768348672951671589432764253819289716543513948276835194627496327185127865394 C6: 1,8 # 14 pairs * PAIR B6: 1,8 COL B B3: 1,8,7 # reduction candidate for 1,8 B3: 1,8 # 19 pairs B3: 7 # 16 pairs * PAIR A9: 1,2 BLK 7 B9: 1,2,7 # reduction candidate for 1,2 B9: 7 => CTR * 952431768...6.2951...5.9432764253819.297185465..946273835194627.96327185271865394 B9: 1,2 # 16 pairs * PAIR C9: 1,7 BLK 7 B9: 1,7,2 # reduction candidate for 1,7 B9: 1,7 => CTR * 952431768...6.2951...5.9432764253819.297185465..946273835194627.963271852..865394 B9: 2 => SOLVED * 952431768348672951671589432764253819289716543513948276835194627496327185127865394 * PAIR C9: 1,7 COL C C3: 1,7,6,8 # reduction candidate for 1,7 C3: 1,7 => SOLVED * 952431768348672951671589432764253819289716543513948276835194627496327185127865394 C3: 6,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-433-base-pr-000.dot * REASONING * DIS # C3: 7,8 => CTR => C3: 1,6 * DIS # B2: 7,8 => CTR => B2: 4 * PRF # B2: 4 => SOL * PRF # C2: 7,8 => SOL * DIS # C2: 3 => CTR => C2: 7,8 * DIS # C3: 7,8 => CTR => C3: 1,6 * PRF # C6: 3 => SOL * DIS # B9: 7 => CTR => B9: 1,2 * DIS # B9: 1,7 => CTR => B9: 2 * PRF # B9: 2 => SOL * PRF # C3: 1,7 => SOL * CNT 11 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A5,A8,A9,B6,B8,C8,C9,E2,E3,F5,F6,I5,I6) * 952431768...6.2951...5.9432764253819...71.54.5..94.27.835194627...327185...865394 * PAIR A3: 1,6 BLK 1 C3: 1,6,7,8 # reduction candidate for 1,6 C3: 7,8 => CTR * 952431768...6.295161.5.9432764253819...71.54.58194627383519462749632718512.865394 * PAIR E2: 7,8 ROW 2 B2: 7,8,4 # reduction candidate for 7,8 B2: 7,8 => CTR * 9524317684.36.2951...5.94327642538193297185465.89462738351946276..327185...865394 B2: 4 => SOLVED * 952431768348672951671589432764253819289716543513948276835194627496327185127865394 * DURATION: 0:00:04.049416 START: 17:34:46.286396 END: 17:34:50.335812 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-433-base-pr-001.dot * REASONING * DIS # C3: 7,8 => CTR => C3: 1,6 * DIS C3: 1,6 # B2: 7,8 => CTR => B2: 4 * PRF C3: 1,6 + B2: 4 => SOL * STA C3: 1,6 + B2: 4 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 433 solution: 952431768348672951671589432764253819289716543513948276835194627496327185127865394 info: 95227 FNBTYK S8.f 44431 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 952431768348672951671589432764253819289716543513948276835194627496327185127865394 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 # C3: 1,6 => UNS * DIS # C3: 7,8 => CTR => C3: 1,6 * DIS # B2: 7,8 => CTR => B2: 4 * PRF # B2: 4 => SOL * PRF # C2: 7,8 => SOL * DIS # C2: 3 => CTR => C2: 7,8 * INC # B3: 7,8 => UNS * DIS # C3: 7,8 => CTR => C3: 1,6 * INC # C3: 1,6 => UNS * INC # C6: 1,8 => UNS * PRF # C6: 3 => SOL * INC # B3: 1,8 => UNS * INC # B3: 7 => UNS * INC # B9: 1,2 => UNS * DIS # B9: 7 => CTR => B9: 1,2 * DIS # B9: 1,7 => CTR => B9: 2 * PRF # B9: 2 => SOL * PRF # C3: 1,7 => SOL * INC # C3: 6,8 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 1,6 => UNS * DIS # C3: 7,8 => CTR => C3: 1,6 * DIS C3: 1,6 # B2: 7,8 => CTR => B2: 4 * PRF C3: 1,6 + B2: 4 => SOL * STA C3: 1,6 + B2: 4 * CNT 4 HDP CHAINS / 3 HYP OPENED