Analysis of xx-top500-074-base.sdk
Contents
Original Sudoku
level: medium
position: .2.7...1........3........9....12.6..9...8....3.....4...1.2..5..4....3............ initial
Autosolve
position: .2973.8148..9.123.13.8.279....129683962384157381...429.1329.5484.8.139.229.4.83.1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 5,6 => CTR => C2: 4,7 * PRF # F6: 5,6 => SOL * DIS # F6: 7 => CTR => F6: 5,6 * DIS # C2: 5,6 => CTR => C2: 4,7 * DIS # E6: 5,6 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # F6: 5,6 => SOL * DIS # F6: 7 => CTR => F6: 5,6 * DIS # C9: 6,7 => CTR => C9: 5 * PRF # C9: 5 => SOL * PRF # C9: 5,7 => SOL * DIS # C9: 6 => CTR => C9: 5,7 * PRF # E9: 6,7 => SOL * DIS # E9: 5 => CTR => E9: 6,7 * DIS # F6: 6,7 => CTR => F6: 5 * PRF # F6: 5 => SOL * PRF # E9: 5,6 => SOL * DIS # E9: 7 => CTR => E9: 5,6 * DIS # C9: 6,7 => CTR => C9: 5 * PRF # C9: 5 => SOL * PRF # E9: 6,7 => SOL * DIS # E9: 5 => CTR => E9: 6,7 * CNT 22 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:
* DIS # C2: 5,6 => CTR => C2: 4,7 * DIS C2: 4,7 # C3: 4 => CTR => C3: 5,6 * PRF C2: 4,7 + C3: 5,6 # F6: 5,6 => SOL * STA C2: 4,7 + C3: 5,6 + F6: 5,6 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.7...1........3........9....12.6..9...8....3.....4...1.2..5..4....3............ | initial |
| .2973.8148..9.123.13.8.279....129683962384157381...429.1329.5484.8.139.229.4.83.1 | autosolve |
| 529736814847951236136842795754129683962384157381675429613297548478513962295468371 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A1: 5,6 F1: 5,6 I2: 5,6 I3: 5,6 A4: 5,7 D6: 5,6 A7: 6,7 B8: 5,7 F7: 6,7 D8: 5,6 H8: 6,7 H9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 4.. / E2 = 4 => 15 pairs (_) / E3 = 4 => 16 pairs (_) B4,C4: 4.. / B4 = 4 => 14 pairs (_) / C4 = 4 => 16 pairs (_) C3,E3: 4.. / C3 = 4 => 15 pairs (_) / E3 = 4 => 16 pairs (_) B2,B4: 4.. / B2 = 4 => 16 pairs (_) / B4 = 4 => 14 pairs (_) I2,I3: 5.. / I2 = 5 => 14 pairs (_) / I3 = 5 => 13 pairs (_) B8,C9: 5.. / B8 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) D8,E9: 5.. / D8 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) A1,F1: 5.. / A1 = 5 => 0 pairs (*) / F1 = 5 => 0 pairs (X) B8,D8: 5.. / B8 = 5 => 0 pairs (X) / D8 = 5 => 0 pairs (_) C9,E9: 5.. / C9 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) A1,A4: 5.. / A1 = 5 => 0 pairs (*) / A4 = 5 => 0 pairs (X) D6,D8: 5.. / D6 = 5 => 0 pairs (X) / D8 = 5 => 0 pairs (_) F1,F6: 5.. / F1 = 5 => 0 pairs (X) / F6 = 5 => 0 pairs (_) I2,I3: 6.. / I2 = 6 => 13 pairs (_) / I3 = 6 => 14 pairs (_) A7,C9: 6.. / A7 = 6 => 0 pairs (*) / C9 = 6 => 0 pairs (X) H8,H9: 6.. / H8 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) A1,F1: 6.. / A1 = 6 => 0 pairs (X) / F1 = 6 => 0 pairs (_) A7,F7: 6.. / A7 = 6 => 0 pairs (*) / F7 = 6 => 0 pairs (X) D8,H8: 6.. / D8 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) A1,A7: 6.. / A1 = 6 => 0 pairs (X) / A7 = 6 => 0 pairs (_) D6,D8: 6.. / D6 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) B2,C2: 7.. / B2 = 7 => 0 pairs (X) / C2 = 7 => 15 pairs (_) E6,F6: 7.. / E6 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) F7,E9: 7.. / F7 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) H8,H9: 7.. / H8 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) A7,F7: 7.. / A7 = 7 => 0 pairs (X) / F7 = 7 => 0 pairs (_) B8,H8: 7.. / B8 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) A4,A7: 7.. / A4 = 7 => 0 pairs (*) / A7 = 7 => 0 pairs (X) E6,E9: 7.. / E6 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) F6,F7: 7.. / F6 = 7 => 0 pairs (X) / F7 = 7 => 0 pairs (_) * DURATION: 0:00:58.125048 START: 05:14:35.596659 END: 05:15:33.721707 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A7,B8,D6,D8,F1,F7,H8,H9,I2,I3) * .2973.8148..9.123.13.8.279....129683962384157381...429.1329.5484.8.139.229.4.83.1 * PAIR A1: 5,6 BLK 1 C2: 5,6,4,7 # reduction candidate for 5,6 C2: 5,6 => CTR * .2973581487.94123.1348.279..4.129683962384157381...429.1329.54845861397229.458361 C2: 4,7 # 13 pairs C3: 5,6,4 # reduction candidate for 5,6 C3: 5,6 # 16 pairs * PAIR F1: 5,6 BLK 2 E2: 5,6,4 # reduction candidate for 5,6 E2: 5,6 # 16 pairs E3: 5,6,4 # reduction candidate for 5,6 E3: 5,6 # 15 pairs * PAIR F1: 5,6 COL F F6: 5,6,7 # reduction candidate for 5,6 F6: 5,6 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 F6: 7 => CTR * .297358148..9.123.13.8.279.5..129683962384157381..7429713296548458.139.229.4.83.1 * PAIR I2: 5,6 ROW 2 C2: 5,6,4,7 # reduction candidate for 5,6 C2: 5,6 => CTR * .2973581487.94123.1348.279..4.129683962384157381...429.1329.54845861397229.458361 C2: 4,7 # 13 pairs E2: 5,6,4 # reduction candidate for 5,6 E2: 5,6 # 16 pairs * PAIR I3: 5,6 ROW 3 C3: 5,6,4 # reduction candidate for 5,6 C3: 5,6 # 16 pairs E3: 5,6,4 # reduction candidate for 5,6 E3: 5,6 # 15 pairs * PAIR A4: 5,7 BLK 4 B4: 5,7,4 # reduction candidate for 5,7 B4: 5,7 # 16 pairs C4: 5,7,4 # reduction candidate for 5,7 C4: 5,7 # 14 pairs * PAIR D6: 5,6 BLK 5 E6: 5,6,7 # reduction candidate for 5,6 E6: 5,6 => CTR * .2973.8148..9.123.13.8.279....129683962384157381..7429713296548458.139.229.4.83.1 E6: 7 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 F6: 5,6,7 # reduction candidate for 5,6 F6: 5,6 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 F6: 7 => CTR * .297358148..9.123.13.8.279.5..129683962384157381..7429713296548458.139.229.4.83.1 * PAIR A7: 6,7 BLK 7 C9: 6,7,5 # reduction candidate for 6,7 C9: 6,7 => CTR * .297358148..9.123.13.8.279.5..129683962384157381576429.1329.54845861397229.458361 C9: 5 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 * PAIR B8: 5,7 BLK 7 C9: 5,7,6 # reduction candidate for 5,7 C9: 5,7 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 C9: 6 => CTR * .2973.8148..9.123.13.8.279....129683962384157381...429.1329.5484586139722964.83.1 * PAIR B8: 5,7 COL B B2: 5,7,4 # reduction candidate for 5,7 B2: 5,7 # 14 pairs B4: 5,7,4 # reduction candidate for 5,7 B4: 5,7 # 16 pairs * PAIR F7: 6,7 BLK 8 E9: 6,7,5 # reduction candidate for 6,7 E9: 6,7 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 E9: 5 => CTR * .2973581487.9.123.13.8.279....129683962384157381.7.429.132975484.8613972297458361 * PAIR F7: 6,7 COL F F6: 6,7,5 # reduction candidate for 6,7 F6: 6,7 => CTR * .297358148..9.123.13.8.279.5..129683962384157381...429713296548458.139.229.4.83.1 F6: 5 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 * PAIR D8: 5,6 BLK 8 E9: 5,6,7 # reduction candidate for 5,6 E9: 5,6 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 E9: 7 => CTR * .2973.8148..9.123.13.8.279....129683962384157381...429.1329.5484.851396229.4.83.1 * PAIR H9: 6,7 ROW 9 C9: 6,7,5 # reduction candidate for 6,7 C9: 6,7 => CTR * .297358148..9.123.13.8.279.5..129683962384157381576429.1329.54845861397229.458361 C9: 5 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 E9: 6,7,5 # reduction candidate for 6,7 E9: 6,7 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 E9: 5 => CTR * .2973581487.9.123.13.8.279....129683962384157381.7.429.132975484.8613972297458361 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-074-base-pr-000.dot * REASONING * DIS # C2: 5,6 => CTR => C2: 4,7 * PRF # F6: 5,6 => SOL * DIS # F6: 7 => CTR => F6: 5,6 * DIS # C2: 5,6 => CTR => C2: 4,7 * DIS # E6: 5,6 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # F6: 5,6 => SOL * DIS # F6: 7 => CTR => F6: 5,6 * DIS # C9: 6,7 => CTR => C9: 5 * PRF # C9: 5 => SOL * PRF # C9: 5,7 => SOL * DIS # C9: 6 => CTR => C9: 5,7 * PRF # E9: 6,7 => SOL * DIS # E9: 5 => CTR => E9: 6,7 * DIS # F6: 6,7 => CTR => F6: 5 * PRF # F6: 5 => SOL * PRF # E9: 5,6 => SOL * DIS # E9: 7 => CTR => E9: 5,6 * DIS # C9: 6,7 => CTR => C9: 5 * PRF # C9: 5 => SOL * PRF # E9: 6,7 => SOL * DIS # E9: 5 => CTR => E9: 6,7 * CNT 22 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A7,B8,D6,D8,F1,F7,H8,H9,I2,I3) * .2973.8148..9.123.13.8.279....129683962384157381...429.1329.5484.8.139.229.4.83.1 * PAIR A1: 5,6 BLK 1 C2: 5,6,4,7 # reduction candidate for 5,6 C2: 5,6 => CTR * .2973581487.94123.1348.279..4.129683962384157381...429.1329.54845861397229.458361 C3: 5,6,4 # reduction candidate for 5,6 C3: 5,6 # 16 pairs * RESTART * PAIR A1: 5,6 BLK 1 C3: 5,6,4 # reduction candidate for 5,6 C3: 4 => CTR * 6297358148579.123.13.8.279....129683962384157381...429.1329.5484.8.139.229.4.83.1 * PAIR F1: 5,6 COL F F6: 5,6,7 # reduction candidate for 5,6 F6: 5,6 => SOLVED * 529736814847951236136842795754129683962384157381675429613297548478513962295468371 * DURATION: 0:00:06.953132 START: 05:16:16.031775 END: 05:16:22.984907 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-074-base-pr-001.dot * REASONING * DIS # C2: 5,6 => CTR => C2: 4,7 * DIS C2: 4,7 # C3: 4 => CTR => C3: 5,6 * PRF C2: 4,7 + C3: 5,6 # F6: 5,6 => SOL * STA C2: 4,7 + C3: 5,6 + F6: 5,6 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 074 solution: 529736814847951236136842795754129683962384157381675429613297548478513962295468371 info: 1491 FNBHWXY S8.f 16912 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 529736814847951236136842795754129683962384157381675429613297548478513962295468371 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 # C2: 5,6 => CTR => C2: 4,7 * INC # C2: 4,7 => UNS * INC # C3: 5,6 => UNS * INC # E2: 5,6 => UNS * INC # E3: 5,6 => UNS * PRF # F6: 5,6 => SOL * DIS # F6: 7 => CTR => F6: 5,6 * DIS # C2: 5,6 => CTR => C2: 4,7 * INC # C2: 4,7 => UNS * INC # E2: 5,6 => UNS * INC # C3: 5,6 => UNS * INC # E3: 5,6 => UNS * INC # B4: 5,7 => UNS * INC # C4: 5,7 => UNS * DIS # E6: 5,6 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # F6: 5,6 => SOL * DIS # F6: 7 => CTR => F6: 5,6 * DIS # C9: 6,7 => CTR => C9: 5 * PRF # C9: 5 => SOL * PRF # C9: 5,7 => SOL * DIS # C9: 6 => CTR => C9: 5,7 * INC # B2: 5,7 => UNS * INC # B4: 5,7 => UNS * PRF # E9: 6,7 => SOL * DIS # E9: 5 => CTR => E9: 6,7 * DIS # F6: 6,7 => CTR => F6: 5 * PRF # F6: 5 => SOL * PRF # E9: 5,6 => SOL * DIS # E9: 7 => CTR => E9: 5,6 * DIS # C9: 6,7 => CTR => C9: 5 * PRF # C9: 5 => SOL * PRF # E9: 6,7 => SOL * DIS # E9: 5 => CTR => E9: 6,7 * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 5,6 => CTR => C2: 4,7 * INC C2: 4,7 # C3: 5,6 => UNS * INC C2: 4,7 # C3: 5,6 => UNS * DIS C2: 4,7 # C3: 4 => CTR => C3: 5,6 * PRF C2: 4,7 + C3: 5,6 # F6: 5,6 => SOL * STA C2: 4,7 + C3: 5,6 + F6: 5,6 * CNT 5 HDP CHAINS / 5 HYP OPENED