Analysis of xx-top500-007-base.sdk
Contents
Original Sudoku
level: medium
position: ....1.4.7.2.3......6......8.3.2.....5.....1...........4...5....1......8....6...2. initial
Autosolve
position: ....12467.2436.915.614.523863724185954..3617221.5...4.4.215..9.1.672..84...6.4.21 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 8,9 => CTR => A1: 3 * PRF # F6: 7,8 => SOL * DIS # F6: 9 => CTR => F6: 7,8 * PRF # E6: 7,9 => SOL * DIS # E6: 8 => CTR => E6: 7,9 * DIS # E6: 8,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # F6: 8,9 => SOL * DIS # F6: 7 => CTR => F6: 8,9 * DIS # E6: 8,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # F6: 8,9 => SOL * DIS # F6: 7 => CTR => F6: 8,9 * DIS # G7: 3,6 => CTR => G7: 7 * PRF # G7: 7 => SOL * DIS # B9: 5,9 => CTR => B9: 7,8 * DIS # B9: 5,9 => CTR => B9: 7,8 * DIS # B1: 8 => CTR => B1: 5,9 * DIS # B9: 8,9 => CTR => B9: 5,7 * DIS # E6: 8,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * DIS # G7: 3,6 => CTR => G7: 7 * PRF # G7: 7 => SOL * DIS # B9: 8,9 => CTR => B9: 5,7 * CNT 24 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 8,9 => CTR => A1: 3 * PRF A1: 3 # F6: 7,8 => SOL * STA A1: 3 + F6: 7,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....1.4.7.2.3......6......8.3.2.....5.....1...........4...5....1......8....6...2. | initial |
| ....12467.2436.915.614.523863724185954..3617221.5...4.4.215..9.1.672..84...6.4.21 | autosolve |
| 395812467824367915761495238637241859548936172219578643482153796156729384973684521 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) C1: 3,5 A2: 7,8 A3: 7,9 D1: 8,9 F2: 7,8 E3: 7,9 C5: 8,9 C6: 8,9 D5: 8,9 G6: 3,6 I6: 3,6 B7: 7,8 B8: 5,9 C9: 3,5 F7: 3,8 F8: 3,9 E9: 8,9 I7: 3,6 G8: 3,5 G9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 3.. / A1 = 3 => 21 pairs (_) / C1 = 3 => 0 pairs (X) G6,I6: 3.. / G6 = 3 => 0 pairs (X) / I6 = 3 => 18 pairs (_) A9,C9: 3.. / A9 = 3 => 0 pairs (X) / C9 = 3 => 21 pairs (_) F7,F8: 3.. / F7 = 3 => 0 pairs (*) / F8 = 3 => 0 pairs (X) F8,G8: 3.. / F8 = 3 => 0 pairs (X) / G8 = 3 => 0 pairs (_) A1,A9: 3.. / A1 = 3 => 21 pairs (_) / A9 = 3 => 0 pairs (X) C1,C9: 3.. / C1 = 3 => 0 pairs (X) / C9 = 3 => 21 pairs (_) I6,I7: 3.. / I6 = 3 => 18 pairs (_) / I7 = 3 => 0 pairs (X) B1,C1: 5.. / B1 = 5 => 0 pairs (X) / C1 = 5 => 21 pairs (_) G8,G9: 5.. / G8 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) B8,G8: 5.. / B8 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) C1,C9: 5.. / C1 = 5 => 21 pairs (_) / C9 = 5 => 0 pairs (X) G6,I6: 6.. / G6 = 6 => 18 pairs (_) / I6 = 6 => 0 pairs (X) G7,I7: 6.. / G7 = 6 => 0 pairs (X) / I7 = 6 => 18 pairs (_) G6,G7: 6.. / G6 = 6 => 18 pairs (_) / G7 = 6 => 0 pairs (X) I6,I7: 6.. / I6 = 6 => 0 pairs (X) / I7 = 6 => 18 pairs (_) A2,A3: 7.. / A2 = 7 => 0 pairs (X) / A3 = 7 => 0 pairs (_) F2,E3: 7.. / F2 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) E6,F6: 7.. / E6 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) B7,B9: 7.. / B7 = 7 => 0 pairs (X) / B9 = 7 => 0 pairs (_) G7,G9: 7.. / G7 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) A2,F2: 7.. / A2 = 7 => 0 pairs (X) / F2 = 7 => 0 pairs (_) A3,E3: 7.. / A3 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) B7,G7: 7.. / B7 = 7 => 0 pairs (X) / G7 = 7 => 0 pairs (_) B9,G9: 7.. / B9 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) E3,E6: 7.. / E3 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) F2,F6: 7.. / F2 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) D1,F2: 8.. / D1 = 8 => 0 pairs (*) / F2 = 8 => 0 pairs (X) C5,C6: 8.. / C5 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) F7,E9: 8.. / F7 = 8 => 0 pairs (X) / E9 = 8 => 0 pairs (_) A2,F2: 8.. / A2 = 8 => 0 pairs (*) / F2 = 8 => 0 pairs (X) C5,D5: 8.. / C5 = 8 => 0 pairs (*) / D5 = 8 => 0 pairs (X) B7,F7: 8.. / B7 = 8 => 0 pairs (*) / F7 = 8 => 0 pairs (X) D1,D5: 8.. / D1 = 8 => 0 pairs (*) / D5 = 8 => 0 pairs (X) E6,E9: 8.. / E6 = 8 => 0 pairs (X) / E9 = 8 => 0 pairs (_) D1,E3: 9.. / D1 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) C5,C6: 9.. / C5 = 9 => 0 pairs (X) / C6 = 9 => 0 pairs (_) F8,E9: 9.. / F8 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) A3,E3: 9.. / A3 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) C5,D5: 9.. / C5 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) B8,F8: 9.. / B8 = 9 => 0 pairs (X) / F8 = 9 => 0 pairs (_) D1,D5: 9.. / D1 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) F6,F8: 9.. / F6 = 9 => 0 pairs (X) / F8 = 9 => 0 pairs (_) * DURATION: 0:01:30.575116 START: 02:49:00.572548 END: 02:50:31.147664 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B7,B8,C1,C5,C6,C9,D1,D5,E3,E9,F2,F7,F8,G6,G8,G9,I6,I7) * ....12467.2436.915.614.523863724185954..3617221.5...4.4.215..9.1.672..84...6.4.21 * PAIR D1: 8,9 ROW 1 A1: 8,9,3 # reduction candidate for 8,9 A1: 8,9 => CTR * .53.12467.2436.915.614.523863724185954..3617221.5...4.472158.9.196723584385694721 A1: 3 # 21 pairs B1: 8,9,5 # reduction candidate for 8,9 B1: 8,9 # 21 pairs * PAIR F2: 7,8 COL F F6: 7,8,9 # reduction candidate for 7,8 F6: 7,8 => SOLVED * 395812467824367915761495238637241859548936172219578643482153796156729384973684521 F6: 9 => CTR * ....12467.2436791576149523863724185954.93617221.5...4.4.215..9.1.672..84...6.4.21 * PAIR E3: 7,9 COL E E6: 7,9,8 # reduction candidate for 7,9 E6: 7,9 => SOLVED * 395812467824367915761495238637241859548936172219578643482153796156729384973684521 E6: 8 => CTR * ....12467.2436.915.6147523863724185954..3617221.587.4.4.2158.9.1.672..84...6.4.21 * PAIR C6: 8,9 ROW 6 E6: 8,9,7 # reduction candidate for 8,9 E6: 8,9 => CTR * ..591246772436891596147523863724185954..3617221.5.7.4.4.215..9.1.6729384...684521 E6: 7 => SOLVED * 395812467824367915761495238637241859548936172219578643482153796156729384973684521 F6: 8,9,7 # reduction candidate for 8,9 F6: 8,9 => SOLVED * 395812467824367915761495238637241859548936172219578643482153796156729384973684521 F6: 7 => CTR * ..5.124677243689159614.523863724185954..3617221.5.7.4.4.215..9.1.6729384...684521 * PAIR D5: 8,9 BLK 5 E6: 8,9,7 # reduction candidate for 8,9 E6: 8,9 => CTR * ..591246772436891596147523863724185954..3617221.5.7.4.4.215..9.1.6729384...684521 E6: 7 => SOLVED * 395812467824367915761495238637241859548936172219578643482153796156729384973684521 F6: 8,9,7 # reduction candidate for 8,9 F6: 8,9 => SOLVED * 395812467824367915761495238637241859548936172219578643482153796156729384973684521 F6: 7 => CTR * ..5.124677243689159614.523863724185954..3617221.5.7.4.4.215..9.1.6729384...684521 * PAIR G6: 3,6 COL G G7: 3,6,7 # reduction candidate for 3,6 G7: 3,6 => CTR * ....12467.2436.915.614.523863724185954..3617221.5...4.472158.9.1.6723584...694721 G7: 7 => SOLVED * 395812467824367915761495238637241859548936172219578643482153796156729384973684521 * PAIR B7: 7,8 BLK 7 B9: 7,8,5,9 # reduction candidate for 7,8 B9: 5,9 => CTR * ....12467.2436.915.614.523863724185954..3617221.5...4.472158.9.1.67235848.3694721 B9: 7,8 # 23 pairs * PAIR B8: 5,9 BLK 7 B9: 5,9,7,8 # reduction candidate for 5,9 B9: 5,9 => CTR * ....12467.2436.915.614.523863724185954..3617221.5...4.472158.9.1.67235848.3694721 B9: 7,8 # 23 pairs * PAIR B8: 5,9 COL B B1: 5,9,8 # reduction candidate for 5,9 B1: 8 => CTR * .85912467724368915961475238637241859549836172218597.4.47215369.1.672..84...6.4.21 B1: 5,9 # 23 pairs * PAIR E9: 8,9 ROW 9 A9: 8,9,3 # reduction candidate for 8,9 A9: 8,9 # 21 pairs B9: 8,9,5,7 # reduction candidate for 8,9 B9: 8,9 => CTR * ....12467.2436.915.614.523863724185954..3617221.5...4.472158.9.1.6723584..5694721 B9: 5,7 # 21 pairs * PAIR E9: 8,9 COL E E6: 8,9,7 # reduction candidate for 8,9 E6: 8,9 => CTR * ..591246772436891596147523863724185954..3617221.5.7.4.4.215..9.1.6729384...684521 E6: 7 => SOLVED * 395812467824367915761495238637241859548936172219578643482153796156729384973684521 * PAIR I7: 3,6 BLK 9 G7: 3,6,7 # reduction candidate for 3,6 G7: 3,6 => CTR * ....12467.2436.915.614.523863724185954..3617221.5...4.472158.9.1.6723584...694721 G7: 7 => SOLVED * 395812467824367915761495238637241859548936172219578643482153796156729384973684521 * PAIR G9: 5,7 ROW 9 B9: 5,7,8,9 # reduction candidate for 5,7 B9: 8,9 => CTR * ....12467.2436.915.614.523863724185954..3617221.5...4.472158.9.1.6723584..5694721 B9: 5,7 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-007-base-pr-000.dot * REASONING * DIS # A1: 8,9 => CTR => A1: 3 * PRF # F6: 7,8 => SOL * DIS # F6: 9 => CTR => F6: 7,8 * PRF # E6: 7,9 => SOL * DIS # E6: 8 => CTR => E6: 7,9 * DIS # E6: 8,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # F6: 8,9 => SOL * DIS # F6: 7 => CTR => F6: 8,9 * DIS # E6: 8,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # F6: 8,9 => SOL * DIS # F6: 7 => CTR => F6: 8,9 * DIS # G7: 3,6 => CTR => G7: 7 * PRF # G7: 7 => SOL * DIS # B9: 5,9 => CTR => B9: 7,8 * DIS # B9: 5,9 => CTR => B9: 7,8 * DIS # B1: 8 => CTR => B1: 5,9 * DIS # B9: 8,9 => CTR => B9: 5,7 * DIS # E6: 8,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * DIS # G7: 3,6 => CTR => G7: 7 * PRF # G7: 7 => SOL * DIS # B9: 8,9 => CTR => B9: 5,7 * CNT 24 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B7,B8,C1,C5,C6,C9,D1,D5,E3,E9,F2,F7,F8,G6,G8,G9,I6,I7) * ....12467.2436.915.614.523863724185954..3617221.5...4.4.215..9.1.672..84...6.4.21 * PAIR D1: 8,9 ROW 1 A1: 8,9,3 # reduction candidate for 8,9 A1: 8,9 => CTR * .53.12467.2436.915.614.523863724185954..3617221.5...4.472158.9.196723584385694721 * RESTART * PAIR RESTART * PAIR F2: 7,8 COL F F6: 7,8,9 # reduction candidate for 7,8 F6: 7,8 => SOLVED * 395812467824367915761495238637241859548936172219578643482153796156729384973684521 * DURATION: 0:00:03.771304 START: 02:51:13.875499 END: 02:51:17.646803 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-007-base-pr-001.dot * REASONING * DIS # A1: 8,9 => CTR => A1: 3 * PRF A1: 3 # F6: 7,8 => SOL * STA A1: 3 + F6: 7,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 007 solution: 395812467824367915761495238637241859548936172219578643482153796156729384973684521 info: 1307 FNBTWXY S8.f 2850 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 395812467824367915761495238637241859548936172219578643482153796156729384973684521 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 # A1: 8,9 => CTR => A1: 3 * INC # A1: 3 => UNS * INC # B1: 8,9 => UNS * PRF # F6: 7,8 => SOL * DIS # F6: 9 => CTR => F6: 7,8 * PRF # E6: 7,9 => SOL * DIS # E6: 8 => CTR => E6: 7,9 * DIS # E6: 8,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # F6: 8,9 => SOL * DIS # F6: 7 => CTR => F6: 8,9 * DIS # E6: 8,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # F6: 8,9 => SOL * DIS # F6: 7 => CTR => F6: 8,9 * DIS # G7: 3,6 => CTR => G7: 7 * PRF # G7: 7 => SOL * INC # B9: 7,8 => UNS * DIS # B9: 5,9 => CTR => B9: 7,8 * DIS # B9: 5,9 => CTR => B9: 7,8 * INC # B9: 7,8 => UNS * INC # B1: 5,9 => UNS * DIS # B1: 8 => CTR => B1: 5,9 * INC # A9: 8,9 => UNS * DIS # B9: 8,9 => CTR => B9: 5,7 * INC # B9: 5,7 => UNS * DIS # E6: 8,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * DIS # G7: 3,6 => CTR => G7: 7 * PRF # G7: 7 => SOL * INC # B9: 5,7 => UNS * DIS # B9: 8,9 => CTR => B9: 5,7 * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 8,9 => CTR => A1: 3 * PRF A1: 3 # F6: 7,8 => SOL * STA A1: 3 + F6: 7,8 * CNT 2 HDP CHAINS / 2 HYP OPENED