Analysis of xx-top500-012-base.sdk
Contents
Original Sudoku
level: medium
position: ...3..2..91.................475.......17...........89.....96..42...8...........1. initial
Autosolve
position: ..83612.991.8....6..69..1.8847529361691738425...6148971..296.8426418.9.3.894.3612 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 5,7 => CTR => B3: 2,3 * PRF # B7: 3 => SOL * PRF # H2: 5,7 => SOL * DIS # E2: 5,7 => CTR => E2: 4 * DIS # A3: 3,5 => CTR => A3: 4,7 * PRF # B7: 3,5 => SOL * DIS # B7: 7 => CTR => B7: 3,5 * PRF # B7: 3 => SOL * DIS # E2: 5,7 => CTR => E2: 4 * PRF # B7: 3 => SOL * PRF # H2: 5,7 => SOL * CNT 11 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 5,7 => CTR => B3: 2,3 * PRF B3: 2,3 # B7: 3 => SOL * STA B3: 2,3 + B7: 3 * CNT 2 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...3..2..91.................475.......17...........89.....96..42...8...........1. | initial |
| ..83612.991.8....6..69..1.8847529361691738425...6148971..296.8426418.9.3.894.3612 | autosolve |
| 578361249913842576426975138847529361691738425352614897135296784264187953789453612 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B1: 5,7 G2: 5,7 A6: 3,5 C7: 3,5 A9: 5,7 F8: 5,7 E9: 5,7 G7: 5,7 H8: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,B3: 2.. / C2 = 2 => 12 pairs (_) / B3 = 2 => 12 pairs (_) F2,F3: 2.. / F2 = 2 => 12 pairs (_) / F3 = 2 => 12 pairs (_) B6,C6: 2.. / B6 = 2 => 12 pairs (_) / C6 = 2 => 12 pairs (_) C2,F2: 2.. / C2 = 2 => 12 pairs (_) / F2 = 2 => 12 pairs (_) B3,F3: 2.. / B3 = 2 => 12 pairs (_) / F3 = 2 => 12 pairs (_) B3,B6: 2.. / B3 = 2 => 12 pairs (_) / B6 = 2 => 12 pairs (_) C2,C6: 2.. / C2 = 2 => 12 pairs (_) / C6 = 2 => 12 pairs (_) H2,H3: 3.. / H2 = 3 => 11 pairs (_) / H3 = 3 => 0 pairs (*) B7,C7: 3.. / B7 = 3 => 0 pairs (*) / C7 = 3 => 0 pairs (X) C2,H2: 3.. / C2 = 3 => 0 pairs (*) / H2 = 3 => 0 pairs (X) A3,A6: 3.. / A3 = 3 => 0 pairs (X) / A6 = 3 => 12 pairs (_) A1,A3: 4.. / A1 = 4 => 12 pairs (_) / A3 = 4 => 14 pairs (_) E2,E3: 4.. / E2 = 4 => 10 pairs (_) / E3 = 4 => 0 pairs (X) A1,H1: 4.. / A1 = 4 => 12 pairs (_) / H1 = 4 => 14 pairs (_) E2,H2: 4.. / E2 = 4 => 10 pairs (_) / H2 = 4 => 0 pairs (X) F8,E9: 5.. / F8 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) G7,H8: 5.. / G7 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) F8,H8: 5.. / F8 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) A9,E9: 5.. / A9 = 5 => 0 pairs (X) / E9 = 5 => 0 pairs (_) G2,G7: 5.. / G2 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) B7,A9: 7.. / B7 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) F8,E9: 7.. / F8 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) G7,H8: 7.. / G7 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) B7,G7: 7.. / B7 = 7 => 0 pairs (X) / G7 = 7 => 0 pairs (_) F8,H8: 7.. / F8 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) A9,E9: 7.. / A9 = 7 => 0 pairs (*) / E9 = 7 => 0 pairs (X) G2,G7: 7.. / G2 = 7 => 0 pairs (X) / G7 = 7 => 0 pairs (_) * DURATION: 0:00:46.227368 START: 03:00:22.506989 END: 03:01:08.734357 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B1,C7,E9,F8,G2,G7,H8) * ..83612.991.8....6..69..1.8847529361691738425...6148971..296.8426418.9.3.894.3612 * PAIR B1: 5,7 BLK 1 A1: 5,7,4 # reduction candidate for 5,7 A1: 5,7 # 14 pairs A3: 5,7,3,4 # reduction candidate for 5,7 A3: 5,7 # 16 pairs B3: 5,7,2,3 # reduction candidate for 5,7 B3: 5,7 => CTR * ..83612.99128...363.69.21.8847529361691738425523614897135296784264187953789453612 B3: 2,3 # 10 pairs * PAIR B1: 5,7 ROW 1 H1: 5,7,4 # reduction candidate for 5,7 H1: 4 # 14 pairs H1: 5,7 # 12 pairs * PAIR B1: 5,7 COL B B7: 5,7,3 # reduction candidate for 5,7 B7: 3 => SOLVED * 578361249913842576426975138847529361691738425352614897135296784264187953789453612 B7: 5,7 # 14 pairs * PAIR G2: 5,7 BLK 3 H1: 5,7,4 # reduction candidate for 5,7 H1: 5,7 # 12 pairs H2: 5,7,3,4 # reduction candidate for 5,7 H2: 5,7 => SOLVED * 578361249913842576426975138847529361691738425352614897135296784264187953789453612 H2: 3,4 # 10 pairs H3: 5,7,3,4 # reduction candidate for 5,7 H3: 5,7 # 12 pairs * PAIR G2: 5,7 ROW 2 E2: 5,7,4 # reduction candidate for 5,7 E2: 5,7 => CTR * 4583612.991.8...46..694.1388475293616917384253..614897135296784264187953789453612 E2: 4 # 10 pairs F2: 5,7,2 # reduction candidate for 5,7 F2: 5,7 # 12 pairs * PAIR A6: 3,5 BLK 4 B6: 3,5,2 # reduction candidate for 3,5 B6: 3,5 # 12 pairs C6: 3,5,2 # reduction candidate for 3,5 C6: 3,5 # 12 pairs * PAIR A6: 3,5 COL A A3: 3,5,4,7 # reduction candidate for 3,5 A3: 3,5 => CTR * 45836127991.87.5463.69..1.8847529361691738425...6148971..296784264187953789453612 A3: 4,7 # 14 pairs * PAIR C7: 3,5 BLK 7 B7: 3,5,7 # reduction candidate for 3,5 B7: 3,5 => SOLVED * 578361249913842576426975138847529361691738425352614897135296784264187953789453612 B7: 7 => CTR * 75836124991284...6..69..1.8847529361691738425...614897173296584264185973589473612 * PAIR C7: 3,5 COL C C2: 3,5,2 # reduction candidate for 3,5 C2: 3,5 # 12 pairs C6: 3,5,2 # reduction candidate for 3,5 C6: 3,5 # 12 pairs * PAIR A9: 5,7 BLK 7 B7: 5,7,3 # reduction candidate for 5,7 B7: 3 => SOLVED * 578361249913842576426975138847529361691738425352614897135296784264187953789453612 B7: 5,7 # 14 pairs * PAIR A9: 5,7 COL A A1: 5,7,4 # reduction candidate for 5,7 A1: 5,7 # 14 pairs A3: 5,7,3,4 # reduction candidate for 5,7 A3: 5,7 # 16 pairs * PAIR F8: 5,7 COL F F2: 5,7,2 # reduction candidate for 5,7 F2: 5,7 # 12 pairs F3: 5,7,2 # reduction candidate for 5,7 F3: 5,7 # 12 pairs * PAIR E9: 5,7 COL E E2: 5,7,4 # reduction candidate for 5,7 E2: 5,7 => CTR * 4583612.991.8...46..694.1388475293616917384253..614897135296784264187953789453612 E2: 4 # 10 pairs E3: 5,7,4 # reduction candidate for 5,7 E3: 5,7 # 10 pairs * PAIR G7: 5,7 ROW 7 B7: 5,7,3 # reduction candidate for 5,7 B7: 3 => SOLVED * 578361249913842576426975138847529361691738425352614897135296784264187953789453612 B7: 5,7 # 14 pairs * PAIR H8: 5,7 COL H H1: 5,7,4 # reduction candidate for 5,7 H1: 5,7 # 12 pairs H2: 5,7,3,4 # reduction candidate for 5,7 H2: 5,7 => SOLVED * 578361249913842576426975138847529361691738425352614897135296784264187953789453612 H2: 3,4 # 10 pairs H3: 5,7,3,4 # reduction candidate for 5,7 H3: 5,7 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-012-base-pr-000.dot * REASONING * DIS # B3: 5,7 => CTR => B3: 2,3 * PRF # B7: 3 => SOL * PRF # H2: 5,7 => SOL * DIS # E2: 5,7 => CTR => E2: 4 * DIS # A3: 3,5 => CTR => A3: 4,7 * PRF # B7: 3,5 => SOL * DIS # B7: 7 => CTR => B7: 3,5 * PRF # B7: 3 => SOL * DIS # E2: 5,7 => CTR => E2: 4 * PRF # B7: 3 => SOL * PRF # H2: 5,7 => SOL * CNT 11 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B1,C7,E9,F8,G2,G7,H8) * ..83612.991.8....6..69..1.8847529361691738425...6148971..296.8426418.9.3.894.3612 * PAIR B1: 5,7 BLK 1 A1: 5,7,4 # reduction candidate for 5,7 A1: 5,7 # 14 pairs A3: 5,7,3,4 # reduction candidate for 5,7 A3: 5,7 # 16 pairs B3: 5,7,2,3 # reduction candidate for 5,7 B3: 5,7 => CTR * ..83612.99128...363.69.21.8847529361691738425523614897135296784264187953789453612 * PAIR B1: 5,7 ROW 1 H1: 5,7,4 # reduction candidate for 5,7 H1: 4 # 14 pairs H1: 5,7 # 13 pairs * PAIR B1: 5,7 COL B B7: 5,7,3 # reduction candidate for 5,7 B7: 3 => SOLVED * 578361249913842576426975138847529361691738425352614897135296784264187953789453612 * DURATION: 0:00:07.707472 START: 03:01:46.392753 END: 03:01:54.100225 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-012-base-pr-001.dot * REASONING * DIS # B3: 5,7 => CTR => B3: 2,3 * PRF B3: 2,3 # B7: 3 => SOL * STA B3: 2,3 + B7: 3 * CNT 2 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 012 solution: 578361249913842576426975138847529361691738425352614897135296784264187953789453612 info: 1308 FNBWXY S8.f 48865 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 578361249913842576426975138847529361691738425352614897135296784264187953789453612 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 # A1: 5,7 => UNS * INC # A3: 5,7 => UNS * DIS # B3: 5,7 => CTR => B3: 2,3 * INC # B3: 2,3 => UNS * INC # H1: 5,7 => UNS * INC # H1: 4 => UNS * INC # B7: 5,7 => UNS * PRF # B7: 3 => SOL * INC # H1: 5,7 => UNS * PRF # H2: 5,7 => SOL * INC # H2: 3,4 => UNS * INC # H3: 5,7 => UNS * DIS # E2: 5,7 => CTR => E2: 4 * INC # E2: 4 => UNS * INC # F2: 5,7 => UNS * INC # B6: 3,5 => UNS * INC # C6: 3,5 => UNS * DIS # A3: 3,5 => CTR => A3: 4,7 * INC # A3: 4,7 => UNS * PRF # B7: 3,5 => SOL * DIS # B7: 7 => CTR => B7: 3,5 * INC # C2: 3,5 => UNS * INC # C6: 3,5 => UNS * INC # B7: 5,7 => UNS * PRF # B7: 3 => SOL * INC # A1: 5,7 => UNS * INC # A3: 5,7 => UNS * INC # F2: 5,7 => UNS * INC # F3: 5,7 => UNS * DIS # E2: 5,7 => CTR => E2: 4 * INC # E2: 4 => UNS * INC # E3: 5,7 => UNS * INC # B7: 5,7 => UNS * PRF # B7: 3 => SOL * INC # H1: 5,7 => UNS * PRF # H2: 5,7 => SOL * INC # H2: 3,4 => UNS * INC # H3: 5,7 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 5,7 => UNS * INC # A3: 5,7 => UNS * DIS # B3: 5,7 => CTR => B3: 2,3 * INC B3: 2,3 # H1: 5,7 => UNS * INC B3: 2,3 # H1: 4 => UNS * INC B3: 2,3 # B7: 5,7 => UNS * PRF B3: 2,3 # B7: 3 => SOL * STA B3: 2,3 + B7: 3 * CNT 7 HDP CHAINS / 7 HYP OPENED