Analysis of xx-top500-194-base.sdk
Contents
Original Sudoku
level: medium
position: ...3.2...6.....4....1......78.5.........4.6........1..5......32.3.....8.....1.... initial
Autosolve
position: 94.3.28166281..4.33.148629.7845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 5,7 => CTR => E2: 9 * PRF # E2: 9 => SOL * PRF # E2: 7,9 => SOL * DIS # E2: 5 => CTR => E2: 7,9 * PRF # F6: 7,9 => SOL * DIS # E2: 5,7 => CTR => E2: 9 * PRF # E2: 9 => SOL * PRF # I5: 5,7 => SOL * PRF # F6: 7,9 => SOL * PRF # I5: 5,7 => SOL * PRF # E2: 7,9 => SOL * DIS # E2: 5 => CTR => E2: 7,9 * CNT 12 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 # E2: 5,7 => CTR => E2: 9 * PRF E2: 9 => SOL * STA E2: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...3.2...6.....4....1......78.5.........4.6........1..5......32.3.....8.....1.... | initial |
| 94.3.28166281..4.33.148629.7845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564 | autosolve |
| 947352816628197453351486297784561329193248675265739148516874932439625781872913564 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) C1: 5,7 B3: 5,7 E1: 5,7 F2: 7,9 H2: 5,7 I3: 5,7 B5: 5,9 C6: 5,9 D6: 7,9 H5: 5,7 C8: 7,9 B9: 7,9 E7: 7,9 D9: 7,9 G7: 7,9 G8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,B3: 5.. / C1 = 5 => 0 pairs (X) / B3 = 5 => 0 pairs (_) E1,E2: 5.. / E1 = 5 => 0 pairs (*) / E2 = 5 => 0 pairs (X) H2,I3: 5.. / H2 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) B5,C6: 5.. / B5 = 5 => 0 pairs (X) / C6 = 5 => 0 pairs (_) C1,E1: 5.. / C1 = 5 => 0 pairs (X) / E1 = 5 => 0 pairs (_) E2,H2: 5.. / E2 = 5 => 0 pairs (X) / H2 = 5 => 0 pairs (_) B3,I3: 5.. / B3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) C6,I6: 5.. / C6 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) B3,B5: 5.. / B3 = 5 => 0 pairs (*) / B5 = 5 => 0 pairs (X) C1,C6: 5.. / C1 = 5 => 0 pairs (X) / C6 = 5 => 0 pairs (_) H2,H5: 5.. / H2 = 5 => 0 pairs (*) / H5 = 5 => 0 pairs (X) C1,B3: 7.. / C1 = 7 => 0 pairs (*) / B3 = 7 => 0 pairs (X) H2,I3: 7.. / H2 = 7 => 0 pairs (X) / I3 = 7 => 0 pairs (_) C8,B9: 7.. / C8 = 7 => 0 pairs (X) / B9 = 7 => 0 pairs (_) E7,D9: 7.. / E7 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) G7,G8: 7.. / G7 = 7 => 0 pairs (X) / G8 = 7 => 0 pairs (_) C1,E1: 7.. / C1 = 7 => 0 pairs (*) / E1 = 7 => 0 pairs (X) B3,I3: 7.. / B3 = 7 => 0 pairs (X) / I3 = 7 => 0 pairs (_) E7,G7: 7.. / E7 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) C8,G8: 7.. / C8 = 7 => 0 pairs (X) / G8 = 7 => 0 pairs (_) B9,D9: 7.. / B9 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) B3,B9: 7.. / B3 = 7 => 0 pairs (X) / B9 = 7 => 0 pairs (_) C1,C8: 7.. / C1 = 7 => 0 pairs (*) / C8 = 7 => 0 pairs (X) D6,D9: 7.. / D6 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) H2,H5: 7.. / H2 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) F5,F6: 8.. / F5 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) I5,I6: 8.. / I5 = 8 => 18 pairs (_) / I6 = 8 => 0 pairs (*) F5,I5: 8.. / F5 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) F6,I6: 8.. / F6 = 8 => 18 pairs (_) / I6 = 8 => 0 pairs (*) E2,F2: 9.. / E2 = 9 => 0 pairs (*) / F2 = 9 => 0 pairs (X) B5,C6: 9.. / B5 = 9 => 0 pairs (*) / C6 = 9 => 0 pairs (X) C8,B9: 9.. / C8 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) E7,D9: 9.. / E7 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) G7,G8: 9.. / G7 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) B5,F5: 9.. / B5 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) E7,G7: 9.. / E7 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) C8,G8: 9.. / C8 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) B9,D9: 9.. / B9 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) B5,B9: 9.. / B5 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) C6,C8: 9.. / C6 = 9 => 0 pairs (X) / C8 = 9 => 0 pairs (_) D6,D9: 9.. / D6 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) E2,E7: 9.. / E2 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) * DURATION: 0:01:28.600128 START: 09:22:30.593779 END: 09:23:59.193907 2017-05-04 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B5,B9,C1,C6,C8,D6,D9,E1,E7,F2,G7,G8,H2,H5,I3) * 94.3.28166281..4.33.148629.7845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564 * PAIR E1: 5,7 BLK 2 E2: 5,7,9 # reduction candidate for 5,7 E2: 5,7 => CTR * 94.3.28166281.94.33.148629.78456132919324.6..26593.14.51689473243.625.818.2.13564 E2: 9 => SOLVED * 947352816628197453351486297784561329193248675265739148516874932439625781872913564 * PAIR F2: 7,9 BLK 2 E2: 7,9,5 # reduction candidate for 7,9 E2: 7,9 => SOLVED * 947352816628197453351486297784561329193248675265739148516874932439625781872913564 E2: 5 => CTR * 94.3.28166281594733714862957845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564 * PAIR F2: 7,9 COL F F5: 7,9,8 # reduction candidate for 7,9 F5: 7,9 # 18 pairs F6: 7,9,8 # reduction candidate for 7,9 F6: 7,9 => SOLVED * 947352816628197453351486297784561329193248675265739148516874932439625781872913564 F6: 8 # 18 pairs * PAIR H2: 5,7 ROW 2 E2: 5,7,9 # reduction candidate for 5,7 E2: 5,7 => CTR * 94.3.28166281.94.33.148629.78456132919324.6..26593.14.51689473243.625.818.2.13564 E2: 9 => SOLVED * 947352816628197453351486297784561329193248675265739148516874932439625781872913564 * PAIR I3: 5,7 COL I I5: 5,7,8 # reduction candidate for 5,7 I5: 5,7 => SOLVED * 947352816628197453351486297784561329193248675265739148516874932439625781872913564 I5: 8 # 18 pairs I6: 5,7,8 # reduction candidate for 5,7 I6: 5,7 # 18 pairs * PAIR D6: 7,9 BLK 5 F5: 7,9,8 # reduction candidate for 7,9 F5: 7,9 # 18 pairs F6: 7,9,8 # reduction candidate for 7,9 F6: 7,9 => SOLVED * 947352816628197453351486297784561329193248675265739148516874932439625781872913564 F6: 8 # 18 pairs * PAIR H5: 5,7 BLK 6 I5: 5,7,8 # reduction candidate for 5,7 I5: 5,7 => SOLVED * 947352816628197453351486297784561329193248675265739148516874932439625781872913564 I5: 8 # 18 pairs I6: 5,7,8 # reduction candidate for 5,7 I6: 5,7 # 18 pairs * PAIR E7: 7,9 COL E E2: 7,9,5 # reduction candidate for 7,9 E2: 7,9 => SOLVED * 947352816628197453351486297784561329193248675265739148516874932439625781872913564 E2: 5 => CTR * 94.3.28166281594733714862957845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-194-base-pr-000.dot * REASONING * DIS # E2: 5,7 => CTR => E2: 9 * PRF # E2: 9 => SOL * PRF # E2: 7,9 => SOL * DIS # E2: 5 => CTR => E2: 7,9 * PRF # F6: 7,9 => SOL * DIS # E2: 5,7 => CTR => E2: 9 * PRF # E2: 9 => SOL * PRF # I5: 5,7 => SOL * PRF # F6: 7,9 => SOL * PRF # I5: 5,7 => SOL * PRF # E2: 7,9 => SOL * DIS # E2: 5 => CTR => E2: 7,9 * CNT 12 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B5,B9,C1,C6,C8,D6,D9,E1,E7,F2,G7,G8,H2,H5,I3) * 94.3.28166281..4.33.148629.7845613291.324.6..26..3.14.5168.4.3243.625.818.2.13564 * PAIR E1: 5,7 BLK 2 E2: 5,7,9 # reduction candidate for 5,7 E2: 5,7 => CTR * 94.3.28166281.94.33.148629.78456132919324.6..26593.14.51689473243.625.818.2.13564 E2: 9 => SOLVED * 947352816628197453351486297784561329193248675265739148516874932439625781872913564 * DURATION: 0:00:03.501297 START: 09:24:28.463768 END: 09:24:31.965065 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-194-base-pr-001.dot * REASONING * DIS # E2: 5,7 => CTR => E2: 9 * PRF E2: 9 => SOL * STA E2: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 194 solution: 947352816628197453351486297784561329193248675265739148516874932439625781872913564 info: 1849 FNBTWX S8.f 47765 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 947352816628197453351486297784561329193248675265739148516874932439625781872913564 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 # E2: 5,7 => CTR => E2: 9 * PRF # E2: 9 => SOL * PRF # E2: 7,9 => SOL * DIS # E2: 5 => CTR => E2: 7,9 * INC # F5: 7,9 => UNS * PRF # F6: 7,9 => SOL * INC # F6: 8 => UNS * DIS # E2: 5,7 => CTR => E2: 9 * PRF # E2: 9 => SOL * PRF # I5: 5,7 => SOL * INC # I5: 8 => UNS * INC # I6: 5,7 => UNS * INC # F5: 7,9 => UNS * PRF # F6: 7,9 => SOL * INC # F6: 8 => UNS * PRF # I5: 5,7 => SOL * INC # I5: 8 => UNS * INC # I6: 5,7 => UNS * PRF # E2: 7,9 => SOL * DIS # E2: 5 => CTR => E2: 7,9 * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E2: 5,7 => CTR => E2: 9 * PRF E2: 9 => SOL * STA E2: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED