Analysis of xx-top500-337-base.sdk
Contents
Original Sudoku
level: medium
position: .61.........2..8......5....3.....2...5..1.......7.........4..612..3.....8......4. initial
Autosolve
position: .61.38.2.4..2.18.6.2865.1..347586219652.1....18972.6.....842.6121436....8.61...42 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 7,9 => CTR => B2: 3 * DIS # H3: 7,9 => CTR => H3: 3 * DIS # A7: 7,9 => CTR => A7: 5 * DIS # F3: 7 => CTR => F3: 4,9 * PRF # G1: 5,7 => SOL * DIS # F3: 4 => CTR => F3: 7,9 * DIS # B2: 7,9 => CTR => B2: 3 * DIS # F5: 4,9 => CTR => F5: 3 * DIS # F5: 9 => CTR => F5: 3,4 * DIS # I6: 5 => CTR => I6: 3,4 * DIS # I6: 4 => CTR => I6: 3,5 * DIS # F9: 7,9 => CTR => F9: 5 * DIS # G9: 7,9 => CTR => G9: 3,5 * CNT 13 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 7,9 => CTR => B2: 3 * DIS B2: 3 # H3: 7,9 => CTR => H3: 3 * DIS B2: 3 + H3: 3 # F3: 4 => CTR => F3: 7,9 * PRF B2: 3 + H3: 3 + F3: 7,9 # G1: 5 => SOL * STA B2: 3 + H3: 3 + F3: 7,9 + G1: 5 * CNT 4 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .61.........2..8......5....3.....2...5..1.......7.........4..612..3.....8......4. | initial |
| .61.38.2.4..2.18.6.2865.1..347586219652.1....18972.6.....842.6121436....8.61...42 | autosolve |
| 961438527435271896728659134347586219652913478189724653593842761214367985876195342 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) C2: 3,5 A3: 7,9 D1: 4,9 E2: 7,9 D5: 4,9 F6: 3,4 G5: 4,7 H6: 3,5 C7: 3,5 E9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 3.. / B2 = 3 => 14 pairs (_) / C2 = 3 => 0 pairs (X) H3,I3: 3.. / H3 = 3 => 16 pairs (_) / I3 = 3 => 0 pairs (X) F5,F6: 3.. / F5 = 3 => 13 pairs (_) / F6 = 3 => 0 pairs (X) G7,G9: 3.. / G7 = 3 => 0 pairs (X) / G9 = 3 => 13 pairs (_) B9,G9: 3.. / B9 = 3 => 0 pairs (X) / G9 = 3 => 13 pairs (_) C2,C7: 3.. / C2 = 3 => 0 pairs (X) / C7 = 3 => 14 pairs (_) D1,F3: 4.. / D1 = 4 => 13 pairs (_) / F3 = 4 => 0 pairs (X) F3,I3: 4.. / F3 = 4 => 0 pairs (X) / I3 = 4 => 13 pairs (_) F6,I6: 4.. / F6 = 4 => 13 pairs (_) / I6 = 4 => 0 pairs (X) D1,D5: 4.. / D1 = 4 => 13 pairs (_) / D5 = 4 => 0 pairs (X) G1,G5: 4.. / G1 = 4 => 0 pairs (X) / G5 = 4 => 13 pairs (_) A1,C2: 5.. / A1 = 5 => 0 pairs (X) / C2 = 5 => 14 pairs (_) H6,I6: 5.. / H6 = 5 => 14 pairs (_) / I6 = 5 => 0 pairs (X) A7,C7: 5.. / A7 = 5 => 14 pairs (_) / C7 = 5 => 0 pairs (X) F8,F9: 5.. / F8 = 5 => 0 pairs (X) / F9 = 5 => 11 pairs (_) C2,H2: 5.. / C2 = 5 => 14 pairs (_) / H2 = 5 => 0 pairs (X) F9,G9: 5.. / F9 = 5 => 11 pairs (_) / G9 = 5 => 0 pairs (X) A1,A7: 5.. / A1 = 5 => 0 pairs (X) / A7 = 5 => 14 pairs (_) C2,C7: 5.. / C2 = 5 => 14 pairs (_) / C7 = 5 => 0 pairs (X) E2,F3: 7.. / E2 = 7 => 16 pairs (_) / F3 = 7 => 0 pairs (X) E2,E9: 7.. / E2 = 7 => 16 pairs (_) / E9 = 7 => 0 pairs (X) H5,I5: 8.. / H5 = 8 => 10 pairs (_) / I5 = 8 => 12 pairs (_) H8,I8: 8.. / H8 = 8 => 12 pairs (_) / I8 = 8 => 10 pairs (_) H5,H8: 8.. / H5 = 8 => 10 pairs (_) / H8 = 8 => 12 pairs (_) I5,I8: 8.. / I5 = 8 => 12 pairs (_) / I8 = 8 => 10 pairs (_) D5,F5: 9.. / D5 = 9 => 13 pairs (_) / F5 = 9 => 0 pairs (X) D1,D5: 9.. / D1 = 9 => 0 pairs (X) / D5 = 9 => 13 pairs (_) E2,E9: 9.. / E2 = 9 => 0 pairs (X) / E9 = 9 => 16 pairs (_) * DURATION: 0:00:52.434366 START: 14:16:42.571177 END: 14:17:35.005543 2017-05-04 * CP COUNT: (28) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C2,C7,D1,D5,E2,E9,F6,G5,H6) * .61.38.2.4..2.18.6.2865.1..347586219652.1....18972.6.....842.6121436....8.61...42 * PAIR A3: 7,9 BLK 1 A1: 7,9,5 # reduction candidate for 7,9 A1: 7,9 # 14 pairs B2: 7,9,3 # reduction candidate for 7,9 B2: 7,9 => CTR * 561.38.2.4.32.1856.2865.1.3347586219652.13...189724635..5842.6121436....8.61...42 B2: 3 # 14 pairs * PAIR A3: 7,9 ROW 3 F3: 7,9,4 # reduction candidate for 7,9 F3: 7,9 # 13 pairs H3: 7,9,3 # reduction candidate for 7,9 H3: 7,9 => CTR * 7619384254.52718969286541733475862196524197381897236545..842.6121436..878.6197542 H3: 3 # 16 pairs * PAIR A3: 7,9 COL A A7: 7,9,5 # reduction candidate for 7,9 A7: 7,9 => CTR * 561.38.2.4.32.1856.2865.1.3347586219652.13...189724635..5842.6121436....8.61...42 A7: 5 # 14 pairs * PAIR D1: 4,9 BLK 2 F3: 4,9,7 # reduction candidate for 4,9 F3: 7 => CTR * .614389254.52918769286571343475862196529134871897246535..842.6121436..988.6179542 F3: 4,9 # 16 pairs * PAIR D1: 4,9 ROW 1 G1: 4,9,5,7 # reduction candidate for 4,9 G1: 5,7 => SOLVED * 961438527435271896728659134347586219652913478189724653593842761214367985876195342 G1: 4,9 # 14 pairs * PAIR E2: 7,9 BLK 2 F3: 7,9,4 # reduction candidate for 7,9 F3: 4 => CTR * .619384254.52718969286541..3475862196524197..1897236545..842.6121436....8.619..42 F3: 7,9 # 13 pairs * PAIR E2: 7,9 ROW 2 B2: 7,9,3 # reduction candidate for 7,9 B2: 7,9 => CTR * 561.38.2.4.32.1856.2865.1.3347586219652.13...189724635..5842.6121436....8.61...42 B2: 3 # 14 pairs H2: 7,9,5 # reduction candidate for 7,9 H2: 7,9 # 14 pairs * PAIR D5: 4,9 BLK 5 F5: 4,9,3 # reduction candidate for 4,9 F5: 4,9 => CTR * .61.384254.52.18.6.286541..3475862196524197..18972365457384296121436.5..89617..42 F5: 3 # 13 pairs * PAIR F6: 3,4 BLK 5 F5: 3,4,9 # reduction candidate for 3,4 F5: 9 => CTR * .619384254.52718969286541..3475862196524197..1897236545..842.6121436....8.619..42 F5: 3,4 # 13 pairs * PAIR F6: 3,4 ROW 6 I6: 3,4,5 # reduction candidate for 3,4 I6: 5 => CTR * .61.38.2.4..2.18.6.2865.1..347586219652.1....189724635...842.6121436....8.61...42 I6: 3,4 # 14 pairs * PAIR G5: 4,7 BLK 6 I5: 4,7,3,8 # reduction candidate for 4,7 I5: 4,7 # 12 pairs I5: 3,8 # 11 pairs * PAIR G5: 4,7 COL G G1: 4,7,5,9 # reduction candidate for 4,7 G1: 4,7 # 17 pairs G1: 5,9 # 16 pairs * PAIR H6: 3,5 BLK 6 I6: 3,5,4 # reduction candidate for 3,5 I6: 4 => CTR * .61.384254.52.18.6.286541..3475862196524197..18972365457384296121436.5..89617..42 I6: 3,5 # 13 pairs * PAIR E9: 7,9 BLK 8 F8: 7,9,5 # reduction candidate for 7,9 F8: 7,9 # 11 pairs F9: 7,9,5 # reduction candidate for 7,9 F9: 7,9 => CTR * 561.38.2.4.32.1856.2865.1.3347586219652.13...189724635..5842361214365...8361..542 F9: 5 # 11 pairs * PAIR E9: 7,9 ROW 9 B9: 7,9,3 # reduction candidate for 7,9 B9: 7,9 # 13 pairs G9: 7,9,3,5 # reduction candidate for 7,9 G9: 7,9 => CTR * 561.38.2.4.32.1856.2865.1.3347586219652.13...189724635..584236121436.5..8361.5.42 G9: 3,5 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-337-base-pr-000.dot * REASONING * DIS # B2: 7,9 => CTR => B2: 3 * DIS # H3: 7,9 => CTR => H3: 3 * DIS # A7: 7,9 => CTR => A7: 5 * DIS # F3: 7 => CTR => F3: 4,9 * PRF # G1: 5,7 => SOL * DIS # F3: 4 => CTR => F3: 7,9 * DIS # B2: 7,9 => CTR => B2: 3 * DIS # F5: 4,9 => CTR => F5: 3 * DIS # F5: 9 => CTR => F5: 3,4 * DIS # I6: 5 => CTR => I6: 3,4 * DIS # I6: 4 => CTR => I6: 3,5 * DIS # F9: 7,9 => CTR => F9: 5 * DIS # G9: 7,9 => CTR => G9: 3,5 * CNT 13 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C2,C7,D1,D5,E2,E9,F6,G5,H6) * .61.38.2.4..2.18.6.2865.1..347586219652.1....18972.6.....842.6121436....8.61...42 * PAIR A3: 7,9 BLK 1 A1: 7,9,5 # reduction candidate for 7,9 A1: 7,9 # 14 pairs B2: 7,9,3 # reduction candidate for 7,9 B2: 7,9 => CTR * 561.38.2.4.32.1856.2865.1.3347586219652.13...189724635..5842.6121436....8.61...42 * RESTART * PAIR A3: 7,9 ROW 3 F3: 7,9,4 # reduction candidate for 7,9 F3: 7,9 # 13 pairs H3: 7,9,3 # reduction candidate for 7,9 H3: 7,9 => CTR * .61.38.2.4352.18.6.286541.3347586219652419738189723654573842961214367...8.61.5342 * RESTART * PAIR A3: 7,9 ROW 3 F3: 7,9,4 # reduction candidate for 7,9 F3: 4 => CTR * .61.38.2.435271896928654137347586219652419783189723654573842961214367...8.61.5342 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A3,B7,B9,E2,E9,F3,F8,G7,H2,H5,I1,I5) * .61438.2.4352.18.6.2865.1343475862196529134..1897246535.3842.6121436....8.61.5342 * PAIR A1: 7,9 ROW 1 G1: 7,9,5 # reduction candidate for 7,9 G1: 5 => SOLVED * 961438527435271896728659134347586219652913478189724653593842761214367985876195342 * DURATION: 0:00:10.313103 START: 14:18:11.276246 END: 14:18:21.589349 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-337-base-pr-001.dot * REASONING * DIS # B2: 7,9 => CTR => B2: 3 * DIS B2: 3 # H3: 7,9 => CTR => H3: 3 * DIS B2: 3 + H3: 3 # F3: 4 => CTR => F3: 7,9 * PRF B2: 3 + H3: 3 + F3: 7,9 # G1: 5 => SOL * STA B2: 3 + H3: 3 + F3: 7,9 + G1: 5 * CNT 4 HDP CHAINS / 8 HYP OPENED
Header Info
Top 500 Minimum 17 337 solution: 961438527435271896728659134347586219652913478189724653593842761214367985876195342 info: 3103 FNBTWXY S8.f 21708 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 961438527435271896728659134347586219652913478189724653593842761214367985876195342 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: 7,9 => UNS * DIS # B2: 7,9 => CTR => B2: 3 * INC # B2: 3 => UNS * INC # F3: 7,9 => UNS * DIS # H3: 7,9 => CTR => H3: 3 * INC # H3: 3 => UNS * DIS # A7: 7,9 => CTR => A7: 5 * INC # A7: 5 => UNS * INC # F3: 4,9 => UNS * DIS # F3: 7 => CTR => F3: 4,9 * INC # G1: 4,9 => UNS * PRF # G1: 5,7 => SOL * INC # F3: 7,9 => UNS * DIS # F3: 4 => CTR => F3: 7,9 * DIS # B2: 7,9 => CTR => B2: 3 * INC # B2: 3 => UNS * INC # H2: 7,9 => UNS * DIS # F5: 4,9 => CTR => F5: 3 * INC # F5: 3 => UNS * INC # F5: 3,4 => UNS * DIS # F5: 9 => CTR => F5: 3,4 * INC # I6: 3,4 => UNS * DIS # I6: 5 => CTR => I6: 3,4 * INC # I5: 4,7 => UNS * INC # I5: 3,8 => UNS * INC # G1: 4,7 => UNS * INC # G1: 5,9 => UNS * INC # I6: 3,5 => UNS * DIS # I6: 4 => CTR => I6: 3,5 * INC # F8: 7,9 => UNS * DIS # F9: 7,9 => CTR => F9: 5 * INC # F9: 5 => UNS * INC # B9: 7,9 => UNS * DIS # G9: 7,9 => CTR => G9: 3,5 * INC # G9: 3,5 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 7,9 => UNS * DIS # B2: 7,9 => CTR => B2: 3 * INC B2: 3 # F3: 7,9 => UNS * DIS B2: 3 # H3: 7,9 => CTR => H3: 3 * INC B2: 3 + H3: 3 # F3: 7,9 => UNS * DIS B2: 3 + H3: 3 # F3: 4 => CTR => F3: 7,9 * INC B2: 3 + H3: 3 + F3: 7,9 # G1: 7,9 => UNS * PRF B2: 3 + H3: 3 + F3: 7,9 # G1: 5 => SOL * STA B2: 3 + H3: 3 + F3: 7,9 + G1: 5 * CNT 8 HDP CHAINS / 8 HYP OPENED