Analysis of xx-top500-196-base.sdk
Contents
Original Sudoku
level: medium
position: 7...5...........41....2.......6..2........37..18.......6.1.8...3.....5.....4..... initial
Autosolve
position: 7...51..........411...24......6.921.6...1237.218.......6.1.8...3.12..5.....4.51.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I4: 4,5 => CTR => I4: 8 * PRF # I4: 8 => SOL * DIS # A7: 9 => CTR => A7: 4,5 * PRF # I4: 4,8 => SOL * DIS # I4: 5 => CTR => I4: 4,8 * PRF # I5: 5,8 => SOL * DIS # I5: 4 => CTR => I5: 5,8 * DIS # D6: 3,7 => CTR => D6: 5 * PRF # D6: 5 => SOL * DIS # F2: 3,7 => CTR => F2: 6 * PRF # B8: 8,9 => SOL * DIS # B9: 8,9 => CTR => B9: 2,7 * DIS # A2: 5 => CTR => A2: 8,9 * DIS # I8: 6,7 => CTR => I8: 4,9 * DIS # F2: 3 => CTR => F2: 6,7 * CNT 15 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I4: 4,5 => CTR => I4: 8 * PRF I4: 8 => SOL * STA I4: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7...5...........41....2.......6..2........37..18.......6.1.8...3.....5.....4..... | initial |
| 7...51..........411...24......6.921.6...1237.218.......6.1.8...3.12..5.....4.51.. | autosolve |
| 784951632952386741136724859573649218649812375218573496465138927391267584827495163 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A4: 4,5 B4: 3,7 C4: 3,7 E4: 4,8 D5: 5,8 E6: 4,7 F6: 3,7 A9: 8,9 F8: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 2.. / B2 = 2 => 0 pairs (X) / C2 = 2 => 10 pairs (_) H1,I1: 2.. / H1 = 2 => 10 pairs (_) / I1 = 2 => 9 pairs (_) B2,B9: 2.. / B2 = 2 => 0 pairs (X) / B9 = 2 => 10 pairs (_) B4,C4: 3.. / B4 = 3 => 9 pairs (_) / C4 = 3 => 8 pairs (_) D6,F6: 3.. / D6 = 3 => 0 pairs (X) / F6 = 3 => 10 pairs (_) E7,E9: 3.. / E7 = 3 => 10 pairs (_) / E9 = 3 => 11 pairs (_) F2,F6: 3.. / F2 = 3 => 0 pairs (X) / F6 = 3 => 10 pairs (_) B1,C1: 4.. / B1 = 4 => 0 pairs (X) / C1 = 4 => 10 pairs (_) E4,E6: 4.. / E4 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) B8,I8: 4.. / B8 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) A4,A7: 4.. / A4 = 4 => 0 pairs (X) / A7 = 4 => 0 pairs (_) G6,G7: 4.. / G6 = 4 => 0 pairs (*) / G7 = 4 => 0 pairs (X) H3,I3: 5.. / H3 = 5 => 10 pairs (_) / I3 = 5 => 0 pairs (X) D5,D6: 5.. / D5 = 5 => 0 pairs (X) / D6 = 5 => 0 pairs (_) A7,C7: 5.. / A7 = 5 => 0 pairs (X) / C7 = 5 => 11 pairs (_) A4,I4: 5.. / A4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) B2,B5: 5.. / B2 = 5 => 14 pairs (_) / B5 = 5 => 0 pairs (X) H3,H6: 5.. / H3 = 5 => 10 pairs (_) / H6 = 5 => 0 pairs (X) C1,C3: 6.. / C1 = 6 => 0 pairs (X) / C3 = 6 => 9 pairs (_) E2,F2: 6.. / E2 = 6 => 0 pairs (X) / F2 = 6 => 11 pairs (_) F2,F8: 6.. / F2 = 6 => 11 pairs (_) / F8 = 6 => 0 pairs (X) B4,C4: 7.. / B4 = 7 => 8 pairs (_) / C4 = 7 => 9 pairs (_) E4,D5: 8.. / E4 = 8 => 0 pairs (X) / D5 = 8 => 0 pairs (_) I4,I5: 8.. / I4 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) H8,H9: 8.. / H8 = 8 => 9 pairs (_) / H9 = 8 => 0 pairs (X) E4,I4: 8.. / E4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) D5,I5: 8.. / D5 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) B8,H8: 8.. / B8 = 8 => 0 pairs (X) / H8 = 8 => 9 pairs (_) A2,A9: 8.. / A2 = 8 => 0 pairs (X) / A9 = 8 => 9 pairs (_) E2,E4: 8.. / E2 = 8 => 0 pairs (*) / E4 = 8 => 0 pairs (X) B5,C5: 9.. / B5 = 9 => 15 pairs (_) / C5 = 9 => 12 pairs (_) * DURATION: 0:00:50.561178 START: 09:26:24.604206 END: 09:27:15.165384 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B4,C4,D5,E4,E6,F6,F8) * 7...51..........411...24......6.921.6...1237.218.......6.1.8...3.12..5.....4.51.. * PAIR A4: 4,5 BLK 4 B5: 4,5,9 # reduction candidate for 4,5 B5: 4,5 # 12 pairs C5: 4,5,9 # reduction candidate for 4,5 C5: 4,5 # 15 pairs * PAIR A4: 4,5 ROW 4 I4: 4,5,8 # reduction candidate for 4,5 I4: 4,5 => CTR * 7...51..........411...24......68921.6..512378218.4.....6.1.84..3412..58....4.51.. I4: 8 => SOLVED * 784951632952386741136724859573649218649812375218573496465138927391267584827495163 * PAIR A4: 4,5 COL A A7: 4,5,9 # reduction candidate for 4,5 A7: 9 => CTR * 7...51..........411...24...4..6892156...1237.218.......6.1.8...3.12..5.....4.51.. A7: 4,5 # 14 pairs * PAIR E4: 4,8 ROW 4 I4: 4,8,5 # reduction candidate for 4,8 I4: 4,8 => SOLVED * 784951632952386741136724859573649218649812375218573496465138927391267584827495163 I4: 5 => CTR * 7...51..........411...24......6892156..512378218.4.....6.1.84..3412..58....4.51.. * PAIR D5: 5,8 ROW 5 I5: 5,8,4 # reduction candidate for 5,8 I5: 5,8 => SOLVED * 784951632952386741136724859573649218649812375218573496465138927391267584827495163 I5: 4 => CTR * 7...51..........411...24......6.92186..81237421854.....6.1.8...3.12..5.....4.51.. * PAIR F6: 3,7 BLK 5 D6: 3,7,5 # reduction candidate for 3,7 D6: 3,7 => CTR * 7...51....52....411...24...5..6892146..512378218.4....4651.8...3.12..5...2.4.51.. D6: 5 => SOLVED * 784951632952386741136724859573649218649812375218573496465138927391267584827495163 * PAIR F6: 3,7 COL F F2: 3,7,6 # reduction candidate for 3,7 F2: 3,7 => CTR * 7...51.......6..411...24......68921.6..512378218.4.....6.1.84..3412.658....4.51.. F2: 6 # 11 pairs * PAIR A9: 8,9 BLK 7 B8: 8,9,4,7 # reduction candidate for 8,9 B8: 8,9 => SOLVED * 784951632952386741136724859573649218649812375218573496465138927391267584827495163 B8: 4,7 # 10 pairs B9: 8,9,2,7 # reduction candidate for 8,9 B9: 8,9 => CTR * 7...51....2.....411...24......6.921.659812374218.......6.1.8...3.12..5.....4.51.. B9: 2,7 # 10 pairs * PAIR A9: 8,9 ROW 9 H9: 8,9,2,3,6 # reduction candidate for 8,9 H9: 8,9 # 14 pairs H9: 2,3,6 # 9 pairs * PAIR A9: 8,9 COL A A2: 8,9,5 # reduction candidate for 8,9 A2: 5 => CTR * 7...51...5......411...24...4..6892156...1237.218.......6.1.8...3.12..5.....4.51.. A2: 8,9 # 14 pairs * PAIR F8: 6,7 BLK 8 E8: 6,7,9 # reduction candidate for 6,7 E8: 6,7 # 14 pairs E9: 6,7,3,9 # reduction candidate for 6,7 E9: 6,7 # 12 pairs * PAIR F8: 6,7 ROW 8 I8: 6,7,4,9 # reduction candidate for 6,7 I8: 6,7 => CTR * 7.4.51..........411.6.24...4..6892156...1237.218.......6.1.8...3412..58....4.51.. I8: 4,9 # 10 pairs * PAIR F8: 6,7 COL F F2: 6,7,3 # reduction candidate for 6,7 F2: 3 => CTR * 7...51.......63.411...24......68921.6..512378218347....6.1.84..3412.658....4.51.. F2: 6,7 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-196-base-pr-000.dot * REASONING * DIS # I4: 4,5 => CTR => I4: 8 * PRF # I4: 8 => SOL * DIS # A7: 9 => CTR => A7: 4,5 * PRF # I4: 4,8 => SOL * DIS # I4: 5 => CTR => I4: 4,8 * PRF # I5: 5,8 => SOL * DIS # I5: 4 => CTR => I5: 5,8 * DIS # D6: 3,7 => CTR => D6: 5 * PRF # D6: 5 => SOL * DIS # F2: 3,7 => CTR => F2: 6 * PRF # B8: 8,9 => SOL * DIS # B9: 8,9 => CTR => B9: 2,7 * DIS # A2: 5 => CTR => A2: 8,9 * DIS # I8: 6,7 => CTR => I8: 4,9 * DIS # F2: 3 => CTR => F2: 6,7 * CNT 15 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B4,C4,D5,E4,E6,F6,F8) * 7...51..........411...24......6.921.6...1237.218.......6.1.8...3.12..5.....4.51.. * PAIR A4: 4,5 BLK 4 B5: 4,5,9 # reduction candidate for 4,5 B5: 4,5 # 12 pairs C5: 4,5,9 # reduction candidate for 4,5 C5: 4,5 # 15 pairs * PAIR A4: 4,5 ROW 4 I4: 4,5,8 # reduction candidate for 4,5 I4: 4,5 => CTR * 7...51..........411...24......68921.6..512378218.4.....6.1.84..3412..58....4.51.. I4: 8 => SOLVED * 784951632952386741136724859573649218649812375218573496465138927391267584827495163 * DURATION: 0:00:05.003121 START: 09:27:42.222760 END: 09:27:47.225881 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-196-base-pr-001.dot * REASONING * DIS # I4: 4,5 => CTR => I4: 8 * PRF I4: 8 => SOL * STA I4: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 196 solution: 784951632952386741136724859573649218649812375218573496465138927391267584827495163 info: 1880 FNBHWY S8.f 36719 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 784951632952386741136724859573649218649812375218573496465138927391267584827495163 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 # B5: 4,5 => UNS * INC # C5: 4,5 => UNS * DIS # I4: 4,5 => CTR => I4: 8 * PRF # I4: 8 => SOL * INC # A7: 4,5 => UNS * DIS # A7: 9 => CTR => A7: 4,5 * PRF # I4: 4,8 => SOL * DIS # I4: 5 => CTR => I4: 4,8 * PRF # I5: 5,8 => SOL * DIS # I5: 4 => CTR => I5: 5,8 * DIS # D6: 3,7 => CTR => D6: 5 * PRF # D6: 5 => SOL * DIS # F2: 3,7 => CTR => F2: 6 * INC # F2: 6 => UNS * PRF # B8: 8,9 => SOL * INC # B8: 4,7 => UNS * DIS # B9: 8,9 => CTR => B9: 2,7 * INC # B9: 2,7 => UNS * INC # H9: 8,9 => UNS * INC # H9: 2,3,6 => UNS * INC # A2: 8,9 => UNS * DIS # A2: 5 => CTR => A2: 8,9 * INC # E8: 6,7 => UNS * INC # E9: 6,7 => UNS * DIS # I8: 6,7 => CTR => I8: 4,9 * INC # I8: 4,9 => UNS * INC # F2: 6,7 => UNS * DIS # F2: 3 => CTR => F2: 6,7 * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B5: 4,5 => UNS * INC # C5: 4,5 => UNS * DIS # I4: 4,5 => CTR => I4: 8 * PRF I4: 8 => SOL * STA I4: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED