Analysis of xx-top500-211-base.sdk
Contents
Original Sudoku
level: medium
position: 4...6...........51....2.......7..2........43..18.......7.1.8...3.....6.....5..... initial
Autosolve
position: 4...61..........511...25......7.921.7...1243.218.......7.1.8...3.12..6.....5.61.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I4: 5,6 => CTR => I4: 8 * PRF # I4: 8 => SOL * DIS # A7: 9 => CTR => A7: 5,6 * PRF # I4: 5,8 => SOL * DIS # I4: 6 => CTR => I4: 5,8 * PRF # I5: 6,8 => SOL * DIS # I5: 5 => CTR => I5: 6,8 * DIS # D6: 3,4 => CTR => D6: 6 * PRF # D6: 6 => SOL * DIS # F2: 3,4 => CTR => F2: 7 * PRF # B8: 8,9 => SOL * DIS # B9: 8,9 => CTR => B9: 2,4 * DIS # A2: 6 => CTR => A2: 8,9 * DIS # H8: 4,7 => CTR => H8: 8,9 * DIS # I8: 4,7 => CTR => I8: 5,9 * DIS # F2: 3 => CTR => F2: 4,7 * CNT 16 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I4: 5,6 => 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
| 4...6...........51....2.......7..2........43..18.......7.1.8...3.....6.....5..... | initial |
| 4...61..........511...25......7.921.7...1243.218.......7.1.8...3.12..6.....5.61.. | autosolve |
| 485361729962487351137925864643759218759812436218643597576138942391274685824596173 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) H3: 4,6 I3: 4,6 A4: 5,6 B4: 3,4 C4: 3,4 E4: 5,8 D5: 6,8 E6: 4,5 F6: 3,4 A9: 8,9 F8: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 2.. / B2 = 2 => 0 pairs (X) / C2 = 2 => 12 pairs (_) H1,I1: 2.. / H1 = 2 => 12 pairs (_) / I1 = 2 => 13 pairs (_) B2,B9: 2.. / B2 = 2 => 0 pairs (X) / B9 = 2 => 12 pairs (_) B4,C4: 3.. / B4 = 3 => 11 pairs (_) / C4 = 3 => 10 pairs (_) D6,F6: 3.. / D6 = 3 => 0 pairs (X) / F6 = 3 => 12 pairs (_) E7,E9: 3.. / E7 = 3 => 12 pairs (_) / E9 = 3 => 12 pairs (_) E9,I9: 3.. / E9 = 3 => 12 pairs (_) / I9 = 3 => 12 pairs (_) F2,F6: 3.. / F2 = 3 => 0 pairs (X) / F6 = 3 => 12 pairs (_) H3,I3: 4.. / H3 = 4 => 0 pairs (X) / I3 = 4 => 10 pairs (_) B4,C4: 4.. / B4 = 4 => 10 pairs (_) / C4 = 4 => 11 pairs (_) D2,D6: 4.. / D2 = 4 => 14 pairs (_) / D6 = 4 => 0 pairs (X) B1,C1: 5.. / B1 = 5 => 0 pairs (X) / C1 = 5 => 12 pairs (_) E4,E6: 5.. / E4 = 5 => 0 pairs (*) / E6 = 5 => 0 pairs (X) B8,I8: 5.. / B8 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) A4,A7: 5.. / A4 = 5 => 0 pairs (X) / A7 = 5 => 0 pairs (_) G6,G7: 5.. / G6 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) H3,I3: 6.. / H3 = 6 => 10 pairs (_) / I3 = 6 => 0 pairs (X) D5,D6: 6.. / D5 = 6 => 0 pairs (X) / D6 = 6 => 0 pairs (_) A7,C7: 6.. / A7 = 6 => 0 pairs (X) / C7 = 6 => 13 pairs (_) A4,I4: 6.. / A4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) B2,B5: 6.. / B2 = 6 => 15 pairs (_) / B5 = 6 => 0 pairs (X) H3,H6: 6.. / H3 = 6 => 10 pairs (_) / H6 = 6 => 0 pairs (X) C1,C3: 7.. / C1 = 7 => 0 pairs (X) / C3 = 7 => 11 pairs (_) E2,F2: 7.. / E2 = 7 => 0 pairs (X) / F2 = 7 => 13 pairs (_) C3,G3: 7.. / C3 = 7 => 11 pairs (_) / G3 = 7 => 0 pairs (X) F2,F8: 7.. / F2 = 7 => 13 pairs (_) / F8 = 7 => 0 pairs (X) 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 => 11 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 => 11 pairs (_) A2,A9: 8.. / A2 = 8 => 0 pairs (X) / A9 = 8 => 11 pairs (_) E2,E4: 8.. / E2 = 8 => 0 pairs (*) / E4 = 8 => 0 pairs (X) B5,C5: 9.. / B5 = 9 => 16 pairs (_) / C5 = 9 => 14 pairs (_) * DURATION: 0:00:59.370779 START: 10:02:35.944831 END: 10:03:35.315610 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B4,C4,D5,E4,E6,F6,F8,H3,I3) * 4...61..........511...25......7.921.7...1243.218.......7.1.8...3.12..6.....5.61.. * PAIR A4: 5,6 BLK 4 B5: 5,6,9 # reduction candidate for 5,6 B5: 5,6 # 14 pairs C5: 5,6,9 # reduction candidate for 5,6 C5: 5,6 # 16 pairs * PAIR A4: 5,6 ROW 4 I4: 5,6,8 # reduction candidate for 5,6 I4: 5,6 => CTR * 4...61..........511...25......78921.7..612438218.5.....7.1.85..3512..68....5.61.. I4: 8 => SOLVED * 485361729962487351137925864643759218759812436218643597576138942391274685824596173 * PAIR A4: 5,6 COL A A7: 5,6,9 # reduction candidate for 5,6 A7: 9 => CTR * 4...61..........511...25...5..7892167...1243.218.......7.1.8...3.12..6.....5.61.. A7: 5,6 # 15 pairs * PAIR E4: 5,8 ROW 4 I4: 5,8,6 # reduction candidate for 5,8 I4: 5,8 => SOLVED * 485361729962487351137925864643759218759812436218643597576138942391274685824596173 I4: 6 => CTR * 4...61..........511...25......7892167..612438218.5.....7.1.85..3512..68....5.61.. * PAIR D5: 6,8 ROW 5 I5: 6,8,5 # reduction candidate for 6,8 I5: 6,8 => SOLVED * 485361729962487351137925864643759218759812436218643597576138942391274685824596173 I5: 5 => CTR * 4...61..........511...25......7.92187..81243521865.....7.1.8...3.12..6.....5.61.. * PAIR F6: 3,4 BLK 5 D6: 3,4,6 # reduction candidate for 3,4 D6: 3,4 => CTR * 4...61....62....511...25...6..7892157..612438218.5....5761.8...3.12..6...2.5.61.. D6: 6 => SOLVED * 485361729962487351137925864643759218759812436218643597576138942391274685824596173 * PAIR F6: 3,4 COL F F2: 3,4,7 # reduction candidate for 3,4 F2: 3,4 => CTR * 4...61.......7..511...25......78921.7..612438218.5.....7.1.85..3512.768....5.61.. F2: 7 # 13 pairs * PAIR A9: 8,9 BLK 7 B8: 8,9,4,5 # reduction candidate for 8,9 B8: 8,9 => SOLVED * 485361729962487351137925864643759218759812436218643597576138942391274685824596173 B8: 4,5 # 12 pairs B9: 8,9,2,4 # reduction candidate for 8,9 B9: 8,9 => CTR * 4...61....2.....511...25......7.921.769812435218.......7.1.8...3.12..6.....5.61.. B9: 2,4 # 12 pairs * PAIR A9: 8,9 ROW 9 H9: 8,9,2,4,7 # reduction candidate for 8,9 H9: 8,9 # 16 pairs H9: 2,4,7 # 11 pairs * PAIR A9: 8,9 COL A A2: 8,9,6 # reduction candidate for 8,9 A2: 6 => CTR * 4...61...6......511...25...5..7892167...1243.218.......7.1.8...3.12..6.....5.61.. A2: 8,9 # 15 pairs * PAIR F8: 4,7 BLK 8 E8: 4,7,9 # reduction candidate for 4,7 E8: 4,7 # 16 pairs E9: 4,7,3,9 # reduction candidate for 4,7 E9: 4,7 # 13 pairs * PAIR F8: 4,7 ROW 8 H8: 4,7,8,9 # reduction candidate for 4,7 H8: 4,7 => CTR * 4...61...8......511...25......7892167..612438218.5....6751.8...38129.6.59..5.618. H8: 8,9 # 12 pairs I8: 4,7,5,9 # reduction candidate for 4,7 I8: 4,7 => CTR * 4.5.61..........511.7.25...5..7892167...1243.218.......7.1.8...3512..68....5.61.. I8: 5,9 # 12 pairs * PAIR F8: 4,7 COL F F2: 4,7,3 # reduction candidate for 4,7 F2: 3 => CTR * 4...61.......73.511...25......78921.7..612438218354....7.1.85..3512.768....5.61.. F2: 4,7 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-211-base-pr-000.dot * REASONING * DIS # I4: 5,6 => CTR => I4: 8 * PRF # I4: 8 => SOL * DIS # A7: 9 => CTR => A7: 5,6 * PRF # I4: 5,8 => SOL * DIS # I4: 6 => CTR => I4: 5,8 * PRF # I5: 6,8 => SOL * DIS # I5: 5 => CTR => I5: 6,8 * DIS # D6: 3,4 => CTR => D6: 6 * PRF # D6: 6 => SOL * DIS # F2: 3,4 => CTR => F2: 7 * PRF # B8: 8,9 => SOL * DIS # B9: 8,9 => CTR => B9: 2,4 * DIS # A2: 6 => CTR => A2: 8,9 * DIS # H8: 4,7 => CTR => H8: 8,9 * DIS # I8: 4,7 => CTR => I8: 5,9 * DIS # F2: 3 => CTR => F2: 4,7 * CNT 16 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B4,C4,D5,E4,E6,F6,F8,H3,I3) * 4...61..........511...25......7.921.7...1243.218.......7.1.8...3.12..6.....5.61.. * PAIR A4: 5,6 BLK 4 B5: 5,6,9 # reduction candidate for 5,6 B5: 5,6 # 14 pairs C5: 5,6,9 # reduction candidate for 5,6 C5: 5,6 # 16 pairs * PAIR A4: 5,6 ROW 4 I4: 5,6,8 # reduction candidate for 5,6 I4: 5,6 => CTR * 4...61..........511...25......78921.7..612438218.5.....7.1.85..3512..68....5.61.. I4: 8 => SOLVED * 485361729962487351137925864643759218759812436218643597576138942391274685824596173 * DURATION: 0:00:05.221856 START: 10:04:05.172435 END: 10:04:10.394291 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-211-base-pr-001.dot * REASONING * DIS # I4: 5,6 => CTR => I4: 8 * PRF I4: 8 => SOL * STA I4: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 211 solution: 485361729962487351137925864643759218759812436218643597576138942391274685824596173 info: 1943 FNBHWY S8.f 30747 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 485361729962487351137925864643759218759812436218643597576138942391274685824596173 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: 5,6 => UNS * INC # C5: 5,6 => UNS * DIS # I4: 5,6 => CTR => I4: 8 * PRF # I4: 8 => SOL * INC # A7: 5,6 => UNS * DIS # A7: 9 => CTR => A7: 5,6 * PRF # I4: 5,8 => SOL * DIS # I4: 6 => CTR => I4: 5,8 * PRF # I5: 6,8 => SOL * DIS # I5: 5 => CTR => I5: 6,8 * DIS # D6: 3,4 => CTR => D6: 6 * PRF # D6: 6 => SOL * DIS # F2: 3,4 => CTR => F2: 7 * INC # F2: 7 => UNS * PRF # B8: 8,9 => SOL * INC # B8: 4,5 => UNS * DIS # B9: 8,9 => CTR => B9: 2,4 * INC # B9: 2,4 => UNS * INC # H9: 8,9 => UNS * INC # H9: 2,4,7 => UNS * INC # A2: 8,9 => UNS * DIS # A2: 6 => CTR => A2: 8,9 * INC # E8: 4,7 => UNS * INC # E9: 4,7 => UNS * DIS # H8: 4,7 => CTR => H8: 8,9 * INC # H8: 8,9 => UNS * DIS # I8: 4,7 => CTR => I8: 5,9 * INC # I8: 5,9 => UNS * INC # F2: 4,7 => UNS * DIS # F2: 3 => CTR => F2: 4,7 * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B5: 5,6 => UNS * INC # C5: 5,6 => UNS * DIS # I4: 5,6 => CTR => I4: 8 * PRF I4: 8 => SOL * STA I4: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED