Analysis of xx-top500-138-base.sdk
Contents
Original Sudoku
level: medium
position: 18.4.........9.6..3.........7...3.4...9.2...........1.6....1......5..9........2.. initial
Autosolve
position: 182436.9....1986233962..18427.613.49.19.2.3...63..9.1262.9.143..3.5.29..9..3..2.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 5,7 => CTR => C2: 4 * PRF # C2: 4 => SOL * PRF # C2: 4,5 => SOL * DIS # C2: 7 => CTR => C2: 4,5 * DIS # G6: 5,7 => CTR => G6: 8 * PRF # G6: 8 => SOL * DIS # I5: 5,7 => CTR => I5: 6 * DIS # I9: 5,7 => CTR => I9: 1,6,8 * DIS # A6: 5,8 => CTR => A6: 4 * DIS # C9: 5,8 => CTR => C9: 1,4,7 * PRF # A5: 4,5 => SOL * DIS # A5: 8 => CTR => A5: 4,5 * DIS # G6: 5 => CTR => G6: 7,8 * DIS # A6: 8 => CTR => A6: 4,5 * PRF # G6: 5,8 => SOL * DIS # G6: 7 => CTR => G6: 5,8 * DIS # C7: 7,8 => CTR => C7: 5 * PRF # C7: 5 => SOL * PRF # C8: 7,8 => SOL * DIS # C9: 7,8 => CTR => C9: 1,4,5 * DIS # E8: 7,8 => CTR => E8: 4,6 * DIS # I8: 7,8 => CTR => I8: 1,6 * DIS # C9: 4,5 => CTR => C9: 1,7,8 * DIS # E8: 7,8 => CTR => E8: 4,6 * DIS # E9: 7,8 => CTR => E9: 4,6 * DIS # C7: 7,8 => CTR => C7: 5 * PRF # C7: 5 => SOL * PRF # I7: 7,8 => SOL * DIS # I7: 5 => CTR => I7: 7,8 * DIS # E9: 4,7 => CTR => E9: 6,8 * DIS # C9: 4,7 => CTR => C9: 1,5,8 * DIS # I8: 6,7 => CTR => I8: 1,8 * DIS # H9: 6,7 => CTR => H9: 5 * PRF # H9: 5 => SOL * DIS # I9: 6,7 => CTR => I9: 1,5,8 * DIS # E8: 6,7 => CTR => E8: 4,8 * PRF # H5: 6,7 => SOL * DIS # H5: 5 => CTR => H5: 6,7 * CNT 38 HDP CHAINS / 60 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 5,7 => CTR => C2: 4 * PRF C2: 4 => SOL * STA C2: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 18.4.........9.6..3.........7...3.4...9.2...........1.6....1......5..9........2.. | initial |
| 182436.9....1986233962..18427.613.49.19.2.3...63..9.1262.9.143..3.5.29..9..3..2.. | autosolve |
| 182436795754198623396275184278613549519824376463759812625981437837542961941367258 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A2: 5,7 B2: 4,5 E3: 5,7 F3: 5,7 G1: 5,7 I1: 5,7 C4: 5,8 D5: 7,8 F5: 4,5 D6: 7,8 E6: 4,5 G4: 5,8 A8: 7,8 B9: 4,5 E7: 7,8 F9: 4,7 H8: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C8,C9: 1.. / C8 = 1 => 0 pairs (X) / C9 = 1 => 17 pairs (_) I8,I9: 1.. / I8 = 1 => 17 pairs (_) / I9 = 1 => 0 pairs (X) C8,I8: 1.. / C8 = 1 => 0 pairs (X) / I8 = 1 => 17 pairs (_) C9,I9: 1.. / C9 = 1 => 17 pairs (_) / I9 = 1 => 0 pairs (X) B2,C2: 4.. / B2 = 4 => 0 pairs (X) / C2 = 4 => 0 pairs (_) A5,A6: 4.. / A5 = 4 => 0 pairs (X) / A6 = 4 => 22 pairs (_) F5,E6: 4.. / F5 = 4 => 22 pairs (_) / E6 = 4 => 0 pairs (X) A5,F5: 4.. / A5 = 4 => 0 pairs (X) / F5 = 4 => 22 pairs (_) A6,E6: 4.. / A6 = 4 => 22 pairs (_) / E6 = 4 => 0 pairs (X) C8,E8: 4.. / C8 = 4 => 0 pairs (X) / E8 = 4 => 0 pairs (_) B2,B9: 4.. / B2 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) F5,F9: 4.. / F5 = 4 => 22 pairs (_) / F9 = 4 => 0 pairs (X) E3,F3: 5.. / E3 = 5 => 0 pairs (X) / F3 = 5 => 22 pairs (_) G1,I1: 5.. / G1 = 5 => 0 pairs (X) / I1 = 5 => 0 pairs (_) F5,E6: 5.. / F5 = 5 => 0 pairs (X) / E6 = 5 => 22 pairs (_) C4,G4: 5.. / C4 = 5 => 0 pairs (X) / G4 = 5 => 0 pairs (_) C7,I7: 5.. / C7 = 5 => 0 pairs (*) / I7 = 5 => 0 pairs (X) B2,B9: 5.. / B2 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) E3,E6: 5.. / E3 = 5 => 0 pairs (X) / E6 = 5 => 22 pairs (_) F3,F5: 5.. / F3 = 5 => 22 pairs (_) / F5 = 5 => 0 pairs (X) H5,H9: 5.. / H5 = 5 => 0 pairs (X) / H9 = 5 => 0 pairs (_) H5,I5: 6.. / H5 = 6 => 0 pairs (X) / I5 = 6 => 18 pairs (_) E8,E9: 6.. / E8 = 6 => 0 pairs (X) / E9 = 6 => 20 pairs (_) A2,C2: 7.. / A2 = 7 => 0 pairs (*) / C2 = 7 => 0 pairs (X) E3,F3: 7.. / E3 = 7 => 22 pairs (_) / F3 = 7 => 0 pairs (X) G1,I1: 7.. / G1 = 7 => 0 pairs (*) / I1 = 7 => 0 pairs (X) D5,D6: 7.. / D5 = 7 => 0 pairs (X) / D6 = 7 => 0 pairs (_) D6,G6: 7.. / D6 = 7 => 0 pairs (*) / G6 = 7 => 0 pairs (X) A2,A8: 7.. / A2 = 7 => 0 pairs (*) / A8 = 7 => 0 pairs (X) F3,F9: 7.. / F3 = 7 => 0 pairs (X) / F9 = 7 => 22 pairs (_) G1,G6: 7.. / G1 = 7 => 0 pairs (*) / G6 = 7 => 0 pairs (X) D5,D6: 8.. / D5 = 8 => 0 pairs (*) / D6 = 8 => 0 pairs (X) G4,G6: 8.. / G4 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) C4,G4: 8.. / C4 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) A5,D5: 8.. / A5 = 8 => 0 pairs (X) / D5 = 8 => 0 pairs (_) * DURATION: 0:01:00.578250 START: 07:27:09.803009 END: 07:28:10.381259 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B2,B9,C4,D5,D6,E3,E6,E7,F3,F5,F9,G1,G4,H8,I1) * 182436.9....1986233962..18427.613.49.19.2.3...63..9.1262.9.143..3.5.29..9..3..2.. * PAIR A2: 5,7 BLK 1 C2: 5,7,4 # reduction candidate for 5,7 C2: 5,7 => CTR * 182436597547198623396275184275613849.197243564638597126289.1435.3.5.29..95.3..2.. C2: 4 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 * PAIR B2: 4,5 BLK 1 C2: 4,5,7 # reduction candidate for 4,5 C2: 4,5 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 C2: 7 => CTR * 182436.9.5471986233962.7184275613849.19.253...63..9.1262.9.143.73.5.296.95.36.27. * PAIR G1: 5,7 COL G G6: 5,7,8 # reduction candidate for 5,7 G6: 5,7 => CTR * 1824365975471986233962..184275613849.19.2.356.63.59712628971435.3.5.29..95.3..2.. G6: 8 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 * PAIR I1: 5,7 COL I I5: 5,7,6 # reduction candidate for 5,7 I5: 5,7 => CTR * 182436.9.7541986233962..18427.613.49.19.2.36..63..9.1262597143883154297.9..3..25. I5: 6 # 18 pairs I7: 5,7,8 # reduction candidate for 5,7 I7: 5,7 # 21 pairs I9: 5,7,1,6,8 # reduction candidate for 5,7 I9: 5,7 => CTR * 182436.9....1986233962..18427.613.49.19.2.356.63.5971262.97143..3.5.29.19.138.26. I9: 1,6,8 # 17 pairs * PAIR C4: 5,8 BLK 4 A5: 5,8,4 # reduction candidate for 5,8 A5: 5,8 # 22 pairs A6: 5,8,4 # reduction candidate for 5,8 A6: 5,8 => CTR * 182436.9....1986233962..18427.613.494198253...63749.1262.9.143..345.29.19513.42.. A6: 4 # 22 pairs * PAIR C4: 5,8 COL C C7: 5,8,7 # reduction candidate for 5,8 C7: 5,8 # 19 pairs C9: 5,8,1,4,7 # reduction candidate for 5,8 C9: 5,8 => CTR * 182436.9..5419862339627518427.613.49.19.243..463.59.1262.9.143..315429..94.367251 C9: 1,4,7 # 17 pairs * PAIR F5: 4,5 ROW 5 A5: 4,5,8 # reduction candidate for 4,5 A5: 4,5 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 A5: 8 => CTR * 182436.9....1986233962..18427.613.498197243..46385971262.9.143.73.5.296.9..36725. * PAIR D6: 7,8 ROW 6 G6: 7,8,5 # reduction candidate for 7,8 G6: 5 => CTR * 182436795...1986233962..18427.613849.19.2.3...637.95126259.143..3.5.29..9..3..2.. G6: 7,8 # 19 pairs * PAIR E6: 4,5 ROW 6 A6: 4,5,8 # reduction candidate for 4,5 A6: 8 => CTR * 182436.9....1986233962..18427.613.494198253..86374951262.9.143.7345.296195136427. A6: 4,5 # 19 pairs * PAIR G4: 5,8 BLK 6 G6: 5,8,7 # reduction candidate for 5,8 G6: 5,8 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 G6: 7 => CTR * 1824365975471986233962751842756138498197243564638597126289.1435.3.5.29..95.3..2.. * PAIR A8: 7,8 BLK 7 C7: 7,8,5 # reduction candidate for 7,8 C7: 7,8 => CTR * 182436597547198623396275184275613849.197243564638597126289.1435.3.5.29..95.3..2.. C7: 5 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 C8: 7,8,1,4 # reduction candidate for 7,8 C8: 7,8 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 C8: 1,4 # 18 pairs C9: 7,8,1,4,5 # reduction candidate for 7,8 C9: 7,8 => CTR * 182436.9..5419862339627518427.613.49.19.243..463.59.1262.9.143..315429..94.367251 C9: 1,4,5 # 17 pairs * PAIR A8: 7,8 ROW 8 E8: 7,8,4,6 # reduction candidate for 7,8 E8: 7,8 => CTR * 182436.9..4.1986233962.718427.613.494198253...63..9.1262.9.143..345.29.1951364278 E8: 4,6 # 18 pairs I8: 7,8,1,6 # reduction candidate for 7,8 I8: 7,8 => CTR * 182436.9..5419862339627518427.613.49.19.2437646375981262.9.143..3154296.9..367251 I8: 1,6 # 18 pairs * PAIR B9: 4,5 BLK 7 C9: 4,5,1,7,8 # reduction candidate for 4,5 C9: 4,5 => CTR * 182436.9....1986233962..18427.613.49.19.2.3...63..9.1262.9.143..315429..9..3672.. C9: 1,7,8 # 17 pairs * PAIR E7: 7,8 BLK 8 E8: 7,8,4,6 # reduction candidate for 7,8 E8: 7,8 => CTR * 182436.9..4.1986233962.718427.613.494198253...63..9.1262.9.143..345.29.1951364278 E8: 4,6 # 18 pairs E9: 7,8,4,6 # reduction candidate for 7,8 E9: 7,8 => CTR * 182436.9.7451986233962.7184278613549419825367563749812627981435.3.56297.9..3.42.. E9: 4,6 # 20 pairs * PAIR E7: 7,8 ROW 7 C7: 7,8,5 # reduction candidate for 7,8 C7: 7,8 => CTR * 182436597547198623396275184275613849.197243564638597126289.1435.3.5.29..95.3..2.. C7: 5 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 I7: 7,8,5 # reduction candidate for 7,8 I7: 7,8 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 I7: 5 => CTR * 182436597547198623396275184275613849.197243564638597126289.1435.3.5.29..95.3..2.. * PAIR F9: 4,7 BLK 8 E8: 4,7,6,8 # reduction candidate for 4,7 E8: 4,7 # 23 pairs E9: 4,7,6,8 # reduction candidate for 4,7 E9: 4,7 => CTR * 1824365977451986233962..18427.613.49.19.2.3...63..9.1262.9814358345629719513..268 E9: 6,8 # 18 pairs * PAIR F9: 4,7 ROW 9 C9: 4,7,1,5,8 # reduction candidate for 4,7 C9: 4,7 => CTR * 182436.9....1986233962..18427.613.49.19.2.3...63..9.1262.9.143..315429..9..3672.. C9: 1,5,8 # 17 pairs * PAIR H8: 6,7 BLK 9 I8: 6,7,1,8 # reduction candidate for 6,7 I8: 6,7 => CTR * 182436.9..5419862339627518427.613.49.19.243..463.59.1262.9.143..315429..9..367251 I8: 1,8 # 18 pairs H9: 6,7,5 # reduction candidate for 6,7 H9: 6,7 => CTR * 182436597547198623396275184275613849.197243564638597126289.143..3.5.29..9..3..2.. H9: 5 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 I9: 6,7,1,5,8 # reduction candidate for 6,7 I9: 6,7 => CTR * 182436.9....1986233962..18427.613.49.19.2.3...63..9.1262.971438.3.5629719.138425. I9: 1,5,8 # 17 pairs * PAIR H8: 6,7 ROW 8 E8: 6,7,4,8 # reduction candidate for 6,7 E8: 6,7 => CTR * 182436.9..4.1986233962..18427.613.49.19.2.356.63.5971262.9.14358345.29.1951347268 E8: 4,8 # 21 pairs * PAIR H8: 6,7 COL H H5: 6,7,5 # reduction candidate for 6,7 H5: 6,7 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 H5: 5 => CTR * 182436597547198623396275184275613849.197243564638597126289.143..3.5.29..9..3..2.. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-138-base-pr-000.dot * REASONING * DIS # C2: 5,7 => CTR => C2: 4 * PRF # C2: 4 => SOL * PRF # C2: 4,5 => SOL * DIS # C2: 7 => CTR => C2: 4,5 * DIS # G6: 5,7 => CTR => G6: 8 * PRF # G6: 8 => SOL * DIS # I5: 5,7 => CTR => I5: 6 * DIS # I9: 5,7 => CTR => I9: 1,6,8 * DIS # A6: 5,8 => CTR => A6: 4 * DIS # C9: 5,8 => CTR => C9: 1,4,7 * PRF # A5: 4,5 => SOL * DIS # A5: 8 => CTR => A5: 4,5 * DIS # G6: 5 => CTR => G6: 7,8 * DIS # A6: 8 => CTR => A6: 4,5 * PRF # G6: 5,8 => SOL * DIS # G6: 7 => CTR => G6: 5,8 * DIS # C7: 7,8 => CTR => C7: 5 * PRF # C7: 5 => SOL * PRF # C8: 7,8 => SOL * DIS # C9: 7,8 => CTR => C9: 1,4,5 * DIS # E8: 7,8 => CTR => E8: 4,6 * DIS # I8: 7,8 => CTR => I8: 1,6 * DIS # C9: 4,5 => CTR => C9: 1,7,8 * DIS # E8: 7,8 => CTR => E8: 4,6 * DIS # E9: 7,8 => CTR => E9: 4,6 * DIS # C7: 7,8 => CTR => C7: 5 * PRF # C7: 5 => SOL * PRF # I7: 7,8 => SOL * DIS # I7: 5 => CTR => I7: 7,8 * DIS # E9: 4,7 => CTR => E9: 6,8 * DIS # C9: 4,7 => CTR => C9: 1,5,8 * DIS # I8: 6,7 => CTR => I8: 1,8 * DIS # H9: 6,7 => CTR => H9: 5 * PRF # H9: 5 => SOL * DIS # I9: 6,7 => CTR => I9: 1,5,8 * DIS # E8: 6,7 => CTR => E8: 4,8 * PRF # H5: 6,7 => SOL * DIS # H5: 5 => CTR => H5: 6,7 * CNT 38 HDP CHAINS / 60 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B2,B9,C4,D5,D6,E3,E6,E7,F3,F5,F9,G1,G4,H8,I1) * 182436.9....1986233962..18427.613.49.19.2.3...63..9.1262.9.143..3.5.29..9..3..2.. * PAIR A2: 5,7 BLK 1 C2: 5,7,4 # reduction candidate for 5,7 C2: 5,7 => CTR * 182436597547198623396275184275613849.197243564638597126289.1435.3.5.29..95.3..2.. C2: 4 => SOLVED * 182436795754198623396275184278613549519824376463759812625981437837542961941367258 * DURATION: 0:00:03.082531 START: 07:29:09.151828 END: 07:29:12.234359 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-138-base-pr-001.dot * REASONING * DIS # C2: 5,7 => CTR => C2: 4 * PRF C2: 4 => SOL * STA C2: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 138 solution: 182436795754198623396275184278613549519824376463759812625981437837542961941367258 info: 1813 FNBTWY S8.f 26635 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 182436795754198623396275184278613549519824376463759812625981437837542961941367258 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 # C2: 5,7 => CTR => C2: 4 * PRF # C2: 4 => SOL * PRF # C2: 4,5 => SOL * DIS # C2: 7 => CTR => C2: 4,5 * DIS # G6: 5,7 => CTR => G6: 8 * PRF # G6: 8 => SOL * DIS # I5: 5,7 => CTR => I5: 6 * INC # I5: 6 => UNS * INC # I7: 5,7 => UNS * DIS # I9: 5,7 => CTR => I9: 1,6,8 * INC # I9: 1,6,8 => UNS * INC # A5: 5,8 => UNS * DIS # A6: 5,8 => CTR => A6: 4 * INC # A6: 4 => UNS * INC # C7: 5,8 => UNS * DIS # C9: 5,8 => CTR => C9: 1,4,7 * INC # C9: 1,4,7 => UNS * PRF # A5: 4,5 => SOL * DIS # A5: 8 => CTR => A5: 4,5 * INC # G6: 7,8 => UNS * DIS # G6: 5 => CTR => G6: 7,8 * INC # A6: 4,5 => UNS * DIS # A6: 8 => CTR => A6: 4,5 * PRF # G6: 5,8 => SOL * DIS # G6: 7 => CTR => G6: 5,8 * DIS # C7: 7,8 => CTR => C7: 5 * PRF # C7: 5 => SOL * PRF # C8: 7,8 => SOL * INC # C8: 1,4 => UNS * DIS # C9: 7,8 => CTR => C9: 1,4,5 * INC # C9: 1,4,5 => UNS * DIS # E8: 7,8 => CTR => E8: 4,6 * INC # E8: 4,6 => UNS * DIS # I8: 7,8 => CTR => I8: 1,6 * INC # I8: 1,6 => UNS * DIS # C9: 4,5 => CTR => C9: 1,7,8 * INC # C9: 1,7,8 => UNS * DIS # E8: 7,8 => CTR => E8: 4,6 * INC # E8: 4,6 => UNS * DIS # E9: 7,8 => CTR => E9: 4,6 * INC # E9: 4,6 => UNS * DIS # C7: 7,8 => CTR => C7: 5 * PRF # C7: 5 => SOL * PRF # I7: 7,8 => SOL * DIS # I7: 5 => CTR => I7: 7,8 * INC # E8: 4,7 => UNS * DIS # E9: 4,7 => CTR => E9: 6,8 * INC # E9: 6,8 => UNS * DIS # C9: 4,7 => CTR => C9: 1,5,8 * INC # C9: 1,5,8 => UNS * DIS # I8: 6,7 => CTR => I8: 1,8 * INC # I8: 1,8 => UNS * DIS # H9: 6,7 => CTR => H9: 5 * PRF # H9: 5 => SOL * DIS # I9: 6,7 => CTR => I9: 1,5,8 * INC # I9: 1,5,8 => UNS * DIS # E8: 6,7 => CTR => E8: 4,8 * INC # E8: 4,8 => UNS * PRF # H5: 6,7 => SOL * DIS # H5: 5 => CTR => H5: 6,7 * CNT 60 HDP CHAINS / 60 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 5,7 => CTR => C2: 4 * PRF C2: 4 => SOL * STA C2: 4 * CNT 2 HDP CHAINS / 1 HYP OPENED