Analysis of xx-top500-221-base.sdk
Contents
Original Sudoku
level: medium
position: ....7..2...3...5..6........17.....4..4.8........3.....5.....8.3...24.........6... initial
Autosolve
position: 45..73.2...3...5..6......3.17....34.34.8.7....6.3.4...524791863.36248......536... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 6,9 => CTR => D2: 1,4 * DIS # A9: 7,9 => CTR => A9: 8 * DIS # A9: 7,9 => CTR => A9: 8 * DIS # H6: 7,9 => CTR => H6: 1,5,8 * CNT 4 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 6,9 => CTR => D2: 1,4 * DIS D2: 1,4 # D1: 1 => CTR => D1: 6,9 * DIS D2: 1,4 + D1: 6,9 # A9: 7,9 => CTR => A9: 8 * DIS D2: 1,4 + D1: 6,9 + A9: 8 # C9: 1 => CTR => C9: 7,9 * DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # H2: 7,9 => CTR => H2: 1 * DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 # H8: 5 => CTR => H8: 7,9 * PRF D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 # F3: 2,9 => SOL * STA D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 + F3: 2,9 * CNT 7 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....7..2...3...5..6........17.....4..4.8........3.....5.....8.3...24.........6... | initial |
| 45..73.2...3...5..6......3.17....34.34.8.7....6.3.4...524791863.36248......536... | autosolve |
| 451673928793482516682159437178965342349827651265314789524791863936248175817536294 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A2: 2,7 C3: 2,7 F2: 2,9 D4: 6,9 A8: 7,9 G9: 2,4 H9: 7,9 I9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E5,E6: 1.. / E5 = 1 => 10 pairs (_) / E6 = 1 => 8 pairs (_) B9,C9: 1.. / B9 = 1 => 16 pairs (_) / C9 = 1 => 0 pairs (X) C1,C9: 1.. / C1 = 1 => 16 pairs (_) / C9 = 1 => 0 pairs (X) A2,C3: 2.. / A2 = 2 => 0 pairs (X) / C3 = 2 => 18 pairs (_) G9,I9: 2.. / G9 = 2 => 7 pairs (_) / I9 = 2 => 6 pairs (_) A2,A6: 2.. / A2 = 2 => 0 pairs (X) / A6 = 2 => 18 pairs (_) D2,D3: 4.. / D2 = 4 => 9 pairs (_) / D3 = 4 => 7 pairs (_) G9,I9: 4.. / G9 = 4 => 6 pairs (_) / I9 = 4 => 7 pairs (_) D2,I2: 4.. / D2 = 4 => 9 pairs (_) / I2 = 4 => 7 pairs (_) G3,G9: 4.. / G3 = 4 => 7 pairs (_) / G9 = 4 => 6 pairs (_) E3,F3: 5.. / E3 = 5 => 19 pairs (_) / F3 = 5 => 10 pairs (_) H8,I8: 5.. / H8 = 5 => 9 pairs (_) / I8 = 5 => 8 pairs (_) F3,F4: 5.. / F3 = 5 => 10 pairs (_) / F4 = 5 => 19 pairs (_) G1,G5: 6.. / G1 = 6 => 9 pairs (_) / G5 = 6 => 9 pairs (_) A2,C3: 7.. / A2 = 7 => 18 pairs (_) / C3 = 7 => 0 pairs (X) C3,C9: 7.. / C3 = 7 => 0 pairs (X) / C9 = 7 => 18 pairs (_) E2,E3: 8.. / E2 = 8 => 17 pairs (_) / E3 = 8 => 16 pairs (_) C1,I1: 8.. / C1 = 8 => 0 pairs (X) / I1 = 8 => 11 pairs (_) C4,I4: 8.. / C4 = 8 => 11 pairs (_) / I4 = 8 => 0 pairs (X) A6,A9: 8.. / A6 = 8 => 0 pairs (X) / A9 = 8 => 11 pairs (_) H2,H6: 8.. / H2 = 8 => 0 pairs (X) / H6 = 8 => 11 pairs (_) D4,F4: 9.. / D4 = 9 => 13 pairs (_) / F4 = 9 => 0 pairs (X) * DURATION: 0:00:37.502342 START: 10:20:32.575954 END: 10:21:10.078296 2017-05-04 * CP COUNT: (22) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,C3,D4,F2,G9,H9,I9) * 45..73.2...3...5..6......3.17....34.34.8.7....6.3.4...524791863.36248......536... * PAIR F2: 2,9 BLK 2 F3: 2,9,5 # reduction candidate for 2,9 F3: 2,9 # 19 pairs F3: 5 # 10 pairs * PAIR F2: 2,9 COL F F4: 2,9,5 # reduction candidate for 2,9 F4: 5 # 19 pairs F4: 2,9 # 10 pairs * PAIR D4: 6,9 COL D D1: 6,9,1 # reduction candidate for 6,9 D1: 6,9 # 11 pairs D2: 6,9,1,4 # reduction candidate for 6,9 D2: 6,9 => CTR * 45.173.2.2.3..95746.74...3.17.9..34.34.8.7....6.3.4.8.524791863.36248.....15364.2 D2: 1,4 # 9 pairs * PAIR A8: 7,9 BLK 7 A9: 7,9,8 # reduction candidate for 7,9 A9: 7,9 => CTR * 45..73.2.2.3..95876.7.8..3.17....34.34.8.7...86.3.4...524791863.36248......536... A9: 8 # 11 pairs C9: 7,9,1,8 # reduction candidate for 7,9 C9: 7,9 # 16 pairs * PAIR A8: 7,9 ROW 8 G8: 7,9,1 # reduction candidate for 7,9 G8: 7,9 # 11 pairs H8: 7,9,1,5 # reduction candidate for 7,9 H8: 7,9 # 12 pairs I8: 7,9,1,5 # reduction candidate for 7,9 I8: 7,9 # 11 pairs * PAIR H9: 7,9 BLK 9 G8: 7,9,1 # reduction candidate for 7,9 G8: 7,9 # 11 pairs H8: 7,9,1,5 # reduction candidate for 7,9 H8: 7,9 # 12 pairs I8: 7,9,1,5 # reduction candidate for 7,9 I8: 7,9 # 11 pairs * PAIR H9: 7,9 ROW 9 A9: 7,9,8 # reduction candidate for 7,9 A9: 7,9 => CTR * 45..73.2.2.3..95876.7.8..3.17....34.34.8.7...86.3.4...524791863.36248......536... A9: 8 # 11 pairs C9: 7,9,1,8 # reduction candidate for 7,9 C9: 7,9 # 16 pairs * PAIR H9: 7,9 COL H H2: 7,9,1,8 # reduction candidate for 7,9 H2: 7,9 # 16 pairs H6: 7,9,1,5,8 # reduction candidate for 7,9 H6: 7,9 => CTR * 45..73.2...3...58.6...85.3.17....34.34.8.7....6.3.4...524791863.36248....81536... H6: 1,5,8 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-221-base-pr-000.dot * REASONING * DIS # D2: 6,9 => CTR => D2: 1,4 * DIS # A9: 7,9 => CTR => A9: 8 * DIS # A9: 7,9 => CTR => A9: 8 * DIS # H6: 7,9 => CTR => H6: 1,5,8 * CNT 4 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,C3,D4,F2,G9,H9,I9) * 45..73.2...3...5..6......3.17....34.34.8.7....6.3.4...524791863.36248......536... * PAIR F2: 2,9 BLK 2 F3: 2,9,5 # reduction candidate for 2,9 F3: 2,9 # 19 pairs F3: 5 # 10 pairs * PAIR F2: 2,9 COL F F4: 2,9,5 # reduction candidate for 2,9 F4: 5 # 19 pairs F4: 2,9 # 10 pairs * PAIR D4: 6,9 COL D D1: 6,9,1 # reduction candidate for 6,9 D1: 6,9 # 11 pairs D2: 6,9,1,4 # reduction candidate for 6,9 D2: 6,9 => CTR * 45.173.2.2.3..95746.74...3.17.9..34.34.8.7....6.3.4.8.524791863.36248.....15364.2 * RESTART * PAIR D4: 6,9 COL D D1: 6,9,1 # reduction candidate for 6,9 D1: 1 => CTR * 45.173.2...346.5..6..985.3.17.6.934.34.8.7....6.3.4...524791863.36248.....1536... * PAIR RESTART * PAIR A8: 7,9 BLK 7 A9: 7,9,8 # reduction candidate for 7,9 A9: 7,9 => CTR * 45..73.2.2.3..95876.7.8..3.17....34.34.8.7...86.3.4...524791863.36248......536... C9: 7,9,1 # reduction candidate for 7,9 C9: 7,9 # 16 pairs * RESTART * PAIR A8: 7,9 BLK 7 C9: 7,9,1 # reduction candidate for 7,9 C9: 1 => CTR * 459673128..3...5..6.7....3.178...34.34.8.7....6.3.4.8.524791863736248...891536.7. * PAIR A8: 7,9 ROW 8 G8: 7,9,1 # reduction candidate for 7,9 G8: 7,9 # 19 pairs H8: 7,9,1,5 # reduction candidate for 7,9 H8: 7,9 # 18 pairs I8: 7,9,1,5 # reduction candidate for 7,9 I8: 7,9 # 18 pairs * PAIR H9: 7,9 BLK 9 G8: 7,9,1 # reduction candidate for 7,9 G8: 7,9 # 19 pairs H8: 7,9,1,5 # reduction candidate for 7,9 H8: 7,9 # 18 pairs I8: 7,9,1,5 # reduction candidate for 7,9 I8: 7,9 # 18 pairs * PAIR H9: 7,9 COL H H2: 7,9,1 # reduction candidate for 7,9 H2: 7,9 => CTR * 451973628.83.6259.692.85.3.1786.934.34.8.7..626.3.4.8.524791863936248...81.536... * PAIR RESTART * PAIR H9: 7,9 BLK 9 H8: 7,9,5 # reduction candidate for 7,9 H8: 5 => CTR * 451.73.282.34.951769718..3.178...34.34.8.7....6.3.4.8.524791863736248.5.819536.7. * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A6,A8,B2,B3,C3,C5,C9,D1,D4,E6,F2,G1,G9,H8,H9,I4,I9) * 451.73.28..34..51.6..1...3.178...34.34.8.7.5..653.4.8.524791863.362481.581.536... * PAIR F2: 2,9 BLK 2 F3: 2,9,5 # reduction candidate for 2,9 F3: 2,9 => SOLVED * 451673928793482516682159437178965342349827651265314789524791863936248175817536294 * DURATION: 0:00:24.629928 START: 10:21:29.885178 END: 10:21:54.515106 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-221-base-pr-001.dot * REASONING * DIS # D2: 6,9 => CTR => D2: 1,4 * DIS D2: 1,4 # D1: 1 => CTR => D1: 6,9 * DIS D2: 1,4 + D1: 6,9 # A9: 7,9 => CTR => A9: 8 * DIS D2: 1,4 + D1: 6,9 + A9: 8 # C9: 1 => CTR => C9: 7,9 * DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # H2: 7,9 => CTR => H2: 1 * DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 # H8: 5 => CTR => H8: 7,9 * PRF D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 # F3: 2,9 => SOL * STA D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 + F3: 2,9 * CNT 7 HDP CHAINS / 22 HYP OPENED
Header Info
Top 500 Minimum 17 221 solution: 451673928793482516682159437178965342349827651265314789524791863936248175817536294 info: 1962 FNBTHWXY S8.f 5607 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 451673928793482516682159437178965342349827651265314789524791863936248175817536294 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 # F3: 2,9 => UNS * INC # F3: 5 => UNS * INC # F4: 2,9 => UNS * INC # F4: 5 => UNS * INC # D1: 6,9 => UNS * DIS # D2: 6,9 => CTR => D2: 1,4 * INC # D2: 1,4 => UNS * DIS # A9: 7,9 => CTR => A9: 8 * INC # A9: 8 => UNS * INC # C9: 7,9 => UNS * INC # G8: 7,9 => UNS * INC # H8: 7,9 => UNS * INC # I8: 7,9 => UNS * INC # G8: 7,9 => UNS * INC # H8: 7,9 => UNS * INC # I8: 7,9 => UNS * DIS # A9: 7,9 => CTR => A9: 8 * INC # A9: 8 => UNS * INC # C9: 7,9 => UNS * INC # H2: 7,9 => UNS * DIS # H6: 7,9 => CTR => H6: 1,5,8 * INC # H6: 1,5,8 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F3: 2,9 => UNS * INC # F3: 5 => UNS * INC # F4: 2,9 => UNS * INC # F4: 5 => UNS * INC # D1: 6,9 => UNS * DIS # D2: 6,9 => CTR => D2: 1,4 * INC D2: 1,4 # D1: 6,9 => UNS * DIS D2: 1,4 # D1: 1 => CTR => D1: 6,9 * DIS D2: 1,4 + D1: 6,9 # A9: 7,9 => CTR => A9: 8 * INC D2: 1,4 + D1: 6,9 + A9: 8 # C9: 7,9 => UNS * INC D2: 1,4 + D1: 6,9 + A9: 8 # C9: 7,9 => UNS * DIS D2: 1,4 + D1: 6,9 + A9: 8 # C9: 1 => CTR => C9: 7,9 * INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # G8: 7,9 => UNS * INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # H8: 7,9 => UNS * INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # I8: 7,9 => UNS * INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # G8: 7,9 => UNS * INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # H8: 7,9 => UNS * INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # I8: 7,9 => UNS * DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 # H2: 7,9 => CTR => H2: 1 * INC D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 # H8: 7,9 => UNS * DIS D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 # H8: 5 => CTR => H8: 7,9 * PRF D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 # F3: 2,9 => SOL * STA D2: 1,4 + D1: 6,9 + A9: 8 + C9: 7,9 + H2: 1 + H8: 7,9 + F3: 2,9 * CNT 22 HDP CHAINS / 22 HYP OPENED