Analysis of xx-top500-451-base.sdk
Contents
Original Sudoku
level: medium
position: 8.1............27........9.6....14...9..5.............2.....1.6.5.97.......3..... initial
Autosolve
position: 8.1......9.....27........9.6....14...9..5..1..1.......279...1361539768..4..312.5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 5,6 => CTR => C3: 2,7 * PRF # A6: 3,7 => SOL * DIS # A6: 5 => CTR => A6: 3,7 * DIS # F5: 3,7 => CTR => F5: 4,8 * DIS # G5: 3,7 => CTR => G5: 6 * PRF # G5: 6 => SOL * PRF # I5: 3,7 => SOL * DIS # I5: 2 => CTR => I5: 3,7 * DIS # A3: 3,7 => CTR => A3: 5 * PRF # A3: 5 => SOL * PRF # H6: 2,8 => SOL * DIS # H6: 6 => CTR => H6: 2,8 * PRF # B4: 2,8 => SOL * DIS # B4: 3 => CTR => B4: 2,8 * DIS # C4: 2,8 => CTR => C4: 5,7 * PRF # C4: 5,7 => SOL * DIS # D4: 2,8 => CTR => D4: 7 * PRF # D4: 7 => SOL * DIS # E4: 2,8 => CTR => E4: 3,9 * DIS # G6: 3,5,6 => CTR => G6: 7,9 * PRF # I4: 7,9 => SOL * DIS # I4: 2,3,5 => CTR => I4: 7,9 * DIS # I6: 7,9 => CTR => I6: 2,3,5 * CNT 23 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 5,6 => CTR => C3: 2,7 * PRF C3: 2,7 # A6: 3,7 => SOL * STA C3: 2,7 + A6: 3,7 * CNT 2 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8.1............27........9.6....14...9..5.............2.....1.6.5.97.......3..... | initial |
| 8.1......9.....27........9.6....14...9..5..1..1.......279...1361539768..4..312.5. | autosolve |
| 831297564946583271527164398685731429792458613314629785279845136153976842468312957 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C2: 5,6 H1: 4,6 I2: 1,8 I3: 1,8 A5: 3,7 H4: 2,8 B9: 6,8 C9: 6,8 E7: 4,8 H8: 2,4 I8: 2,4 G9: 7,9 I9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 11 pairs (_) / D3 = 1 => 11 pairs (_) I2,I3: 1.. / I2 = 1 => 11 pairs (_) / I3 = 1 => 11 pairs (_) D2,I2: 1.. / D2 = 1 => 11 pairs (_) / I2 = 1 => 11 pairs (_) D3,I3: 1.. / D3 = 1 => 11 pairs (_) / I3 = 1 => 11 pairs (_) H8,I8: 2.. / H8 = 2 => 0 pairs (X) / I8 = 2 => 0 pairs (_) B2,B3: 4.. / B2 = 4 => 13 pairs (_) / B3 = 4 => 14 pairs (_) H1,I1: 4.. / H1 = 4 => 0 pairs (X) / I1 = 4 => 0 pairs (_) C5,C6: 4.. / C5 = 4 => 14 pairs (_) / C6 = 4 => 13 pairs (_) H8,I8: 4.. / H8 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) H1,H8: 4.. / H1 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) I1,I8: 4.. / I1 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) D7,F7: 5.. / D7 = 5 => 14 pairs (_) / F7 = 5 => 14 pairs (_) C4,I4: 5.. / C4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) A3,A6: 5.. / A3 = 5 => 0 pairs (*) / A6 = 5 => 0 pairs (X) B9,C9: 6.. / B9 = 6 => 0 pairs (*) / C9 = 6 => 0 pairs (X) D5,G5: 6.. / D5 = 6 => 0 pairs (X) / G5 = 6 => 0 pairs (_) H1,H6: 6.. / H1 = 6 => 0 pairs (*) / H6 = 6 => 0 pairs (X) A3,C3: 7.. / A3 = 7 => 0 pairs (X) / C3 = 7 => 15 pairs (_) D1,F1: 7.. / D1 = 7 => 0 pairs (X) / F1 = 7 => 0 pairs (_) G9,I9: 7.. / G9 = 7 => 0 pairs (X) / I9 = 7 => 12 pairs (_) I2,I3: 8.. / I2 = 8 => 11 pairs (_) / I3 = 8 => 11 pairs (_) H4,H6: 8.. / H4 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) B9,C9: 8.. / B9 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) B4,B9: 8.. / B4 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) E1,F1: 9.. / E1 = 9 => 0 pairs (*) / F1 = 9 => 0 pairs (X) G9,I9: 9.. / G9 = 9 => 12 pairs (_) / I9 = 9 => 0 pairs (X) E4,I4: 9.. / E4 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) F1,F6: 9.. / F1 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) G6,G9: 9.. / G6 = 9 => 0 pairs (X) / G9 = 9 => 12 pairs (_) * DURATION: 0:00:48.867347 START: 18:09:16.394478 END: 18:10:05.261825 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B9,C2,C9,E7,G9,H1,H4,H8,I2,I3,I8,I9) * 8.1......9.....27........9.6....14...9..5..1..1.......279...1361539768..4..312.5. * PAIR C2: 5,6 BLK 1 C3: 5,6,2,7 # reduction candidate for 5,6 C3: 5,6 => CTR * 8.1......9.....27.7......9.6....14.539..5..1.51.......279...1361539768..4..312.5. C3: 2,7 # 14 pairs * PAIR C2: 5,6 ROW 2 D2: 5,6,1,4,8 # reduction candidate for 5,6 D2: 5,6 # 13 pairs D2: 1,4,8 # 13 pairs * PAIR I2: 1,8 ROW 2 D2: 1,8,4,5,6 # reduction candidate for 1,8 D2: 1,8 # 14 pairs D2: 4,5,6 # 11 pairs * PAIR I3: 1,8 ROW 3 D3: 1,8,2,4,5,6 # reduction candidate for 1,8 D3: 1,8 # 14 pairs D3: 2,4,5,6 # 11 pairs * PAIR A5: 3,7 BLK 4 A6: 3,7,5 # reduction candidate for 3,7 A6: 3,7 => SOLVED * 831297564946583271527164398685731429792458613314629785279845136153976842468312957 A6: 5 => CTR * 8.1..9...9.....27........9.63..914.579..5..1.51...7...279...1361539768..486312759 * PAIR A5: 3,7 ROW 5 F5: 3,7,4,8 # reduction candidate for 3,7 F5: 3,7 => CTR * 8.1......9.....27........9.6....14...9..5.612.1.....8.279...1361539768..4..312.5. F5: 4,8 # 16 pairs G5: 3,7,6 # reduction candidate for 3,7 G5: 3,7 => CTR * 8.1....439.5...27........9.6...91485.9.65..1251..3796.279...136153976824486312.5. G5: 6 => SOLVED * 831297564946583271527164398685731429792458613314629785279845136153976842468312957 I5: 3,7,2 # reduction candidate for 3,7 I5: 3,7 => SOLVED * 831297564946583271527164398685731429792458613314629785279845136153976842468312957 I5: 2 => CTR * 8.1..9.439.5...27........9.63..9148579.65.31251...796.279...136153976824486312.5. * PAIR A5: 3,7 COL A A3: 3,7,5 # reduction candidate for 3,7 A3: 3,7 => CTR * 8.1..9...9.....27........9.63..914.579..5..1.51...7...279...1361539768..486312759 A3: 5 => SOLVED * 831297564946583271527164398685731429792458613314629785279845136153976842468312957 * PAIR H4: 2,8 BLK 6 H6: 2,8,6 # reduction candidate for 2,8 H6: 2,8 => SOLVED * 831297564946583271527164398685731429792458613314629785279845136153976842468312957 H6: 6 => CTR * 8.1..9.439.5...27........9.63..9148579.65.31251...796.279...136153976824486312.5. * PAIR H4: 2,8 ROW 4 B4: 2,8,3 # reduction candidate for 2,8 B4: 2,8 => SOLVED * 831297564946583271527164398685731429792458613314629785279845136153976842468312957 B4: 3 => CTR * 8.1......9.5...27.3.7....9.63.7914.579..5..1.51.......279...1361539768..486312.5. C4: 2,8,5,7 # reduction candidate for 2,8 C4: 2,8 => CTR * 8.1......9.....27........9.6..7914.5.9..5..1..1.......279...1361539768..4..312.5. C4: 5,7 => SOLVED * 831297564946583271527164398685731429792458613314629785279845136153976842468312957 D4: 2,8,7 # reduction candidate for 2,8 D4: 2,8 => CTR * 8.1......9.....27........9.63..914..79..5..1.51.......279...1361539768..4..312.5. D4: 7 => SOLVED * 831297564946583271527164398685731429792458613314629785279845136153976842468312957 E4: 2,8,3,9 # reduction candidate for 2,8 E4: 2,8 => CTR * 8.1......9.....27........9.6357.14.979..5..1..1.......279...1361539768..4..312957 E4: 3,9 # 14 pairs * PAIR E7: 4,8 BLK 8 D7: 4,8,5 # reduction candidate for 4,8 D7: 4,8 # 14 pairs F7: 4,8,5 # reduction candidate for 4,8 F7: 4,8 # 14 pairs * PAIR E7: 4,8 COL E E2: 4,8,3,6 # reduction candidate for 4,8 E2: 4,8 # 14 pairs E3: 4,8,2,3,6 # reduction candidate for 4,8 E3: 4,8 # 15 pairs E6: 4,8,2,3,6,9 # reduction candidate for 4,8 E6: 4,8 # 15 pairs * PAIR G9: 7,9 COL G G6: 7,9,3,5,6 # reduction candidate for 7,9 G6: 3,5,6 => CTR * 8.1....4.9.5...27.7.2....9.627..148.39.65.712.1.....6.279...136153976824486312957 G6: 7,9 # 16 pairs * PAIR I9: 7,9 COL I I4: 7,9,2,3,5 # reduction candidate for 7,9 I4: 7,9 => SOLVED * 831297564946583271527164398685731429792458613314629785279845136153976842468312957 I4: 2,3,5 => CTR * 8.17.9...9.....27........9.6.7.914.539..5..1.51.......279...1361539768..4..312.5. I6: 7,9,2,3,5 # reduction candidate for 7,9 I6: 7,9 => CTR * 8.17.9...9.....27........9.6.7.914.539..5..1251....3.9279...1361539768244..312957 I6: 2,3,5 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-451-base-pr-000.dot * REASONING * DIS # C3: 5,6 => CTR => C3: 2,7 * PRF # A6: 3,7 => SOL * DIS # A6: 5 => CTR => A6: 3,7 * DIS # F5: 3,7 => CTR => F5: 4,8 * DIS # G5: 3,7 => CTR => G5: 6 * PRF # G5: 6 => SOL * PRF # I5: 3,7 => SOL * DIS # I5: 2 => CTR => I5: 3,7 * DIS # A3: 3,7 => CTR => A3: 5 * PRF # A3: 5 => SOL * PRF # H6: 2,8 => SOL * DIS # H6: 6 => CTR => H6: 2,8 * PRF # B4: 2,8 => SOL * DIS # B4: 3 => CTR => B4: 2,8 * DIS # C4: 2,8 => CTR => C4: 5,7 * PRF # C4: 5,7 => SOL * DIS # D4: 2,8 => CTR => D4: 7 * PRF # D4: 7 => SOL * DIS # E4: 2,8 => CTR => E4: 3,9 * DIS # G6: 3,5,6 => CTR => G6: 7,9 * PRF # I4: 7,9 => SOL * DIS # I4: 2,3,5 => CTR => I4: 7,9 * DIS # I6: 7,9 => CTR => I6: 2,3,5 * CNT 23 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B9,C2,C9,E7,G9,H1,H4,H8,I2,I3,I8,I9) * 8.1......9.....27........9.6....14...9..5..1..1.......279...1361539768..4..312.5. * PAIR C2: 5,6 BLK 1 C3: 5,6,2,7 # reduction candidate for 5,6 C3: 5,6 => CTR * 8.1......9.....27.7......9.6....14.539..5..1.51.......279...1361539768..4..312.5. * PAIR C2: 5,6 ROW 2 D2: 5,6,1,4,8 # reduction candidate for 5,6 D2: 5,6 # 14 pairs D2: 1,4,8 # 14 pairs * PAIR I2: 1,8 ROW 2 D2: 1,8,4,5,6 # reduction candidate for 1,8 D2: 1,8 # 15 pairs D2: 4,5,6 # 12 pairs * PAIR I3: 1,8 ROW 3 D3: 1,8,2,4,5,6 # reduction candidate for 1,8 D3: 1,8 # 15 pairs D3: 2,4,5,6 # 12 pairs * PAIR A5: 3,7 BLK 4 A6: 3,7,5 # reduction candidate for 3,7 A6: 3,7 => SOLVED * 831297564946583271527164398685731429792458613314629785279845136153976842468312957 * DURATION: 0:00:08.565264 START: 18:10:43.496870 END: 18:10:52.062134 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-451-base-pr-001.dot * REASONING * DIS # C3: 5,6 => CTR => C3: 2,7 * PRF C3: 2,7 # A6: 3,7 => SOL * STA C3: 2,7 + A6: 3,7 * CNT 2 HDP CHAINS / 8 HYP OPENED
Header Info
Top 500 Minimum 17 451 solution: 831297564946583271527164398685731429792458613314629785279845136153976842468312957 info: 95386 FNBHXYK S8.f 38447 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 831297564946583271527164398685731429792458613314629785279845136153976842468312957 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 # C3: 5,6 => CTR => C3: 2,7 * INC # C3: 2,7 => UNS * INC # D2: 5,6 => UNS * INC # D2: 1,4,8 => UNS * INC # D2: 1,8 => UNS * INC # D2: 4,5,6 => UNS * INC # D3: 1,8 => UNS * INC # D3: 2,4,5,6 => UNS * PRF # A6: 3,7 => SOL * DIS # A6: 5 => CTR => A6: 3,7 * DIS # F5: 3,7 => CTR => F5: 4,8 * INC # F5: 4,8 => UNS * DIS # G5: 3,7 => CTR => G5: 6 * PRF # G5: 6 => SOL * PRF # I5: 3,7 => SOL * DIS # I5: 2 => CTR => I5: 3,7 * DIS # A3: 3,7 => CTR => A3: 5 * PRF # A3: 5 => SOL * PRF # H6: 2,8 => SOL * DIS # H6: 6 => CTR => H6: 2,8 * PRF # B4: 2,8 => SOL * DIS # B4: 3 => CTR => B4: 2,8 * DIS # C4: 2,8 => CTR => C4: 5,7 * PRF # C4: 5,7 => SOL * DIS # D4: 2,8 => CTR => D4: 7 * PRF # D4: 7 => SOL * DIS # E4: 2,8 => CTR => E4: 3,9 * INC # E4: 3,9 => UNS * INC # D7: 4,8 => UNS * INC # F7: 4,8 => UNS * INC # E2: 4,8 => UNS * INC # E3: 4,8 => UNS * INC # E6: 4,8 => UNS * INC # G6: 7,9 => UNS * DIS # G6: 3,5,6 => CTR => G6: 7,9 * PRF # I4: 7,9 => SOL * DIS # I4: 2,3,5 => CTR => I4: 7,9 * DIS # I6: 7,9 => CTR => I6: 2,3,5 * INC # I6: 2,3,5 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C3: 5,6 => CTR => C3: 2,7 * INC C3: 2,7 # D2: 5,6 => UNS * INC C3: 2,7 # D2: 1,4,8 => UNS * INC C3: 2,7 # D2: 1,8 => UNS * INC C3: 2,7 # D2: 4,5,6 => UNS * INC C3: 2,7 # D3: 1,8 => UNS * INC C3: 2,7 # D3: 2,4,5,6 => UNS * PRF C3: 2,7 # A6: 3,7 => SOL * STA C3: 2,7 + A6: 3,7 * CNT 8 HDP CHAINS / 8 HYP OPENED