Analysis of xx-top500-333-base.sdk
Contents
Original Sudoku
level: medium
position: ..8..1.......2..3.5.....4....76..5...1..3..............2.....1....5..7..6..4..... initial
Autosolve
position: 2.8..1.......2.13.5.1...4.23.76..521.1.23......21......2.....1.1..5.27..6..41.2.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E6: 4,5 => CTR => E6: 7,8,9 * DIS # F6: 4,5 => CTR => F6: 7,8,9 * DIS # I2: 6,9 => CTR => I2: 5,7,8 * DIS # B1: 6,9 => CTR => B1: 3,4,7 * DIS # G6: 6,9 => CTR => G6: 3,8 * CNT 5 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E6: 4,5 => CTR => E6: 7,8,9 * PRF E6: 7,8,9 # G7: 6,9 => SOL * STA E6: 7,8,9 + G7: 6,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..8..1.......2..3.5.....4....76..5...1..3..............2.....1....5..7..6..4..... | initial |
| 2.8..1.......2.13.5.1...4.23.76..521.1.23......21......2.....1.1..5.27..6..41.2.. | autosolve |
| 248351967769824135531976482397648521416235879852197346925783614184562793673419258 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) E1: 4,5 F2: 4,5 G1: 6,9 C5: 5,6 B6: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B3: 3.. / B1 = 3 => 0 pairs (X) / B3 = 3 => 5 pairs (_) G6,I6: 3.. / G6 = 3 => 5 pairs (_) / I6 = 3 => 0 pairs (X) B1,D1: 3.. / B1 = 3 => 0 pairs (X) / D1 = 3 => 5 pairs (_) C8,I8: 3.. / C8 = 3 => 6 pairs (_) / I8 = 3 => 6 pairs (_) G6,G7: 3.. / G6 = 3 => 5 pairs (_) / G7 = 3 => 0 pairs (X) E1,F2: 4.. / E1 = 4 => 0 pairs (X) / F2 = 4 => 13 pairs (_) B1,E1: 4.. / B1 = 4 => 13 pairs (_) / E1 = 4 => 0 pairs (X) E1,F2: 5.. / E1 = 5 => 13 pairs (_) / F2 = 5 => 0 pairs (X) C5,B6: 5.. / C5 = 5 => 0 pairs (X) / B6 = 5 => 13 pairs (_) F2,I2: 5.. / F2 = 5 => 0 pairs (X) / I2 = 5 => 13 pairs (_) C5,F5: 5.. / C5 = 5 => 0 pairs (X) / F5 = 5 => 13 pairs (_) C7,I7: 5.. / C7 = 5 => 13 pairs (_) / I7 = 5 => 0 pairs (X) B6,B9: 5.. / B6 = 5 => 13 pairs (_) / B9 = 5 => 0 pairs (X) E1,E6: 5.. / E1 = 5 => 13 pairs (_) / E6 = 5 => 0 pairs (X) H1,H9: 5.. / H1 = 5 => 0 pairs (X) / H9 = 5 => 13 pairs (_) E3,F3: 6.. / E3 = 6 => 6 pairs (_) / F3 = 6 => 5 pairs (_) C5,B6: 6.. / C5 = 6 => 13 pairs (_) / B6 = 6 => 0 pairs (X) C2,C5: 6.. / C2 = 6 => 0 pairs (X) / C5 = 6 => 13 pairs (_) F3,F7: 6.. / F3 = 6 => 5 pairs (_) / F7 = 6 => 6 pairs (_) A7,B9: 7.. / A7 = 7 => 0 pairs (X) / B9 = 7 => 13 pairs (_) B9,F9: 7.. / B9 = 7 => 13 pairs (_) / F9 = 7 => 0 pairs (X) A2,A7: 7.. / A2 = 7 => 13 pairs (_) / A7 = 7 => 0 pairs (X) I2,H3: 8.. / I2 = 8 => 0 pairs (X) / H3 = 8 => 6 pairs (_) D2,I2: 8.. / D2 = 8 => 6 pairs (_) / I2 = 8 => 0 pairs (X) * DURATION: 0:00:38.763102 START: 14:09:45.712764 END: 14:10:24.475866 2017-05-04 * CP COUNT: (24) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C5,E1,F2,G1) * 2.8..1.......2.13.5.1...4.23.76..521.1.23......21......2.....1.1..5.27..6..41.2.. * PAIR E1: 4,5 COL E E6: 4,5,7,8,9 # reduction candidate for 4,5 E6: 4,5 => CTR * 248351...769824135531...4823.76..521416235....52147....25....141.45.27.367341.25. E6: 7,8,9 # 13 pairs * PAIR F2: 4,5 COL F F5: 4,5,7,8,9 # reduction candidate for 4,5 F5: 4,5 # 7 pairs F6: 4,5,7,8,9 # reduction candidate for 4,5 F6: 4,5 => CTR * 2.8..1.5...6.2513.5.1...4.23.76..521.1523.....621......2.....151..5.27..65.4172.. F6: 7,8,9 # 5 pairs * PAIR G1: 6,9 BLK 3 H1: 6,9,5,7 # reduction candidate for 6,9 H1: 6,9 # 16 pairs I1: 6,9,5,7 # reduction candidate for 6,9 I1: 6,9 # 9 pairs I2: 6,9,5,7,8 # reduction candidate for 6,9 I2: 6,9 => CTR * 2.8..1......82513.5.1...4823.76..521.1523.....6215.....2.....151..5.27..65.417298 I2: 5,7,8 # 5 pairs * PAIR G1: 6,9 ROW 1 B1: 6,9,3,4,7 # reduction candidate for 6,9 B1: 6,9 => CTR * 2.8341.......2513.531...4.23.76..521.1523.....6215.....2.....151..5.27..65.4172.. B1: 3,4,7 # 5 pairs * PAIR G1: 6,9 COL G G5: 6,9,8 # reduction candidate for 6,9 G5: 6,9 # 8 pairs G6: 6,9,3,8 # reduction candidate for 6,9 G6: 6,9 => CTR * 2.8.51...7...241355.1...4823.76..521.1623.8...521....3.2....31.1.35.27..67.4132.. G6: 3,8 # 6 pairs G7: 6,9,3,8 # reduction candidate for 6,9 G7: 6,9 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-333-base-pr-000.dot * REASONING * DIS # E6: 4,5 => CTR => E6: 7,8,9 * DIS # F6: 4,5 => CTR => F6: 7,8,9 * DIS # I2: 6,9 => CTR => I2: 5,7,8 * DIS # B1: 6,9 => CTR => B1: 3,4,7 * DIS # G6: 6,9 => CTR => G6: 3,8 * CNT 5 HDP CHAINS / 15 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C5,E1,F2,G1) * 2.8..1.......2.13.5.1...4.23.76..521.1.23......21......2.....1.1..5.27..6..41.2.. * PAIR E1: 4,5 COL E E6: 4,5,7,8,9 # reduction candidate for 4,5 E6: 4,5 => CTR * 248351...769824135531...4823.76..521416235....52147....25....141.45.27.367341.25. * PAIR RESTART * PAIR G1: 6,9 BLK 3 H1: 6,9,7 # reduction candidate for 6,9 H1: 6,9 # 16 pairs I1: 6,9,7 # reduction candidate for 6,9 I1: 6,9 # 15 pairs * PAIR G1: 6,9 COL G G7: 6,9,8 # reduction candidate for 6,9 G7: 6,9 => SOLVED * 248351967769824135531976482397648521416235879852197346925783614184562793673419258 * DURATION: 0:00:07.150971 START: 14:10:37.455215 END: 14:10:44.606186 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-333-base-pr-001.dot * REASONING * DIS # E6: 4,5 => CTR => E6: 7,8,9 * PRF E6: 7,8,9 # G7: 6,9 => SOL * STA E6: 7,8,9 + G7: 6,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 333 solution: 248351967769824135531976482397648521416235879852197346925783614184562793673419258 info: 3044 FNBHWXY S8.f 14526 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 248351967769824135531976482397648521416235879852197346925783614184562793673419258 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 # E6: 4,5 => CTR => E6: 7,8,9 * INC # E6: 7,8,9 => UNS * INC # F5: 4,5 => UNS * DIS # F6: 4,5 => CTR => F6: 7,8,9 * INC # F6: 7,8,9 => UNS * INC # H1: 6,9 => UNS * INC # I1: 6,9 => UNS * DIS # I2: 6,9 => CTR => I2: 5,7,8 * INC # I2: 5,7,8 => UNS * DIS # B1: 6,9 => CTR => B1: 3,4,7 * INC # B1: 3,4,7 => UNS * INC # G5: 6,9 => UNS * DIS # G6: 6,9 => CTR => G6: 3,8 * INC # G6: 3,8 => UNS * INC # G7: 6,9 => UNS * CNT 15 HDP CHAINS / 15 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E6: 4,5 => CTR => E6: 7,8,9 * INC E6: 7,8,9 # H1: 6,9 => UNS * INC E6: 7,8,9 # I1: 6,9 => UNS * PRF E6: 7,8,9 # G7: 6,9 => SOL * STA E6: 7,8,9 + G7: 6,9 * CNT 4 HDP CHAINS / 4 HYP OPENED