Analysis of xx-top500-254-base.sdk
Contents
Original Sudoku
level: medium
position: 27.5...4......96...............93....5.....2..........6..82....8.....3.9......1.. initial
Autosolve
position: 273568941.8.2.963..963..2.8.28.9351695168..2336.15289.639821...812..5369.4.936182 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A2: 4,5 => SOL * PRF # E3: 4,7 => SOL * PRF # I7: 5,7 => SOL * DIS # I7: 4 => CTR => I7: 5,7 * DIS # I7: 4,7 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # E3: 4,7 => SOL * DIS # I7: 4,7 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # I7: 5,7 => SOL * DIS # I7: 4 => CTR => I7: 5,7 * CNT 11 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A2: 4,5 => SOL * STA A2: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 27.5...4......96...............93....5.....2..........6..82....8.....3.9......1.. | initial |
| 273568941.8.2.963..963..2.8.28.9351695168..2336.15289.639821...812..5369.4.936182 | autosolve |
| 273568941584219637196347258428793516951684723367152894639821475812475369745936182 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) C2: 4,5 F3: 4,7 I2: 5,7 H3: 5,7 A4: 4,7 C6: 4,7 D4: 4,7 F5: 4,7 G5: 4,7 I6: 4,7 A9: 5,7 C9: 5,7 D8: 4,7 E8: 4,7 G7: 4,7 H7: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 18 pairs (_) / A3 = 1 => 0 pairs (*) E2,E3: 1.. / E2 = 1 => 0 pairs (*) / E3 = 1 => 0 pairs (X) A2,E2: 1.. / A2 = 1 => 18 pairs (_) / E2 = 1 => 0 pairs (*) A3,E3: 1.. / A3 = 1 => 0 pairs (*) / E3 = 1 => 0 pairs (X) A4,C6: 4.. / A4 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) D4,F5: 4.. / D4 = 4 => 0 pairs (X) / F5 = 4 => 0 pairs (_) G5,I6: 4.. / G5 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) D8,E8: 4.. / D8 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) G7,I7: 4.. / G7 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) A4,D4: 4.. / A4 = 4 => 0 pairs (*) / D4 = 4 => 0 pairs (X) F5,G5: 4.. / F5 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) C6,I6: 4.. / C6 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) C2,C6: 4.. / C2 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) D4,D8: 4.. / D4 = 4 => 0 pairs (X) / D8 = 4 => 0 pairs (_) F3,F5: 4.. / F3 = 4 => 0 pairs (X) / F5 = 4 => 0 pairs (_) G5,G7: 4.. / G5 = 4 => 0 pairs (X) / G7 = 4 => 0 pairs (_) I6,I7: 4.. / I6 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) I2,H3: 5.. / I2 = 5 => 0 pairs (X) / H3 = 5 => 0 pairs (_) A9,C9: 5.. / A9 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) H7,I7: 5.. / H7 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) A3,H3: 5.. / A3 = 5 => 0 pairs (X) / H3 = 5 => 0 pairs (_) C2,C9: 5.. / C2 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) H3,H7: 5.. / H3 = 5 => 0 pairs (*) / H7 = 5 => 0 pairs (X) I2,I7: 5.. / I2 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) I2,H3: 7.. / I2 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) A4,C6: 7.. / A4 = 7 => 0 pairs (X) / C6 = 7 => 0 pairs (_) D4,F5: 7.. / D4 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) G5,I6: 7.. / G5 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) A9,C9: 7.. / A9 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) D8,E8: 7.. / D8 = 7 => 0 pairs (X) / E8 = 7 => 0 pairs (_) E2,I2: 7.. / E2 = 7 => 0 pairs (X) / I2 = 7 => 0 pairs (_) A4,D4: 7.. / A4 = 7 => 0 pairs (X) / D4 = 7 => 0 pairs (_) F5,G5: 7.. / F5 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) C6,I6: 7.. / C6 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) A4,A9: 7.. / A4 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) C6,C9: 7.. / C6 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) D4,D8: 7.. / D4 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) F3,F5: 7.. / F3 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) G5,G7: 7.. / G5 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) H3,H7: 7.. / H3 = 7 => 0 pairs (X) / H7 = 7 => 0 pairs (_) * DURATION: 0:01:15.166397 START: 11:27:53.731308 END: 11:29:08.897705 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,C2,C6,C9,D4,D8,E8,F3,F5,G5,G7,H3,H7,I2,I6) * 273568941.8.2.963..963..2.8.28.9351695168..2336.15289.639821...812..5369.4.936182 * PAIR C2: 4,5 BLK 1 A2: 4,5,1 # reduction candidate for 4,5 A2: 4,5 => SOLVED * 273568941584219637196347258428793516951684723367152894639821475812475369745936182 A2: 1 # 18 pairs A3: 4,5,1 # reduction candidate for 4,5 A3: 4,5 # 18 pairs * PAIR F3: 4,7 BLK 2 E2: 4,7,1 # reduction candidate for 4,7 E2: 4,7 # 18 pairs E3: 4,7,1 # reduction candidate for 4,7 E3: 4,7 => SOLVED * 273568941584219637196347258428793516951684723367152894639821475812475369745936182 E3: 1 # 18 pairs * PAIR I2: 5,7 COL I I7: 5,7,4 # reduction candidate for 5,7 I7: 5,7 => SOLVED * 273568941584219637196347258428793516951684723367152894639821475812475369745936182 I7: 4 => CTR * 273568941.8.2.9635596314278.2849351695168742336415289.639821...812..5369.4.936182 * PAIR I6: 4,7 COL I I7: 4,7,5 # reduction candidate for 4,7 I7: 4,7 => CTR * 273568941.8.2.9635596314278.2849351695168742336415289.639821...812..5369.4.936182 I7: 5 => SOLVED * 273568941584219637196347258428793516951684723367152894639821475812475369745936182 * PAIR E8: 4,7 COL E E2: 4,7,1 # reduction candidate for 4,7 E2: 4,7 # 18 pairs E3: 4,7,1 # reduction candidate for 4,7 E3: 4,7 => SOLVED * 273568941584219637196347258428793516951684723367152894639821475812475369745936182 E3: 1 # 18 pairs * PAIR G7: 4,7 BLK 9 I7: 4,7,5 # reduction candidate for 4,7 I7: 4,7 => CTR * 273568941.8.2.9635596314278.2849351695168742336415289.639821...812..5369.4.936182 I7: 5 => SOLVED * 273568941584219637196347258428793516951684723367152894639821475812475369745936182 * PAIR H7: 5,7 BLK 9 I7: 5,7,4 # reduction candidate for 5,7 I7: 5,7 => SOLVED * 273568941584219637196347258428793516951684723367152894639821475812475369745936182 I7: 4 => CTR * 273568941.8.2.9635596314278.2849351695168742336415289.639821...812..5369.4.936182 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-254-base-pr-000.dot * REASONING * PRF # A2: 4,5 => SOL * PRF # E3: 4,7 => SOL * PRF # I7: 5,7 => SOL * DIS # I7: 4 => CTR => I7: 5,7 * DIS # I7: 4,7 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # E3: 4,7 => SOL * DIS # I7: 4,7 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # I7: 5,7 => SOL * DIS # I7: 4 => CTR => I7: 5,7 * CNT 11 HDP CHAINS / 17 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,C2,C6,C9,D4,D8,E8,F3,F5,G5,G7,H3,H7,I2,I6) * 273568941.8.2.963..963..2.8.28.9351695168..2336.15289.639821...812..5369.4.936182 * PAIR C2: 4,5 BLK 1 A2: 4,5,1 # reduction candidate for 4,5 A2: 4,5 => SOLVED * 273568941584219637196347258428793516951684723367152894639821475812475369745936182 * DURATION: 0:00:02.044816 START: 11:29:30.288809 END: 11:29:32.333625 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-254-base-pr-001.dot * REASONING * PRF # A2: 4,5 => SOL * STA A2: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 254 solution: 273568941584219637196347258428793516951684723367152894639821475812475369745936182 info: 2077 FNBWXY S8.f 42285 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 273568941584219637196347258428793516951684723367152894639821475812475369745936182 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:
* PRF # A2: 4,5 => SOL * INC # A2: 1 => UNS * INC # A3: 4,5 => UNS * INC # E2: 4,7 => UNS * PRF # E3: 4,7 => SOL * INC # E3: 1 => UNS * PRF # I7: 5,7 => SOL * DIS # I7: 4 => CTR => I7: 5,7 * DIS # I7: 4,7 => CTR => I7: 5 * PRF # I7: 5 => SOL * INC # E2: 4,7 => UNS * PRF # E3: 4,7 => SOL * INC # E3: 1 => UNS * DIS # I7: 4,7 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # I7: 5,7 => SOL * DIS # I7: 4 => CTR => I7: 5,7 * CNT 17 HDP CHAINS / 17 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A2: 4,5 => SOL * STA A2: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED