Analysis of xx-top500-096-base.sdk
Contents
Original Sudoku
level: medium
position: 75.....2...86..........1....4..2........5.9........8.66.98............5.3........ initial
Autosolve
position: 75.....2...86.2.9....5.1....4..2........5.9.25.....8.66.98.5..........5.3.5...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A8: 1,4 => CTR => A8: 2,8 * DIS # B5: 1,3 => CTR => B5: 6,7,8 * DIS # B6: 1,3 => CTR => B6: 2,7,9 * DIS # B5: 1,8 => CTR => B5: 3,6,7 * DIS # A8: 1,8 => CTR => A8: 2,4 * DIS # B5: 1,3,7 => CTR => B5: 6,8 * CNT 6 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A8: 1,4 => CTR => A8: 2,8 * DIS A8: 2,8 # B3: 6 => CTR => B3: 2,9 * DIS A8: 2,8 + B3: 2,9 # I3: 3,4 => CTR => I3: 7 * PRF A8: 2,8 + B3: 2,9 + I3: 7 # E6: 3,4 => SOL * STA A8: 2,8 + B3: 2,9 + I3: 7 + E6: 3,4 * CNT 4 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 75.....2...86..........1....4..2........5.9........8.66.98............5.3........ | initial |
| 75.....2...86.2.9....5.1....4..2........5.9.25.....8.66.98.5..........5.3.5...... | autosolve |
| 751489623438672591926531487847926315163758942592143876679815234284367159315294768 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A2: 1,4 B2: 1,3 H3: 6,8 A5: 1,8 F4: 6,8 F5: 6,8 H9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B6,C6: 2.. / B6 = 2 => 0 pairs (X) / C6 = 2 => 11 pairs (_) D8,D9: 2.. / D8 = 2 => 0 pairs (X) / D9 = 2 => 7 pairs (_) B7,G7: 2.. / B7 = 2 => 0 pairs (X) / G7 = 2 => 8 pairs (_) A3,A8: 2.. / A3 = 2 => 0 pairs (X) / A8 = 2 => 11 pairs (_) H5,H6: 4.. / H5 = 4 => 7 pairs (_) / H6 = 4 => 8 pairs (_) A8,C8: 4.. / A8 = 4 => 0 pairs (X) / C8 = 4 => 7 pairs (_) D5,H5: 4.. / D5 = 4 => 8 pairs (_) / H5 = 4 => 7 pairs (_) G2,I2: 5.. / G2 = 5 => 7 pairs (_) / I2 = 5 => 7 pairs (_) G4,I4: 5.. / G4 = 5 => 7 pairs (_) / I4 = 5 => 7 pairs (_) G2,G4: 5.. / G2 = 5 => 7 pairs (_) / G4 = 5 => 7 pairs (_) I2,I4: 5.. / I2 = 5 => 7 pairs (_) / I4 = 5 => 7 pairs (_) F4,F5: 6.. / F4 = 6 => 11 pairs (_) / F5 = 6 => 0 pairs (X) E8,E9: 6.. / E8 = 6 => 7 pairs (_) / E9 = 6 => 0 pairs (X) C1,G1: 6.. / C1 = 6 => 0 pairs (X) / G1 = 6 => 9 pairs (_) C4,F4: 6.. / C4 = 6 => 0 pairs (X) / F4 = 6 => 11 pairs (_) E8,G8: 6.. / E8 = 6 => 7 pairs (_) / G8 = 6 => 0 pairs (X) B3,B5: 6.. / B3 = 6 => 0 pairs (X) / B5 = 6 => 11 pairs (_) H3,H9: 6.. / H3 = 6 => 0 pairs (X) / H9 = 6 => 7 pairs (_) E2,E3: 7.. / E2 = 7 => 7 pairs (_) / E3 = 7 => 10 pairs (_) E1,E3: 8.. / E1 = 8 => 7 pairs (_) / E3 = 8 => 0 pairs (X) F4,F5: 8.. / F4 = 8 => 0 pairs (X) / F5 = 8 => 11 pairs (_) E1,I1: 8.. / E1 = 8 => 7 pairs (_) / I1 = 8 => 0 pairs (X) A4,F4: 8.. / A4 = 8 => 11 pairs (_) / F4 = 8 => 0 pairs (X) H3,H9: 8.. / H3 = 8 => 7 pairs (_) / H9 = 8 => 0 pairs (X) A3,B3: 9.. / A3 = 9 => 11 pairs (_) / B3 = 9 => 0 pairs (X) A4,B6: 9.. / A4 = 9 => 0 pairs (X) / B6 = 9 => 11 pairs (_) I8,I9: 9.. / I8 = 9 => 8 pairs (_) / I9 = 9 => 8 pairs (_) A4,D4: 9.. / A4 = 9 => 0 pairs (X) / D4 = 9 => 11 pairs (_) A3,A4: 9.. / A3 = 9 => 11 pairs (_) / A4 = 9 => 0 pairs (X) B3,B6: 9.. / B3 = 9 => 0 pairs (X) / B6 = 9 => 11 pairs (_) * DURATION: 0:00:47.039691 START: 06:03:26.238133 END: 06:04:13.277824 2017-05-04 * CP COUNT: (30) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B2,F4,F5,H3,H9) * 75.....2...86.2.9....5.1....4..2........5.9.25.....8.66.98.5..........5.3.5...... * PAIR A2: 1,4 BLK 1 C1: 1,4,3,6 # reduction candidate for 1,4 C1: 1,4 # 10 pairs C1: 3,6 # 8 pairs * PAIR A2: 1,4 ROW 2 G2: 1,4,3,5,7 # reduction candidate for 1,4 G2: 1,4 # 7 pairs I2: 1,4,3,5,7 # reduction candidate for 1,4 I2: 1,4 # 7 pairs * PAIR A2: 1,4 COL A A8: 1,4,2,8 # reduction candidate for 1,4 A8: 1,4 => CTR * 75.....2...86.2.9.29.5.1...94..28...86..5.9.25.....8.66.98.5..........5.3.5...... A8: 2,8 # 15 pairs * PAIR B2: 1,3 BLK 1 C1: 1,3,4,6 # reduction candidate for 1,3 C1: 1,3 # 10 pairs C1: 4,6 # 8 pairs * PAIR B2: 1,3 ROW 2 G2: 1,3,4,5,7 # reduction candidate for 1,3 G2: 1,3 # 8 pairs I2: 1,3,4,5,7 # reduction candidate for 1,3 I2: 1,3 # 8 pairs * PAIR B2: 1,3 COL B B5: 1,3,6,7,8 # reduction candidate for 1,3 B5: 1,3 => CTR * 75.....2...86.2.9..6.5.1.8..4..2........5.9.2592...8.66.98.5..........5.3.5....6. B5: 6,7,8 # 7 pairs B6: 1,3,2,7,9 # reduction candidate for 1,3 B6: 1,3 => CTR * 75.....2...86.2.9..9.5.1...94..28....6..5.9.25.....8.66.98.5..........5.3.5...... B6: 2,7,9 # 7 pairs * PAIR A5: 1,8 BLK 4 A4: 1,8,9 # reduction candidate for 1,8 A4: 1,8 # 11 pairs B5: 1,8,3,6,7 # reduction candidate for 1,8 B5: 1,8 => CTR * 75.....2...86.2.9..6.5.1.8..4..2........5.9.2592...8.66.98.5..........5.3.5....6. B5: 3,6,7 # 7 pairs * PAIR A5: 1,8 COL A A8: 1,8,2,4 # reduction candidate for 1,8 A8: 1,8 => CTR * 75.....2...86.2.9.29.5.1...94..28....6..5.9.25.....8.66.98.5..........5.3.5...... A8: 2,4 # 8 pairs * PAIR F5: 6,8 ROW 5 B5: 6,8,1,3,7 # reduction candidate for 6,8 B5: 1,3,7 => CTR * 75.....2...86.2.9..6.5.1.8..4..2........5.9.2592...8.66.98.5..........5.3.5....6. B5: 6,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-096-base-pr-000.dot * REASONING * DIS # A8: 1,4 => CTR => A8: 2,8 * DIS # B5: 1,3 => CTR => B5: 6,7,8 * DIS # B6: 1,3 => CTR => B6: 2,7,9 * DIS # B5: 1,8 => CTR => B5: 3,6,7 * DIS # A8: 1,8 => CTR => A8: 2,4 * DIS # B5: 1,3,7 => CTR => B5: 6,8 * CNT 6 HDP CHAINS / 21 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B2,F4,F5,H3,H9) * 75.....2...86.2.9....5.1....4..2........5.9.25.....8.66.98.5..........5.3.5...... * PAIR A2: 1,4 BLK 1 C1: 1,4,3,6 # reduction candidate for 1,4 C1: 1,4 # 10 pairs C1: 3,6 # 8 pairs * PAIR A2: 1,4 ROW 2 G2: 1,4,3,5,7 # reduction candidate for 1,4 G2: 1,4 # 7 pairs I2: 1,4,3,5,7 # reduction candidate for 1,4 I2: 1,4 # 7 pairs * PAIR A2: 1,4 COL A A8: 1,4,2,8 # reduction candidate for 1,4 A8: 1,4 => CTR * 75.....2...86.2.9.29.5.1...94..28...86..5.9.25.....8.66.98.5..........5.3.5...... * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A3,A4,A8,B5,B6,C3,C5,E3,F4,F5,G2,I1,I2,I8,I9) * 751.8.62.438672.9....5.1.8..4..2....1...5.9.25.....8.66.98.5.....4.6..5.3.5....6. * PAIR A3: 2,9 BLK 1 B3: 2,9,6 # reduction candidate for 2,9 B3: 6 => CTR * 751.8.62.438672.9.9625.1.8.84..2....1...5.9.25.....8.66.98.5.....4.6..5.3.5....6. * PAIR E3: 3,4 ROW 3 G3: 3,4,7 # reduction candidate for 3,4 G3: 3,4 # 12 pairs I3: 3,4,7 # reduction candidate for 3,4 I3: 3,4 => CTR * 751.8962.438672.9.9265.178.84.926...16..589.2592..48.66.98452..28416..593.529.468 * RESTART * PAIR E3: 3,4 COL E E6: 3,4,1 # reduction candidate for 3,4 E6: 3,4 => SOLVED * 751489623438672591926531487847926315163758942592143876679815234284367159315294768 * DURATION: 0:00:13.887004 START: 06:04:30.645313 END: 06:04:44.532317 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-096-base-pr-001.dot * REASONING * DIS # A8: 1,4 => CTR => A8: 2,8 * DIS A8: 2,8 # B3: 6 => CTR => B3: 2,9 * DIS A8: 2,8 + B3: 2,9 # I3: 3,4 => CTR => I3: 7 * PRF A8: 2,8 + B3: 2,9 + I3: 7 # E6: 3,4 => SOL * STA A8: 2,8 + B3: 2,9 + I3: 7 + E6: 3,4 * CNT 4 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 096 solution: 751489623438672591926531487847926315163758942592143876679815234284367159315294768 info: 1573 FNBHXY S8.f 39272 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 751489623438672591926531487847926315163758942592143876679815234284367159315294768 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 # C1: 1,4 => UNS * INC # C1: 3,6 => UNS * INC # G2: 1,4 => UNS * INC # I2: 1,4 => UNS * DIS # A8: 1,4 => CTR => A8: 2,8 * INC # A8: 2,8 => UNS * INC # C1: 1,3 => UNS * INC # C1: 4,6 => UNS * INC # G2: 1,3 => UNS * INC # I2: 1,3 => UNS * DIS # B5: 1,3 => CTR => B5: 6,7,8 * INC # B5: 6,7,8 => UNS * DIS # B6: 1,3 => CTR => B6: 2,7,9 * INC # B6: 2,7,9 => UNS * INC # A4: 1,8 => UNS * DIS # B5: 1,8 => CTR => B5: 3,6,7 * INC # B5: 3,6,7 => UNS * DIS # A8: 1,8 => CTR => A8: 2,4 * INC # A8: 2,4 => UNS * INC # B5: 6,8 => UNS * DIS # B5: 1,3,7 => CTR => B5: 6,8 * CNT 21 HDP CHAINS / 21 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 1,4 => UNS * INC # C1: 3,6 => UNS * INC # G2: 1,4 => UNS * INC # I2: 1,4 => UNS * DIS # A8: 1,4 => CTR => A8: 2,8 * INC A8: 2,8 # B3: 2,9 => UNS * DIS A8: 2,8 # B3: 6 => CTR => B3: 2,9 * INC A8: 2,8 + B3: 2,9 # G3: 3,4 => UNS * DIS A8: 2,8 + B3: 2,9 # I3: 3,4 => CTR => I3: 7 * PRF A8: 2,8 + B3: 2,9 + I3: 7 # E6: 3,4 => SOL * STA A8: 2,8 + B3: 2,9 + I3: 7 + E6: 3,4 * CNT 10 HDP CHAINS / 10 HYP OPENED