Analysis of xx-top500-348-base.sdk
Contents
Original Sudoku
level: medium
position: 4.....7..3..2.........1.....1..4..5...6..32..............6....1.4.....8.2....7... initial
Autosolve
position: 4.1...7..3..27.14.6..41.....1..4..5...6..3214..4..1......6.4..114....68.26.1.74.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 5,9 => CTR => E1: 3,6 * DIS # E9: 3,9 => CTR => E9: 5,8 * DIS # H6: 3,9 => CTR => H6: 6,7 * CNT 3 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:
* DIS # E1: 5,9 => CTR => E1: 3,6 * DIS E1: 3,6 # E9: 3,9 => CTR => E9: 5,8 * DIS E1: 3,6 + E9: 5,8 # H6: 3,9 => CTR => H6: 6,7 * DIS E1: 3,6 + E9: 5,8 + H6: 6,7 # H3: 2 => CTR => H3: 3,9 * DIS E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # I6: 6,7 => CTR => I6: 3,8,9 * DIS E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 # E7: 5,8 => CTR => E7: 2,3,9 * PRF E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 + E7: 2,3,9 # I1: 2,6 => SOL * STA E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 + E7: 2,3,9 + I1: 2,6 * CNT 7 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.....7..3..2.........1.....1..4..5...6..32..............6....1.4.....8.2....7... | initial |
| 4.1...7..3..27.14.6..41.....1..4..5...6..3214..4..1......6.4..114....68.26.1.74.. | autosolve |
| 491538762358276149672419835713842956986753214524961378837694521149325687265187493 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C4: 2,3 B6: 2,3 F4: 2,6 E5: 5,9 E6: 2,6 H7: 2,7 I8: 2,7 H9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C4,B6: 2.. / C4 = 2 => 0 pairs (X) / B6 = 2 => 8 pairs (_) F4,E6: 2.. / F4 = 2 => 8 pairs (_) / E6 = 2 => 0 pairs (X) H7,I8: 2.. / H7 = 2 => 8 pairs (_) / I8 = 2 => 0 pairs (X) C4,F4: 2.. / C4 = 2 => 0 pairs (X) / F4 = 2 => 8 pairs (_) B6,E6: 2.. / B6 = 2 => 8 pairs (_) / E6 = 2 => 0 pairs (X) E7,H7: 2.. / E7 = 2 => 0 pairs (X) / H7 = 2 => 8 pairs (_) C3,C4: 2.. / C3 = 2 => 8 pairs (_) / C4 = 2 => 0 pairs (X) F4,F8: 2.. / F4 = 2 => 8 pairs (_) / F8 = 2 => 0 pairs (X) D1,E1: 3.. / D1 = 3 => 9 pairs (_) / E1 = 3 => 8 pairs (_) C4,B6: 3.. / C4 = 3 => 8 pairs (_) / B6 = 3 => 0 pairs (X) B6,B7: 3.. / B6 = 3 => 0 pairs (X) / B7 = 3 => 8 pairs (_) D1,D8: 3.. / D1 = 3 => 9 pairs (_) / D8 = 3 => 8 pairs (_) G7,I9: 5.. / G7 = 5 => 12 pairs (_) / I9 = 5 => 10 pairs (_) A6,D6: 5.. / A6 = 5 => 8 pairs (_) / D6 = 5 => 11 pairs (_) G3,G7: 5.. / G3 = 5 => 10 pairs (_) / G7 = 5 => 12 pairs (_) F4,E6: 6.. / F4 = 6 => 0 pairs (X) / E6 = 6 => 8 pairs (_) F2,I2: 6.. / F2 = 6 => 8 pairs (_) / I2 = 6 => 0 pairs (X) F4,I4: 6.. / F4 = 6 => 0 pairs (X) / I4 = 6 => 8 pairs (_) E1,E6: 6.. / E1 = 6 => 0 pairs (X) / E6 = 6 => 8 pairs (_) H1,H6: 6.. / H1 = 6 => 8 pairs (_) / H6 = 6 => 0 pairs (X) B3,C3: 7.. / B3 = 7 => 8 pairs (_) / C3 = 7 => 0 pairs (X) H7,I8: 7.. / H7 = 7 => 0 pairs (X) / I8 = 7 => 8 pairs (_) C8,I8: 7.. / C8 = 7 => 0 pairs (X) / I8 = 7 => 8 pairs (_) H6,H7: 7.. / H6 = 7 => 8 pairs (_) / H7 = 7 => 0 pairs (X) E7,E9: 8.. / E7 = 8 => 14 pairs (_) / E9 = 8 => 8 pairs (_) C9,E9: 8.. / C9 = 8 => 14 pairs (_) / E9 = 8 => 8 pairs (_) * DURATION: 0:00:47.548912 START: 14:37:39.655859 END: 14:38:27.204771 2017-05-04 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C4,E5,E6,F4,H7,H9,I8) * 4.1...7..3..27.14.6..41.....1..4..5...6..3214..4..1......6.4..114....68.26.1.74.. * PAIR E5: 5,9 BLK 5 D5: 5,9,7,8 # reduction candidate for 5,9 D5: 5,9 # 15 pairs D6: 5,9,7,8 # reduction candidate for 5,9 D6: 5,9 # 11 pairs * PAIR E5: 5,9 ROW 5 A5: 5,9,7,8 # reduction candidate for 5,9 A5: 5,9 # 12 pairs B5: 5,9,7,8 # reduction candidate for 5,9 B5: 5,9 # 12 pairs * PAIR E5: 5,9 COL E E1: 5,9,3,6 # reduction candidate for 5,9 E1: 5,9 => CTR * 4.13..76.3..27614.6..41.....1..42.56..6..3214.24.61....3.6.4..114..3.68226.1.74.. E1: 3,6 # 9 pairs E7: 5,9,2,3,8 # reduction candidate for 5,9 E7: 5,9 # 16 pairs E8: 5,9,2,3 # reduction candidate for 5,9 E8: 5,9 # 12 pairs E9: 5,9,3,8 # reduction candidate for 5,9 E9: 5,9 # 14 pairs * PAIR H9: 3,9 BLK 9 G7: 3,9,5 # reduction candidate for 3,9 G7: 3,9 # 10 pairs I9: 3,9,5 # reduction candidate for 3,9 I9: 3,9 # 12 pairs * PAIR H9: 3,9 ROW 9 C9: 3,9,5,8 # reduction candidate for 3,9 C9: 3,9 # 11 pairs E9: 3,9,5,8 # reduction candidate for 3,9 E9: 3,9 => CTR * 4.1.3.7623.527614.6.241.593.13.42856.56..3214.24.61.7..3.684921149.25687268197435 E9: 5,8 # 9 pairs * PAIR H9: 3,9 COL H H3: 3,9,2 # reduction candidate for 3,9 H3: 3,9 # 11 pairs H6: 3,9,6,7 # reduction candidate for 3,9 H6: 3,9 => CTR * 4.1...76.3..27614.6..41.....1..42.56..6..3214.24.61..7.3.6.4.71147...68226.1.74.. H6: 6,7 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-348-base-pr-000.dot * REASONING * DIS # E1: 5,9 => CTR => E1: 3,6 * DIS # E9: 3,9 => CTR => E9: 5,8 * DIS # H6: 3,9 => CTR => H6: 6,7 * CNT 3 HDP CHAINS / 17 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,C4,E5,E6,F4,H7,H9,I8) * 4.1...7..3..27.14.6..41.....1..4..5...6..3214..4..1......6.4..114....68.26.1.74.. * PAIR E5: 5,9 BLK 5 D5: 5,9,7,8 # reduction candidate for 5,9 D5: 5,9 # 15 pairs D6: 5,9,7,8 # reduction candidate for 5,9 D6: 5,9 # 11 pairs * PAIR E5: 5,9 ROW 5 A5: 5,9,7,8 # reduction candidate for 5,9 A5: 5,9 # 12 pairs B5: 5,9,7,8 # reduction candidate for 5,9 B5: 5,9 # 12 pairs * PAIR E5: 5,9 COL E E1: 5,9,3,6 # reduction candidate for 5,9 E1: 5,9 => CTR * 4.13..76.3..27614.6..41.....1..42.56..6..3214.24.61....3.6.4..114..3.68226.1.74.. E7: 5,9,2,3,8 # reduction candidate for 5,9 E7: 5,9 # 16 pairs E8: 5,9,2,3 # reduction candidate for 5,9 E8: 5,9 # 12 pairs E9: 5,9,3,8 # reduction candidate for 5,9 E9: 5,9 # 14 pairs * PAIR RESTART * PAIR E5: 5,9 BLK 5 D5: 5,9,7,8 # reduction candidate for 5,9 D5: 5,9 # 16 pairs D6: 5,9,7,8 # reduction candidate for 5,9 D6: 5,9 # 12 pairs * PAIR E5: 5,9 ROW 5 A5: 5,9,7,8 # reduction candidate for 5,9 A5: 5,9 # 13 pairs B5: 5,9,7,8 # reduction candidate for 5,9 B5: 5,9 # 13 pairs * PAIR E5: 5,9 COL E E7: 5,9,2,3,8 # reduction candidate for 5,9 E7: 5,9 # 16 pairs E8: 5,9,2,3 # reduction candidate for 5,9 E8: 5,9 # 12 pairs E9: 5,9,3,8 # reduction candidate for 5,9 E9: 5,9 # 14 pairs * PAIR H9: 3,9 BLK 9 G7: 3,9,5 # reduction candidate for 3,9 G7: 3,9 # 11 pairs I9: 3,9,5 # reduction candidate for 3,9 I9: 3,9 # 13 pairs * PAIR H9: 3,9 ROW 9 C9: 3,9,5,8 # reduction candidate for 3,9 C9: 3,9 # 12 pairs E9: 3,9,5,8 # reduction candidate for 3,9 E9: 3,9 => CTR * 4.153.7623.527614.6.241.593.13.42856.56..3214.24.61.7..3.684921149.25687268197435 * RESTART * PAIR H9: 3,9 ROW 9 C9: 3,9,5,8 # reduction candidate for 3,9 C9: 5,8 # 13 pairs C9: 3,9 # 12 pairs * PAIR H9: 3,9 COL H H3: 3,9,2 # reduction candidate for 3,9 H3: 3,9 # 13 pairs H6: 3,9,6,7 # reduction candidate for 3,9 H6: 3,9 => CTR * 4.1...76.3..27614.6..41.....1..42.56..6..3214.24.61..7.3.6.4.71147...68226.1.74.. * RESTART * PAIR H9: 3,9 COL H H3: 3,9,2 # reduction candidate for 3,9 H3: 2 => CTR * 4.1...7..3..27.14.6..41..2..12.46.5...6..3214.34.21......6.4.71147..268.26.1.74.. * PAIR RESTART * PAIR H9: 3,9 BLK 9 G7: 3,9,5 # reduction candidate for 3,9 G7: 3,9 # 15 pairs I9: 3,9,5 # reduction candidate for 3,9 I9: 3,9 # 16 pairs * PAIR H9: 3,9 ROW 9 C9: 3,9,5,8 # reduction candidate for 3,9 C9: 5,8 # 16 pairs C9: 3,9 # 15 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B6,C4,E1,E5,E6,E9,F4,H1,H3,H6,H7,H9,I8) * 4.1...7..3..27.14.6..41.....1..4..5...6..3214..4..1......6.4..114....68.26.1.74.. * PAIR H1: 2,6 BLK 3 I1: 2,6,5,8,9 # reduction candidate for 2,6 I1: 5,8,9 # 13 pairs I1: 2,6 # 9 pairs * PAIR H3: 3,9 BLK 3 G3: 3,9,5,8 # reduction candidate for 3,9 G3: 3,9 # 18 pairs I3: 3,9,2,5,8 # reduction candidate for 3,9 I3: 3,9 # 18 pairs * PAIR E5: 5,9 BLK 5 D5: 5,9,7,8 # reduction candidate for 5,9 D5: 5,9 # 20 pairs D6: 5,9,7,8 # reduction candidate for 5,9 D6: 5,9 # 16 pairs * PAIR E5: 5,9 ROW 5 A5: 5,9,7,8 # reduction candidate for 5,9 A5: 5,9 # 17 pairs B5: 5,9,7,8 # reduction candidate for 5,9 B5: 5,9 # 17 pairs * PAIR E5: 5,9 COL E E7: 5,9,2,3,8 # reduction candidate for 5,9 E7: 5,9 # 16 pairs E8: 5,9,2,3 # reduction candidate for 5,9 E8: 5,9 # 15 pairs * PAIR H6: 6,7 BLK 6 I4: 6,7,3,8,9 # reduction candidate for 6,7 I4: 6,7 # 14 pairs I6: 6,7,3,8,9 # reduction candidate for 6,7 I6: 6,7 => CTR * 4.1.6.72.3..27.1466..41.....1..46.5...6..3214.34.21.67...6.4.71147..268.26.1.74.. * RESTART * PAIR E9: 5,8 BLK 8 E7: 5,8,2,3,9 # reduction candidate for 5,8 E7: 5,8 => CTR * 4.193.762398276145672415....13.42.56.86.93214.24.61.7.837654.2114532968726.1.74.. * PAIR H9: 3,9 BLK 9 G7: 3,9,5 # reduction candidate for 3,9 G7: 3,9 # 17 pairs I9: 3,9,5 # reduction candidate for 3,9 I9: 3,9 # 15 pairs * PAIR H9: 3,9 ROW 9 C9: 3,9,5 # reduction candidate for 3,9 C9: 3,9 # 17 pairs C9: 5 # 15 pairs * LEVEL 0 PASS 1 ROUND 3 (AUTO SOLVE) (B6,C4,E1,E5,E6,F4,H1,H3,H6,H7,H9,I4,I8) * 4.1...7..3..27.14.6..41.....1..4..5...6..3214..4..1......6.4..114....68.26.1874.. * PAIR H1: 2,6 BLK 3 I1: 2,6,5,8,9 # reduction candidate for 2,6 I1: 2,6 => SOLVED * 491538762358276149672419835713842956986753214524961378837694521149325687265187493 * DURATION: 0:00:49.559741 START: 14:38:43.867026 END: 14:39:33.426767 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-348-base-pr-001.dot * REASONING * DIS # E1: 5,9 => CTR => E1: 3,6 * DIS E1: 3,6 # E9: 3,9 => CTR => E9: 5,8 * DIS E1: 3,6 + E9: 5,8 # H6: 3,9 => CTR => H6: 6,7 * DIS E1: 3,6 + E9: 5,8 + H6: 6,7 # H3: 2 => CTR => H3: 3,9 * DIS E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # I6: 6,7 => CTR => I6: 3,8,9 * DIS E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 # E7: 5,8 => CTR => E7: 2,3,9 * PRF E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 + E7: 2,3,9 # I1: 2,6 => SOL * STA E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 + E7: 2,3,9 + I1: 2,6 * CNT 7 HDP CHAINS / 47 HYP OPENED
Header Info
Top 500 Minimum 17 348 solution: 491538762358276149672419835713842956986753214524961378837694521149325687265187493 info: 4834 FNBTHWXY S8.f 45069 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 491538762358276149672419835713842956986753214524961378837694521149325687265187493 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 # D5: 5,9 => UNS * INC # D6: 5,9 => UNS * INC # A5: 5,9 => UNS * INC # B5: 5,9 => UNS * DIS # E1: 5,9 => CTR => E1: 3,6 * INC # E1: 3,6 => UNS * INC # E7: 5,9 => UNS * INC # E8: 5,9 => UNS * INC # E9: 5,9 => UNS * INC # G7: 3,9 => UNS * INC # I9: 3,9 => UNS * INC # C9: 3,9 => UNS * DIS # E9: 3,9 => CTR => E9: 5,8 * INC # E9: 5,8 => UNS * INC # H3: 3,9 => UNS * DIS # H6: 3,9 => CTR => H6: 6,7 * INC # H6: 6,7 => UNS * CNT 17 HDP CHAINS / 17 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D5: 5,9 => UNS * INC # D6: 5,9 => UNS * INC # A5: 5,9 => UNS * INC # B5: 5,9 => UNS * DIS # E1: 5,9 => CTR => E1: 3,6 * INC E1: 3,6 # E7: 5,9 => UNS * INC E1: 3,6 # E8: 5,9 => UNS * INC E1: 3,6 # E9: 5,9 => UNS * INC E1: 3,6 # D5: 5,9 => UNS * INC E1: 3,6 # D6: 5,9 => UNS * INC E1: 3,6 # A5: 5,9 => UNS * INC E1: 3,6 # B5: 5,9 => UNS * INC E1: 3,6 # E7: 5,9 => UNS * INC E1: 3,6 # E8: 5,9 => UNS * INC E1: 3,6 # E9: 5,9 => UNS * INC E1: 3,6 # G7: 3,9 => UNS * INC E1: 3,6 # I9: 3,9 => UNS * INC E1: 3,6 # C9: 3,9 => UNS * DIS E1: 3,6 # E9: 3,9 => CTR => E9: 5,8 * INC E1: 3,6 + E9: 5,8 # C9: 3,9 => UNS * INC E1: 3,6 + E9: 5,8 # C9: 5,8 => UNS * INC E1: 3,6 + E9: 5,8 # H3: 3,9 => UNS * DIS E1: 3,6 + E9: 5,8 # H6: 3,9 => CTR => H6: 6,7 * INC E1: 3,6 + E9: 5,8 + H6: 6,7 # H3: 3,9 => UNS * DIS E1: 3,6 + E9: 5,8 + H6: 6,7 # H3: 2 => CTR => H3: 3,9 * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # G7: 3,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # I9: 3,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # C9: 3,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # C9: 5,8 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # I1: 2,6 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # I1: 5,8,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # G3: 3,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # I3: 3,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # D5: 5,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # D6: 5,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # A5: 5,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # B5: 5,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # E7: 5,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # E8: 5,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # I4: 6,7 => UNS * DIS E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 # I6: 6,7 => CTR => I6: 3,8,9 * DIS E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 # E7: 5,8 => CTR => E7: 2,3,9 * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 + E7: 2,3,9 # G7: 3,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 + E7: 2,3,9 # I9: 3,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 + E7: 2,3,9 # C9: 3,9 => UNS * INC E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 + E7: 2,3,9 # C9: 5 => UNS * PRF E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 + E7: 2,3,9 # I1: 2,6 => SOL * STA E1: 3,6 + E9: 5,8 + H6: 6,7 + H3: 3,9 + I6: 3,8,9 + E7: 2,3,9 + I1: 2,6 * CNT 47 HDP CHAINS / 47 HYP OPENED