Analysis of xx-top500-216-base.sdk
Contents
Original Sudoku
level: medium
position: ....6..8..2.........1.......7....1.25...3..........4....42.1...3..7..6.........5. initial
Autosolve
position: ....6..8..2.........1.......7....1.25...3..........4.5..42.1...3..7..6.........5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 1,7 => CTR => I2: 3,4,6,9 * DIS # E6: 2 => CTR => E6: 1,7 * DIS # F1: 2,7 => CTR => F1: 3,4,5,9 * DIS # F3: 2,7 => CTR => F3: 3,4,5,8,9 * DIS # G3: 2,7 => CTR => G3: 3,5,9 * DIS # E6: 2,7 => CTR => E6: 1 * DIS # I1: 1,4 => CTR => I1: 3,7,9 * DIS # I2: 1,4 => CTR => I2: 3,6,7,9 * DIS # D2: 1,4 => CTR => D2: 3,5,8,9 * DIS # H8: 1,4 => CTR => H8: 2 * DIS # F3: 2,4 => CTR => F3: 3,5,7,8,9 * DIS # H8: 1 => CTR => H8: 2,4 * DIS # E6: 7 => CTR => E6: 1,2 * DIS # I9: 7,9 => CTR => I9: 1,4,8 * CNT 14 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I2: 1,7 => CTR => I2: 3,4,6,9 * DIS I2: 3,4,6,9 # E6: 2 => CTR => E6: 1,7 * PRF I2: 3,4,6,9 + E6: 1,7 # D3: 3,9 => SOL * STA I2: 3,4,6,9 + E6: 1,7 + D3: 3,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....6..8..2.........1.......7....1.25...3..........4....42.1...3..7..6.........5. | initial |
| ....6..8..2.........1.......7....1.25...3..........4.5..42.1...3..7..6.........5. | autosolve |
| 947165283823974516651328947478596132516432879239817465764251398385749621192683754 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) E2: 1,7 E3: 2,7 H2: 1,4 H3: 2,4 A6: 1,2 A9: 1,2 D9: 3,6 F9: 3,6 H7: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,I1: 1.. / D1 = 1 => 13 pairs (_) / I1 = 1 => 0 pairs (X) B5,D5: 1.. / B5 = 1 => 13 pairs (_) / D5 = 1 => 0 pairs (X) A6,A9: 1.. / A6 = 1 => 0 pairs (X) / A9 = 1 => 13 pairs (_) E2,E6: 1.. / E2 = 1 => 0 pairs (X) / E6 = 1 => 13 pairs (_) H2,H8: 1.. / H2 = 1 => 13 pairs (_) / H8 = 1 => 0 pairs (X) H8,G9: 2.. / H8 = 2 => 13 pairs (_) / G9 = 2 => 0 pairs (X) F1,G1: 2.. / F1 = 2 => 0 pairs (X) / G1 = 2 => 13 pairs (_) C5,F5: 2.. / C5 = 2 => 0 pairs (X) / F5 = 2 => 13 pairs (_) C8,H8: 2.. / C8 = 2 => 0 pairs (X) / H8 = 2 => 13 pairs (_) A6,A9: 2.. / A6 = 2 => 13 pairs (_) / A9 = 2 => 0 pairs (X) E3,E6: 2.. / E3 = 2 => 13 pairs (_) / E6 = 2 => 0 pairs (X) H3,H8: 2.. / H3 = 2 => 0 pairs (X) / H8 = 2 => 13 pairs (_) H4,H6: 3.. / H4 = 3 => 9 pairs (_) / H6 = 3 => 10 pairs (_) D9,F9: 3.. / D9 = 3 => 7 pairs (_) / F9 = 3 => 7 pairs (_) G7,I7: 3.. / G7 = 3 => 9 pairs (_) / I7 = 3 => 9 pairs (_) C4,H4: 3.. / C4 = 3 => 10 pairs (_) / H4 = 3 => 9 pairs (_) A4,B5: 4.. / A4 = 4 => 10 pairs (_) / B5 = 4 => 0 pairs (X) E9,I9: 4.. / E9 = 4 => 9 pairs (_) / I9 = 4 => 11 pairs (_) B7,E7: 5.. / B7 = 5 => 10 pairs (_) / E7 = 5 => 9 pairs (_) I2,I3: 6.. / I2 = 6 => 9 pairs (_) / I3 = 6 => 9 pairs (_) A7,B7: 6.. / A7 = 6 => 9 pairs (_) / B7 = 6 => 9 pairs (_) D9,F9: 6.. / D9 = 6 => 7 pairs (_) / F9 = 6 => 7 pairs (_) A7,C9: 7.. / A7 = 7 => 19 pairs (_) / C9 = 7 => 9 pairs (_) G5,I5: 8.. / G5 = 8 => 10 pairs (_) / I5 = 8 => 10 pairs (_) * DURATION: 0:00:39.411123 START: 10:11:41.628387 END: 10:12:21.039510 2017-05-04 * CP COUNT: (24) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,D9,E2,E3,F9,H2,H3,H7) * ....6..8..2.........1.......7....1.25...3..........4.5..42.1...3..7..6.........5. * PAIR E2: 1,7 ROW 2 I2: 1,7,3,4,6,9 # reduction candidate for 1,7 I2: 1,7 => CTR * ....6..8..2.....4...1....26.7....1.25...3........2.4.5..42.1...3.27..61.1......5. I2: 3,4,6,9 # 9 pairs * PAIR E2: 1,7 COL E E6: 1,7,2 # reduction candidate for 1,7 E6: 2 => CTR * ....6..8..2..1..4...1.7..2..7....1.25...3........2.4.5..42.1...3.27..61.1......5. E6: 1,7 # 13 pairs * PAIR E3: 2,7 BLK 2 F1: 2,7,3,4,5,9 # reduction candidate for 2,7 F1: 2,7 => CTR * ....6..8..2..1..4...1....2..7....1.25...3........2.4.5..42.1...3.27..61.1......5. F1: 3,4,5,9 # 13 pairs F3: 2,7,3,4,5,8,9 # reduction candidate for 2,7 F3: 2,7 => CTR * ....6.28..2..1..4...1.......7....1.25...3..........4.5..42.1...3..7..6.........5. F3: 3,4,5,8,9 # 9 pairs * PAIR E3: 2,7 ROW 3 G3: 2,7,3,5,9 # reduction candidate for 2,7 G3: 2,7 => CTR * ...16..8..2..7..1...1.2.74..7....1.251..32...2...174.5764251.9.3..7..6211.2...85. G3: 3,5,9 # 9 pairs * PAIR E3: 2,7 COL E E6: 2,7,1 # reduction candidate for 2,7 E6: 2,7 => CTR * ....6..8..2..1..4...1....2..7....1.25...3........2.4.5..42.1...3.27..61.1......5. E6: 1 # 13 pairs * PAIR H2: 1,4 BLK 3 I1: 1,4,3,7,9 # reduction candidate for 1,4 I1: 1,4 => CTR * ....6..8..2.........1....2..7....1.25...3........2.4.5..42.1...3.27..6..1......5. I1: 3,7,9 # 13 pairs I2: 1,4,3,6,7,9 # reduction candidate for 1,4 I2: 1,4 => CTR * ...16..8..2..7......1.2...6.7....1.25...3..........4.5..42.1...3..7..6.........5. I2: 3,6,7,9 # 9 pairs * PAIR H2: 1,4 ROW 2 D2: 1,4,3,5,8,9 # reduction candidate for 1,4 D2: 1,4 => CTR * ..7.6.28..2.47..1...1.2..4..7....1.251..3........1.4.5..42.1...3..7..62.1.2....5. D2: 3,5,8,9 # 9 pairs * PAIR H2: 1,4 COL H H8: 1,4,2 # reduction candidate for 1,4 H8: 1,4 => CTR * ....6..8..2.........1....2..7....1.25...3........2.4.5..42.1...3.27..6..1......5. H8: 2 # 13 pairs * PAIR H3: 2,4 ROW 3 F3: 2,4,3,5,7,8,9 # reduction candidate for 2,4 F3: 2,4 => CTR * ....6.28..2..1..4...1.7.....7....1.25...3........2.4.5..42.1...3..7..6..2......5. F3: 3,5,7,8,9 # 9 pairs * PAIR H3: 2,4 COL H H8: 2,4,1 # reduction candidate for 2,4 H8: 1 => CTR * ....6..8..2.........1....2..7....1.25...3........2.4.5..42.1...3.27..61.1......5. H8: 2,4 # 13 pairs * PAIR A6: 1,2 ROW 6 E6: 1,2,7 # reduction candidate for 1,2 E6: 7 => CTR * ....6..8..2..1..4...1.2.....7....1.25...3..........4.5..42.1...3..7..6.........5. E6: 1,2 # 10 pairs * PAIR H7: 7,9 BLK 9 G7: 7,9,3,8 # reduction candidate for 7,9 G7: 7,9 # 13 pairs I7: 7,9,3,8 # reduction candidate for 7,9 I7: 7,9 # 13 pairs G9: 7,9,2,8 # reduction candidate for 7,9 G9: 7,9 # 13 pairs I9: 7,9,1,4,8 # reduction candidate for 7,9 I9: 7,9 => CTR * ....6..8..2.........1....2..7....1.25...3........2.4.5..42.1...3.27..6..1...4..5. I9: 1,4,8 # 9 pairs * PAIR H7: 7,9 ROW 7 A7: 7,9,6,8 # reduction candidate for 7,9 A7: 7,9 # 12 pairs A7: 6,8 # 10 pairs * PAIR H7: 7,9 COL H H5: 7,9,6 # reduction candidate for 7,9 H5: 7,9 # 13 pairs H6: 7,9,3,6 # reduction candidate for 7,9 H6: 7,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-216-base-pr-000.dot * REASONING * DIS # I2: 1,7 => CTR => I2: 3,4,6,9 * DIS # E6: 2 => CTR => E6: 1,7 * DIS # F1: 2,7 => CTR => F1: 3,4,5,9 * DIS # F3: 2,7 => CTR => F3: 3,4,5,8,9 * DIS # G3: 2,7 => CTR => G3: 3,5,9 * DIS # E6: 2,7 => CTR => E6: 1 * DIS # I1: 1,4 => CTR => I1: 3,7,9 * DIS # I2: 1,4 => CTR => I2: 3,6,7,9 * DIS # D2: 1,4 => CTR => D2: 3,5,8,9 * DIS # H8: 1,4 => CTR => H8: 2 * DIS # F3: 2,4 => CTR => F3: 3,5,7,8,9 * DIS # H8: 1 => CTR => H8: 2,4 * DIS # E6: 7 => CTR => E6: 1,2 * DIS # I9: 7,9 => CTR => I9: 1,4,8 * CNT 14 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,D9,E2,E3,F9,H2,H3,H7) * ....6..8..2.........1.......7....1.25...3..........4.5..42.1...3..7..6.........5. * PAIR E2: 1,7 ROW 2 I2: 1,7,3,4,6,9 # reduction candidate for 1,7 I2: 1,7 => CTR * ....6..8..2.....4...1....26.7....1.25...3........2.4.5..42.1...3.27..61.1......5. * PAIR E2: 1,7 COL E E6: 1,7,2 # reduction candidate for 1,7 E6: 2 => CTR * ....6..8..2..1..4...1.7..2..7....1.25...3........2.4.5..42.1...3.27..61.1......5. * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B3,B9,C2,D2,D9,E4,E9,F8,F9,G2,G3,H4,H6) * 94716528382..74.166.1.2..4747.5..1.25164328792...174.57642513983..74.6211.2...754 * PAIR D2: 3,9 BLK 2 D3: 3,9,8 # reduction candidate for 3,9 D3: 3,9 => SOLVED * 947165283823974516651328947478596132516432879239817465764251398385749621192683754 * DURATION: 0:00:07.124058 START: 10:12:51.657089 END: 10:12:58.781147 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-216-base-pr-001.dot * REASONING * DIS # I2: 1,7 => CTR => I2: 3,4,6,9 * DIS I2: 3,4,6,9 # E6: 2 => CTR => E6: 1,7 * PRF I2: 3,4,6,9 + E6: 1,7 # D3: 3,9 => SOL * STA I2: 3,4,6,9 + E6: 1,7 + D3: 3,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 216 solution: 947165283823974516651328947478596132516432879239817465764251398385749621192683754 info: 1949 FNBHXY S8.f 5212 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 947165283823974516651328947478596132516432879239817465764251398385749621192683754 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 # I2: 1,7 => CTR => I2: 3,4,6,9 * INC # I2: 3,4,6,9 => UNS * INC # E6: 1,7 => UNS * DIS # E6: 2 => CTR => E6: 1,7 * DIS # F1: 2,7 => CTR => F1: 3,4,5,9 * INC # F1: 3,4,5,9 => UNS * DIS # F3: 2,7 => CTR => F3: 3,4,5,8,9 * INC # F3: 3,4,5,8,9 => UNS * DIS # G3: 2,7 => CTR => G3: 3,5,9 * INC # G3: 3,5,9 => UNS * DIS # E6: 2,7 => CTR => E6: 1 * INC # E6: 1 => UNS * DIS # I1: 1,4 => CTR => I1: 3,7,9 * INC # I1: 3,7,9 => UNS * DIS # I2: 1,4 => CTR => I2: 3,6,7,9 * INC # I2: 3,6,7,9 => UNS * DIS # D2: 1,4 => CTR => D2: 3,5,8,9 * INC # D2: 3,5,8,9 => UNS * DIS # H8: 1,4 => CTR => H8: 2 * INC # H8: 2 => UNS * DIS # F3: 2,4 => CTR => F3: 3,5,7,8,9 * INC # F3: 3,5,7,8,9 => UNS * INC # H8: 2,4 => UNS * DIS # H8: 1 => CTR => H8: 2,4 * INC # E6: 1,2 => UNS * DIS # E6: 7 => CTR => E6: 1,2 * INC # G7: 7,9 => UNS * INC # I7: 7,9 => UNS * INC # G9: 7,9 => UNS * DIS # I9: 7,9 => CTR => I9: 1,4,8 * INC # I9: 1,4,8 => UNS * INC # A7: 7,9 => UNS * INC # A7: 6,8 => UNS * INC # H5: 7,9 => UNS * INC # H6: 7,9 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I2: 1,7 => CTR => I2: 3,4,6,9 * INC I2: 3,4,6,9 # E6: 1,7 => UNS * DIS I2: 3,4,6,9 # E6: 2 => CTR => E6: 1,7 * PRF I2: 3,4,6,9 + E6: 1,7 # D3: 3,9 => SOL * STA I2: 3,4,6,9 + E6: 1,7 + D3: 3,9 * CNT 4 HDP CHAINS / 4 HYP OPENED