Analysis of xx-top500-327-base.sdk
Contents
Original Sudoku
level: medium
position: .......124...9...........5..7.2.....6.....4.....1.8....18..........3.7..5.2...... initial
Autosolve
position: .......124...9...........54.7.2.....6.....4.....1.8...718......9...3.7..532...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 3,8 => CTR => A3: 1,2 * DIS # D1: 3,8 => CTR => D1: 4,5,6,7 * DIS # G1: 3,8 => CTR => G1: 6,9 * PRF # A4: 3,8 => SOL * DIS # A4: 1 => CTR => A4: 3,8 * DIS # H6: 2,3 => CTR => H6: 6,7,9 * DIS # A3: 2,3 => CTR => A3: 1,8 * PRF # A3: 1,8 => SOL * DIS # I5: 5,7 => CTR => I5: 1,3,8,9 * DIS # E1: 5,7 => CTR => E1: 4,6,8 * DIS # I8: 5,8 => CTR => I8: 1 * PRF # I8: 1 => SOL * DIS # H5: 3,7,9 => CTR => H5: 2,8 * CNT 13 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 3,8 => CTR => A3: 1,2 * DIS A3: 1,2 # D1: 3,8 => CTR => D1: 4,5,6,7 * DIS A3: 1,2 + D1: 4,5,6,7 # G1: 3,8 => CTR => G1: 6,9 * PRF A3: 1,2 + D1: 4,5,6,7 + G1: 6,9 # A4: 3,8 => SOL * STA A3: 1,2 + D1: 4,5,6,7 + G1: 6,9 + A4: 3,8 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......124...9...........5..7.2.....6.....4.....1.8....18..........3.7..5.2...... | initial |
| .......124...9...........54.7.2.....6.....4.....1.8...718......9...3.7..532...... | autosolve |
| 367485912425391867189726354873254196651973428294168573718649235946532781532817649 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A1: 3,8 A6: 2,3 E5: 5,7 B8: 4,6 C8: 4,6 D8: 5,8 H8: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,F2: 1.. / C2 = 1 => 0 pairs (X) / F2 = 1 => 0 pairs (_) C5,I5: 1.. / C5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) F8,I8: 1.. / F8 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) A3,A4: 1.. / A3 = 1 => 0 pairs (*) / A4 = 1 => 0 pairs (X) E3,E9: 1.. / E3 = 1 => 0 pairs (X) / E9 = 1 => 0 pairs (_) G4,G9: 1.. / G4 = 1 => 0 pairs (*) / G9 = 1 => 0 pairs (X) B2,F2: 2.. / B2 = 2 => 0 pairs (*) / F2 = 2 => 0 pairs (X) B5,H5: 2.. / B5 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) F8,H8: 2.. / F8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) A3,A6: 2.. / A3 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) E3,E7: 2.. / E3 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) G6,G7: 2.. / G6 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) B8,C8: 4.. / B8 = 4 => 5 pairs (_) / C8 = 4 => 5 pairs (_) H7,H9: 4.. / H7 = 4 => 7 pairs (_) / H9 = 4 => 7 pairs (_) B6,B8: 4.. / B6 = 4 => 5 pairs (_) / B8 = 4 => 5 pairs (_) B8,C8: 6.. / B8 = 6 => 5 pairs (_) / C8 = 6 => 5 pairs (_) C1,C3: 7.. / C1 = 7 => 7 pairs (_) / C3 = 7 => 7 pairs (_) H2,I2: 7.. / H2 = 7 => 7 pairs (_) / I2 = 7 => 7 pairs (_) A4,B5: 8.. / A4 = 8 => 0 pairs (*) / B5 = 8 => 0 pairs (X) G1,G3: 9.. / G1 = 9 => 7 pairs (_) / G3 = 9 => 7 pairs (_) * DURATION: 0:00:27.874101 START: 14:01:52.548464 END: 14:02:20.422565 2017-05-04 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B8,C8,D8,E5,H8) * .......124...9...........54.7.2.....6.....4.....1.8...718......9...3.7..532...... * PAIR A1: 3,8 BLK 1 A3: 3,8,1,2 # reduction candidate for 3,8 A3: 3,8 => CTR * .......124...9...........5417.2.....68....4212..1.8...718...2..9...3.7..532...... A3: 1,2 # 8 pairs * PAIR A1: 3,8 ROW 1 D1: 3,8,4,5,6,7 # reduction candidate for 3,8 D1: 3,8 => CTR * 8..3...124...92...2......5417.2.....62....4.13..1.82..718.2....9...3172.532.8.1.. D1: 4,5,6,7 # 7 pairs G1: 3,8,6,9 # reduction candidate for 3,8 G1: 3,8 => CTR * 8.....31245..92...26....95417.2.....62....4.13..1.82..718.2....946.3172.532.8.1.. G1: 6,9 # 8 pairs * PAIR A1: 3,8 COL A A4: 3,8,1 # reduction candidate for 3,8 A4: 3,8 => SOLVED * 367485912425391867189726354873254196651973428294168573718649235946532781532817649 A4: 1 => CTR * .......124...9...........5417.2.....68....421...1.8...718...2..9...3.7..532...... * PAIR A6: 2,3 ROW 6 G6: 2,3,5,6 # reduction candidate for 2,3 G6: 2,3 # 8 pairs H6: 2,3,6,7,9 # reduction candidate for 2,3 H6: 2,3 => CTR * .......1242..9........2..54.7.2..1..6.1...42.2..1.853.718...24.9...32781532...6.9 H6: 6,7,9 # 7 pairs * PAIR A6: 2,3 COL A A3: 2,3,1,8 # reduction candidate for 2,3 A3: 2,3 => CTR * .......124...9...........5417.2.....68....421...1.8...718...2..9...3.7..532...... A3: 1,8 => SOLVED * 367485912425391867189726354873254196651973428294168573718649235946532781532817649 * PAIR E5: 5,7 BLK 5 D5: 5,7,3,9 # reduction candidate for 5,7 D5: 5,7 # 13 pairs F5: 5,7,3,9 # reduction candidate for 5,7 F5: 5,7 # 13 pairs E6: 5,7,4,6 # reduction candidate for 5,7 E6: 5,7 # 13 pairs * PAIR E5: 5,7 ROW 5 I5: 5,7,1,3,8,9 # reduction candidate for 5,7 I5: 5,7 => CTR * 85.....1242..918..1...2..543752..1.8681.5.4272..1785..718...2359..532781532817649 I5: 1,3,8,9 # 7 pairs * PAIR E5: 5,7 COL E E1: 5,7,4,6,8 # reduction candidate for 5,7 E1: 5,7 => CTR * 8......124...92...2......5417.2.....62....4.13..1.82..718.2....9...3172.532.8.1.. E1: 4,6,8 # 7 pairs * PAIR D8: 5,8 ROW 8 I8: 5,8,1 # reduction candidate for 5,8 I8: 5,8 => CTR * .......124.1.9........1..5417.2.....6.....4.....1.8...718......9...3172.532...... I8: 1 => SOLVED * 367485912425391867189726354873254196651973428294168573718649235946532781532817649 * PAIR D8: 5,8 COL D D1: 5,8,3,4,6,7 # reduction candidate for 5,8 D1: 5,8 # 11 pairs D2: 5,8,3,6 # reduction candidate for 5,8 D2: 5,8 # 8 pairs * PAIR H8: 2,8 COL H H5: 2,8,3,7,9 # reduction candidate for 2,8 H5: 3,7,9 => CTR * 8......124...92...2......5417.2.....62....4.83..1.8...718.2....9...3.72.532...18. H5: 2,8 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-327-base-pr-000.dot * REASONING * DIS # A3: 3,8 => CTR => A3: 1,2 * DIS # D1: 3,8 => CTR => D1: 4,5,6,7 * DIS # G1: 3,8 => CTR => G1: 6,9 * PRF # A4: 3,8 => SOL * DIS # A4: 1 => CTR => A4: 3,8 * DIS # H6: 2,3 => CTR => H6: 6,7,9 * DIS # A3: 2,3 => CTR => A3: 1,8 * PRF # A3: 1,8 => SOL * DIS # I5: 5,7 => CTR => I5: 1,3,8,9 * DIS # E1: 5,7 => CTR => E1: 4,6,8 * DIS # I8: 5,8 => CTR => I8: 1 * PRF # I8: 1 => SOL * DIS # H5: 3,7,9 => CTR => H5: 2,8 * CNT 13 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B8,C8,D8,E5,H8) * .......124...9...........54.7.2.....6.....4.....1.8...718......9...3.7..532...... * PAIR A1: 3,8 BLK 1 A3: 3,8,1,2 # reduction candidate for 3,8 A3: 3,8 => CTR * .......124...9...........5417.2.....68....4212..1.8...718...2..9...3.7..532...... * PAIR A1: 3,8 ROW 1 D1: 3,8,4,5,6,7 # reduction candidate for 3,8 D1: 3,8 => CTR * 8..3...124...92...2......5417.2.....62....4.13..1.82..718.2....9...3172.532.8.1.. G1: 3,8,6,9 # reduction candidate for 3,8 G1: 3,8 => CTR * 8.....31245..92...26....95417.2.....62....4.13..1.82..718.2....946.3172.532.8.1.. * RESTART * PAIR A1: 3,8 COL A A4: 3,8,1 # reduction candidate for 3,8 A4: 3,8 => SOLVED * 367485912425391867189726354873254196651973428294168573718649235946532781532817649 * DURATION: 0:00:05.429933 START: 14:02:38.977640 END: 14:02:44.407573 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-327-base-pr-001.dot * REASONING * DIS # A3: 3,8 => CTR => A3: 1,2 * DIS A3: 1,2 # D1: 3,8 => CTR => D1: 4,5,6,7 * DIS A3: 1,2 + D1: 4,5,6,7 # G1: 3,8 => CTR => G1: 6,9 * PRF A3: 1,2 + D1: 4,5,6,7 + G1: 6,9 # A4: 3,8 => SOL * STA A3: 1,2 + D1: 4,5,6,7 + G1: 6,9 + A4: 3,8 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 327 solution: 367485912425391867189726354873254196651973428294168573718649235946532781532817649 info: 2964 FNBHWY S8.f 9 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 367485912425391867189726354873254196651973428294168573718649235946532781532817649 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 # A3: 3,8 => CTR => A3: 1,2 * INC # A3: 1,2 => UNS * DIS # D1: 3,8 => CTR => D1: 4,5,6,7 * INC # D1: 4,5,6,7 => UNS * DIS # G1: 3,8 => CTR => G1: 6,9 * INC # G1: 6,9 => UNS * PRF # A4: 3,8 => SOL * DIS # A4: 1 => CTR => A4: 3,8 * INC # G6: 2,3 => UNS * DIS # H6: 2,3 => CTR => H6: 6,7,9 * INC # H6: 6,7,9 => UNS * DIS # A3: 2,3 => CTR => A3: 1,8 * PRF # A3: 1,8 => SOL * INC # D5: 5,7 => UNS * INC # F5: 5,7 => UNS * INC # E6: 5,7 => UNS * DIS # I5: 5,7 => CTR => I5: 1,3,8,9 * INC # I5: 1,3,8,9 => UNS * DIS # E1: 5,7 => CTR => E1: 4,6,8 * INC # E1: 4,6,8 => UNS * DIS # I8: 5,8 => CTR => I8: 1 * PRF # I8: 1 => SOL * INC # D1: 5,8 => UNS * INC # D2: 5,8 => UNS * INC # H5: 2,8 => UNS * DIS # H5: 3,7,9 => CTR => H5: 2,8 * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 3,8 => CTR => A3: 1,2 * DIS A3: 1,2 # D1: 3,8 => CTR => D1: 4,5,6,7 * DIS A3: 1,2 + D1: 4,5,6,7 # G1: 3,8 => CTR => G1: 6,9 * PRF A3: 1,2 + D1: 4,5,6,7 + G1: 6,9 # A4: 3,8 => SOL * STA A3: 1,2 + D1: 4,5,6,7 + G1: 6,9 + A4: 3,8 * CNT 4 HDP CHAINS / 4 HYP OPENED