Analysis of xx-top500-106-base.sdk
Contents
Original Sudoku
level: medium
position: 7.....1.....3........6......38..........1.2....6....5..1....46.2...7.......5...3. initial
Autosolve
position: 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 2,4 => CTR => F1: 8,9 * PRF # F1: 8,9 => SOL * DIS # H1: 2,4 => CTR => H1: 8,9 * PRF # H1: 8,9 => SOL * PRF # I2: 5,9 => SOL * DIS # I2: 4 => CTR => I2: 5,9 * DIS # I3: 5,9 => CTR => I3: 4,8 * PRF # I3: 4,8 => SOL * DIS # I3: 5,8 => CTR => I3: 4,9 * DIS # E6: 4,8 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # F6: 4,8 => SOL * DIS # F6: 9 => CTR => F6: 4,8 * DIS # D1: 9 => CTR => D1: 4,8 * PRF # H1: 4,8 => SOL * DIS # H1: 2,9 => CTR => H1: 4,8 * DIS # H3: 4,8 => CTR => H3: 2,7,9 * DIS # E6: 4,8 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # F6: 4,8 => SOL * DIS # F6: 9 => CTR => F6: 4,8 * PRF # I3: 4,8 => SOL * DIS # I3: 5,9 => CTR => I3: 4,8 * DIS # D1: 8,9 => CTR => D1: 4 * PRF # D1: 4 => SOL * PRF # F1: 8,9 => SOL * DIS # F1: 2,4 => CTR => F1: 8,9 * DIS # F6: 8,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * PRF # E2: 2,4 => SOL * DIS # E2: 9 => CTR => E2: 2,4 * DIS # E3: 2,4 => CTR => E3: 8,9 * PRF # E3: 8,9 => SOL * DIS # F1: 2,4 => CTR => F1: 8,9 * PRF # F1: 8,9 => SOL * PRF # I8: 5,8 => SOL * DIS # I8: 9 => CTR => I8: 5,8 * DIS # I8: 8,9 => CTR => I8: 5 * PRF # I8: 5 => SOL * PRF # H1: 8,9 => SOL * DIS # H1: 2,4 => CTR => H1: 8,9 * DIS # H3: 8,9 => CTR => H3: 2,4,7 * CNT 42 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 2,4 => CTR => F1: 8,9 * PRF F1: 8,9 => SOL * STA F1: 8,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7.....1.....3........6......38..........1.2....6....5..1....46.2...7.......5...3. | initial |
| 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 | autosolve |
| 762459183854321679391687524438265917975813246126794358517938462243176895689542731 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 2,4 B2: 5,9 B3: 5,9 F2: 1,7 F3: 1,7 G3: 5,8 D5: 4,8 H5: 4,8 I6: 4,8 D7: 8,9 F7: 8,9 E9: 2,4 F9: 2,4 G8: 5,8 H8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 14 pairs (_) / C3 = 1 => 14 pairs (_) F2,F3: 1.. / F2 = 1 => 14 pairs (_) / F3 = 1 => 14 pairs (_) C2,F2: 1.. / C2 = 1 => 14 pairs (_) / F2 = 1 => 14 pairs (_) C3,F3: 1.. / C3 = 1 => 14 pairs (_) / F3 = 1 => 14 pairs (_) E9,F9: 2.. / E9 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) F1,F9: 2.. / F1 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) H5,I6: 4.. / H5 = 4 => 0 pairs (*) / I6 = 4 => 0 pairs (X) E9,F9: 4.. / E9 = 4 => 0 pairs (*) / F9 = 4 => 0 pairs (X) D5,H5: 4.. / D5 = 4 => 0 pairs (X) / H5 = 4 => 0 pairs (_) D1,D5: 4.. / D1 = 4 => 0 pairs (*) / D5 = 4 => 0 pairs (X) B2,B3: 5.. / B2 = 5 => 14 pairs (_) / B3 = 5 => 0 pairs (X) G8,I8: 5.. / G8 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) B2,I2: 5.. / B2 = 5 => 14 pairs (_) / I2 = 5 => 0 pairs (X) G3,G8: 5.. / G3 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) F2,F3: 7.. / F2 = 7 => 14 pairs (_) / F3 = 7 => 14 pairs (_) H2,H3: 7.. / H2 = 7 => 14 pairs (_) / H3 = 7 => 14 pairs (_) F2,H2: 7.. / F2 = 7 => 14 pairs (_) / H2 = 7 => 14 pairs (_) F3,H3: 7.. / F3 = 7 => 14 pairs (_) / H3 = 7 => 14 pairs (_) H5,I6: 8.. / H5 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) D7,F7: 8.. / D7 = 8 => 0 pairs (X) / F7 = 8 => 15 pairs (_) D5,H5: 8.. / D5 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) E3,E6: 8.. / E3 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) G3,G8: 8.. / G3 = 8 => 0 pairs (X) / G8 = 8 => 0 pairs (_) B2,B3: 9.. / B2 = 9 => 0 pairs (X) / B3 = 9 => 14 pairs (_) E6,F6: 9.. / E6 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) D7,F7: 9.. / D7 = 9 => 15 pairs (_) / F7 = 9 => 0 pairs (X) H8,I8: 9.. / H8 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) D1,D7: 9.. / D1 = 9 => 0 pairs (X) / D7 = 9 => 15 pairs (_) * DURATION: 0:00:46.924679 START: 06:23:21.441660 END: 06:24:08.366339 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,C1,D5,D7,E9,F2,F3,F7,F9,G3,G8,H5,H8,I6) * 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 * PAIR C1: 2,4 BLK 1 C2: 2,4,1 # reduction candidate for 2,4 C2: 2,4 # 14 pairs C3: 2,4,1 # reduction candidate for 2,4 C3: 2,4 # 14 pairs * PAIR C1: 2,4 ROW 1 F1: 2,4,8,9 # reduction candidate for 2,4 F1: 2,4 => CTR * 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 F1: 8,9 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 H1: 2,4,8,9 # reduction candidate for 2,4 H1: 2,4 => CTR * 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 H1: 8,9 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 * PAIR B2: 5,9 ROW 2 I2: 5,9,4 # reduction candidate for 5,9 I2: 5,9 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 I2: 4 => CTR * 76.45.1.385.3..6.43946815..438265917975.132461267..358517.3.462243176..96895..731 * PAIR B3: 5,9 ROW 3 I3: 5,9,4,8 # reduction candidate for 5,9 I3: 5,9 => CTR * 76.85.1938..3..6..3..6..8..438265917975.132.61267893545179384622431765.86895..731 I3: 4,8 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 * PAIR G3: 5,8 BLK 3 I3: 5,8,4,9 # reduction candidate for 5,8 I3: 5,8 => CTR * 76.85.19385.3..6..39.6.....438265917975.132.6126789354517938462243176...6895..731 I3: 4,9 # 16 pairs * PAIR D5: 4,8 BLK 5 E6: 4,8,9 # reduction candidate for 4,8 E6: 4,8 => CTR * 76.85.1938..3..6..3..6..8..4382659179754132.61267.935.517938462243176.896895..731 E6: 9 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 F6: 4,8,9 # reduction candidate for 4,8 F6: 4,8 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 F6: 9 => CTR * 76.85.1938..3..6..3..6..8..4382659179754132.61267.935.517938462243176.896895..731 * PAIR D5: 4,8 COL D D1: 4,8,9 # reduction candidate for 4,8 D1: 9 => CTR * 76.95.1.38..3..6..3..6.....438265917975413286126798354517839462243176.9.6895..731 D1: 4,8 # 15 pairs * PAIR H5: 4,8 COL H H1: 4,8,2,9 # reduction candidate for 4,8 H1: 4,8 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 H1: 2,9 => CTR * 76..5.1.38..3..6..3..6.....438265917975413286126789354517938462243176.9.6895..731 H3: 4,8,2,7,9 # reduction candidate for 4,8 H3: 4,8 => CTR * 76..5.1238..3.167.3.1627...438265917975.132.6126789354517938462243176.9.689542731 H3: 2,7,9 # 15 pairs * PAIR I6: 4,8 ROW 6 E6: 4,8,9 # reduction candidate for 4,8 E6: 4,8 => CTR * 76.85.1938..3..6..3..6..8..4382659179754132.61267.935.517938462243176.896895..731 E6: 9 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 F6: 4,8,9 # reduction candidate for 4,8 F6: 4,8 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 F6: 9 => CTR * 76.85.1938..3..6..3..6..8..4382659179754132.61267.935.517938462243176.896895..731 * PAIR I6: 4,8 COL I I3: 4,8,5,9 # reduction candidate for 4,8 I3: 4,8 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 I3: 5,9 => CTR * 76.85.1938..3..6..3..6..8..438265917975.132.61267893545179384622431765.86895..731 * PAIR D7: 8,9 COL D D1: 8,9,4 # reduction candidate for 8,9 D1: 8,9 => CTR * 76..5.1.38..3..6..3..6.....4382659179754132861267..354517.3.462243176.9.6895..731 D1: 4 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 * PAIR F7: 8,9 COL F F1: 8,9,2,4 # reduction candidate for 8,9 F1: 8,9 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 F1: 2,4 => CTR * 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 F6: 8,9,4 # reduction candidate for 8,9 F6: 8,9 => CTR * 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 F6: 4 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 * PAIR E9: 2,4 COL E E2: 2,4,9 # reduction candidate for 2,4 E2: 2,4 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 E2: 9 => CTR * 76..5.19385.39.6.439.6....5438265917975.13246126749358517938462243176589689524731 E3: 2,4,8,9 # reduction candidate for 2,4 E3: 2,4 => CTR * 76.85.1938..39.6.53..6.....438265917975.132.6126789354517938462243176...6895..731 E3: 8,9 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 * PAIR F9: 2,4 COL F F1: 2,4,8,9 # reduction candidate for 2,4 F1: 2,4 => CTR * 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 F1: 8,9 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 * PAIR G8: 5,8 BLK 9 I8: 5,8,9 # reduction candidate for 5,8 I8: 5,8 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 I8: 9 => CTR * 76..5.1.38..3..6..3..6..8..4382659179758132461267..3585179384622431765896895..731 * PAIR H8: 8,9 BLK 9 I8: 8,9,5 # reduction candidate for 8,9 I8: 8,9 => CTR * 76.85.1938..3..6..3..6..8..438265917975.132.61267893545179384622431765.86895..731 I8: 5 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 * PAIR H8: 8,9 COL H H1: 8,9,2,4 # reduction candidate for 8,9 H1: 8,9 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 H1: 2,4 => CTR * 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 H3: 8,9,2,4,7 # reduction candidate for 8,9 H3: 8,9 => CTR * 76..5.1238..3.167.3.1627..4438265917975.1324612678.35.517.3.462243176...6895..731 H3: 2,4,7 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-106-base-pr-000.dot * REASONING * DIS # F1: 2,4 => CTR => F1: 8,9 * PRF # F1: 8,9 => SOL * DIS # H1: 2,4 => CTR => H1: 8,9 * PRF # H1: 8,9 => SOL * PRF # I2: 5,9 => SOL * DIS # I2: 4 => CTR => I2: 5,9 * DIS # I3: 5,9 => CTR => I3: 4,8 * PRF # I3: 4,8 => SOL * DIS # I3: 5,8 => CTR => I3: 4,9 * DIS # E6: 4,8 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # F6: 4,8 => SOL * DIS # F6: 9 => CTR => F6: 4,8 * DIS # D1: 9 => CTR => D1: 4,8 * PRF # H1: 4,8 => SOL * DIS # H1: 2,9 => CTR => H1: 4,8 * DIS # H3: 4,8 => CTR => H3: 2,7,9 * DIS # E6: 4,8 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # F6: 4,8 => SOL * DIS # F6: 9 => CTR => F6: 4,8 * PRF # I3: 4,8 => SOL * DIS # I3: 5,9 => CTR => I3: 4,8 * DIS # D1: 8,9 => CTR => D1: 4 * PRF # D1: 4 => SOL * PRF # F1: 8,9 => SOL * DIS # F1: 2,4 => CTR => F1: 8,9 * DIS # F6: 8,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * PRF # E2: 2,4 => SOL * DIS # E2: 9 => CTR => E2: 2,4 * DIS # E3: 2,4 => CTR => E3: 8,9 * PRF # E3: 8,9 => SOL * DIS # F1: 2,4 => CTR => F1: 8,9 * PRF # F1: 8,9 => SOL * PRF # I8: 5,8 => SOL * DIS # I8: 9 => CTR => I8: 5,8 * DIS # I8: 8,9 => CTR => I8: 5 * PRF # I8: 5 => SOL * PRF # H1: 8,9 => SOL * DIS # H1: 2,4 => CTR => H1: 8,9 * DIS # H3: 8,9 => CTR => H3: 2,4,7 * CNT 42 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,C1,D5,D7,E9,F2,F3,F7,F9,G3,G8,H5,H8,I6) * 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 * PAIR C1: 2,4 BLK 1 C2: 2,4,1 # reduction candidate for 2,4 C2: 2,4 # 14 pairs C3: 2,4,1 # reduction candidate for 2,4 C3: 2,4 # 14 pairs * PAIR C1: 2,4 ROW 1 F1: 2,4,8,9 # reduction candidate for 2,4 F1: 2,4 => CTR * 76..5.1.38..3..6..3..6.....438265917975.132.61267..35.517.3.462243176...6895..731 F1: 8,9 => SOLVED * 762459183854321679391687524438265917975813246126794358517938462243176895689542731 * DURATION: 0:00:03.321474 START: 06:25:00.627548 END: 06:25:03.949022 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-106-base-pr-001.dot * REASONING * DIS # F1: 2,4 => CTR => F1: 8,9 * PRF F1: 8,9 => SOL * STA F1: 8,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 106 solution: 762459183854321679391687524438265917975813246126794358517938462243176895689542731 info: 1624 FNBHW S8.f 36343 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 762459183854321679391687524438265917975813246126794358517938462243176895689542731 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 # C2: 2,4 => UNS * INC # C3: 2,4 => UNS * DIS # F1: 2,4 => CTR => F1: 8,9 * PRF # F1: 8,9 => SOL * DIS # H1: 2,4 => CTR => H1: 8,9 * PRF # H1: 8,9 => SOL * PRF # I2: 5,9 => SOL * DIS # I2: 4 => CTR => I2: 5,9 * DIS # I3: 5,9 => CTR => I3: 4,8 * PRF # I3: 4,8 => SOL * DIS # I3: 5,8 => CTR => I3: 4,9 * INC # I3: 4,9 => UNS * DIS # E6: 4,8 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # F6: 4,8 => SOL * DIS # F6: 9 => CTR => F6: 4,8 * INC # D1: 4,8 => UNS * DIS # D1: 9 => CTR => D1: 4,8 * PRF # H1: 4,8 => SOL * DIS # H1: 2,9 => CTR => H1: 4,8 * DIS # H3: 4,8 => CTR => H3: 2,7,9 * INC # H3: 2,7,9 => UNS * DIS # E6: 4,8 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # F6: 4,8 => SOL * DIS # F6: 9 => CTR => F6: 4,8 * PRF # I3: 4,8 => SOL * DIS # I3: 5,9 => CTR => I3: 4,8 * DIS # D1: 8,9 => CTR => D1: 4 * PRF # D1: 4 => SOL * PRF # F1: 8,9 => SOL * DIS # F1: 2,4 => CTR => F1: 8,9 * DIS # F6: 8,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * PRF # E2: 2,4 => SOL * DIS # E2: 9 => CTR => E2: 2,4 * DIS # E3: 2,4 => CTR => E3: 8,9 * PRF # E3: 8,9 => SOL * DIS # F1: 2,4 => CTR => F1: 8,9 * PRF # F1: 8,9 => SOL * PRF # I8: 5,8 => SOL * DIS # I8: 9 => CTR => I8: 5,8 * DIS # I8: 8,9 => CTR => I8: 5 * PRF # I8: 5 => SOL * PRF # H1: 8,9 => SOL * DIS # H1: 2,4 => CTR => H1: 8,9 * DIS # H3: 8,9 => CTR => H3: 2,4,7 * INC # H3: 2,4,7 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 2,4 => UNS * INC # C3: 2,4 => UNS * DIS # F1: 2,4 => CTR => F1: 8,9 * PRF F1: 8,9 => SOL * STA F1: 8,9 * CNT 4 HDP CHAINS / 3 HYP OPENED