Analysis of xx-top500-107-base.sdk
Contents
Original Sudoku
level: medium
position: 8.....1.....3........7......39..........1.2....7....5..1....47.2...8.......6...3. initial
Autosolve
position: 87..5.1.39..3..7..3..7......39.7.61..86.132.7127...35.618.3.472243187...7956..831 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D1: 2,4 => SOL * DIS # D1: 9 => CTR => D1: 2,4 * DIS # F1: 2,4 => CTR => F1: 6,9 * DIS # H1: 2,4 => CTR => H1: 6,9 * PRF # H1: 6,9 => SOL * PRF # I2: 5,6 => SOL * DIS # I2: 4 => CTR => I2: 5,6 * DIS # I3: 5,6 => CTR => I3: 4,9 * PRF # I3: 4,9 => SOL * DIS # I3: 5,9 => CTR => I3: 4,6 * DIS # D4: 4,5 => CTR => D4: 2,8 * DIS # D5: 4,5 => CTR => D5: 9 * PRF # D5: 9 => SOL * DIS # I6: 4,8 => CTR => I6: 9 * PRF # I6: 9 => SOL * DIS # D4: 4,8 => CTR => D4: 2,5 * DIS # I6: 8 => CTR => I6: 4,9 * DIS # D5: 5 => CTR => D5: 4,9 * PRF # H1: 4,9 => SOL * DIS # H1: 2,6 => CTR => H1: 4,9 * DIS # H3: 4,9 => CTR => H3: 2,6,8 * PRF # D5: 5,9 => SOL * DIS # D5: 4 => CTR => D5: 5,9 * PRF # E2: 2,4 => SOL * DIS # E2: 6 => CTR => E2: 2,4 * DIS # E3: 2,4 => CTR => E3: 6,9 * PRF # E3: 6,9 => SOL * DIS # F1: 2,4 => CTR => F1: 6,9 * DIS # F4: 2,4 => CTR => F4: 5 * PRF # I8: 5,9 => SOL * DIS # I8: 6 => CTR => I8: 5,9 * DIS # I8: 6,9 => CTR => I8: 5 * PRF # I8: 5 => SOL * PRF # H1: 6,9 => SOL * DIS # H1: 2,4 => CTR => H1: 6,9 * DIS # H3: 6,9 => CTR => H3: 2,4,8 * CNT 36 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D1: 2,4 => SOL * STA D1: 2,4 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8.....1.....3........7......39..........1.2....7....5..1....47.2...8.......6...3. | initial |
| 87..5.1.39..3..7..3..7......39.7.61..86.132.7127...35.618.3.472243187...7956..831 | autosolve |
| 872456193954321786361798524439275618586913247127864359618539472243187965795642831 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) C1: 2,4 B2: 5,6 B3: 5,6 F2: 1,8 F3: 1,8 G3: 5,9 A4: 4,5 A5: 4,5 I4: 4,8 H5: 4,9 D7: 5,9 F7: 5,9 E9: 2,4 F9: 2,4 G8: 5,9 H8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 15 pairs (_) / C3 = 1 => 15 pairs (_) F2,F3: 1.. / F2 = 1 => 15 pairs (_) / F3 = 1 => 15 pairs (_) C2,F2: 1.. / C2 = 1 => 15 pairs (_) / F2 = 1 => 15 pairs (_) C3,F3: 1.. / C3 = 1 => 15 pairs (_) / F3 = 1 => 15 pairs (_) D4,F4: 2.. / D4 = 2 => 18 pairs (_) / F4 = 2 => 0 pairs (X) E9,F9: 2.. / E9 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) D1,D4: 2.. / D1 = 2 => 0 pairs (X) / D4 = 2 => 18 pairs (_) A4,A5: 4.. / A4 = 4 => 17 pairs (_) / A5 = 4 => 0 pairs (X) E9,F9: 4.. / E9 = 4 => 0 pairs (*) / F9 = 4 => 0 pairs (X) B2,B3: 5.. / B2 = 5 => 15 pairs (_) / B3 = 5 => 0 pairs (X) A4,A5: 5.. / A4 = 5 => 0 pairs (X) / A5 = 5 => 17 pairs (_) D7,F7: 5.. / D7 = 5 => 15 pairs (_) / F7 = 5 => 0 pairs (X) G8,I8: 5.. / G8 = 5 => 0 pairs (X) / I8 = 5 => 0 pairs (_) B2,I2: 5.. / B2 = 5 => 15 pairs (_) / I2 = 5 => 0 pairs (X) A5,D5: 5.. / A5 = 5 => 17 pairs (_) / D5 = 5 => 0 pairs (X) F4,F7: 5.. / F4 = 5 => 15 pairs (_) / F7 = 5 => 0 pairs (X) G3,G8: 5.. / G3 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) B2,B3: 6.. / B2 = 6 => 0 pairs (X) / B3 = 6 => 15 pairs (_) E6,F6: 6.. / E6 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) H8,I8: 6.. / H8 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) F1,H1: 6.. / F1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) F1,F6: 6.. / F1 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) F2,F3: 8.. / F2 = 8 => 15 pairs (_) / F3 = 8 => 15 pairs (_) H2,H3: 8.. / H2 = 8 => 15 pairs (_) / H3 = 8 => 15 pairs (_) D4,D6: 8.. / D4 = 8 => 0 pairs (X) / D6 = 8 => 16 pairs (_) I4,I6: 8.. / I4 = 8 => 16 pairs (_) / I6 = 8 => 0 pairs (X) F2,H2: 8.. / F2 = 8 => 15 pairs (_) / H2 = 8 => 15 pairs (_) F3,H3: 8.. / F3 = 8 => 15 pairs (_) / H3 = 8 => 15 pairs (_) D4,I4: 8.. / D4 = 8 => 0 pairs (X) / I4 = 8 => 16 pairs (_) D6,I6: 8.. / D6 = 8 => 16 pairs (_) / I6 = 8 => 0 pairs (X) H5,I6: 9.. / H5 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) D7,F7: 9.. / D7 = 9 => 0 pairs (X) / F7 = 9 => 15 pairs (_) D5,H5: 9.. / D5 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) E3,E6: 9.. / E3 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) G3,G8: 9.. / G3 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) * DURATION: 0:01:00.846119 START: 06:25:19.047569 END: 06:26:19.893688 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B2,B3,C1,D7,E9,F2,F3,F7,F9,G3,G8,H5,H8,I4) * 87..5.1.39..3..7..3..7......39.7.61..86.132.7127...35.618.3.472243187...7956..831 * PAIR C1: 2,4 BLK 1 C2: 2,4,1 # reduction candidate for 2,4 C2: 2,4 # 15 pairs C3: 2,4,1 # reduction candidate for 2,4 C3: 2,4 # 15 pairs * PAIR C1: 2,4 ROW 1 D1: 2,4,9 # reduction candidate for 2,4 D1: 2,4 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 D1: 9 => CTR * 87.95.1.39..3..7..3..7......3927.618.86.13297127896354618539472243187.6.7956..831 F1: 2,4,6,9 # reduction candidate for 2,4 F1: 2,4 => CTR * 87.95.1639..3..7..3..7..9...392756185864132.7127..635.618.39472243187.967956..831 F1: 6,9 # 17 pairs H1: 2,4,6,9 # reduction candidate for 2,4 H1: 2,4 => CTR * 87.9561.39..3..7..3..7......3927.618.86.1329712786935461853.472243187...7956..831 H1: 6,9 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 * PAIR B2: 5,6 ROW 2 I2: 5,6,4 # reduction candidate for 5,6 I2: 5,6 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 I2: 4 => CTR * 87..5.1.395.3..7.436.79.5...39.7.618.86.132471278..359618.3.472243187..67956..831 * PAIR B3: 5,6 ROW 3 I3: 5,6,4,9 # reduction candidate for 5,6 I3: 5,6 => CTR * 87..5.1639..3..7..3..7..9...39.7.61..86.132.7127.9635.618.3.4722431875.97956..831 I3: 4,9 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 * PAIR G3: 5,9 BLK 3 I3: 5,9,4,6 # reduction candidate for 5,9 I3: 5,9 => CTR * 87..5.16395.36.7.436.7......39.7.618.86.132.7127.9635.618.3.472243187...7956..831 I3: 4,6 # 17 pairs * PAIR A4: 4,5 ROW 4 D4: 4,5,2,8 # reduction candidate for 4,5 D4: 4,5 => CTR * 87425.1.39..3..7..3..7......39.72618.86.132971278..354618935472243187.6.795624831 D4: 2,8 # 17 pairs F4: 4,5,2 # reduction candidate for 4,5 F4: 4,5 # 18 pairs * PAIR A5: 4,5 ROW 5 D5: 4,5,9 # reduction candidate for 4,5 D5: 4,5 => CTR * 87.9561.39..3..7..3..7......3927.618.86.1329712786935461853.472243187.6.7956..831 D5: 9 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 * PAIR I4: 4,8 BLK 6 I6: 4,8,9 # reduction candidate for 4,8 I6: 4,8 => CTR * 87.9561.39..3..7..3..7......3927.618.86.1329712786935461853.472243187.6.7956..831 I6: 9 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 * PAIR I4: 4,8 ROW 4 D4: 4,8,2,5 # reduction candidate for 4,8 D4: 4,8 => CTR * 87.25.1.39..3..7..3..7......39.7261..86513297127...35.618935472243187.6.795624831 D4: 2,5 # 17 pairs * PAIR H5: 4,9 BLK 6 I6: 4,9,8 # reduction candidate for 4,9 I6: 8 => CTR * 87..561.39..3..7..3..7......39872614486513297127...358618.3.472243187.6.7956..831 I6: 4,9 # 16 pairs * PAIR H5: 4,9 ROW 5 D5: 4,9,5 # reduction candidate for 4,9 D5: 5 => CTR * 87..5.1.39..3..7..3..7......39.7.61..86513297127...35.618935472243187.6.7956..831 D5: 4,9 # 17 pairs * PAIR H5: 4,9 COL H H1: 4,9,2,6 # reduction candidate for 4,9 H1: 4,9 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 H1: 2,6 => CTR * 87..5.1.39..3..7..3..7......39.7.61..86.13297127.9635.618.3.472243187.6.7956..831 H3: 4,9,2,6,8 # reduction candidate for 4,9 H3: 4,9 => CTR * 87..5.1239..3.178.3.1728....3927.618.86.132.7127896354618.3.472243187.6.795642831 H3: 2,6,8 # 16 pairs * PAIR D7: 5,9 COL D D5: 5,9,4 # reduction candidate for 5,9 D5: 5,9 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 D5: 4 => CTR * 87..561.39..3..7..3..7.....439.7.618586413297127869354618935472243187.6.7956.4831 * PAIR E9: 2,4 COL E E2: 2,4,6 # reduction candidate for 2,4 E2: 2,4 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 E2: 6 => CTR * 87..5.16395.36.7.436.7....5.39.7.618.86.13247127846359618.3.472243187596795624831 E3: 2,4,6,9 # reduction candidate for 2,4 E3: 2,4 => CTR * 87..5.1639..36.7..36.7......39.7.61..86.13297127.9635.618.3.472243187...7956..831 E3: 6,9 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 * PAIR F9: 2,4 COL F F1: 2,4,6,9 # reduction candidate for 2,4 F1: 2,4 => CTR * 87.95.1639..3..7..3..7..9...392756185864132.7127..635.618.39472243187.967956..831 F1: 6,9 # 17 pairs F4: 2,4,5 # reduction candidate for 2,4 F4: 2,4 => CTR * 87..5.1.39..3..7..3..7......39.7.61..86.13297127...35.618935472243187.6.7956..831 F4: 5 # 15 pairs * PAIR G8: 5,9 BLK 9 I8: 5,9,6 # reduction candidate for 5,9 I8: 5,9 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 I8: 6 => CTR * 87..5.1.39..3..7..3..7..9...39.7.61..86913247127...3596185394722431875967956..831 * PAIR H8: 6,9 BLK 9 I8: 6,9,5 # reduction candidate for 6,9 I8: 6,9 => CTR * 87..5.1639..3..7..3..7..9...39.7.61..86.132.7127.9635.618.3.4722431875.97956..831 I8: 5 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 * PAIR H8: 6,9 COL H H1: 6,9,2,4 # reduction candidate for 6,9 H1: 6,9 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 H1: 2,4 => CTR * 87.9561.39..3..7..3..7......3927.618.86.1329712786935461853.472243187...7956..831 H3: 6,9,2,4,8 # reduction candidate for 6,9 H3: 6,9 => CTR * 87..5.1239..3.178.3.1728..4.3927.618.86.1324712789.35.618.3.472243187...7956..831 H3: 2,4,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-107-base-pr-000.dot * REASONING * PRF # D1: 2,4 => SOL * DIS # D1: 9 => CTR => D1: 2,4 * DIS # F1: 2,4 => CTR => F1: 6,9 * DIS # H1: 2,4 => CTR => H1: 6,9 * PRF # H1: 6,9 => SOL * PRF # I2: 5,6 => SOL * DIS # I2: 4 => CTR => I2: 5,6 * DIS # I3: 5,6 => CTR => I3: 4,9 * PRF # I3: 4,9 => SOL * DIS # I3: 5,9 => CTR => I3: 4,6 * DIS # D4: 4,5 => CTR => D4: 2,8 * DIS # D5: 4,5 => CTR => D5: 9 * PRF # D5: 9 => SOL * DIS # I6: 4,8 => CTR => I6: 9 * PRF # I6: 9 => SOL * DIS # D4: 4,8 => CTR => D4: 2,5 * DIS # I6: 8 => CTR => I6: 4,9 * DIS # D5: 5 => CTR => D5: 4,9 * PRF # H1: 4,9 => SOL * DIS # H1: 2,6 => CTR => H1: 4,9 * DIS # H3: 4,9 => CTR => H3: 2,6,8 * PRF # D5: 5,9 => SOL * DIS # D5: 4 => CTR => D5: 5,9 * PRF # E2: 2,4 => SOL * DIS # E2: 6 => CTR => E2: 2,4 * DIS # E3: 2,4 => CTR => E3: 6,9 * PRF # E3: 6,9 => SOL * DIS # F1: 2,4 => CTR => F1: 6,9 * DIS # F4: 2,4 => CTR => F4: 5 * PRF # I8: 5,9 => SOL * DIS # I8: 6 => CTR => I8: 5,9 * DIS # I8: 6,9 => CTR => I8: 5 * PRF # I8: 5 => SOL * PRF # H1: 6,9 => SOL * DIS # H1: 2,4 => CTR => H1: 6,9 * DIS # H3: 6,9 => CTR => H3: 2,4,8 * CNT 36 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B2,B3,C1,D7,E9,F2,F3,F7,F9,G3,G8,H5,H8,I4) * 87..5.1.39..3..7..3..7......39.7.61..86.132.7127...35.618.3.472243187...7956..831 * PAIR C1: 2,4 BLK 1 C2: 2,4,1 # reduction candidate for 2,4 C2: 2,4 # 15 pairs C3: 2,4,1 # reduction candidate for 2,4 C3: 2,4 # 15 pairs * PAIR C1: 2,4 ROW 1 D1: 2,4,9 # reduction candidate for 2,4 D1: 2,4 => SOLVED * 872456193954321786361798524439275618586913247127864359618539472243187965795642831 * DURATION: 0:00:04.160883 START: 06:27:14.208645 END: 06:27:18.369528 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-107-base-pr-001.dot * REASONING * PRF # D1: 2,4 => SOL * STA D1: 2,4 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 107 solution: 872456193954321786361798524439275618586913247127864359618539472243187965795642831 info: 1625 FNBHW S8.f 37954 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 872456193954321786361798524439275618586913247127864359618539472243187965795642831 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 * PRF # D1: 2,4 => SOL * DIS # D1: 9 => CTR => D1: 2,4 * DIS # F1: 2,4 => CTR => F1: 6,9 * INC # F1: 6,9 => UNS * DIS # H1: 2,4 => CTR => H1: 6,9 * PRF # H1: 6,9 => SOL * PRF # I2: 5,6 => SOL * DIS # I2: 4 => CTR => I2: 5,6 * DIS # I3: 5,6 => CTR => I3: 4,9 * PRF # I3: 4,9 => SOL * DIS # I3: 5,9 => CTR => I3: 4,6 * INC # I3: 4,6 => UNS * DIS # D4: 4,5 => CTR => D4: 2,8 * INC # D4: 2,8 => UNS * INC # F4: 4,5 => UNS * DIS # D5: 4,5 => CTR => D5: 9 * PRF # D5: 9 => SOL * DIS # I6: 4,8 => CTR => I6: 9 * PRF # I6: 9 => SOL * DIS # D4: 4,8 => CTR => D4: 2,5 * INC # D4: 2,5 => UNS * INC # I6: 4,9 => UNS * DIS # I6: 8 => CTR => I6: 4,9 * INC # D5: 4,9 => UNS * DIS # D5: 5 => CTR => D5: 4,9 * PRF # H1: 4,9 => SOL * DIS # H1: 2,6 => CTR => H1: 4,9 * DIS # H3: 4,9 => CTR => H3: 2,6,8 * INC # H3: 2,6,8 => UNS * PRF # D5: 5,9 => SOL * DIS # D5: 4 => CTR => D5: 5,9 * PRF # E2: 2,4 => SOL * DIS # E2: 6 => CTR => E2: 2,4 * DIS # E3: 2,4 => CTR => E3: 6,9 * PRF # E3: 6,9 => SOL * DIS # F1: 2,4 => CTR => F1: 6,9 * INC # F1: 6,9 => UNS * DIS # F4: 2,4 => CTR => F4: 5 * INC # F4: 5 => UNS * PRF # I8: 5,9 => SOL * DIS # I8: 6 => CTR => I8: 5,9 * DIS # I8: 6,9 => CTR => I8: 5 * PRF # I8: 5 => SOL * PRF # H1: 6,9 => SOL * DIS # H1: 2,4 => CTR => H1: 6,9 * DIS # H3: 6,9 => CTR => H3: 2,4,8 * INC # H3: 2,4,8 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 2,4 => UNS * INC # C3: 2,4 => UNS * PRF # D1: 2,4 => SOL * STA D1: 2,4 * CNT 3 HDP CHAINS / 3 HYP OPENED