Analysis of xx-top500-406-base.sdk
Contents
Original Sudoku
level: medium
position: ..63...75.1..........2.....5.......2.....84......1........4.81.3..5.....2........ initial
Autosolve
position: 846391275.1285.34....2.4.815.84..1.21...2845.42..15.386...428133.15...242.41..5.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F9: 6,7 => CTR => F9: 3,9 * DIS # B5: 7,9 => CTR => B5: 3,6 * DIS # D6: 7,9 => CTR => D6: 6 * DIS # F4: 9 => CTR => F4: 3,7 * DIS # B4: 7 => CTR => B4: 6,9 * DIS # F9: 7,9 => CTR => F9: 3,6 * DIS # D6: 7,9 => CTR => D6: 6 * DIS # F9: 6,9 => CTR => F9: 3,7 * CNT 8 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F9: 6,7 => CTR => F9: 3,9 * PRF F9: 3,9 # F8: 9 => SOL * STA F9: 3,9 + F8: 9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..63...75.1..........2.....5.......2.....84......1........4.81.3..5.....2........ | initial |
| 846391275.1285.34....2.4.815.84..1.21...2845.42..15.386...428133.15...242.41..5.. | autosolve |
| 846391275712856349935274681598437162163928457427615938659742813381569724274183596 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A2: 7,9 A3: 7,9 B3: 3,5 C3: 3,5 F2: 6,7 E3: 6,7 I2: 6,9 G3: 6,9 C6: 7,9 E4: 3,7 H4: 6,9 D7: 7,9 H9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 3.. / B3 = 3 => 12 pairs (_) / C3 = 3 => 22 pairs (_) B5,C5: 3.. / B5 = 3 => 22 pairs (_) / C5 = 3 => 12 pairs (_) E4,F4: 3.. / E4 = 3 => 13 pairs (_) / F4 = 3 => 0 pairs (X) E9,F9: 3.. / E9 = 3 => 0 pairs (X) / F9 = 3 => 13 pairs (_) B3,B5: 3.. / B3 = 3 => 12 pairs (_) / B5 = 3 => 22 pairs (_) C3,C5: 3.. / C3 = 3 => 22 pairs (_) / C5 = 3 => 12 pairs (_) E4,E9: 3.. / E4 = 3 => 13 pairs (_) / E9 = 3 => 0 pairs (X) F4,F9: 3.. / F4 = 3 => 0 pairs (X) / F9 = 3 => 13 pairs (_) B3,C3: 5.. / B3 = 5 => 22 pairs (_) / C3 = 5 => 12 pairs (_) B7,C7: 5.. / B7 = 5 => 12 pairs (_) / C7 = 5 => 22 pairs (_) B3,B7: 5.. / B3 = 5 => 22 pairs (_) / B7 = 5 => 12 pairs (_) C3,C7: 5.. / C3 = 5 => 12 pairs (_) / C7 = 5 => 22 pairs (_) F2,E3: 6.. / F2 = 6 => 14 pairs (_) / E3 = 6 => 16 pairs (_) I2,G3: 6.. / I2 = 6 => 16 pairs (_) / G3 = 6 => 14 pairs (_) B4,B5: 6.. / B4 = 6 => 26 pairs (_) / B5 = 6 => 17 pairs (_) D5,D6: 6.. / D5 = 6 => 0 pairs (X) / D6 = 6 => 15 pairs (_) F2,I2: 6.. / F2 = 6 => 14 pairs (_) / I2 = 6 => 16 pairs (_) E3,G3: 6.. / E3 = 6 => 16 pairs (_) / G3 = 6 => 14 pairs (_) B4,H4: 6.. / B4 = 6 => 26 pairs (_) / H4 = 6 => 17 pairs (_) D6,G6: 6.. / D6 = 6 => 15 pairs (_) / G6 = 6 => 0 pairs (X) H4,H9: 6.. / H4 = 6 => 17 pairs (_) / H9 = 6 => 26 pairs (_) A2,A3: 7.. / A2 = 7 => 14 pairs (_) / A3 = 7 => 16 pairs (_) F2,E3: 7.. / F2 = 7 => 16 pairs (_) / E3 = 7 => 14 pairs (_) I5,G6: 7.. / I5 = 7 => 22 pairs (_) / G6 = 7 => 19 pairs (_) G8,I9: 7.. / G8 = 7 => 22 pairs (_) / I9 = 7 => 19 pairs (_) A2,F2: 7.. / A2 = 7 => 14 pairs (_) / F2 = 7 => 16 pairs (_) A3,E3: 7.. / A3 = 7 => 16 pairs (_) / E3 = 7 => 14 pairs (_) G6,G8: 7.. / G6 = 7 => 19 pairs (_) / G8 = 7 => 22 pairs (_) I5,I9: 7.. / I5 = 7 => 22 pairs (_) / I9 = 7 => 19 pairs (_) B8,B9: 8.. / B8 = 8 => 16 pairs (_) / B9 = 8 => 14 pairs (_) E8,E9: 8.. / E8 = 8 => 14 pairs (_) / E9 = 8 => 16 pairs (_) B8,E8: 8.. / B8 = 8 => 16 pairs (_) / E8 = 8 => 14 pairs (_) B9,E9: 8.. / B9 = 8 => 14 pairs (_) / E9 = 8 => 16 pairs (_) A2,A3: 9.. / A2 = 9 => 16 pairs (_) / A3 = 9 => 14 pairs (_) I2,G3: 9.. / I2 = 9 => 14 pairs (_) / G3 = 9 => 16 pairs (_) A2,I2: 9.. / A2 = 9 => 16 pairs (_) / I2 = 9 => 14 pairs (_) A3,G3: 9.. / A3 = 9 => 14 pairs (_) / G3 = 9 => 16 pairs (_) H4,H9: 9.. / H4 = 9 => 26 pairs (_) / H9 = 9 => 17 pairs (_) * DURATION: 0:01:09.006371 START: 16:42:52.943019 END: 16:44:01.949390 2017-05-04 * CP COUNT: (38) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B3,C3,C6,D7,E3,E4,F2,G3,H4,H9,I2) * 846391275.1285.34....2.4.815.84..1.21...2845.42..15.386...428133.15...242.41..5.. * PAIR F2: 6,7 COL F F8: 6,7,9 # reduction candidate for 6,7 F8: 6,7 # 16 pairs F9: 6,7,3,9 # reduction candidate for 6,7 F9: 6,7 => CTR * 846391275.128573467..26498159847316216..2845.42..15.386..7428133.1589624284136597 F9: 3,9 # 14 pairs * PAIR E3: 6,7 COL E E8: 6,7,8 # reduction candidate for 6,7 E8: 6,7 # 16 pairs E9: 6,7,3,8 # reduction candidate for 6,7 E9: 6,7 # 16 pairs * PAIR I2: 6,9 COL I I5: 6,9,7 # reduction candidate for 6,9 I5: 6,9 # 19 pairs I9: 6,9,7 # reduction candidate for 6,9 I9: 6,9 # 22 pairs * PAIR G3: 6,9 COL G G6: 6,9,7 # reduction candidate for 6,9 G6: 6,9 # 22 pairs G8: 6,9,7 # reduction candidate for 6,9 G8: 6,9 # 19 pairs * PAIR C6: 7,9 BLK 4 B4: 7,9,6 # reduction candidate for 7,9 B4: 7,9 # 17 pairs B5: 7,9,3,6 # reduction candidate for 7,9 B5: 7,9 => CTR * 84639127591285734..352.4.815684..1921936284574279156386597428133.15..724274183569 B5: 3,6 # 14 pairs C5: 7,9,3 # reduction candidate for 7,9 C5: 7,9 # 22 pairs * PAIR C6: 7,9 ROW 6 D6: 7,9,6 # reduction candidate for 7,9 D6: 7,9 => CTR * 8463912759128573467..2649815684731.21..62845.42..156386...428133.15..7242.41..569 D6: 6 # 15 pairs G6: 7,9,6 # reduction candidate for 7,9 G6: 7,9 # 15 pairs * PAIR C6: 7,9 COL C C7: 7,9,5 # reduction candidate for 7,9 C7: 5 # 22 pairs C7: 7,9 # 12 pairs * PAIR E4: 3,7 BLK 5 F4: 3,7,9 # reduction candidate for 3,7 F4: 9 => CTR * 8463912759128573467352649815784391621637284594296157386579428133915...242.41.3597 F4: 3,7 # 22 pairs * PAIR E4: 3,7 COL E E9: 3,7,6,8 # reduction candidate for 3,7 E9: 3,7 # 16 pairs E9: 6,8 # 14 pairs * PAIR H4: 6,9 BLK 6 I5: 6,9,7 # reduction candidate for 6,9 I5: 6,9 # 19 pairs G6: 6,9,7 # reduction candidate for 6,9 G6: 6,9 # 22 pairs * PAIR H4: 6,9 ROW 4 B4: 6,9,7 # reduction candidate for 6,9 B4: 7 => CTR * 8463912759128573467352649815784391621637284594296157386579428133915...242.41.3597 B4: 6,9 # 22 pairs * PAIR D7: 7,9 BLK 8 F8: 7,9,6 # reduction candidate for 7,9 F8: 7,9 # 16 pairs F9: 7,9,3,6 # reduction candidate for 7,9 F9: 7,9 => CTR * 846391275.128573467..2649815.84731.21...2845.42..15.386..7428133.1586.24284139567 F9: 3,6 # 14 pairs * PAIR D7: 7,9 ROW 7 B7: 7,9,5 # reduction candidate for 7,9 B7: 7,9 # 22 pairs C7: 7,9,5 # reduction candidate for 7,9 C7: 7,9 # 12 pairs * PAIR D7: 7,9 COL D D5: 7,9,6 # reduction candidate for 7,9 D5: 7,9 # 15 pairs D6: 7,9,6 # reduction candidate for 7,9 D6: 7,9 => CTR * 8463912759128573467..2649815684731.21..62845.42..156386...428133.15..7242.41..569 D6: 6 # 15 pairs * PAIR H9: 6,9 BLK 9 G8: 6,9,7 # reduction candidate for 6,9 G8: 6,9 # 19 pairs I9: 6,9,7 # reduction candidate for 6,9 I9: 6,9 # 22 pairs * PAIR H9: 6,9 ROW 9 F9: 6,9,3,7 # reduction candidate for 6,9 F9: 6,9 => CTR * 846391275.128573467..2649815.84731.21...2845942.915.386..7428133.158..2428413.5.7 F9: 3,7 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-406-base-pr-000.dot * REASONING * DIS # F9: 6,7 => CTR => F9: 3,9 * DIS # B5: 7,9 => CTR => B5: 3,6 * DIS # D6: 7,9 => CTR => D6: 6 * DIS # F4: 9 => CTR => F4: 3,7 * DIS # B4: 7 => CTR => B4: 6,9 * DIS # F9: 7,9 => CTR => F9: 3,6 * DIS # D6: 7,9 => CTR => D6: 6 * DIS # F9: 6,9 => CTR => F9: 3,7 * CNT 8 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B3,C3,C6,D7,E3,E4,F2,G3,H4,H9,I2) * 846391275.1285.34....2.4.815.84..1.21...2845.42..15.386...428133.15...242.41..5.. * PAIR F2: 6,7 COL F F8: 6,7,9 # reduction candidate for 6,7 F8: 6,7 # 16 pairs F9: 6,7,3,9 # reduction candidate for 6,7 F9: 6,7 => CTR * 846391275.128573467..26498159847316216..2845.42..15.386..7428133.1589624284136597 * RESTART * PAIR F2: 6,7 COL F F8: 6,7,9 # reduction candidate for 6,7 F8: 9 => SOLVED * 846391275712856349935274681598437162163928457427615938659742813381569724274183596 * DURATION: 0:00:05.152052 START: 16:44:38.787998 END: 16:44:43.940050 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-406-base-pr-001.dot * REASONING * DIS # F9: 6,7 => CTR => F9: 3,9 * PRF F9: 3,9 # F8: 9 => SOL * STA F9: 3,9 + F8: 9 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 406 solution: 846391275712856349935274681598437162163928457427615938659742813381569724274183596 info: 94803 FNBXK S8.f 14147 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 846391275712856349935274681598437162163928457427615938659742813381569724274183596 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 # F8: 6,7 => UNS * DIS # F9: 6,7 => CTR => F9: 3,9 * INC # F9: 3,9 => UNS * INC # E8: 6,7 => UNS * INC # E9: 6,7 => UNS * INC # I5: 6,9 => UNS * INC # I9: 6,9 => UNS * INC # G6: 6,9 => UNS * INC # G8: 6,9 => UNS * INC # B4: 7,9 => UNS * DIS # B5: 7,9 => CTR => B5: 3,6 * INC # B5: 3,6 => UNS * INC # C5: 7,9 => UNS * DIS # D6: 7,9 => CTR => D6: 6 * INC # D6: 6 => UNS * INC # G6: 7,9 => UNS * INC # C7: 7,9 => UNS * INC # C7: 5 => UNS * INC # F4: 3,7 => UNS * DIS # F4: 9 => CTR => F4: 3,7 * INC # E9: 3,7 => UNS * INC # E9: 6,8 => UNS * INC # I5: 6,9 => UNS * INC # G6: 6,9 => UNS * INC # B4: 6,9 => UNS * DIS # B4: 7 => CTR => B4: 6,9 * INC # F8: 7,9 => UNS * DIS # F9: 7,9 => CTR => F9: 3,6 * INC # F9: 3,6 => UNS * INC # B7: 7,9 => UNS * INC # C7: 7,9 => UNS * INC # D5: 7,9 => UNS * DIS # D6: 7,9 => CTR => D6: 6 * INC # D6: 6 => UNS * INC # G8: 6,9 => UNS * INC # I9: 6,9 => UNS * DIS # F9: 6,9 => CTR => F9: 3,7 * INC # F9: 3,7 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F8: 6,7 => UNS * DIS # F9: 6,7 => CTR => F9: 3,9 * INC F9: 3,9 # F8: 6,7 => UNS * PRF F9: 3,9 # F8: 9 => SOL * STA F9: 3,9 + F8: 9 * CNT 4 HDP CHAINS / 4 HYP OPENED