Analysis of xx-top500-016-base.sdk
Contents
Original Sudoku
level: medium
position: 1.....8....2.7........3.5..43.....7....5..1.....6.....6..1......5.....3.....2.... initial
Autosolve
position: 175...8.33.2.75.1.....315.743.....752.75.31..5..6.73.262315.7...5.7..23.7..32..5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 8,9 => CTR => B2: 4,6 * PRF # C3: 8,9 => SOL * DIS # D3: 8,9 => CTR => D3: 2,4 * DIS # F1: 6,9 => CTR => F1: 2 * DIS # E8: 6,9 => CTR => E8: 8 * DIS # F4: 2,9 => CTR => F4: 8 * PRF # D1: 2,9 => SOL * DIS # I5: 6,9 => CTR => I5: 4,8 * DIS # C4: 1,8 => CTR => C4: 6,9 * DIS # C8: 8,9 => CTR => C8: 1,4 * DIS # F8: 8,9 => CTR => F8: 4,6 * DIS # I8: 8,9 => CTR => I8: 1,4,6 * CNT 12 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 8,9 => CTR => B2: 4,6 * PRF B2: 4,6 # C3: 8,9 => SOL * STA B2: 4,6 + C3: 8,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.....8....2.7........3.5..43.....7....5..1.....6.....6..1......5.....3.....2.... | initial |
| 175...8.33.2.75.1.....315.743.....752.75.31..5..6.73.262315.7...5.7..23.7..32..5. | autosolve |
| 175962843342875619869431527436218975287593164591647382623154798954786231718329456 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A3: 8,9 E1: 6,9 D4: 2,9 G4: 6,9 A8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,E6: 1.. / E4 = 1 => 5 pairs (_) / E6 = 1 => 0 pairs (X) I8,I9: 1.. / I8 = 1 => 5 pairs (_) / I9 = 1 => 10 pairs (_) C4,E4: 1.. / C4 = 1 => 0 pairs (X) / E4 = 1 => 5 pairs (_) C8,I8: 1.. / C8 = 1 => 10 pairs (_) / I8 = 1 => 5 pairs (_) B6,B9: 1.. / B6 = 1 => 6 pairs (_) / B9 = 1 => 6 pairs (_) H1,H3: 2.. / H1 = 2 => 0 pairs (X) / H3 = 2 => 15 pairs (_) D4,F4: 2.. / D4 = 2 => 15 pairs (_) / F4 = 2 => 0 pairs (X) D3,H3: 2.. / D3 = 2 => 0 pairs (X) / H3 = 2 => 15 pairs (_) F1,F4: 2.. / F1 = 2 => 15 pairs (_) / F4 = 2 => 0 pairs (X) E5,E6: 4.. / E5 = 4 => 9 pairs (_) / E6 = 4 => 7 pairs (_) D1,H1: 4.. / D1 = 4 => 7 pairs (_) / H1 = 4 => 0 pairs (*) E6,H6: 4.. / E6 = 4 => 7 pairs (_) / H6 = 4 => 9 pairs (_) G2,G9: 4.. / G2 = 4 => 9 pairs (_) / G9 = 4 => 10 pairs (_) E1,F1: 6.. / E1 = 6 => 8 pairs (_) / F1 = 6 => 0 pairs (X) C4,B5: 6.. / C4 = 6 => 15 pairs (_) / B5 = 6 => 0 pairs (X) C4,G4: 6.. / C4 = 6 => 15 pairs (_) / G4 = 6 => 0 pairs (X) C3,C4: 6.. / C3 = 6 => 0 pairs (X) / C4 = 6 => 15 pairs (_) E1,E8: 6.. / E1 = 6 => 8 pairs (_) / E8 = 6 => 0 pairs (X) H3,H5: 6.. / H3 = 6 => 0 pairs (X) / H5 = 6 => 15 pairs (_) D2,D3: 8.. / D2 = 8 => 5 pairs (_) / D3 = 8 => 0 pairs (X) B2,D2: 8.. / B2 = 8 => 0 pairs (X) / D2 = 8 => 5 pairs (_) A3,A8: 8.. / A3 = 8 => 6 pairs (_) / A8 = 8 => 0 pairs (X) A3,A8: 9.. / A3 = 9 => 0 pairs (X) / A8 = 9 => 6 pairs (_) * DURATION: 0:00:35.688519 START: 03:08:22.813974 END: 03:08:58.502493 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,D4,E1,G4) * 175...8.33.2.75.1.....315.743.....752.75.31..5..6.73.262315.7...5.7..23.7..32..5. * PAIR A3: 8,9 BLK 1 B2: 8,9,4,6 # reduction candidate for 8,9 B2: 8,9 => CTR * 1754628933928754168649315274362189752875931645..6.73.262315.7..95178.23.74832.651 B2: 4,6 # 8 pairs B3: 8,9,4,6 # reduction candidate for 8,9 B3: 8,9 # 10 pairs C3: 8,9,4,6 # reduction candidate for 8,9 C3: 8,9 => SOLVED * 175962843342875619869431527436218975287593164591647382623154798954786231718329456 C3: 4,6 # 6 pairs * PAIR A3: 8,9 ROW 3 D3: 8,9,2,4 # reduction candidate for 8,9 D3: 8,9 => CTR * 1754628933928754168649315274362189752875931645..6.73.262315.7..95178.23.74832.651 D3: 2,4 # 7 pairs * PAIR E1: 6,9 BLK 2 F1: 6,9,2 # reduction candidate for 6,9 F1: 6,9 => CTR * 175...8.33.2.75.16..6.315.743.9.26752675.31..5..6.73.262315.7...5.7..23.7..326.5. F1: 2 # 15 pairs * PAIR E1: 6,9 COL E E8: 6,9,8 # reduction candidate for 6,9 E8: 6,9 => CTR * 175...8.33.2.75.1...6.315.743....6752675.31..5..6.73.262315.7...5.7..23.7..32..5. E8: 8 # 15 pairs * PAIR D4: 2,9 BLK 5 F4: 2,9,8 # reduction candidate for 2,9 F4: 2,9 => CTR * 175...8.33.2.75.1...6.315.743....6752675.31..5..6.73.262315.7...5.7..23.7..32..5. F4: 8 # 15 pairs * PAIR D4: 2,9 COL D D1: 2,9,4 # reduction candidate for 2,9 D1: 2,9 => SOLVED * 175962843342875619869431527436218975287593164591647382623154798954786231718329456 D1: 4 # 7 pairs D3: 2,9,4,8 # reduction candidate for 2,9 D3: 2,9 # 7 pairs * PAIR G4: 6,9 BLK 6 H5: 6,9,4,8 # reduction candidate for 6,9 H5: 6,9 # 8 pairs I5: 6,9,4,8 # reduction candidate for 6,9 I5: 6,9 => CTR * 1754..8233.2.75.1....2315674369...752.75.31..5..6.73.262315.79..5.7..23.7..32..5. I5: 4,8 # 6 pairs * PAIR G4: 6,9 ROW 4 C4: 6,9,1,8 # reduction candidate for 6,9 C4: 1,8 => CTR * 175...8.33.2.75.1...6.315.743....6752675.31..5..6.73.262315.7...5.7..23.7..32..5. C4: 6,9 # 15 pairs * PAIR G4: 6,9 COL G G2: 6,9,4 # reduction candidate for 6,9 G2: 6,9 # 10 pairs G9: 6,9,4 # reduction candidate for 6,9 G9: 6,9 # 9 pairs * PAIR A8: 8,9 BLK 7 C8: 8,9,1,4 # reduction candidate for 8,9 C8: 8,9 => CTR * 175.968.33.2.75.1.....315.743.9.26752675.31..5..6.73.262315.7...5.7642317..32..56 C8: 1,4 # 6 pairs B9: 8,9,1,4 # reduction candidate for 8,9 B9: 8,9 # 9 pairs C9: 8,9,1,4 # reduction candidate for 8,9 C9: 8,9 # 8 pairs * PAIR A8: 8,9 ROW 8 E8: 8,9,6 # reduction candidate for 8,9 E8: 8,9 # 8 pairs F8: 8,9,4,6 # reduction candidate for 8,9 F8: 8,9 => CTR * 175.968.33.2.75.1.....315.743.9.26752675.31..5..6.73.262315.7...5.76.23.7..32..56 F8: 4,6 # 6 pairs I8: 8,9,1,4,6 # reduction candidate for 8,9 I8: 8,9 => CTR * 175.968.33.2.7541.....315.743691..752.75.31..51.6.73.262315.7...5176423.7..32.651 I8: 1,4,6 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-016-base-pr-000.dot * REASONING * DIS # B2: 8,9 => CTR => B2: 4,6 * PRF # C3: 8,9 => SOL * DIS # D3: 8,9 => CTR => D3: 2,4 * DIS # F1: 6,9 => CTR => F1: 2 * DIS # E8: 6,9 => CTR => E8: 8 * DIS # F4: 2,9 => CTR => F4: 8 * PRF # D1: 2,9 => SOL * DIS # I5: 6,9 => CTR => I5: 4,8 * DIS # C4: 1,8 => CTR => C4: 6,9 * DIS # C8: 8,9 => CTR => C8: 1,4 * DIS # F8: 8,9 => CTR => F8: 4,6 * DIS # I8: 8,9 => CTR => I8: 1,4,6 * CNT 12 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,D4,E1,G4) * 175...8.33.2.75.1.....315.743.....752.75.31..5..6.73.262315.7...5.7..23.7..32..5. * PAIR A3: 8,9 BLK 1 B2: 8,9,4,6 # reduction candidate for 8,9 B2: 8,9 => CTR * 1754628933928754168649315274362189752875931645..6.73.262315.7..95178.23.74832.651 B3: 8,9,4,6 # reduction candidate for 8,9 B3: 8,9 # 10 pairs C3: 8,9,4,6 # reduction candidate for 8,9 C3: 8,9 => SOLVED * 175962843342875619869431527436218975287593164591647382623154798954786231718329456 * DURATION: 0:00:04.312290 START: 03:09:26.443094 END: 03:09:30.755384 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-016-base-pr-001.dot * REASONING * DIS # B2: 8,9 => CTR => B2: 4,6 * PRF B2: 4,6 # C3: 8,9 => SOL * STA B2: 4,6 + C3: 8,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 016 solution: 175962843342875619869431527436218975287593164591647382623154798954786231718329456 info: 1310 FNBWXY S8.f 44468 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 175962843342875619869431527436218975287593164591647382623154798954786231718329456 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 # B2: 8,9 => CTR => B2: 4,6 * INC # B2: 4,6 => UNS * INC # B3: 8,9 => UNS * PRF # C3: 8,9 => SOL * INC # C3: 4,6 => UNS * DIS # D3: 8,9 => CTR => D3: 2,4 * INC # D3: 2,4 => UNS * DIS # F1: 6,9 => CTR => F1: 2 * INC # F1: 2 => UNS * DIS # E8: 6,9 => CTR => E8: 8 * INC # E8: 8 => UNS * DIS # F4: 2,9 => CTR => F4: 8 * INC # F4: 8 => UNS * PRF # D1: 2,9 => SOL * INC # D1: 4 => UNS * INC # D3: 2,9 => UNS * INC # H5: 6,9 => UNS * DIS # I5: 6,9 => CTR => I5: 4,8 * INC # I5: 4,8 => UNS * INC # C4: 6,9 => UNS * DIS # C4: 1,8 => CTR => C4: 6,9 * INC # G2: 6,9 => UNS * INC # G9: 6,9 => UNS * DIS # C8: 8,9 => CTR => C8: 1,4 * INC # C8: 1,4 => UNS * INC # B9: 8,9 => UNS * INC # C9: 8,9 => UNS * INC # E8: 8,9 => UNS * DIS # F8: 8,9 => CTR => F8: 4,6 * INC # F8: 4,6 => UNS * DIS # I8: 8,9 => CTR => I8: 1,4,6 * INC # I8: 1,4,6 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 8,9 => CTR => B2: 4,6 * INC B2: 4,6 # B3: 8,9 => UNS * PRF B2: 4,6 # C3: 8,9 => SOL * STA B2: 4,6 + C3: 8,9 * CNT 3 HDP CHAINS / 3 HYP OPENED