Analysis of zz-www.sudokuoftheday.co.uk-20190211-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: ..58..9...........79....4314.......76.......8.1....2...64..78..8..6.3......9.8.5. initial
Autosolve
position: ..58..9....6....8.798...43148......76.......8.1..8.2...64..78.38..6.3......9.8.5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 7 => CTR => H1: 2,6 * DIS # I9: 2,6 => CTR => I9: 4 * PRF # I9: 4 => SOL * PRF # F6: 5,9 => SOL * DIS # B5: 3,7 => CTR => B5: 2,5 * DIS # C9: 3,7 => CTR => C9: 1,2 * DIS # C9: 2,3 => CTR => C9: 1,7 * DIS # G9: 1,7 => CTR => G9: 6 * DIS # C8: 1,7 => CTR => C8: 2,9 * CNT 9 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 7 => CTR => H1: 2,6 * PRF H1: 2,6 # F6: 5,9 => SOL * STA H1: 2,6 + F6: 5,9 * CNT 2 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..58..9...........79....4314.......76.......8.1....2...64..78..8..6.3......9.8.5. | initial |
| ..58..9....6....8.798...43148......76.......8.1..8.2...64..78.38..6.3......9.8.5. | autosolve |
| 135874962246391785798562431489236517627415398513789246964157823852643179371928654 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) F1: 1,4 D3: 2,5 I1: 2,6 G2: 5,7 I2: 2,5 A6: 5,9 C6: 3,7 D6: 3,7 A7: 5,9 A9: 2,3 G8: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A2: 1.. / A1 = 1 => 15 pairs (_) / A2 = 1 => 13 pairs (_) C8,C9: 1.. / C8 = 1 => 0 pairs (X) / C9 = 1 => 13 pairs (_) G4,G5: 3.. / G4 = 3 => 15 pairs (_) / G5 = 3 => 11 pairs (_) C6,D6: 3.. / C6 = 3 => 10 pairs (_) / D6 = 3 => 11 pairs (_) B1,B2: 4.. / B1 = 4 => 14 pairs (_) / B2 = 4 => 13 pairs (_) E8,E9: 4.. / E8 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) B1,F1: 4.. / B1 = 4 => 14 pairs (_) / F1 = 4 => 13 pairs (_) E9,I9: 4.. / E9 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) D2,D5: 4.. / D2 = 4 => 14 pairs (_) / D5 = 4 => 12 pairs (_) G2,I2: 5.. / G2 = 5 => 0 pairs (X) / I2 = 5 => 20 pairs (_) B5,A6: 5.. / B5 = 5 => 0 pairs (X) / A6 = 5 => 0 pairs (_) A7,B8: 5.. / A7 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) B8,E8: 5.. / B8 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) A6,A7: 5.. / A6 = 5 => 0 pairs (*) / A7 = 5 => 0 pairs (X) B5,B8: 5.. / B5 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) I2,I6: 5.. / I2 = 5 => 20 pairs (_) / I6 = 5 => 0 pairs (X) E3,F3: 6.. / E3 = 6 => 12 pairs (_) / F3 = 6 => 18 pairs (_) H1,I1: 6.. / H1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) G9,I9: 6.. / G9 = 6 => 13 pairs (_) / I9 = 6 => 0 pairs (X) E3,E4: 6.. / E3 = 6 => 12 pairs (_) / E4 = 6 => 18 pairs (_) G4,G9: 6.. / G4 = 6 => 0 pairs (X) / G9 = 6 => 13 pairs (_) H1,G2: 7.. / H1 = 7 => 0 pairs (X) / G2 = 7 => 20 pairs (_) E1,H1: 7.. / E1 = 7 => 20 pairs (_) / H1 = 7 => 0 pairs (X) C6,D6: 7.. / C6 = 7 => 11 pairs (_) / D6 = 7 => 10 pairs (_) H1,H8: 7.. / H1 = 7 => 0 pairs (X) / H8 = 7 => 20 pairs (_) E2,F2: 9.. / E2 = 9 => 15 pairs (_) / F2 = 9 => 11 pairs (_) A7,C8: 9.. / A7 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) A7,H7: 9.. / A7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) A6,A7: 9.. / A6 = 9 => 0 pairs (X) / A7 = 9 => 0 pairs (_) I6,I8: 9.. / I6 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) * DURATION: 0:00:34.504390 START: 03:39:16.972146 END: 03:39:51.476536 2019-05-01 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,A9,C6,D3,D6,F1,G2,G8,I1,I2) * ..58..9....6....8.798...43148......76.......8.1..8.2...64..78.38..6.3......9.8.5. * PAIR F1: 1,4 BLK 2 D2: 1,4,3,7 # reduction candidate for 1,4 D2: 1,4 # 14 pairs F2: 1,4,9 # reduction candidate for 1,4 F2: 1,4 # 15 pairs * PAIR F1: 1,4 COL F F5: 1,4,2,5,9 # reduction candidate for 1,4 F5: 1,4 # 14 pairs F5: 2,5,9 # 11 pairs * PAIR D3: 2,5 BLK 2 E3: 2,5,6 # reduction candidate for 2,5 E3: 2,5 # 18 pairs F3: 2,5,6 # reduction candidate for 2,5 F3: 2,5 # 12 pairs * PAIR D3: 2,5 COL D D4: 2,5,1,3 # reduction candidate for 2,5 D4: 2,5 # 16 pairs D5: 2,5,1,3,4,7 # reduction candidate for 2,5 D5: 2,5 # 20 pairs D7: 2,5,1 # reduction candidate for 2,5 D7: 2,5 # 14 pairs * PAIR I1: 2,6 BLK 3 H1: 2,6,7 # reduction candidate for 2,6 H1: 7 => CTR * ..58..976..6...582798...43148......76.......8.1..8.2.5564..78938.9653.24...9.8.5. H1: 2,6 # 20 pairs * PAIR I1: 2,6 COL I I9: 2,6,4 # reduction candidate for 2,6 I9: 2,6 => CTR * ..587.9262.6...785798...43148......76.......8.1..8.2.9964..78.38..6.3174..1948652 I9: 4 => SOLVED * 135874962246391785798562431489236517627415398513789246964157823852643179371928654 * PAIR A6: 5,9 ROW 6 F6: 5,9,4,6 # reduction candidate for 5,9 F6: 5,9 => SOLVED * 135874962246391785798562431489236517627415398513789246964157823852643179371928654 F6: 4,6 # 12 pairs I6: 5,9,4,6 # reduction candidate for 5,9 I6: 5,9 # 14 pairs * PAIR C6: 3,7 BLK 4 B5: 3,7,2,5 # reduction candidate for 3,7 B5: 3,7 => CTR * ..587.9.2..6...785798...43148......76.......851..8.2.6964..7823852643179371928654 B5: 2,5 # 13 pairs C5: 3,7,2,9 # reduction candidate for 3,7 C5: 3,7 # 15 pairs * PAIR C6: 3,7 COL C C9: 3,7,1,2 # reduction candidate for 3,7 C9: 3,7 => CTR * ..58..976..6...582798...43148......76.......8.1..8.2.5.64..78.38.16.37.....9.8.5. C9: 1,2 # 12 pairs * PAIR D6: 3,7 BLK 5 D5: 3,7,1,2,4,5 # reduction candidate for 3,7 D5: 3,7 # 15 pairs E5: 3,7,1,2,5,9 # reduction candidate for 3,7 E5: 3,7 # 14 pairs * PAIR D6: 3,7 COL D D2: 3,7,1,4 # reduction candidate for 3,7 D2: 1,4 # 14 pairs D2: 3,7 # 13 pairs * PAIR A9: 2,3 BLK 7 B9: 2,3,7 # reduction candidate for 2,3 B9: 2,3 # 17 pairs C9: 2,3,1,7 # reduction candidate for 2,3 C9: 2,3 => CTR * ..58..976..6...582798...43148......76.......8.1..8.2.5.64..78.38.16.37...7.9.8.5. C9: 1,7 # 12 pairs * PAIR A9: 2,3 COL A A1: 2,3,1 # reduction candidate for 2,3 A1: 2,3 # 13 pairs A2: 2,3,1 # reduction candidate for 2,3 A2: 2,3 # 15 pairs * PAIR G8: 1,7 BLK 9 H8: 1,7,2,4,9 # reduction candidate for 1,7 H8: 1,7 # 23 pairs G9: 1,7,6 # reduction candidate for 1,7 G9: 1,7 => CTR * ..58..9....6....8.798...43148....6.76.....3.8.1..862.5564..78938.9653.....1948756 G9: 6 # 13 pairs * PAIR G8: 1,7 ROW 8 C8: 1,7,2,9 # reduction candidate for 1,7 C8: 1,7 => CTR * ..58..9....6...785798...43148......76.......851..8.2..964..78.385.6.317....9.8.5. C8: 2,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190211-absurd-base-pr-000.dot * REASONING * DIS # H1: 7 => CTR => H1: 2,6 * DIS # I9: 2,6 => CTR => I9: 4 * PRF # I9: 4 => SOL * PRF # F6: 5,9 => SOL * DIS # B5: 3,7 => CTR => B5: 2,5 * DIS # C9: 3,7 => CTR => C9: 1,2 * DIS # C9: 2,3 => CTR => C9: 1,7 * DIS # G9: 1,7 => CTR => G9: 6 * DIS # C8: 1,7 => CTR => C8: 2,9 * CNT 9 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,A9,C6,D3,D6,F1,G2,G8,I1,I2) * ..58..9....6....8.798...43148......76.......8.1..8.2...64..78.38..6.3......9.8.5. * PAIR F1: 1,4 BLK 2 D2: 1,4,3,7 # reduction candidate for 1,4 D2: 1,4 # 14 pairs F2: 1,4,9 # reduction candidate for 1,4 F2: 1,4 # 15 pairs * PAIR F1: 1,4 COL F F5: 1,4,2,5,9 # reduction candidate for 1,4 F5: 1,4 # 14 pairs F5: 2,5,9 # 11 pairs * PAIR D3: 2,5 BLK 2 E3: 2,5,6 # reduction candidate for 2,5 E3: 2,5 # 18 pairs F3: 2,5,6 # reduction candidate for 2,5 F3: 2,5 # 12 pairs * PAIR D3: 2,5 COL D D4: 2,5,1,3 # reduction candidate for 2,5 D4: 2,5 # 16 pairs D5: 2,5,1,3,4,7 # reduction candidate for 2,5 D5: 2,5 # 20 pairs D7: 2,5,1 # reduction candidate for 2,5 D7: 2,5 # 14 pairs * PAIR I1: 2,6 BLK 3 H1: 2,6,7 # reduction candidate for 2,6 H1: 7 => CTR * ..58..976..6...582798...43148......76.......8.1..8.2.5564..78938.9653.24...9.8.5. * PAIR A6: 5,9 ROW 6 F6: 5,9,6 # reduction candidate for 5,9 F6: 5,9 => SOLVED * 135874962246391785798562431489236517627415398513789246964157823852643179371928654 * DURATION: 0:00:08.380960 START: 03:40:13.015346 END: 03:40:21.396306 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190211-absurd-base-pr-001.dot * REASONING * DIS # H1: 7 => CTR => H1: 2,6 * PRF H1: 2,6 # F6: 5,9 => SOL * STA H1: 2,6 + F6: 5,9 * CNT 2 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190211, absurd
Solution
position: 135874962246391785798562431489236517627415398513789246964157823852643179371928654 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 # D2: 1,4 => UNS * INC # F2: 1,4 => UNS * INC # F5: 1,4 => UNS * INC # F5: 2,5,9 => UNS * INC # E3: 2,5 => UNS * INC # F3: 2,5 => UNS * INC # D4: 2,5 => UNS * INC # D5: 2,5 => UNS * INC # D7: 2,5 => UNS * INC # H1: 2,6 => UNS * DIS # H1: 7 => CTR => H1: 2,6 * DIS # I9: 2,6 => CTR => I9: 4 * PRF # I9: 4 => SOL * PRF # F6: 5,9 => SOL * INC # F6: 4,6 => UNS * INC # I6: 5,9 => UNS * DIS # B5: 3,7 => CTR => B5: 2,5 * INC # B5: 2,5 => UNS * INC # C5: 3,7 => UNS * DIS # C9: 3,7 => CTR => C9: 1,2 * INC # C9: 1,2 => UNS * INC # D5: 3,7 => UNS * INC # E5: 3,7 => UNS * INC # D2: 3,7 => UNS * INC # D2: 1,4 => UNS * INC # B9: 2,3 => UNS * DIS # C9: 2,3 => CTR => C9: 1,7 * INC # C9: 1,7 => UNS * INC # A1: 2,3 => UNS * INC # A2: 2,3 => UNS * INC # H8: 1,7 => UNS * DIS # G9: 1,7 => CTR => G9: 6 * INC # G9: 6 => UNS * DIS # C8: 1,7 => CTR => C8: 2,9 * INC # C8: 2,9 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 1,4 => UNS * INC # F2: 1,4 => UNS * INC # F5: 1,4 => UNS * INC # F5: 2,5,9 => UNS * INC # E3: 2,5 => UNS * INC # F3: 2,5 => UNS * INC # D4: 2,5 => UNS * INC # D5: 2,5 => UNS * INC # D7: 2,5 => UNS * INC # H1: 2,6 => UNS * DIS # H1: 7 => CTR => H1: 2,6 * PRF H1: 2,6 # F6: 5,9 => SOL * STA H1: 2,6 + F6: 5,9 * CNT 12 HDP CHAINS / 12 HYP OPENED