Analysis of zz-www.sudokuoftheday.co.uk-20190228-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: 7..923.....8.7.......6.........4....6.1..2...95.....8.8...3.2.7..4......27...4..5 initial
Autosolve
position: 7..923.....847....4..6.8...38..4....641..2...95.....8.8...3.247..42.7...27...4..5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C7: 9 => SOL * DIS # G3: 3,9 => CTR => G3: 1,5,7 * DIS # H3: 3,9 => CTR => H3: 1,2,5,7 * PRF # C9: 6 => SOL * PRF # E5: 5,9 => SOL * DIS # F7: 5,9 => CTR => F7: 6 * PRF # F7: 6 => SOL * CNT 7 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C7: 9 => SOL * STA C7: 9 * CNT 1 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7..923.....8.7.......6.........4....6.1..2...95.....8.8...3.2.7..4......27...4..5 | initial |
| 7..923.....847....4..6.8...38..4....641..2...95.....8.8...3.247..42.7...27...4..5 | autosolve |
| 765923814198475326423618579382749651641852793957361482819536247534297168276184935 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) B1: 1,6 C1: 5,6 A2: 1,5 C3: 3,9 F2: 1,5 E3: 1,5 G1: 4,8 H1: 1,5 I1: 4,8 C4: 2,7 C6: 2,7 D4: 5,7 F4: 5,9 D6: 3,7 E6: 1,6 F6: 1,6 I5: 3,9 A8: 1,5 D7: 1,5 D9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,A2: 1.. / B1 = 1 => 0 pairs (X) / A2 = 1 => 0 pairs (_) F2,E3: 1.. / F2 = 1 => 0 pairs (X) / E3 = 1 => 0 pairs (_) E6,F6: 1.. / E6 = 1 => 0 pairs (X) / F6 = 1 => 0 pairs (_) D7,D9: 1.. / D7 = 1 => 21 pairs (_) / D9 = 1 => 0 pairs (*) B1,H1: 1.. / B1 = 1 => 0 pairs (X) / H1 = 1 => 0 pairs (_) A2,F2: 1.. / A2 = 1 => 0 pairs (*) / F2 = 1 => 0 pairs (X) B7,D7: 1.. / B7 = 1 => 0 pairs (*) / D7 = 1 => 0 pairs (X) A2,A8: 1.. / A2 = 1 => 0 pairs (*) / A8 = 1 => 0 pairs (X) E3,E6: 1.. / E3 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) F2,F6: 1.. / F2 = 1 => 0 pairs (X) / F6 = 1 => 0 pairs (_) B2,B3: 2.. / B2 = 2 => 22 pairs (_) / B3 = 2 => 21 pairs (_) C4,C6: 2.. / C4 = 2 => 15 pairs (_) / C6 = 2 => 21 pairs (_) C6,I6: 2.. / C6 = 2 => 21 pairs (_) / I6 = 2 => 15 pairs (_) D5,D6: 3.. / D5 = 3 => 22 pairs (_) / D6 = 3 => 21 pairs (_) B8,C9: 3.. / B8 = 3 => 23 pairs (_) / C9 = 3 => 22 pairs (_) C3,C9: 3.. / C3 = 3 => 23 pairs (_) / C9 = 3 => 22 pairs (_) G1,I1: 4.. / G1 = 4 => 19 pairs (_) / I1 = 4 => 19 pairs (_) G6,I6: 4.. / G6 = 4 => 19 pairs (_) / I6 = 4 => 19 pairs (_) G1,G6: 4.. / G1 = 4 => 19 pairs (_) / G6 = 4 => 19 pairs (_) I1,I6: 4.. / I1 = 4 => 19 pairs (_) / I6 = 4 => 19 pairs (_) C1,A2: 5.. / C1 = 5 => 0 pairs (*) / A2 = 5 => 0 pairs (X) F2,E3: 5.. / F2 = 5 => 0 pairs (*) / E3 = 5 => 0 pairs (X) C7,A8: 5.. / C7 = 5 => 0 pairs (X) / A8 = 5 => 0 pairs (_) C1,H1: 5.. / C1 = 5 => 0 pairs (*) / H1 = 5 => 0 pairs (X) A2,F2: 5.. / A2 = 5 => 0 pairs (X) / F2 = 5 => 0 pairs (_) A8,E8: 5.. / A8 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) A2,A8: 5.. / A2 = 5 => 0 pairs (X) / A8 = 5 => 0 pairs (_) C1,C7: 5.. / C1 = 5 => 0 pairs (*) / C7 = 5 => 0 pairs (X) B1,C1: 6.. / B1 = 6 => 0 pairs (*) / C1 = 6 => 0 pairs (X) E6,F6: 6.. / E6 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) F6,F7: 6.. / F6 = 6 => 0 pairs (X) / F7 = 6 => 0 pairs (_) G3,H3: 7.. / G3 = 7 => 21 pairs (_) / H3 = 7 => 20 pairs (_) C4,C6: 7.. / C4 = 7 => 21 pairs (_) / C6 = 7 => 15 pairs (_) G1,I1: 8.. / G1 = 8 => 19 pairs (_) / I1 = 8 => 19 pairs (_) D5,E5: 8.. / D5 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) D5,D9: 8.. / D5 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) I1,I8: 8.. / I1 = 8 => 19 pairs (_) / I8 = 8 => 19 pairs (_) F4,E5: 9.. / F4 = 9 => 22 pairs (_) / E5 = 9 => 0 pairs (X) F4,F7: 9.. / F4 = 9 => 22 pairs (_) / F7 = 9 => 0 pairs (X) * DURATION: 0:01:03.285691 START: 04:06:06.699511 END: 04:07:09.985202 2019-05-01 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B1,C1,C3,C4,C6,D4,D6,D7,D9,E3,E6,F2,F4,F6,G1,H1,I1,I5) * 7..923.....847....4..6.8...38..4....641..2...95.....8.8...3.247..42.7...27...4..5 * PAIR B1: 1,6 COL B B7: 1,6,9 # reduction candidate for 1,6 B7: 1,6 # 22 pairs B8: 1,6,3,9 # reduction candidate for 1,6 B8: 1,6 # 22 pairs * PAIR C1: 5,6 COL C C7: 5,6,9 # reduction candidate for 5,6 C7: 9 => SOLVED * 765923814198475326423618579382749651641852793957361482819536247534297168276184935 C7: 5,6 # 22 pairs * PAIR C3: 3,9 BLK 1 B2: 3,9,2 # reduction candidate for 3,9 B2: 3,9 # 21 pairs B3: 3,9,2 # reduction candidate for 3,9 B3: 3,9 # 22 pairs * PAIR C3: 3,9 ROW 3 G3: 3,9,1,5,7 # reduction candidate for 3,9 G3: 3,9 => CTR * 7..923.5.5.8471...4..658.7138..4....641..2...95..16.8.8.51392471.42.7...27.864..5 G3: 1,5,7 # 20 pairs H3: 3,9,1,2,5,7 # reduction candidate for 3,9 H3: 3,9 => CTR * 7..923.5.5.8471...4..6587.138..4....641..2...95..16.8.8.51392471.42.7...27.864..5 H3: 1,2,5,7 # 20 pairs I3: 3,9,1,2 # reduction candidate for 3,9 I3: 3,9 # 24 pairs * PAIR C3: 3,9 COL C C9: 3,9,6 # reduction candidate for 3,9 C9: 6 => SOLVED * 765923814198475326423618579382749651641852793957361482819536247534297168276184935 C9: 3,9 # 22 pairs * PAIR E3: 1,5 ROW 3 G3: 1,5,3,7,9 # reduction candidate for 1,5 G3: 1,5 # 21 pairs H3: 1,5,2,3,7,9 # reduction candidate for 1,5 H3: 1,5 # 22 pairs * PAIR H1: 1,5 BLK 3 G3: 1,5,3,7,9 # reduction candidate for 1,5 G3: 1,5 # 21 pairs H3: 1,5,2,3,7,9 # reduction candidate for 1,5 H3: 1,5 # 22 pairs * PAIR H1: 1,5 COL H H4: 1,5,2,6,7,9 # reduction candidate for 1,5 H4: 1,5 # 21 pairs H4: 2,6,7,9 # 20 pairs * PAIR C4: 2,7 ROW 4 H4: 2,7,1,5,6,9 # reduction candidate for 2,7 H4: 2,7 # 24 pairs H4: 1,5,6,9 # 20 pairs * PAIR D4: 5,7 BLK 5 D5: 5,7,3,8 # reduction candidate for 5,7 D5: 5,7 # 23 pairs D5: 3,8 # 22 pairs * PAIR D4: 5,7 ROW 4 G4: 5,7,1,6,9 # reduction candidate for 5,7 G4: 5,7 # 20 pairs H4: 5,7,1,2,6,9 # reduction candidate for 5,7 H4: 5,7 # 23 pairs * PAIR F4: 5,9 BLK 5 E5: 5,9,8 # reduction candidate for 5,9 E5: 5,9 => SOLVED * 765923814198475326423618579382749651641852793957361482819536247534297168276184935 E5: 8 # 21 pairs * PAIR F4: 5,9 ROW 4 G4: 5,9,1,6,7 # reduction candidate for 5,9 G4: 5,9 # 18 pairs H4: 5,9,1,2,6,7 # reduction candidate for 5,9 H4: 5,9 # 20 pairs * PAIR F4: 5,9 COL F F7: 5,9,6 # reduction candidate for 5,9 F7: 5,9 => CTR * 7..923.....8471...4..658...38..4....641..2...95..16.8.8...3.247..42.7...27...4..5 F7: 6 => SOLVED * 765923814198475326423618579382749651641852793957361482819536247534297168276184935 * PAIR D6: 3,7 BLK 5 D5: 3,7,5,8 # reduction candidate for 3,7 D5: 3,7 # 21 pairs D5: 5,8 # 15 pairs * PAIR D6: 3,7 ROW 6 G6: 3,7,4 # reduction candidate for 3,7 G6: 4 # 19 pairs G6: 3,7 # 19 pairs * PAIR I5: 3,9 BLK 6 G5: 3,9,5,7 # reduction candidate for 3,9 G5: 3,9 # 25 pairs H5: 3,9,5,7 # reduction candidate for 3,9 H5: 3,9 # 25 pairs * PAIR I5: 3,9 COL I I2: 3,9,2,6 # reduction candidate for 3,9 I2: 3,9 # 23 pairs I3: 3,9,1,2 # reduction candidate for 3,9 I3: 3,9 # 24 pairs I8: 3,9,1,6,8 # reduction candidate for 3,9 I8: 3,9 # 22 pairs * PAIR D9: 1,8 ROW 9 G9: 1,8,3,6,9 # reduction candidate for 1,8 G9: 1,8 # 22 pairs G9: 3,6,9 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190228-absurd-base-pr-000.dot * REASONING * PRF # C7: 9 => SOL * DIS # G3: 3,9 => CTR => G3: 1,5,7 * DIS # H3: 3,9 => CTR => H3: 1,2,5,7 * PRF # C9: 6 => SOL * PRF # E5: 5,9 => SOL * DIS # F7: 5,9 => CTR => F7: 6 * PRF # F7: 6 => SOL * CNT 7 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B1,C1,C3,C4,C6,D4,D6,D7,D9,E3,E6,F2,F4,F6,G1,H1,I1,I5) * 7..923.....847....4..6.8...38..4....641..2...95.....8.8...3.247..42.7...27...4..5 * PAIR B1: 1,6 COL B B7: 1,6,9 # reduction candidate for 1,6 B7: 1,6 # 22 pairs B8: 1,6,3,9 # reduction candidate for 1,6 B8: 1,6 # 22 pairs * PAIR C1: 5,6 COL C C7: 5,6,9 # reduction candidate for 5,6 C7: 9 => SOLVED * 765923814198475326423618579382749651641852793957361482819536247534297168276184935 * DURATION: 0:00:04.535706 START: 04:07:47.171658 END: 04:07:51.707364 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190228-absurd-base-pr-001.dot * REASONING * PRF # C7: 9 => SOL * STA C7: 9 * CNT 1 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190228, absurd
Solution
position: 765923814198475326423618579382749651641852793957361482819536247534297168276184935 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 # B7: 1,6 => UNS * INC # B8: 1,6 => UNS * INC # C7: 5,6 => UNS * PRF # C7: 9 => SOL * INC # B2: 3,9 => UNS * INC # B3: 3,9 => UNS * DIS # G3: 3,9 => CTR => G3: 1,5,7 * INC # G3: 1,5,7 => UNS * DIS # H3: 3,9 => CTR => H3: 1,2,5,7 * INC # H3: 1,2,5,7 => UNS * INC # I3: 3,9 => UNS * INC # C9: 3,9 => UNS * PRF # C9: 6 => SOL * INC # G3: 1,5 => UNS * INC # H3: 1,5 => UNS * INC # G3: 1,5 => UNS * INC # H3: 1,5 => UNS * INC # H4: 1,5 => UNS * INC # H4: 2,6,7,9 => UNS * INC # H4: 2,7 => UNS * INC # H4: 1,5,6,9 => UNS * INC # D5: 5,7 => UNS * INC # D5: 3,8 => UNS * INC # G4: 5,7 => UNS * INC # H4: 5,7 => UNS * PRF # E5: 5,9 => SOL * INC # E5: 8 => UNS * INC # G4: 5,9 => UNS * INC # H4: 5,9 => UNS * DIS # F7: 5,9 => CTR => F7: 6 * PRF # F7: 6 => SOL * INC # D5: 3,7 => UNS * INC # D5: 5,8 => UNS * INC # G6: 3,7 => UNS * INC # G6: 4 => UNS * INC # G5: 3,9 => UNS * INC # H5: 3,9 => UNS * INC # I2: 3,9 => UNS * INC # I3: 3,9 => UNS * INC # I8: 3,9 => UNS * INC # G9: 1,8 => UNS * INC # G9: 3,6,9 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B7: 1,6 => UNS * INC # B8: 1,6 => UNS * INC # C7: 5,6 => UNS * PRF # C7: 9 => SOL * STA C7: 9 * CNT 4 HDP CHAINS / 4 HYP OPENED