Analysis of zz-www.sudokuoftheday.co.uk-20190304-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: .6....4....2.........78..59...3.6....8142.....9....2...4...9...3.......7.2..78..1 initial
Autosolve
position: .6....4....2......1347826592..396..468142....4938..2...4.139...31.2....7.2..78341 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 5,7 => SOL * DIS # A2: 5,7 => CTR => A2: 8,9 * PRF # D2: 5,9 => SOL * DIS # D2: 6 => CTR => D2: 5,9 * PRF # A1: 5,9 => SOL * DIS # C1: 5,9 => CTR => C1: 7,8 * PRF # C1: 7,8 => SOL * DIS # F1: 1,5 => CTR => F1: 3 * DIS # F2: 1,5 => CTR => F2: 3,4 * PRF # C1: 5,7 => SOL * DIS # F6: 5,7 => CTR => F6: 1 * DIS # F6: 7 => CTR => F6: 1,5 * DIS # G2: 1,8 => CTR => G2: 7 * PRF # C9: 5,9 => SOL * DIS # C9: 6 => CTR => C9: 5,9 * PRF # A1: 5,9 => SOL * PRF # F2: 4,5 => SOL * DIS # F2: 1,3 => CTR => F2: 4,5 * DIS # C9: 5,6 => CTR => C9: 9 * PRF # C9: 9 => SOL * DIS # D2: 5,6 => CTR => D2: 9 * PRF # D2: 9 => SOL * DIS # I7: 5,8 => CTR => I7: 2,6 * CNT 23 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 # C1: 5,7 => SOL * STA C1: 5,7 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6....4....2.........78..59...3.6....8142.....9....2...4...9...3.......7.2..78..1 | initial |
| .6....4....2......1347826592..396..468142....4938..2...4.139...31.2....7.2..78341 | autosolve |
| 967513428852964713134782659275396184681427935493851276748139562316245897529678341 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B2: 5,7 D1: 5,9 E1: 1,5 E2: 4,6 I2: 3,8 B4: 5,7 C4: 5,7 F5: 5,7 E6: 1,5 G4: 1,8 H4: 1,8 I5: 3,5 H6: 6,7 I6: 5,6 A9: 5,9 E8: 4,6 F8: 4,5 D9: 5,6 G7: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E6,F6: 1.. / E6 = 1 => 0 pairs (X) / F6 = 1 => 21 pairs (_) G4,H4: 1.. / G4 = 1 => 20 pairs (_) / H4 = 1 => 0 pairs (X) E1,E6: 1.. / E1 = 1 => 21 pairs (_) / E6 = 1 => 0 pairs (X) G2,G4: 1.. / G2 = 1 => 0 pairs (X) / G4 = 1 => 20 pairs (_) H1,I1: 2.. / H1 = 2 => 19 pairs (_) / I1 = 2 => 19 pairs (_) H7,I7: 2.. / H7 = 2 => 19 pairs (_) / I7 = 2 => 19 pairs (_) H1,H7: 2.. / H1 = 2 => 19 pairs (_) / H7 = 2 => 19 pairs (_) I1,I7: 2.. / I1 = 2 => 19 pairs (_) / I7 = 2 => 19 pairs (_) F1,F2: 3.. / F1 = 3 => 20 pairs (_) / F2 = 3 => 0 pairs (X) H5,I5: 3.. / H5 = 3 => 19 pairs (_) / I5 = 3 => 20 pairs (_) E2,F2: 4.. / E2 = 4 => 0 pairs (X) / F2 = 4 => 0 pairs (_) E8,F8: 4.. / E8 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) E2,E8: 4.. / E2 = 4 => 0 pairs (X) / E8 = 4 => 0 pairs (_) F2,F8: 4.. / F2 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) B4,C4: 5.. / B4 = 5 => 0 pairs (X) / C4 = 5 => 19 pairs (_) F8,D9: 5.. / F8 = 5 => 0 pairs (*) / D9 = 5 => 0 pairs (X) B2,B4: 5.. / B2 = 5 => 19 pairs (_) / B4 = 5 => 0 pairs (X) E1,E6: 5.. / E1 = 5 => 0 pairs (X) / E6 = 5 => 21 pairs (_) D2,E2: 6.. / D2 = 6 => 0 pairs (X) / E2 = 6 => 0 pairs (_) H6,I6: 6.. / H6 = 6 => 0 pairs (X) / I6 = 6 => 22 pairs (_) E8,D9: 6.. / E8 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) C9,D9: 6.. / C9 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) D2,D9: 6.. / D2 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) E2,E8: 6.. / E2 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) I6,I7: 6.. / I6 = 6 => 22 pairs (_) / I7 = 6 => 0 pairs (X) B4,C4: 7.. / B4 = 7 => 19 pairs (_) / C4 = 7 => 0 pairs (X) F5,F6: 7.. / F5 = 7 => 22 pairs (_) / F6 = 7 => 0 pairs (X) A7,C7: 7.. / A7 = 7 => 19 pairs (_) / C7 = 7 => 26 pairs (_) F6,H6: 7.. / F6 = 7 => 0 pairs (X) / H6 = 7 => 22 pairs (_) B2,B4: 7.. / B2 = 7 => 0 pairs (X) / B4 = 7 => 19 pairs (_) G2,G5: 7.. / G2 = 7 => 22 pairs (_) / G5 = 7 => 0 pairs (X) G4,H4: 8.. / G4 = 8 => 0 pairs (X) / H4 = 8 => 20 pairs (_) D1,D2: 9.. / D1 = 9 => 0 pairs (X) / D2 = 9 => 0 pairs (_) G5,H5: 9.. / G5 = 9 => 24 pairs (_) / H5 = 9 => 22 pairs (_) A9,C9: 9.. / A9 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) G8,H8: 9.. / G8 = 9 => 22 pairs (_) / H8 = 9 => 24 pairs (_) A2,D2: 9.. / A2 = 9 => 0 pairs (X) / D2 = 9 => 0 pairs (_) C1,C9: 9.. / C1 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) G5,G8: 9.. / G5 = 9 => 24 pairs (_) / G8 = 9 => 22 pairs (_) H5,H8: 9.. / H5 = 9 => 22 pairs (_) / H8 = 9 => 24 pairs (_) * DURATION: 0:01:00.765513 START: 04:13:03.045028 END: 04:14:03.810541 2019-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B2,B4,C4,D1,D9,E1,E2,E6,E8,F5,F8,G4,G7,H4,H6,I2,I5,I6) * .6....4....2......1347826592..396..468142....4938..2...4.139...31.2....7.2..78341 * PAIR B2: 5,7 BLK 1 A1: 5,7,8,9 # reduction candidate for 5,7 A1: 5,7 # 22 pairs C1: 5,7,8,9 # reduction candidate for 5,7 C1: 5,7 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 C1: 8,9 # 20 pairs A2: 5,7,8,9 # reduction candidate for 5,7 A2: 5,7 => CTR * .6.5134....296471.1347826592..396..4681427...493851276.4.139...31.245..7.2.678341 A2: 8,9 # 20 pairs * PAIR D1: 5,9 BLK 2 D2: 5,9,6 # reduction candidate for 5,9 D2: 5,9 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 D2: 6 => CTR * .6.9..4..9.264....1347826592..396..468142....4938..2...4.139...31.264..752..78341 * PAIR D1: 5,9 ROW 1 A1: 5,9,7,8 # reduction candidate for 5,9 A1: 5,9 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 A1: 7,8 # 20 pairs C1: 5,9,7,8 # reduction candidate for 5,9 C1: 5,9 => CTR * 76..134..852964713134782659275396184681427.3549385127654713986231.2....7.2..78341 C1: 7,8 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 * PAIR E1: 1,5 BLK 2 F1: 1,5,3 # reduction candidate for 1,5 F1: 1,5 => CTR * .6.9..4..9.2..3..81347826592..396..468142....4938..2...4.139...31.2.4..7.2.578341 F1: 3 # 20 pairs F2: 1,5,3,4 # reduction candidate for 1,5 F2: 1,5 => CTR * .69..34....2.4....1347826592..396..468142....4938..2...4.139...31.264..7.26578341 F2: 3,4 # 20 pairs * PAIR I2: 3,8 BLK 3 H1: 3,8,1,2,7 # reduction candidate for 3,8 H1: 3,8 # 24 pairs I1: 3,8,2 # reduction candidate for 3,8 I1: 3,8 # 19 pairs H2: 3,8,1,7 # reduction candidate for 3,8 H2: 3,8 # 22 pairs * PAIR C4: 5,7 COL C C1: 5,7,8,9 # reduction candidate for 5,7 C1: 5,7 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 C1: 8,9 # 20 pairs C7: 5,7,6,8 # reduction candidate for 5,7 C7: 5,7 # 28 pairs * PAIR F5: 5,7 BLK 5 F6: 5,7,1 # reduction candidate for 5,7 F6: 5,7 => CTR * .6.95.4..9.2......1347826592..396..468142....49381.2...4.139...31.2....7.2.578341 F6: 1 # 21 pairs * PAIR F5: 5,7 ROW 5 G5: 5,7,9 # reduction candidate for 5,7 G5: 9 # 24 pairs G5: 5,7 # 22 pairs * PAIR E6: 1,5 BLK 5 F6: 1,5,7 # reduction candidate for 1,5 F6: 7 => CTR * .6.95.4.29.2.....81347826592..396..4681425..3493817265.4.139.2631.2.4..7.2.578341 F6: 1,5 # 22 pairs * PAIR G4: 1,8 COL G G2: 1,8,7 # reduction candidate for 1,8 G2: 1,8 => CTR * .6..5.4.2..2.....81347826592..396814681425793493817265.4.139526315264987926578341 G2: 7 # 22 pairs * PAIR H4: 1,8 COL H H1: 1,8,2,3,7 # reduction candidate for 1,8 H1: 1,8 # 24 pairs H2: 1,8,3,7 # reduction candidate for 1,8 H2: 1,8 # 22 pairs * PAIR I6: 5,6 COL I I7: 5,6,2,8 # reduction candidate for 5,6 I7: 5,6 # 20 pairs I7: 2,8 # 19 pairs * PAIR A9: 5,9 BLK 7 C9: 5,9,6 # reduction candidate for 5,9 C9: 5,9 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 C9: 6 => CTR * .695134....2964...1347826592..396..468142....493851276.4.139...31.245..7.2..78341 * PAIR A9: 5,9 COL A A1: 5,9,7,8 # reduction candidate for 5,9 A1: 5,9 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 A1: 7,8 # 20 pairs A2: 5,9,7,8 # reduction candidate for 5,9 A2: 5,9 # 23 pairs * PAIR F8: 4,5 COL F F2: 4,5,1,3 # reduction candidate for 4,5 F2: 4,5 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 F2: 1,3 => CTR * .69...4....2.4....1347826592..396..468142....4938..2...4.139...31.264..7.26578341 * PAIR D9: 5,6 ROW 9 C9: 5,6,9 # reduction candidate for 5,6 C9: 5,6 => CTR * 7695134....2964...1347826592..396..468142....493851276.4.139...31.245..7925678341 C9: 9 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 * PAIR D9: 5,6 COL D D2: 5,6,9 # reduction candidate for 5,6 D2: 5,6 => CTR * .6.9..4..9.2564...134782659257396..468142....49385127674.139...31.245..7529678341 D2: 9 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 * PAIR G7: 5,8 BLK 9 I7: 5,8,2,6 # reduction candidate for 5,8 I7: 5,8 => CTR * .6...34.2..2.647..1347826592..396..468142..934938..276.46139.2531.245967.2.678341 I7: 2,6 # 22 pairs G8: 5,8,9 # reduction candidate for 5,8 G8: 5,8 # 24 pairs * PAIR G7: 5,8 ROW 7 A7: 5,8,7 # reduction candidate for 5,8 A7: 5,8 # 26 pairs C7: 5,8,6,7 # reduction candidate for 5,8 C7: 5,8 # 25 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190304-absurd-base-pr-000.dot * REASONING * PRF # C1: 5,7 => SOL * DIS # A2: 5,7 => CTR => A2: 8,9 * PRF # D2: 5,9 => SOL * DIS # D2: 6 => CTR => D2: 5,9 * PRF # A1: 5,9 => SOL * DIS # C1: 5,9 => CTR => C1: 7,8 * PRF # C1: 7,8 => SOL * DIS # F1: 1,5 => CTR => F1: 3 * DIS # F2: 1,5 => CTR => F2: 3,4 * PRF # C1: 5,7 => SOL * DIS # F6: 5,7 => CTR => F6: 1 * DIS # F6: 7 => CTR => F6: 1,5 * DIS # G2: 1,8 => CTR => G2: 7 * PRF # C9: 5,9 => SOL * DIS # C9: 6 => CTR => C9: 5,9 * PRF # A1: 5,9 => SOL * PRF # F2: 4,5 => SOL * DIS # F2: 1,3 => CTR => F2: 4,5 * DIS # C9: 5,6 => CTR => C9: 9 * PRF # C9: 9 => SOL * DIS # D2: 5,6 => CTR => D2: 9 * PRF # D2: 9 => SOL * DIS # I7: 5,8 => CTR => I7: 2,6 * CNT 23 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B2,B4,C4,D1,D9,E1,E2,E6,E8,F5,F8,G4,G7,H4,H6,I2,I5,I6) * .6....4....2......1347826592..396..468142....4938..2...4.139...31.2....7.2..78341 * PAIR B2: 5,7 BLK 1 A1: 5,7,8,9 # reduction candidate for 5,7 A1: 5,7 # 22 pairs C1: 5,7,8,9 # reduction candidate for 5,7 C1: 5,7 => SOLVED * 967513428852964713134782659275396184681427935493851276748139562316245897529678341 * DURATION: 0:00:02.961894 START: 04:14:45.976362 END: 04:14:48.938256 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190304-absurd-base-pr-001.dot * REASONING * PRF # C1: 5,7 => SOL * STA C1: 5,7 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190304, absurd
Solution
position: 967513428852964713134782659275396184681427935493851276748139562316245897529678341 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 # A1: 5,7 => UNS * PRF # C1: 5,7 => SOL * INC # C1: 8,9 => UNS * DIS # A2: 5,7 => CTR => A2: 8,9 * INC # A2: 8,9 => UNS * PRF # D2: 5,9 => SOL * DIS # D2: 6 => CTR => D2: 5,9 * PRF # A1: 5,9 => SOL * INC # A1: 7,8 => UNS * DIS # C1: 5,9 => CTR => C1: 7,8 * PRF # C1: 7,8 => SOL * DIS # F1: 1,5 => CTR => F1: 3 * INC # F1: 3 => UNS * DIS # F2: 1,5 => CTR => F2: 3,4 * INC # F2: 3,4 => UNS * INC # H1: 3,8 => UNS * INC # I1: 3,8 => UNS * INC # H2: 3,8 => UNS * PRF # C1: 5,7 => SOL * INC # C1: 8,9 => UNS * INC # C7: 5,7 => UNS * DIS # F6: 5,7 => CTR => F6: 1 * INC # F6: 1 => UNS * INC # G5: 5,7 => UNS * INC # G5: 9 => UNS * INC # F6: 1,5 => UNS * DIS # F6: 7 => CTR => F6: 1,5 * DIS # G2: 1,8 => CTR => G2: 7 * INC # G2: 7 => UNS * INC # H1: 1,8 => UNS * INC # H2: 1,8 => UNS * INC # I7: 5,6 => UNS * INC # I7: 2,8 => UNS * PRF # C9: 5,9 => SOL * DIS # C9: 6 => CTR => C9: 5,9 * PRF # A1: 5,9 => SOL * INC # A1: 7,8 => UNS * INC # A2: 5,9 => UNS * PRF # F2: 4,5 => SOL * DIS # F2: 1,3 => CTR => F2: 4,5 * DIS # C9: 5,6 => CTR => C9: 9 * PRF # C9: 9 => SOL * DIS # D2: 5,6 => CTR => D2: 9 * PRF # D2: 9 => SOL * DIS # I7: 5,8 => CTR => I7: 2,6 * INC # I7: 2,6 => UNS * INC # G8: 5,8 => UNS * INC # A7: 5,8 => UNS * INC # C7: 5,8 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 5,7 => UNS * PRF # C1: 5,7 => SOL * STA C1: 5,7 * CNT 2 HDP CHAINS / 2 HYP OPENED