Analysis of zz-www.sudokuoftheday.co.uk-20190112-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: ...1..6....5....8..6....3.7.....3......9......3175...82...1....1.4869.....7.259.. initial
Autosolve
position: ...1..6...15....89.6.59.3175....31.....9.15...3175...829..178..1548697...87.259.1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 3,7 => CTR => A1: 4,8,9 * DIS # A1: 4,8 => CTR => A1: 3,7,9 * DIS # F3: 2 => CTR => F3: 4,8 * DIS # C1: 2,8 => CTR => C1: 3,9 * DIS # C4: 2,8 => CTR => C4: 6,9 * DIS # A1: 3,7 => CTR => A1: 4,8,9 * DIS # F2: 4 => CTR => F2: 2,6 * DIS # F2: 6 => CTR => F2: 2,4 * DIS # C4: 2,6 => CTR => C4: 8,9 * DIS # H4: 2,6 => CTR => H4: 4,7,9 * DIS # H6: 2,6 => CTR => H6: 4,9 * DIS # F2: 4 => CTR => F2: 2,6 * PRF # H4: 2,4 => SOL * DIS # H5: 2,4 => CTR => H5: 3,6,7 * DIS # I5: 2,4 => CTR => I5: 3,6 * DIS # H6: 2,4 => CTR => H6: 6,9 * DIS # I5: 4,6 => CTR => I5: 2,3 * PRF # H4: 4,6 => SOL * DIS # H5: 4,6 => CTR => H5: 2,3,7 * DIS # H6: 4,6 => CTR => H6: 2,9 * CNT 20 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 3,7 => CTR => A1: 4,8,9 * DIS A1: 4,8,9 # A1: 4,8 => CTR => A1: 9 * DIS A1: 4,8,9 + A1: 9 # F3: 2 => CTR => F3: 4,8 * PRF A1: 4,8,9 + A1: 9 + F3: 4,8 # F2: 2,6 => SOL * STA A1: 4,8,9 + A1: 9 + F3: 4,8 + F2: 2,6 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...1..6....5....8..6....3.7.....3......9......3175...82...1....1.4869.....7.259.. | initial |
| ...1..6...15....89.6.59.3175....31.....9.15...3175...829..178..1548697...87.259.1 | autosolve |
| 943178625715632489862594317579283146628941573431756298296317854154869732387425961 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A2: 3,7 A3: 4,8 C3: 2,8 E1: 3,7 D2: 2,6 E2: 3,7 G2: 2,4 D4: 2,6 E4: 4,8 E5: 4,8 F6: 2,6 G6: 2,4 C7: 3,6 A9: 3,6 D7: 3,4 D9: 3,4 H8: 2,3 I8: 2,3 H9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,F6: 2.. / D4 = 2 => 20 pairs (_) / F6 = 2 => 0 pairs (X) H8,I8: 2.. / H8 = 2 => 21 pairs (_) / I8 = 2 => 19 pairs (_) C3,F3: 2.. / C3 = 2 => 21 pairs (_) / F3 = 2 => 0 pairs (X) D2,D4: 2.. / D2 = 2 => 0 pairs (X) / D4 = 2 => 20 pairs (_) G2,G6: 2.. / G2 = 2 => 0 pairs (X) / G6 = 2 => 23 pairs (_) E1,E2: 3.. / E1 = 3 => 15 pairs (_) / E2 = 3 => 20 pairs (_) H5,I5: 3.. / H5 = 3 => 21 pairs (_) / I5 = 3 => 19 pairs (_) C7,A9: 3.. / C7 = 3 => 18 pairs (_) / A9 = 3 => 17 pairs (_) D7,D9: 3.. / D7 = 3 => 17 pairs (_) / D9 = 3 => 18 pairs (_) H8,I8: 3.. / H8 = 3 => 19 pairs (_) / I8 = 3 => 21 pairs (_) A2,E2: 3.. / A2 = 3 => 15 pairs (_) / E2 = 3 => 20 pairs (_) C7,D7: 3.. / C7 = 3 => 18 pairs (_) / D7 = 3 => 17 pairs (_) A9,D9: 3.. / A9 = 3 => 17 pairs (_) / D9 = 3 => 18 pairs (_) C1,C7: 3.. / C1 = 3 => 17 pairs (_) / C7 = 3 => 18 pairs (_) H5,H8: 3.. / H5 = 3 => 21 pairs (_) / H8 = 3 => 19 pairs (_) I5,I8: 3.. / I5 = 3 => 19 pairs (_) / I8 = 3 => 21 pairs (_) E4,E5: 4.. / E4 = 4 => 0 pairs (X) / E5 = 4 => 18 pairs (_) D7,D9: 4.. / D7 = 4 => 18 pairs (_) / D9 = 4 => 17 pairs (_) F2,G2: 4.. / F2 = 4 => 0 pairs (X) / G2 = 4 => 23 pairs (_) A3,F3: 4.. / A3 = 4 => 29 pairs (_) / F3 = 4 => 21 pairs (_) D9,H9: 4.. / D9 = 4 => 17 pairs (_) / H9 = 4 => 18 pairs (_) G2,G6: 4.. / G2 = 4 => 23 pairs (_) / G6 = 4 => 0 pairs (X) H1,I1: 5.. / H1 = 5 => 22 pairs (_) / I1 = 5 => 21 pairs (_) H7,I7: 5.. / H7 = 5 => 21 pairs (_) / I7 = 5 => 22 pairs (_) H1,H7: 5.. / H1 = 5 => 22 pairs (_) / H7 = 5 => 21 pairs (_) I1,I7: 5.. / I1 = 5 => 21 pairs (_) / I7 = 5 => 22 pairs (_) D2,F2: 6.. / D2 = 6 => 20 pairs (_) / F2 = 6 => 0 pairs (X) D4,F6: 6.. / D4 = 6 => 0 pairs (X) / F6 = 6 => 20 pairs (_) C7,A9: 6.. / C7 = 6 => 17 pairs (_) / A9 = 6 => 18 pairs (_) A9,H9: 6.. / A9 = 6 => 18 pairs (_) / H9 = 6 => 17 pairs (_) D2,D4: 6.. / D2 = 6 => 20 pairs (_) / D4 = 6 => 0 pairs (X) F2,F6: 6.. / F2 = 6 => 0 pairs (X) / F6 = 6 => 20 pairs (_) E1,E2: 7.. / E1 = 7 => 20 pairs (_) / E2 = 7 => 15 pairs (_) H4,H5: 7.. / H4 = 7 => 20 pairs (_) / H5 = 7 => 25 pairs (_) A2,E2: 7.. / A2 = 7 => 20 pairs (_) / E2 = 7 => 15 pairs (_) B4,H4: 7.. / B4 = 7 => 25 pairs (_) / H4 = 7 => 20 pairs (_) F1,F3: 8.. / F1 = 8 => 20 pairs (_) / F3 = 8 => 0 pairs (X) E4,E5: 8.. / E4 = 8 => 18 pairs (_) / E5 = 8 => 0 pairs (X) C4,E4: 8.. / C4 = 8 => 0 pairs (X) / E4 = 8 => 18 pairs (_) A1,C1: 9.. / A1 = 9 => 19 pairs (_) / C1 = 9 => 0 pairs (X) C4,A6: 9.. / C4 = 9 => 19 pairs (_) / A6 = 9 => 0 pairs (X) H4,H6: 9.. / H4 = 9 => 0 pairs (X) / H6 = 9 => 19 pairs (_) C4,H4: 9.. / C4 = 9 => 19 pairs (_) / H4 = 9 => 0 pairs (X) A6,H6: 9.. / A6 = 9 => 0 pairs (X) / H6 = 9 => 19 pairs (_) A1,A6: 9.. / A1 = 9 => 19 pairs (_) / A6 = 9 => 0 pairs (X) C1,C4: 9.. / C1 = 9 => 0 pairs (X) / C4 = 9 => 19 pairs (_) * DURATION: 0:00:58.243650 START: 02:53:10.763215 END: 02:54:09.006865 2019-05-01 * CP COUNT: (46) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A9,C3,C7,D2,D4,D7,D9,E1,E2,E4,E5,F6,G2,G6,H8,H9,I8) * ...1..6...15....89.6.59.3175....31.....9.15...3175...829..178..1548697...87.259.1 * PAIR A2: 3,7 BLK 1 A1: 3,7,4,8,9 # reduction candidate for 3,7 A1: 3,7 => CTR * .291.8654.15..4289468592317572..319...69.157393175.428293417865154869732687325941 A1: 4,8,9 # 19 pairs * PAIR A3: 4,8 BLK 1 A1: 4,8,3,7,9 # reduction candidate for 4,8 A1: 4,8 => CTR * ..913.6..315.7..89.6.59.3175....319.7..9.15..93175...82934178..1548697..687325941 A1: 3,7,9 # 19 pairs * PAIR A3: 4,8 ROW 3 F3: 4,8,2 # reduction candidate for 4,8 F3: 2 => CTR * ...1.8654.156.428946859231754.2831..8..9415...3175642829..178..154869732687325941 F3: 4,8 # 21 pairs * PAIR A3: 4,8 COL A A5: 4,8,6,7 # reduction candidate for 4,8 A5: 4,8 # 34 pairs A5: 6,7 # 23 pairs * PAIR C3: 2,8 BLK 1 C1: 2,8,3,9 # reduction candidate for 2,8 C1: 2,8 => CTR * 9..13.6..315.7..89.6.59.3175.9.831..7.89415..63175...829..178..1548697...87.259.1 C1: 3,9 # 20 pairs * PAIR C3: 2,8 ROW 3 F3: 2,8,4 # reduction candidate for 2,8 F3: 2,8 # 29 pairs F3: 4 # 21 pairs * PAIR C3: 2,8 COL C C4: 2,8,6,9 # reduction candidate for 2,8 C4: 2,8 => CTR * ..91..654.15..428946.59.31757.2431968.69.157393175.428293417865154869732687325941 C4: 6,9 # 19 pairs C5: 2,8,6 # reduction candidate for 2,8 C5: 2,8 # 21 pairs * PAIR E1: 3,7 ROW 1 A1: 3,7,4,8,9 # reduction candidate for 3,7 A1: 3,7 => CTR * .291.8654.15..4289468592317572..319...69.157393175.428293417865154869732687325941 A1: 4,8,9 # 19 pairs * PAIR D2: 2,6 BLK 2 F2: 2,6,4 # reduction candidate for 2,6 F2: 4 => CTR * ..91..6...156.428946.59.3175782431966429.157393175642829..178..154869732.87.259.1 F2: 2,6 # 23 pairs * PAIR G2: 2,4 BLK 3 H1: 2,4,5 # reduction candidate for 2,4 H1: 2,4 # 21 pairs I1: 2,4,5 # reduction candidate for 2,4 I1: 2,4 # 22 pairs * PAIR G2: 2,4 ROW 2 F2: 2,4,6 # reduction candidate for 2,4 F2: 6 => CTR * ...1..6...15..6489.6.59.3175..6.31.....9.15...31752..829..178..1548697...87.259.1 F2: 2,4 # 20 pairs * PAIR D4: 2,6 ROW 4 C4: 2,6,8,9 # reduction candidate for 2,6 C4: 2,6 => CTR * ..91..6...15....89.6.59.3175...8319....94157393175...82934178..154869732687325941 C4: 8,9 # 20 pairs H4: 2,6,4,7,9 # reduction candidate for 2,6 H4: 2,6 => CTR * ...1..6...15....89.6.59.317579.831.4...94157343175.29829..178.6154869732687325941 H4: 4,7,9 # 19 pairs I4: 2,6,4 # reduction candidate for 2,6 I4: 2,6 # 22 pairs * PAIR E5: 4,8 ROW 5 A5: 4,8,6,7 # reduction candidate for 4,8 A5: 4,8 # 34 pairs A5: 6,7 # 23 pairs * PAIR F6: 2,6 ROW 6 H6: 2,6,4,9 # reduction candidate for 2,6 H6: 2,6 => CTR * ..91..6...15..428946.59.31757.243196.4298157393175642829..178..154869732.87.259.1 H6: 4,9 # 20 pairs * PAIR F6: 2,6 COL F F2: 2,6,4 # reduction candidate for 2,6 F2: 4 => CTR * ..91..6...156.428946.59.3175782431966429.157393175642829..178..154869732.87.259.1 F2: 2,6 # 23 pairs * PAIR G6: 2,4 BLK 6 H4: 2,4,6,7,9 # reduction candidate for 2,4 H4: 2,4 => SOLVED * 943178625715632489862594317579283146628941573431756298296317854154869732387425961 H4: 6,7,9 # 19 pairs I4: 2,4,6 # reduction candidate for 2,4 I4: 2,4 # 23 pairs H5: 2,4,3,6,7 # reduction candidate for 2,4 H5: 2,4 => CTR * 9..1..6...15....89.6.59.3175.9.83176...941523.3175..9829..178..154869732.87.259.1 H5: 3,6,7 # 19 pairs I5: 2,4,3,6 # reduction candidate for 2,4 I5: 2,4 => CTR * 9..1..6...15....89.6.59.3175.9.83176...941532.3175..9829..178..154869723.87.259.1 I5: 3,6 # 20 pairs H6: 2,4,6,9 # reduction candidate for 2,4 H6: 2,4 => CTR * ..91..654.156.428946.59.3175782.3196...9.1573931756..8293417865154869732687325941 H6: 6,9 # 20 pairs * PAIR H8: 2,3 COL H H5: 2,3,4,6,7 # reduction candidate for 2,3 H5: 2,3 # 23 pairs H5: 4,6,7 # 20 pairs * PAIR I8: 2,3 COL I I5: 2,3,4,6 # reduction candidate for 2,3 I5: 4,6 => CTR * 9..1..6...15....89.6.59.3175.9.8317....9415366317524982963178..154869723387425961 I5: 2,3 # 22 pairs * PAIR H9: 4,6 BLK 9 H7: 4,6,5 # reduction candidate for 4,6 H7: 4,6 # 22 pairs I7: 4,6,5 # reduction candidate for 4,6 I7: 4,6 # 21 pairs * PAIR H9: 4,6 COL H H4: 4,6,2,7,9 # reduction candidate for 4,6 H4: 4,6 => SOLVED * 943178625715632489862594317579283146628941573431756298296317854154869732387425961 H4: 2,7,9 # 19 pairs H5: 4,6,2,3,7 # reduction candidate for 4,6 H5: 4,6 => CTR * 9..1..625.15...489.6259.3175.9.8317..2.941563.3175..9829..178..154869732.87.259.1 H5: 2,3,7 # 19 pairs H6: 4,6,2,9 # reduction candidate for 4,6 H6: 4,6 => CTR * ..91..625.15...489.6259.31757.2.319..2.9.15739317562482934178..154869732.87.259.1 H6: 2,9 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190112-absurd-base-pr-000.dot * REASONING * DIS # A1: 3,7 => CTR => A1: 4,8,9 * DIS # A1: 4,8 => CTR => A1: 3,7,9 * DIS # F3: 2 => CTR => F3: 4,8 * DIS # C1: 2,8 => CTR => C1: 3,9 * DIS # C4: 2,8 => CTR => C4: 6,9 * DIS # A1: 3,7 => CTR => A1: 4,8,9 * DIS # F2: 4 => CTR => F2: 2,6 * DIS # F2: 6 => CTR => F2: 2,4 * DIS # C4: 2,6 => CTR => C4: 8,9 * DIS # H4: 2,6 => CTR => H4: 4,7,9 * DIS # H6: 2,6 => CTR => H6: 4,9 * DIS # F2: 4 => CTR => F2: 2,6 * PRF # H4: 2,4 => SOL * DIS # H5: 2,4 => CTR => H5: 3,6,7 * DIS # I5: 2,4 => CTR => I5: 3,6 * DIS # H6: 2,4 => CTR => H6: 6,9 * DIS # I5: 4,6 => CTR => I5: 2,3 * PRF # H4: 4,6 => SOL * DIS # H5: 4,6 => CTR => H5: 2,3,7 * DIS # H6: 4,6 => CTR => H6: 2,9 * CNT 20 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A9,C3,C7,D2,D4,D7,D9,E1,E2,E4,E5,F6,G2,G6,H8,H9,I8) * ...1..6...15....89.6.59.3175....31.....9.15...3175...829..178..1548697...87.259.1 * PAIR A2: 3,7 BLK 1 A1: 3,7,4,8,9 # reduction candidate for 3,7 A1: 3,7 => CTR * .291.8654.15..4289468592317572..319...69.157393175.428293417865154869732687325941 * PAIR A3: 4,8 BLK 1 A1: 4,8,9 # reduction candidate for 4,8 A1: 4,8 => CTR * ..913.6..315.7..89.6.59.3175....319.7..9.15..93175...82934178..1548697..687325941 * PAIR A3: 4,8 ROW 3 F3: 4,8,2 # reduction candidate for 4,8 F3: 2 => CTR * 9..1.86...15..42894685923175.9.831.....9415...3175..9829..178..1548697...87.259.1 * PAIR RESTART * PAIR D2: 2,6 BLK 2 F2: 2,6,4 # reduction candidate for 2,6 F2: 2,6 => SOLVED * 943178625715632489862594317579283146628941573431756298296317854154869732387425961 * DURATION: 0:00:06.114050 START: 02:54:46.607526 END: 02:54:52.721576 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190112-absurd-base-pr-001.dot * REASONING * DIS # A1: 3,7 => CTR => A1: 4,8,9 * DIS A1: 4,8,9 # A1: 4,8 => CTR => A1: 9 * DIS A1: 4,8,9 + A1: 9 # F3: 2 => CTR => F3: 4,8 * PRF A1: 4,8,9 + A1: 9 + F3: 4,8 # F2: 2,6 => SOL * STA A1: 4,8,9 + A1: 9 + F3: 4,8 + F2: 2,6 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190112, absurd
Solution
position: 943178625715632489862594317579283146628941573431756298296317854154869732387425961 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 # A1: 3,7 => CTR => A1: 4,8,9 * INC # A1: 4,8,9 => UNS * DIS # A1: 4,8 => CTR => A1: 3,7,9 * INC # A1: 3,7,9 => UNS * INC # F3: 4,8 => UNS * DIS # F3: 2 => CTR => F3: 4,8 * INC # A5: 4,8 => UNS * INC # A5: 6,7 => UNS * DIS # C1: 2,8 => CTR => C1: 3,9 * INC # C1: 3,9 => UNS * INC # F3: 2,8 => UNS * INC # F3: 4 => UNS * DIS # C4: 2,8 => CTR => C4: 6,9 * INC # C4: 6,9 => UNS * INC # C5: 2,8 => UNS * DIS # A1: 3,7 => CTR => A1: 4,8,9 * INC # A1: 4,8,9 => UNS * INC # F2: 2,6 => UNS * DIS # F2: 4 => CTR => F2: 2,6 * INC # H1: 2,4 => UNS * INC # I1: 2,4 => UNS * INC # F2: 2,4 => UNS * DIS # F2: 6 => CTR => F2: 2,4 * DIS # C4: 2,6 => CTR => C4: 8,9 * INC # C4: 8,9 => UNS * DIS # H4: 2,6 => CTR => H4: 4,7,9 * INC # H4: 4,7,9 => UNS * INC # I4: 2,6 => UNS * INC # A5: 4,8 => UNS * INC # A5: 6,7 => UNS * DIS # H6: 2,6 => CTR => H6: 4,9 * INC # H6: 4,9 => UNS * INC # F2: 2,6 => UNS * DIS # F2: 4 => CTR => F2: 2,6 * PRF # H4: 2,4 => SOL * INC # H4: 6,7,9 => UNS * INC # I4: 2,4 => UNS * DIS # H5: 2,4 => CTR => H5: 3,6,7 * INC # H5: 3,6,7 => UNS * DIS # I5: 2,4 => CTR => I5: 3,6 * INC # I5: 3,6 => UNS * DIS # H6: 2,4 => CTR => H6: 6,9 * INC # H6: 6,9 => UNS * INC # H5: 2,3 => UNS * INC # H5: 4,6,7 => UNS * INC # I5: 2,3 => UNS * DIS # I5: 4,6 => CTR => I5: 2,3 * INC # H7: 4,6 => UNS * INC # I7: 4,6 => UNS * PRF # H4: 4,6 => SOL * INC # H4: 2,7,9 => UNS * DIS # H5: 4,6 => CTR => H5: 2,3,7 * INC # H5: 2,3,7 => UNS * DIS # H6: 4,6 => CTR => H6: 2,9 * INC # H6: 2,9 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 3,7 => CTR => A1: 4,8,9 * DIS A1: 4,8,9 # A1: 4,8 => CTR => A1: 9 * INC A1: 4,8,9 + A1: 9 # F3: 4,8 => UNS * DIS A1: 4,8,9 + A1: 9 # F3: 2 => CTR => F3: 4,8 * PRF A1: 4,8,9 + A1: 9 + F3: 4,8 # F2: 2,6 => SOL * STA A1: 4,8,9 + A1: 9 + F3: 4,8 + F2: 2,6 * CNT 5 HDP CHAINS / 5 HYP OPENED