Analysis of zz-www.sudokuoftheday.co.uk-20190330-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: .8.7.4..2.....3...75.....81......436.9.3.5........7...9.....14..7...92....15.2... initial
Autosolve
position: .837.4..22.9..3..4754..6381527..1436.963.5...3.8.675.9932678145.75..926...15.2... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E2: 1,5 => SOL * DIS # E2: 8 => CTR => E2: 1,5 * PRF # E2: 1,8 => SOL * DIS # E2: 5 => CTR => E2: 1,8 * DIS # G9: 7,8 => CTR => G9: 9 * PRF # G9: 9 => SOL * DIS # I9: 3 => CTR => I9: 7,8 * DIS # A9: 4,8 => CTR => A9: 6 * PRF # A9: 6 => SOL * DIS # A9: 8 => CTR => A9: 4,6 * DIS # E8: 3 => CTR => E8: 1,4 * PRF # E8: 3,4 => SOL * DIS # E8: 1 => CTR => E8: 3,4 * DIS # I9: 7 => CTR => I9: 3,8 * DIS # G9: 8 => CTR => G9: 7,9 * CNT 15 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E2: 1,5 => SOL * STA E2: 1,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.7.4..2.....3...75.....81......436.9.3.5........7...9.....14..7...92....15.2... | initial |
| .837.4..22.9..3..4754..6381527..1436.963.5...3.8.675.9932678145.75..926...15.2... | autosolve |
| 183754692269813754754296381527981436496325817318467529932678145875149263641532978 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (26) A1: 1,6 B2: 1,6 E1: 1,5 D2: 1,8 D3: 2,9 E3: 2,9 G1: 6,9 H1: 5,9 G2: 6,7 H2: 5,7 A5: 1,4 B6: 1,4 D4: 8,9 E4: 8,9 E5: 2,4 D6: 2,4 G5: 7,8 H5: 1,2 I5: 7,8 H6: 1,2 A8: 4,8 B9: 4,6 D8: 1,4 E9: 3,4 I8: 3,8 H9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B2: 1.. / A1 = 1 => 0 pairs (*) / B2 = 1 => 0 pairs (X) A5,B6: 1.. / A5 = 1 => 0 pairs (X) / B6 = 1 => 0 pairs (_) H5,H6: 1.. / H5 = 1 => 0 pairs (*) / H6 = 1 => 0 pairs (X) D8,E8: 1.. / D8 = 1 => 0 pairs (*) / E8 = 1 => 0 pairs (X) A1,E1: 1.. / A1 = 1 => 0 pairs (*) / E1 = 1 => 0 pairs (X) A5,H5: 1.. / A5 = 1 => 0 pairs (X) / H5 = 1 => 0 pairs (_) B6,H6: 1.. / B6 = 1 => 0 pairs (*) / H6 = 1 => 0 pairs (X) A1,A5: 1.. / A1 = 1 => 0 pairs (*) / A5 = 1 => 0 pairs (X) B2,B6: 1.. / B2 = 1 => 0 pairs (X) / B6 = 1 => 0 pairs (_) D2,D8: 1.. / D2 = 1 => 0 pairs (X) / D8 = 1 => 0 pairs (_) D3,E3: 2.. / D3 = 2 => 0 pairs (*) / E3 = 2 => 0 pairs (X) E5,D6: 2.. / E5 = 2 => 0 pairs (*) / D6 = 2 => 0 pairs (X) H5,H6: 2.. / H5 = 2 => 0 pairs (X) / H6 = 2 => 0 pairs (_) E5,H5: 2.. / E5 = 2 => 0 pairs (*) / H5 = 2 => 0 pairs (X) D6,H6: 2.. / D6 = 2 => 0 pairs (X) / H6 = 2 => 0 pairs (_) D3,D6: 2.. / D3 = 2 => 0 pairs (*) / D6 = 2 => 0 pairs (X) E3,E5: 2.. / E3 = 2 => 0 pairs (X) / E5 = 2 => 0 pairs (_) E8,E9: 3.. / E8 = 3 => 0 pairs (X) / E9 = 3 => 26 pairs (_) I8,I9: 3.. / I8 = 3 => 26 pairs (_) / I9 = 3 => 0 pairs (X) E8,I8: 3.. / E8 = 3 => 0 pairs (X) / I8 = 3 => 26 pairs (_) E9,I9: 3.. / E9 = 3 => 26 pairs (_) / I9 = 3 => 0 pairs (X) A5,B6: 4.. / A5 = 4 => 0 pairs (*) / B6 = 4 => 0 pairs (X) E5,D6: 4.. / E5 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) A5,E5: 4.. / A5 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) B6,D6: 4.. / B6 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) B6,B9: 4.. / B6 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) D6,D8: 4.. / D6 = 4 => 0 pairs (*) / D8 = 4 => 0 pairs (X) E1,E2: 5.. / E1 = 5 => 0 pairs (*) / E2 = 5 => 0 pairs (X) H1,H2: 5.. / H1 = 5 => 0 pairs (X) / H2 = 5 => 0 pairs (_) E1,H1: 5.. / E1 = 5 => 0 pairs (*) / H1 = 5 => 0 pairs (X) E2,H2: 5.. / E2 = 5 => 0 pairs (X) / H2 = 5 => 0 pairs (_) A1,B2: 6.. / A1 = 6 => 0 pairs (X) / B2 = 6 => 0 pairs (_) G1,G2: 6.. / G1 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) A9,B9: 6.. / A9 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) A1,G1: 6.. / A1 = 6 => 0 pairs (X) / G1 = 6 => 0 pairs (_) B2,G2: 6.. / B2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) A1,A9: 6.. / A1 = 6 => 0 pairs (X) / A9 = 6 => 0 pairs (_) B2,B9: 6.. / B2 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) G2,H2: 7.. / G2 = 7 => 0 pairs (*) / H2 = 7 => 0 pairs (X) G5,I5: 7.. / G5 = 7 => 0 pairs (X) / I5 = 7 => 26 pairs (_) H2,H9: 7.. / H2 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) I5,I9: 7.. / I5 = 7 => 26 pairs (_) / I9 = 7 => 0 pairs (X) D2,E2: 8.. / D2 = 8 => 0 pairs (*) / E2 = 8 => 0 pairs (X) D4,E4: 8.. / D4 = 8 => 0 pairs (X) / E4 = 8 => 0 pairs (_) G5,I5: 8.. / G5 = 8 => 26 pairs (_) / I5 = 8 => 0 pairs (X) A8,A9: 8.. / A8 = 8 => 26 pairs (_) / A9 = 8 => 0 pairs (X) A8,I8: 8.. / A8 = 8 => 26 pairs (_) / I8 = 8 => 0 pairs (X) D2,D4: 8.. / D2 = 8 => 0 pairs (*) / D4 = 8 => 0 pairs (X) E2,E4: 8.. / E2 = 8 => 0 pairs (X) / E4 = 8 => 0 pairs (_) G5,G9: 8.. / G5 = 8 => 26 pairs (_) / G9 = 8 => 0 pairs (X) D3,E3: 9.. / D3 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) G1,H1: 9.. / G1 = 9 => 0 pairs (X) / H1 = 9 => 0 pairs (_) D4,E4: 9.. / D4 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) G9,H9: 9.. / G9 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) D3,D4: 9.. / D3 = 9 => 0 pairs (X) / D4 = 9 => 0 pairs (_) E3,E4: 9.. / E3 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) G1,G9: 9.. / G1 = 9 => 0 pairs (X) / G9 = 9 => 0 pairs (_) H1,H9: 9.. / H1 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) * DURATION: 0:01:16.935678 START: 04:54:57.501283 END: 04:56:14.436961 2019-05-01 * CP COUNT: (58) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,A8,B2,B6,B9,D2,D3,D4,D6,D8,E1,E3,E4,E5,E9,G1,G2,G5,H1,H2,H5,H6,H9,I5,I8) * .837.4..22.9..3..4754..6381527..1436.963.5...3.8.675.9932678145.75..926...15.2... * PAIR E1: 1,5 BLK 2 E2: 1,5,8 # reduction candidate for 1,5 E2: 1,5 => SOLVED * 183754692269813754754296381527981436496325817318467529932678145875149263641532978 E2: 8 => CTR * .83754.922.9183.54754..6381527891436.963.5...3184675.9932678145.75..926...15.2... * PAIR D2: 1,8 BLK 2 E2: 1,8,5 # reduction candidate for 1,8 E2: 1,8 => SOLVED * 183754692269813754754296381527981436496325817318467529932678145875149263641532978 E2: 5 => CTR * .837149522198536747542963815279814361963.5...3.8.675.9932678145.751.926...15.2.9. * PAIR G5: 7,8 COL G G9: 7,8,9 # reduction candidate for 7,8 G9: 7,8 => CTR * 683714952219853674754.963815279814361963.5...3.8.675.9932678145.75..926..615.2.9. G9: 9 => SOLVED * 183754692269813754754296381527981436496325817318467529932678145875149263641532978 * PAIR I5: 7,8 COL I I9: 7,8,3 # reduction candidate for 7,8 I9: 3 => CTR * 683714952219853674754..6381527981436.963.5..73.8.675.9932678145.75..9268861542..3 I9: 7,8 # 26 pairs * PAIR A8: 4,8 BLK 7 A9: 4,8,6 # reduction candidate for 4,8 A9: 4,8 => CTR * 683714952219853674754..6381527981436196345.2.3482675.9932678145.75..926...15.2... A9: 6 => SOLVED * 183754692269813754754296381527981436496325817318467529932678145875149263641532978 * PAIR B9: 4,6 BLK 7 A9: 4,6,8 # reduction candidate for 4,6 A9: 8 => CTR * 683714952219853674754..6381527981436196345.2.348.675.9932678145.75..926...15.2... A9: 4,6 # 26 pairs * PAIR D8: 1,4 BLK 8 E8: 1,4,3 # reduction candidate for 1,4 E8: 3 => CTR * 683714952219853674754..6381527981436.963.5...3.8.675.9932678145.75139268861542..3 E8: 1,4 # 26 pairs * PAIR E9: 3,4 BLK 8 E8: 3,4,1 # reduction candidate for 3,4 E8: 3,4 => SOLVED * 183754692269813754754296381527981436496325817318467529932678145875149263641532978 E8: 1 => CTR * 183754692269183754754..6381527891436496325...3.8.675.9932678145.75.19263..1532... * PAIR I8: 3,8 BLK 9 I9: 3,8,7 # reduction candidate for 3,8 I9: 7 => CTR * 683714952219853674754.963815279814361963.57.83.8.675.9932678145875..9263.61532897 I9: 3,8 # 26 pairs * PAIR H9: 7,9 BLK 9 G9: 7,9,8 # reduction candidate for 7,9 G9: 8 => CTR * 683714952219853674754.963815279814361963.57.83.8.675.9932678145875..9263.61532897 G9: 7,9 # 26 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190330-absurd-base-pr-000.dot * REASONING * PRF # E2: 1,5 => SOL * DIS # E2: 8 => CTR => E2: 1,5 * PRF # E2: 1,8 => SOL * DIS # E2: 5 => CTR => E2: 1,8 * DIS # G9: 7,8 => CTR => G9: 9 * PRF # G9: 9 => SOL * DIS # I9: 3 => CTR => I9: 7,8 * DIS # A9: 4,8 => CTR => A9: 6 * PRF # A9: 6 => SOL * DIS # A9: 8 => CTR => A9: 4,6 * DIS # E8: 3 => CTR => E8: 1,4 * PRF # E8: 3,4 => SOL * DIS # E8: 1 => CTR => E8: 3,4 * DIS # I9: 7 => CTR => I9: 3,8 * DIS # G9: 8 => CTR => G9: 7,9 * CNT 15 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,A8,B2,B6,B9,D2,D3,D4,D6,D8,E1,E3,E4,E5,E9,G1,G2,G5,H1,H2,H5,H6,H9,I5,I8) * .837.4..22.9..3..4754..6381527..1436.963.5...3.8.675.9932678145.75..926...15.2... * PAIR E1: 1,5 BLK 2 E2: 1,5,8 # reduction candidate for 1,5 E2: 1,5 => SOLVED * 183754692269813754754296381527981436496325817318467529932678145875149263641532978 * DURATION: 0:00:01.630311 START: 04:56:32.129912 END: 04:56:33.760223 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190330-absurd-base-pr-001.dot * REASONING * PRF # E2: 1,5 => SOL * STA E2: 1,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190330, absurd
Solution
position: 183754692269813754754296381527981436496325817318467529932678145875149263641532978 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:
* PRF # E2: 1,5 => SOL * DIS # E2: 8 => CTR => E2: 1,5 * PRF # E2: 1,8 => SOL * DIS # E2: 5 => CTR => E2: 1,8 * DIS # G9: 7,8 => CTR => G9: 9 * PRF # G9: 9 => SOL * INC # I9: 7,8 => UNS * DIS # I9: 3 => CTR => I9: 7,8 * DIS # A9: 4,8 => CTR => A9: 6 * PRF # A9: 6 => SOL * INC # A9: 4,6 => UNS * DIS # A9: 8 => CTR => A9: 4,6 * INC # E8: 1,4 => UNS * DIS # E8: 3 => CTR => E8: 1,4 * PRF # E8: 3,4 => SOL * DIS # E8: 1 => CTR => E8: 3,4 * INC # I9: 3,8 => UNS * DIS # I9: 7 => CTR => I9: 3,8 * INC # G9: 7,9 => UNS * DIS # G9: 8 => CTR => G9: 7,9 * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # E2: 1,5 => SOL * STA E2: 1,5 * CNT 1 HDP CHAINS / 1 HYP OPENED