Analysis of zz-www.sudokuoftheday.co.uk-20190130-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: 1.7.38...48.7..............6....12...3.9...1..41.5..738.....7.57....4.28.56...1.. initial
Autosolve
position: 1.7.38..248.7....1........767.3.12...3.9...16.41.5..738.4...7.57..5.4.28.56...1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 2 => CTR => B3: 6,9 * DIS # G1: 6,9 => CTR => G1: 4,5 * DIS # H1: 6,9 => CTR => H1: 4,5 * DIS # G1: 4,6 => CTR => G1: 5,9 * PRF # C5: 2,5 => SOL * PRF # A3: 2,5 => SOL * PRF # A3: 2,9 => SOL * DIS # E5: 7 => CTR => E5: 4,8 * DIS # H4: 4,8 => CTR => H4: 5,9 * DIS # F9: 3,9 => CTR => F9: 2,7 * DIS # D6: 8 => CTR => D6: 2,6 * DIS # F2: 2,6 => CTR => F2: 5,9 * DIS # F3: 2,6 => CTR => F3: 5,9 * DIS # F7: 2,6 => CTR => F7: 3,9 * DIS # H4: 4,9 => CTR => H4: 5,8 * DIS # H4: 8,9 => CTR => H4: 4,5 * DIS # B7: 1,9 => CTR => B7: 2 * DIS # A9: 2 => CTR => A9: 3,9 * DIS # D6: 6 => CTR => D6: 2,8 * PRF # E5: 7,8 => SOL * DIS # E5: 4 => CTR => E5: 7,8 * DIS # H9: 3 => CTR => H9: 4,9 * CNT 22 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 2 => CTR => B3: 6,9 * DIS B3: 6,9 # G1: 6,9 => CTR => G1: 4,5 * DIS B3: 6,9 + G1: 4,5 # H1: 6,9 => CTR => H1: 4,5 * PRF B3: 6,9 + G1: 4,5 + H1: 4,5 # C5: 2,5 => SOL * STA B3: 6,9 + G1: 4,5 + H1: 4,5 + C5: 2,5 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.7.38...48.7..............6....12...3.9...1..41.5..738.....7.57....4.28.56...1.. | initial |
| 1.7.38..248.7....1........767.3.12...3.9...16.41.5..738.4...7.57..5.4.28.56...1.. | autosolve |
| 197638542485729631263415987678341259532987416941256873824193765719564328356872194 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B1: 6,9 D1: 4,6 A5: 2,5 A6: 2,9 E4: 4,8 F5: 2,7 F6: 2,6 I4: 4,9 G6: 8,9 B8: 1,9 C8: 3,9 D9: 2,8 E9: 7,8 I9: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,E3: 1.. / D3 = 1 => 16 pairs (_) / E3 = 1 => 15 pairs (_) B7,B8: 1.. / B7 = 1 => 0 pairs (X) / B8 = 1 => 15 pairs (_) B8,E8: 1.. / B8 = 1 => 15 pairs (_) / E8 = 1 => 0 pairs (X) D3,D7: 1.. / D3 = 1 => 16 pairs (_) / D7 = 1 => 15 pairs (_) B7,A9: 2.. / B7 = 2 => 22 pairs (_) / A9 = 2 => 0 pairs (X) B3,B7: 2.. / B3 = 2 => 0 pairs (X) / B7 = 2 => 22 pairs (_) C8,A9: 3.. / C8 = 3 => 18 pairs (_) / A9 = 3 => 0 pairs (*) F7,F9: 3.. / F7 = 3 => 15 pairs (_) / F9 = 3 => 0 pairs (X) F7,H7: 3.. / F7 = 3 => 15 pairs (_) / H7 = 3 => 0 pairs (X) C8,G8: 3.. / C8 = 3 => 18 pairs (_) / G8 = 3 => 0 pairs (*) A3,A9: 3.. / A3 = 3 => 18 pairs (_) / A9 = 3 => 0 pairs (*) D1,D3: 4.. / D1 = 4 => 15 pairs (_) / D3 = 4 => 22 pairs (_) E4,E5: 4.. / E4 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) H9,I9: 4.. / H9 = 4 => 0 pairs (X) / I9 = 4 => 15 pairs (_) E5,G5: 4.. / E5 = 4 => 0 pairs (X) / G5 = 4 => 0 pairs (_) I4,I9: 4.. / I4 = 4 => 0 pairs (X) / I9 = 4 => 15 pairs (_) F2,F3: 5.. / F2 = 5 => 14 pairs (_) / F3 = 5 => 16 pairs (_) G1,H1: 5.. / G1 = 5 => 16 pairs (_) / H1 = 5 => 0 pairs (X) H4,G5: 5.. / H4 = 5 => 16 pairs (_) / G5 = 5 => 0 pairs (X) C2,F2: 5.. / C2 = 5 => 16 pairs (_) / F2 = 5 => 14 pairs (_) C4,H4: 5.. / C4 = 5 => 0 pairs (X) / H4 = 5 => 16 pairs (_) A3,A5: 5.. / A3 = 5 => 0 pairs (X) / A5 = 5 => 16 pairs (_) G1,G5: 5.. / G1 = 5 => 16 pairs (_) / G5 = 5 => 0 pairs (X) H1,H4: 5.. / H1 = 5 => 0 pairs (X) / H4 = 5 => 16 pairs (_) B1,B3: 6.. / B1 = 6 => 21 pairs (_) / B3 = 6 => 22 pairs (_) D6,F6: 6.. / D6 = 6 => 0 pairs (X) / F6 = 6 => 15 pairs (_) H7,G8: 6.. / H7 = 6 => 18 pairs (_) / G8 = 6 => 20 pairs (_) E8,G8: 6.. / E8 = 6 => 18 pairs (_) / G8 = 6 => 20 pairs (_) E5,F5: 7.. / E5 = 7 => 0 pairs (X) / F5 = 7 => 14 pairs (_) E9,F9: 7.. / E9 = 7 => 14 pairs (_) / F9 = 7 => 0 pairs (X) E5,E9: 7.. / E5 = 7 => 0 pairs (X) / E9 = 7 => 14 pairs (_) F5,F9: 7.. / F5 = 7 => 14 pairs (_) / F9 = 7 => 0 pairs (X) G3,H3: 8.. / G3 = 8 => 0 pairs (X) / H3 = 8 => 14 pairs (_) C4,C5: 8.. / C4 = 8 => 0 pairs (*) / C5 = 8 => 0 pairs (X) D9,E9: 8.. / D9 = 8 => 14 pairs (_) / E9 = 8 => 0 pairs (X) D6,G6: 8.. / D6 = 8 => 0 pairs (X) / G6 = 8 => 14 pairs (_) D6,D9: 8.. / D6 = 8 => 0 pairs (X) / D9 = 8 => 14 pairs (_) H3,H4: 8.. / H3 = 8 => 14 pairs (_) / H4 = 8 => 0 pairs (X) C4,A6: 9.. / C4 = 9 => 0 pairs (X) / A6 = 9 => 14 pairs (_) A6,G6: 9.. / A6 = 9 => 14 pairs (_) / G6 = 9 => 0 pairs (X) I4,I9: 9.. / I4 = 9 => 15 pairs (_) / I9 = 9 => 0 pairs (X) * DURATION: 0:00:44.996858 START: 03:19:44.676322 END: 03:20:29.673180 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B1,B8,C8,D1,D9,E4,E9,F5,F6,G6,I4,I9) * 1.7.38..248.7....1........767.3.12...3.9...16.41.5..738.4...7.57..5.4.28.56...1.. * PAIR B1: 6,9 BLK 1 B3: 6,9,2 # reduction candidate for 6,9 B3: 2 => CTR * 167438..248.7....132.....87678341259532987416941.5.8738.4...7.57.35.4.2825687.14. B3: 6,9 # 22 pairs * PAIR B1: 6,9 ROW 1 G1: 6,9,4,5 # reduction candidate for 6,9 G1: 6,9 => CTR * 1.7438.5248.7256.15.....4876753812..2389475169412568738241937657195643283568721.. G1: 4,5 # 15 pairs H1: 6,9,4,5 # reduction candidate for 6,9 H1: 6,9 => CTR * 1.74385.248.7....1......487679381254.3.9...16.41.5..738.4...7.57..5.4.28.56...149 H1: 4,5 # 15 pairs * PAIR D1: 4,6 BLK 2 D3: 4,6,1,2 # reduction candidate for 4,6 D3: 4,6 # 17 pairs D3: 1,2 # 16 pairs * PAIR D1: 4,6 ROW 1 G1: 4,6,5,9 # reduction candidate for 4,6 G1: 4,6 => CTR * 197.38.5248.7.5..156...94876753812..23894751694125.873824...7.57195643283568721.. G1: 5,9 # 15 pairs H1: 4,6,5,9 # reduction candidate for 4,6 H1: 4,6 # 25 pairs * PAIR A5: 2,5 BLK 4 C5: 2,5,8 # reduction candidate for 2,5 C5: 2,5 => SOLVED * 197638542485729631263415987678341259532987416941256873824193765719564328356872194 C5: 8 # 26 pairs * PAIR A5: 2,5 COL A A3: 2,5,3,9 # reduction candidate for 2,5 A3: 2,5 => SOLVED * 197638542485729631263415987678341259532987416941256873824193765719564328356872194 A3: 3,9 # 17 pairs * PAIR A6: 2,9 COL A A3: 2,9,3,5 # reduction candidate for 2,9 A3: 2,9 => SOLVED * 197638542485729631263415987678341259532987416941256873824193765719564328356872194 A3: 3,5 # 15 pairs A9: 2,9,3 # reduction candidate for 2,9 A9: 2,9 # 18 pairs * PAIR E4: 4,8 BLK 5 E5: 4,8,7 # reduction candidate for 4,8 E5: 7 => CTR * 1.7.38..248.7....1........767.3412.9.3.972416.41.5..738.4...7.57..5.4.28.56...1.. E5: 4,8 # 14 pairs * PAIR E4: 4,8 ROW 4 H4: 4,8,5,9 # reduction candidate for 4,8 H4: 4,8 => CTR * 1.7.38.5248.7.5..15......87675381249238947516941256873824193765719564328356872194 H4: 5,9 # 15 pairs * PAIR F5: 2,7 COL F F9: 2,7,3,9 # reduction candidate for 2,7 F9: 3,9 => CTR * 16743859248.7..36132.....8767.3.12..532987416941.5.8738.4...7.57.35.4.2825687.1.4 F9: 2,7 # 22 pairs * PAIR F6: 2,6 BLK 5 D6: 2,6,8 # reduction candidate for 2,6 D6: 8 => CTR * 1.7.38..248.7....1........767.3.12...3.9...16.418569738.4...7.57..5.4.28.562871.9 D6: 2,6 # 14 pairs * PAIR F6: 2,6 COL F F2: 2,6,5,9 # reduction candidate for 2,6 F2: 2,6 => CTR * 1.7.385.24857....1329..5.87678341259532987416941.5.8738.4...7.57.35.4.2825687.1.4 F2: 5,9 # 15 pairs F3: 2,6,5,9 # reduction candidate for 2,6 F3: 2,6 => CTR * 1674385924897253613251964.767.3.125.5329.7.169416528738.42..7.57.35.4.2825687.1.. F3: 5,9 # 15 pairs F7: 2,6,3,9 # reduction candidate for 2,6 F7: 2,6 => CTR * 1.7.385.248.7..3.132....987678341259532987416941.5.8738.4...7357.35.4628256873194 F7: 3,9 # 15 pairs * PAIR I4: 4,9 BLK 6 H4: 4,9,5,8 # reduction candidate for 4,9 H4: 4,9 => CTR * 1.7.38.5248.7.5.315.3....876753812..23894751694125687382419.7.57195643283568721.. H4: 5,8 # 15 pairs * PAIR G6: 8,9 BLK 6 H4: 8,9,4,5 # reduction candidate for 8,9 H4: 8,9 => CTR * 1.7.38.5248.7.5..15......87675381294238947516941256873824193765719564328356872149 H4: 4,5 # 15 pairs * PAIR G6: 8,9 COL G G3: 8,9,3,4,6 # reduction candidate for 8,9 G3: 8,9 # 19 pairs G3: 3,4,6 # 14 pairs * PAIR B8: 1,9 BLK 7 B7: 1,9,2 # reduction candidate for 1,9 B7: 1,9 => CTR * 167438..248.7....132.....87678341259532987416941.5.8738.4...7.57.35.4.2825687.14. B7: 2 # 22 pairs * PAIR B8: 1,9 ROW 8 E8: 1,9,6 # reduction candidate for 1,9 E8: 1,9 # 20 pairs E8: 6 # 18 pairs * PAIR C8: 3,9 BLK 7 A9: 3,9,2 # reduction candidate for 3,9 A9: 2 => CTR * 1674385.248.7..3.132.....87678341259532987416941.5.8738.4...7.57.35.4.2825687.1.4 A9: 3,9 # 22 pairs * PAIR C8: 3,9 ROW 8 G8: 3,9,6 # reduction candidate for 3,9 G8: 6 # 20 pairs G8: 3,9 # 18 pairs * PAIR C8: 3,9 COL C C2: 3,9,2,5 # reduction candidate for 3,9 C2: 3,9 # 19 pairs C3: 3,9,2,5 # reduction candidate for 3,9 C3: 3,9 # 16 pairs * PAIR D9: 2,8 COL D D6: 2,8,6 # reduction candidate for 2,8 D6: 6 => CTR * 1.7438..248.7....132.1..48767.3.12..53.9.7.169416528738.4...7.57..5.4.2825687.1.. D6: 2,8 # 15 pairs * PAIR E9: 7,8 COL E E5: 7,8,4 # reduction candidate for 7,8 E5: 7,8 => SOLVED * 197638542485729631263415987678341259532987416941256873824193765719564328356872194 E5: 4 => CTR * 1.7.38.5248.7.5.315.3....876753812..23894751694125687382419.7.57195643283568721.. * PAIR I9: 4,9 BLK 9 H9: 4,9,3 # reduction candidate for 4,9 H9: 3 => CTR * 1674385.248.7..3.132.....87678341259532987416941.5.8738.4..37.57.35.4.28256879134 H9: 4,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190130-absurd-base-pr-000.dot * REASONING * DIS # B3: 2 => CTR => B3: 6,9 * DIS # G1: 6,9 => CTR => G1: 4,5 * DIS # H1: 6,9 => CTR => H1: 4,5 * DIS # G1: 4,6 => CTR => G1: 5,9 * PRF # C5: 2,5 => SOL * PRF # A3: 2,5 => SOL * PRF # A3: 2,9 => SOL * DIS # E5: 7 => CTR => E5: 4,8 * DIS # H4: 4,8 => CTR => H4: 5,9 * DIS # F9: 3,9 => CTR => F9: 2,7 * DIS # D6: 8 => CTR => D6: 2,6 * DIS # F2: 2,6 => CTR => F2: 5,9 * DIS # F3: 2,6 => CTR => F3: 5,9 * DIS # F7: 2,6 => CTR => F7: 3,9 * DIS # H4: 4,9 => CTR => H4: 5,8 * DIS # H4: 8,9 => CTR => H4: 4,5 * DIS # B7: 1,9 => CTR => B7: 2 * DIS # A9: 2 => CTR => A9: 3,9 * DIS # D6: 6 => CTR => D6: 2,8 * PRF # E5: 7,8 => SOL * DIS # E5: 4 => CTR => E5: 7,8 * DIS # H9: 3 => CTR => H9: 4,9 * CNT 22 HDP CHAINS / 54 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B1,B8,C8,D1,D9,E4,E9,F5,F6,G6,I4,I9) * 1.7.38..248.7....1........767.3.12...3.9...16.41.5..738.4...7.57..5.4.28.56...1.. * PAIR B1: 6,9 BLK 1 B3: 6,9,2 # reduction candidate for 6,9 B3: 2 => CTR * 167438..248.7....132.....87678341259532987416941.5.8738.4...7.57.35.4.2825687.14. * PAIR B1: 6,9 ROW 1 G1: 6,9,4,5 # reduction candidate for 6,9 G1: 6,9 => CTR * 1.7438.5248.725..15.26....76753.12..2389.7516941256873824..37.57195643283568721.. H1: 6,9,4,5 # reduction candidate for 6,9 H1: 6,9 => CTR * 1.74385.248.7...31......487679381254.3.9...16.41.56.73824..37.571.5.4.28.56...149 * PAIR RESTART * PAIR A5: 2,5 BLK 4 C5: 2,5,8 # reduction candidate for 2,5 C5: 2,5 => SOLVED * 197638542485729631263415987678341259532987416941256873824193765719564328356872194 * DURATION: 0:00:04.814446 START: 03:21:03.320546 END: 03:21:08.134992 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190130-absurd-base-pr-001.dot * REASONING * DIS # B3: 2 => CTR => B3: 6,9 * DIS B3: 6,9 # G1: 6,9 => CTR => G1: 4,5 * DIS B3: 6,9 + G1: 4,5 # H1: 6,9 => CTR => H1: 4,5 * PRF B3: 6,9 + G1: 4,5 + H1: 4,5 # C5: 2,5 => SOL * STA B3: 6,9 + G1: 4,5 + H1: 4,5 + C5: 2,5 * 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, 20190130, absurd
Solution
position: 197638542485729631263415987678341259532987416941256873824193765719564328356872194 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 # B3: 6,9 => UNS * DIS # B3: 2 => CTR => B3: 6,9 * DIS # G1: 6,9 => CTR => G1: 4,5 * INC # G1: 4,5 => UNS * DIS # H1: 6,9 => CTR => H1: 4,5 * INC # H1: 4,5 => UNS * INC # D3: 4,6 => UNS * INC # D3: 1,2 => UNS * DIS # G1: 4,6 => CTR => G1: 5,9 * INC # G1: 5,9 => UNS * INC # H1: 4,6 => UNS * PRF # C5: 2,5 => SOL * INC # C5: 8 => UNS * PRF # A3: 2,5 => SOL * INC # A3: 3,9 => UNS * PRF # A3: 2,9 => SOL * INC # A3: 3,5 => UNS * INC # A9: 2,9 => UNS * INC # E5: 4,8 => UNS * DIS # E5: 7 => CTR => E5: 4,8 * DIS # H4: 4,8 => CTR => H4: 5,9 * INC # H4: 5,9 => UNS * INC # F9: 2,7 => UNS * DIS # F9: 3,9 => CTR => F9: 2,7 * INC # D6: 2,6 => UNS * DIS # D6: 8 => CTR => D6: 2,6 * DIS # F2: 2,6 => CTR => F2: 5,9 * INC # F2: 5,9 => UNS * DIS # F3: 2,6 => CTR => F3: 5,9 * INC # F3: 5,9 => UNS * DIS # F7: 2,6 => CTR => F7: 3,9 * INC # F7: 3,9 => UNS * DIS # H4: 4,9 => CTR => H4: 5,8 * INC # H4: 5,8 => UNS * DIS # H4: 8,9 => CTR => H4: 4,5 * INC # H4: 4,5 => UNS * INC # G3: 8,9 => UNS * INC # G3: 3,4,6 => UNS * DIS # B7: 1,9 => CTR => B7: 2 * INC # B7: 2 => UNS * INC # E8: 1,9 => UNS * INC # E8: 6 => UNS * INC # A9: 3,9 => UNS * DIS # A9: 2 => CTR => A9: 3,9 * INC # G8: 3,9 => UNS * INC # G8: 6 => UNS * INC # C2: 3,9 => UNS * INC # C3: 3,9 => UNS * INC # D6: 2,8 => UNS * DIS # D6: 6 => CTR => D6: 2,8 * PRF # E5: 7,8 => SOL * DIS # E5: 4 => CTR => E5: 7,8 * INC # H9: 4,9 => UNS * DIS # H9: 3 => CTR => H9: 4,9 * CNT 54 HDP CHAINS / 54 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 6,9 => UNS * DIS # B3: 2 => CTR => B3: 6,9 * DIS B3: 6,9 # G1: 6,9 => CTR => G1: 4,5 * DIS B3: 6,9 + G1: 4,5 # H1: 6,9 => CTR => H1: 4,5 * PRF B3: 6,9 + G1: 4,5 + H1: 4,5 # C5: 2,5 => SOL * STA B3: 6,9 + G1: 4,5 + H1: 4,5 + C5: 2,5 * CNT 5 HDP CHAINS / 5 HYP OPENED