Analysis of zz-www.sudokuoftheday.co.uk-20060511-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: .56.....8..2......48....2.7......4..39...6.8...1..463.....7.1..6..2.3.5.1..549... initial
Autosolve
position: 756.....8912..7...483...2.7.6....4..394..6.8...1..463....6781..6..213.5.1..549... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F4: 5 => CTR => F4: 1,2 * DIS # D1: 1,9 => CTR => D1: 3,4 * DIS # D4: 1,9 => CTR => D4: 3,7,8 * PRF # F4: 2 => SOL * PRF # D1: 3,9 => SOL * DIS # I2: 4,6 => CTR => I2: 3,5 * DIS # I2: 4,6 => CTR => I2: 3,5 * PRF # B9: 2,7 => SOL * DIS # B9: 3 => CTR => B9: 2,7 * PRF # D4: 1,7 => SOL * DIS # E4: 2,5 => CTR => E4: 3,8,9 * DIS # E6: 2,5 => CTR => E6: 8,9 * PRF # I5: 2,5 => SOL * DIS # I5: 1 => CTR => I5: 2,5 * PRF # C8: 7,8 => SOL * DIS # C8: 9 => CTR => C8: 7,8 * DIS # G9: 7,8 => CTR => G9: 3 * PRF # G9: 3 => SOL * DIS # H7: 4,9 => CTR => H7: 2 * PRF # H7: 2 => SOL * PRF # I7: 4,9 => SOL * CNT 21 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F4: 5 => CTR => F4: 1,2 * DIS F4: 1,2 # D1: 1,9 => CTR => D1: 3,4 * DIS F4: 1,2 + D1: 3,4 # H3: 6 => CTR => H3: 1,9 * DIS F4: 1,2 + D1: 3,4 + H3: 1,9 # D4: 1,9 => CTR => D4: 3,7,8 * PRF F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 # I2: 3,5 => SOL * STA F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 + I2: 3,5 * CNT 5 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .56.....8..2......48....2.7......4..39...6.8...1..463.....7.1..6..2.3.5.1..549... | initial |
| 756.....8912..7...483...2.7.6....4..394..6.8...1..463....6781..6..213.5.1..549... | autosolve |
| 756321948912487563483965217865732491394156782271894635539678124647213859128549376 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) F1: 1,2 D3: 1,9 F3: 1,5 G1: 3,9 G2: 3,5 H2: 4,6 C4: 5,7 B6: 2,7 D5: 1,7 E5: 2,5 G5: 5,7 A7: 2,5 C7: 5,9 B8: 4,7 C9: 7,8 I8: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H3: 1.. / H1 = 1 => 19 pairs (_) / H3 = 1 => 19 pairs (_) I4,I5: 1.. / I4 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) D5,I5: 1.. / D5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) E1,F1: 2.. / E1 = 2 => 0 pairs (*) / F1 = 2 => 0 pairs (X) E5,I5: 2.. / E5 = 2 => 20 pairs (_) / I5 = 2 => 0 pairs (*) F1,F4: 2.. / F1 = 2 => 19 pairs (_) / F4 = 2 => 0 pairs (*) D4,E4: 3.. / D4 = 3 => 17 pairs (_) / E4 = 3 => 20 pairs (_) B7,B9: 3.. / B7 = 3 => 0 pairs (*) / B9 = 3 => 0 pairs (X) B7,I7: 3.. / B7 = 3 => 0 pairs (*) / I7 = 3 => 0 pairs (X) D1,D2: 4.. / D1 = 4 => 18 pairs (_) / D2 = 4 => 23 pairs (_) B7,B8: 4.. / B7 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) D1,H1: 4.. / D1 = 4 => 18 pairs (_) / H1 = 4 => 23 pairs (_) B8,I8: 4.. / B8 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) E3,F3: 5.. / E3 = 5 => 0 pairs (X) / F3 = 5 => 17 pairs (_) G2,I2: 5.. / G2 = 5 => 0 pairs (*) / I2 = 5 => 0 pairs (X) A7,C7: 5.. / A7 = 5 => 0 pairs (*) / C7 = 5 => 0 pairs (X) C4,C7: 5.. / C4 = 5 => 0 pairs (*) / C7 = 5 => 0 pairs (X) F3,F4: 5.. / F3 = 5 => 17 pairs (_) / F4 = 5 => 0 pairs (X) G2,G5: 5.. / G2 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) E2,E3: 6.. / E2 = 6 => 23 pairs (_) / E3 = 6 => 18 pairs (_) H9,I9: 6.. / H9 = 6 => 0 pairs (X) / I9 = 6 => 17 pairs (_) E3,H3: 6.. / E3 = 6 => 18 pairs (_) / H3 = 6 => 23 pairs (_) I2,I9: 6.. / I2 = 6 => 0 pairs (X) / I9 = 6 => 17 pairs (_) C4,B6: 7.. / C4 = 7 => 0 pairs (X) / B6 = 7 => 0 pairs (_) H4,G5: 7.. / H4 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) D5,G5: 7.. / D5 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) B6,D6: 7.. / B6 = 7 => 0 pairs (*) / D6 = 7 => 0 pairs (X) H4,H9: 7.. / H4 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) D2,E2: 8.. / D2 = 8 => 19 pairs (_) / E2 = 8 => 18 pairs (_) A4,A6: 8.. / A4 = 8 => 18 pairs (_) / A6 = 8 => 22 pairs (_) C8,C9: 8.. / C8 = 8 => 0 pairs (X) / C9 = 8 => 28 pairs (_) G8,G9: 8.. / G8 = 8 => 28 pairs (_) / G9 = 8 => 0 pairs (X) C8,G8: 8.. / C8 = 8 => 0 pairs (X) / G8 = 8 => 28 pairs (_) C9,G9: 8.. / C9 = 8 => 28 pairs (_) / G9 = 8 => 0 pairs (X) C7,C8: 9.. / C7 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) G1,G8: 9.. / G1 = 9 => 27 pairs (_) / G8 = 9 => 0 pairs (X) * DURATION: 0:00:39.017984 START: 23:04:32.917117 END: 23:05:11.935101 2019-04-30 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B6,B8,C4,C7,C9,D3,D5,E5,F1,F3,G1,G2,G5,H2,I8) * 756.....8912..7...483...2.7.6....4..394..6.8...1..463....6781..6..213.5.1..549... * PAIR F1: 1,2 COL F F4: 1,2,5 # reduction candidate for 1,2 F4: 5 => CTR * 756..2918912..7.4.483951267867..54..394.267855217846392456781936.92138541.8549... F4: 1,2 # 17 pairs * PAIR D3: 1,9 BLK 2 D1: 1,9,3,4 # reduction candidate for 1,9 D1: 1,9 => CTR * 756.32948912487.6.48396521786.3.14..3947.6581.718.463....6781..64.213.591..549..6 D1: 3,4 # 17 pairs * PAIR D3: 1,9 ROW 3 H3: 1,9,6 # reduction candidate for 1,9 H3: 6 # 23 pairs H3: 1,9 # 18 pairs * PAIR D3: 1,9 COL D D4: 1,9,3,7,8 # reduction candidate for 1,9 D4: 1,9 => CTR * 756.....8912.87...483.652.786..3.4..3947.6581.718546395.96781..64.213.5.1..549... D4: 3,7,8 # 16 pairs * PAIR F3: 1,5 COL F F4: 1,5,2 # reduction candidate for 1,5 F4: 2 => SOLVED * 756321948912487563483965217865732491394156782271894635539678124647213859128549376 F4: 1,5 # 19 pairs * PAIR G1: 3,9 ROW 1 D1: 3,9,1,4 # reduction candidate for 3,9 D1: 3,9 => SOLVED * 756321948912487563483965217865732491394156782271894635539678124647213859128549376 D1: 1,4 # 17 pairs E1: 3,9,2 # reduction candidate for 3,9 E1: 3,9 # 19 pairs * PAIR G2: 3,5 BLK 3 I2: 3,5,4,6 # reduction candidate for 3,5 I2: 4,6 => CTR * 756...3.8912..75.4483...2.7.6....4..3941.678...1..463....67814.6..213.5.1..549.76 I2: 3,5 # 27 pairs * PAIR H2: 4,6 BLK 3 I2: 4,6,3,5 # reduction candidate for 4,6 I2: 4,6 => CTR * 756...3.8912..75.4483...2.7.6....4..3941.678...1..463....67814.6..213.5.1..549.76 I2: 3,5 # 27 pairs * PAIR B6: 2,7 COL B B9: 2,7,3 # reduction candidate for 2,7 B9: 2,7 => SOLVED * 756321948912487563483965217865732491394156782271894635539678124647213859128549376 B9: 3 => CTR * 756...9.8912..73.5483...2.7.6....47.3947.6581.71..463..2.6781.36..213.5.13.549... * PAIR D5: 1,7 BLK 5 D4: 1,7,3,8,9 # reduction candidate for 1,7 D4: 1,7 => SOLVED * 756321948912487563483965217865732491394156782271894635539678124647213859128549376 D4: 3,8,9 # 16 pairs * PAIR E5: 2,5 BLK 5 E4: 2,5,3,8,9 # reduction candidate for 2,5 E4: 2,5 => CTR * 756.....8912..75..483...2.786532147.394..6.8...1..46355.96781..6..213.5.1..549... E4: 3,8,9 # 16 pairs F4: 2,5,1 # reduction candidate for 2,5 F4: 2,5 # 22 pairs E6: 2,5,8,9 # reduction candidate for 2,5 E6: 2,5 => CTR * 756..2..8912..7...483..52.7.6...14..3947.6581.71.5463....6781..64.213.591..549... E6: 8,9 # 17 pairs * PAIR E5: 2,5 ROW 5 I5: 2,5,1 # reduction candidate for 2,5 I5: 2,5 => SOLVED * 756321948912487563483965217865732491394156782271894635539678124647213859128549376 I5: 1 => CTR * 756..2..8912..73.5483...2.7.6....47.394726581.71..463....6781..64.213.591..549..6 * PAIR A7: 2,5 COL A A4: 2,5,8 # reduction candidate for 2,5 A4: 2,5 # 22 pairs A6: 2,5,8 # reduction candidate for 2,5 A6: 2,5 # 18 pairs * PAIR C9: 7,8 BLK 7 C8: 7,8,9 # reduction candidate for 7,8 C8: 7,8 => SOLVED * 756321948912487563483965217865732491394156782271894635539678124647213859128549376 C8: 9 => CTR * 756...9.8912..7...483...2.7.67...4..394..678..217.463.2456781936.92138541.8549... * PAIR C9: 7,8 ROW 9 G9: 7,8,3 # reduction candidate for 7,8 G9: 7,8 => CTR * 756.....8912..7...483...2.7.6....47.3947.6581.71..463....6781..64.213.591..549... G9: 3 => SOLVED * 756321948912487563483965217865732491394156782271894635539678124647213859128549376 * PAIR I8: 4,9 BLK 9 H7: 4,9,2 # reduction candidate for 4,9 H7: 4,9 => CTR * 756...9.8912..7...483...2.7.67...42.394.26785.217.46392456781936.92138541.8549..6 H7: 2 => SOLVED * 756321948912487563483965217865732491394156782271894635539678124647213859128549376 I7: 4,9,2,3 # reduction candidate for 4,9 I7: 4,9 => SOLVED * 756321948912487563483965217865732491394156782271894635539678124647213859128549376 I7: 2,3 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060511-absurd-base-pr-000.dot * REASONING * DIS # F4: 5 => CTR => F4: 1,2 * DIS # D1: 1,9 => CTR => D1: 3,4 * DIS # D4: 1,9 => CTR => D4: 3,7,8 * PRF # F4: 2 => SOL * PRF # D1: 3,9 => SOL * DIS # I2: 4,6 => CTR => I2: 3,5 * DIS # I2: 4,6 => CTR => I2: 3,5 * PRF # B9: 2,7 => SOL * DIS # B9: 3 => CTR => B9: 2,7 * PRF # D4: 1,7 => SOL * DIS # E4: 2,5 => CTR => E4: 3,8,9 * DIS # E6: 2,5 => CTR => E6: 8,9 * PRF # I5: 2,5 => SOL * DIS # I5: 1 => CTR => I5: 2,5 * PRF # C8: 7,8 => SOL * DIS # C8: 9 => CTR => C8: 7,8 * DIS # G9: 7,8 => CTR => G9: 3 * PRF # G9: 3 => SOL * DIS # H7: 4,9 => CTR => H7: 2 * PRF # H7: 2 => SOL * PRF # I7: 4,9 => SOL * CNT 21 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B6,B8,C4,C7,C9,D3,D5,E5,F1,F3,G1,G2,G5,H2,I8) * 756.....8912..7...483...2.7.6....4..394..6.8...1..463....6781..6..213.5.1..549... * PAIR F1: 1,2 COL F F4: 1,2,5 # reduction candidate for 1,2 F4: 5 => CTR * 756..2918912..7.4.483951267867..54..394.267855217846392456781936.92138541.8549... * PAIR RESTART * PAIR D3: 1,9 BLK 2 D1: 1,9,3,4 # reduction candidate for 1,9 D1: 1,9 => CTR * 756.32948912487.6.48396521786.3.14..3947.6581.718.463....6781..64.213.591..549..6 * PAIR D3: 1,9 ROW 3 H3: 1,9,6 # reduction candidate for 1,9 H3: 6 => CTR * 756....18912..7...483195267.6...14..3947.6581.71..463....6781..64.213.591..549..6 * PAIR D3: 1,9 COL D D4: 1,9,3,7,8 # reduction candidate for 1,9 D4: 1,9 => CTR * 756.....8912.87...483.652.786..3.4..3947.6581.718546395.96781..64.213.5.1..549... * PAIR RESTART * PAIR G2: 3,5 BLK 3 I2: 3,5,4,6 # reduction candidate for 3,5 I2: 3,5 => SOLVED * 756321948912487563483965217865732491394156782271894635539678124647213859128549376 * DURATION: 0:00:06.663989 START: 23:05:37.265448 END: 23:05:43.929437 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060511-absurd-base-pr-001.dot * REASONING * DIS # F4: 5 => CTR => F4: 1,2 * DIS F4: 1,2 # D1: 1,9 => CTR => D1: 3,4 * DIS F4: 1,2 + D1: 3,4 # H3: 6 => CTR => H3: 1,9 * DIS F4: 1,2 + D1: 3,4 + H3: 1,9 # D4: 1,9 => CTR => D4: 3,7,8 * PRF F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 # I2: 3,5 => SOL * STA F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 + I2: 3,5 * CNT 5 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060511, absurd
Solution
position: 756321948912487563483965217865732491394156782271894635539678124647213859128549376 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 # F4: 1,2 => UNS * DIS # F4: 5 => CTR => F4: 1,2 * DIS # D1: 1,9 => CTR => D1: 3,4 * INC # D1: 3,4 => UNS * INC # H3: 1,9 => UNS * INC # H3: 6 => UNS * DIS # D4: 1,9 => CTR => D4: 3,7,8 * INC # D4: 3,7,8 => UNS * INC # F4: 1,5 => UNS * PRF # F4: 2 => SOL * PRF # D1: 3,9 => SOL * INC # D1: 1,4 => UNS * INC # E1: 3,9 => UNS * INC # I2: 3,5 => UNS * DIS # I2: 4,6 => CTR => I2: 3,5 * DIS # I2: 4,6 => CTR => I2: 3,5 * INC # I2: 3,5 => UNS * PRF # B9: 2,7 => SOL * DIS # B9: 3 => CTR => B9: 2,7 * PRF # D4: 1,7 => SOL * INC # D4: 3,8,9 => UNS * DIS # E4: 2,5 => CTR => E4: 3,8,9 * INC # E4: 3,8,9 => UNS * INC # F4: 2,5 => UNS * DIS # E6: 2,5 => CTR => E6: 8,9 * INC # E6: 8,9 => UNS * PRF # I5: 2,5 => SOL * DIS # I5: 1 => CTR => I5: 2,5 * INC # A4: 2,5 => UNS * INC # A6: 2,5 => UNS * PRF # C8: 7,8 => SOL * DIS # C8: 9 => CTR => C8: 7,8 * DIS # G9: 7,8 => CTR => G9: 3 * PRF # G9: 3 => SOL * DIS # H7: 4,9 => CTR => H7: 2 * PRF # H7: 2 => SOL * PRF # I7: 4,9 => SOL * INC # I7: 2,3 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F4: 1,2 => UNS * DIS # F4: 5 => CTR => F4: 1,2 * DIS F4: 1,2 # D1: 1,9 => CTR => D1: 3,4 * INC F4: 1,2 + D1: 3,4 # H3: 1,9 => UNS * DIS F4: 1,2 + D1: 3,4 # H3: 6 => CTR => H3: 1,9 * DIS F4: 1,2 + D1: 3,4 + H3: 1,9 # D4: 1,9 => CTR => D4: 3,7,8 * PRF F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 # I2: 3,5 => SOL * STA F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 + I2: 3,5 * CNT 7 HDP CHAINS / 7 HYP OPENED