Analysis of zz-www.sudokuoftheday.co.uk-20060722-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: ..6.9...8.4.6...1.5.3...4.....357....2...6.75.....2....8.2.....4.9......35....9.4 initial
Autosolve
position: ..6.94.38.4.6...1.5.3...4.....357....2...6375735..2....8.249.534.9......352...9.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 1,7 => CTR => B3: 9 * DIS # D1: 1,7 => CTR => D1: 5 * DIS # B8: 6 => CTR => B8: 1,7 * DIS # E2: 3 => CTR => E2: 2,7 * DIS # D3: 7 => CTR => D3: 1,8 * DIS # H6: 6,8 => CTR => H6: 4,9 * DIS # B8: 7 => CTR => B8: 1,6 * DIS # G7: 7 => CTR => G7: 1,6 * DIS # B8: 6 => CTR => B8: 1,7 * DIS # G7: 6 => CTR => G7: 1,7 * DIS # D9: 1,8 => CTR => D9: 7 * DIS # H8: 6,8 => CTR => H8: 2 * DIS # H6: 6,8 => CTR => H6: 4,9 * CNT 13 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 1,7 => CTR => B3: 9 * DIS B3: 9 # B8: 6 => CTR => B8: 1,7 * DIS B3: 9 + B8: 1,7 # E2: 3 => CTR => E2: 2,7 * DIS B3: 9 + B8: 1,7 + E2: 2,7 # I3: 6 => CTR => I3: 2,7 * PRF B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # G6: 6 => SOL * STA B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 + G6: 6 * CNT 5 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6.9...8.4.6...1.5.3...4.....357....2...6.75.....2....8.2.....4.9......35....9.4 | initial |
| ..6.94.38.4.6...1.5.3...4.....357....2...6375735..2....8.249.534.9......352...9.4 | autosolve |
| 176594238248673519593128467961357842824916375735482691687249153419835726352761984 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 1,2 B1: 1,7 C2: 7,8 F2: 3,5 E3: 2,7 F3: 1,8 D5: 4,9 E5: 1,8 D6: 4,9 E6: 1,8 A7: 1,6 C7: 1,7 D8: 5,8 E8: 3,6 F8: 3,5 E9: 6,7 F9: 1,8 H9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E5,E6: 1.. / E5 = 1 => 22 pairs (_) / E6 = 1 => 23 pairs (_) D9,F9: 1.. / D9 = 1 => 0 pairs (X) / F9 = 1 => 18 pairs (_) F3,F9: 1.. / F3 = 1 => 0 pairs (X) / F9 = 1 => 18 pairs (_) A1,A2: 2.. / A1 = 2 => 22 pairs (_) / A2 = 2 => 0 pairs (*) E2,E3: 2.. / E2 = 2 => 0 pairs (X) / E3 = 2 => 19 pairs (_) A1,G1: 2.. / A1 = 2 => 22 pairs (_) / G1 = 2 => 0 pairs (*) E2,F2: 3.. / E2 = 3 => 0 pairs (X) / F2 = 3 => 14 pairs (_) E8,F8: 3.. / E8 = 3 => 14 pairs (_) / F8 = 3 => 0 pairs (X) E2,E8: 3.. / E2 = 3 => 0 pairs (X) / E8 = 3 => 14 pairs (_) F2,F8: 3.. / F2 = 3 => 14 pairs (_) / F8 = 3 => 0 pairs (X) C4,C5: 4.. / C4 = 4 => 24 pairs (_) / C5 = 4 => 21 pairs (_) D5,D6: 4.. / D5 = 4 => 24 pairs (_) / D6 = 4 => 21 pairs (_) H4,H6: 4.. / H4 = 4 => 21 pairs (_) / H6 = 4 => 24 pairs (_) C4,H4: 4.. / C4 = 4 => 24 pairs (_) / H4 = 4 => 21 pairs (_) C5,D5: 4.. / C5 = 4 => 21 pairs (_) / D5 = 4 => 24 pairs (_) D6,H6: 4.. / D6 = 4 => 21 pairs (_) / H6 = 4 => 24 pairs (_) D1,F2: 5.. / D1 = 5 => 14 pairs (_) / F2 = 5 => 0 pairs (X) G1,G2: 5.. / G1 = 5 => 0 pairs (X) / G2 = 5 => 14 pairs (_) D8,F8: 5.. / D8 = 5 => 0 pairs (X) / F8 = 5 => 14 pairs (_) D1,G1: 5.. / D1 = 5 => 14 pairs (_) / G1 = 5 => 0 pairs (X) F2,G2: 5.. / F2 = 5 => 0 pairs (X) / G2 = 5 => 14 pairs (_) D1,D8: 5.. / D1 = 5 => 14 pairs (_) / D8 = 5 => 0 pairs (X) F2,F8: 5.. / F2 = 5 => 0 pairs (X) / F8 = 5 => 14 pairs (_) H3,I3: 6.. / H3 = 6 => 17 pairs (_) / I3 = 6 => 20 pairs (_) A4,B4: 6.. / A4 = 6 => 0 pairs (X) / B4 = 6 => 27 pairs (_) A7,B8: 6.. / A7 = 6 => 27 pairs (_) / B8 = 6 => 0 pairs (X) E8,E9: 6.. / E8 = 6 => 0 pairs (X) / E9 = 6 => 14 pairs (_) A7,G7: 6.. / A7 = 6 => 27 pairs (_) / G7 = 6 => 0 pairs (X) E9,H9: 6.. / E9 = 6 => 14 pairs (_) / H9 = 6 => 0 pairs (X) A4,A7: 6.. / A4 = 6 => 0 pairs (X) / A7 = 6 => 27 pairs (_) B4,B8: 6.. / B4 = 6 => 27 pairs (_) / B8 = 6 => 0 pairs (X) C7,B8: 7.. / C7 = 7 => 23 pairs (_) / B8 = 7 => 0 pairs (X) D9,E9: 7.. / D9 = 7 => 14 pairs (_) / E9 = 7 => 0 pairs (X) C7,G7: 7.. / C7 = 7 => 23 pairs (_) / G7 = 7 => 0 pairs (X) C2,C7: 7.. / C2 = 7 => 0 pairs (X) / C7 = 7 => 23 pairs (_) A2,C2: 8.. / A2 = 8 => 0 pairs (X) / C2 = 8 => 23 pairs (_) D3,F3: 8.. / D3 = 8 => 0 pairs (X) / F3 = 8 => 18 pairs (_) E5,E6: 8.. / E5 = 8 => 23 pairs (_) / E6 = 8 => 22 pairs (_) F3,F9: 8.. / F3 = 8 => 18 pairs (_) / F9 = 8 => 0 pairs (X) A2,B3: 9.. / A2 = 9 => 0 pairs (X) / B3 = 9 => 27 pairs (_) D5,D6: 9.. / D5 = 9 => 21 pairs (_) / D6 = 9 => 24 pairs (_) A2,I2: 9.. / A2 = 9 => 0 pairs (X) / I2 = 9 => 27 pairs (_) A5,D5: 9.. / A5 = 9 => 24 pairs (_) / D5 = 9 => 21 pairs (_) B3,B4: 9.. / B3 = 9 => 27 pairs (_) / B4 = 9 => 0 pairs (X) * DURATION: 0:00:59.453287 START: 00:53:22.741350 END: 00:54:22.194637 2019-05-01 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B1,C2,C7,D5,D6,D8,E3,E5,E6,E8,E9,F2,F3,F8,F9,H9) * ..6.94.38.4.6...1.5.3...4.....357....2...6375735..2....8.249.534.9......352...9.4 * PAIR B1: 1,7 BLK 1 B3: 1,7,9 # reduction candidate for 1,7 B3: 1,7 => CTR * 2.6594738948673512573.284..69.3578...2.9.63757354.2....87249.53469.35...352.6.984 B3: 9 # 27 pairs * PAIR B1: 1,7 ROW 1 D1: 1,7,5 # reduction candidate for 1,7 D1: 1,7 => CTR * 2.6.94538.4.635.1.5.3.2.496...357....2...6375735..2....8.249.534.9563...352.7.964 D1: 5 # 14 pairs * PAIR B1: 1,7 COL B B8: 1,7,6 # reduction candidate for 1,7 B8: 6 => CTR * 2165947389486735125731284..6913578..82.916375735482...187249653469835.2.352761984 B8: 1,7 # 27 pairs * PAIR E3: 2,7 BLK 2 E2: 2,7,3 # reduction candidate for 2,7 E2: 3 => CTR * ..6.94538.4.635.1.5.3.2.496...357....2...6375735..2....8.249.534.9563...352.7.964 E2: 2,7 # 14 pairs * PAIR E3: 2,7 ROW 3 I3: 2,7,6,9 # reduction candidate for 2,7 I3: 6,9 # 19 pairs I3: 2,7 # 19 pairs * PAIR F3: 1,8 BLK 2 D3: 1,8,7 # reduction candidate for 1,8 D3: 7 => CTR * ..6194538.4.635.1.513728496.9.357....2.9.63757354.2689681249753479......352.71964 D3: 1,8 # 21 pairs * PAIR E5: 1,8 ROW 5 A5: 1,8,9 # reduction candidate for 1,8 A5: 1,8 # 21 pairs C5: 1,8,4 # reduction candidate for 1,8 C5: 1,8 # 24 pairs * PAIR D6: 4,9 ROW 6 H6: 4,9,6,8 # reduction candidate for 4,9 H6: 6,8 => CTR * 2.65947389486...1.5.3...496.91357.42824916375735482169187249653469.35.21352.6.984 H6: 4,9 # 20 pairs * PAIR E6: 1,8 ROW 6 G6: 1,8,6 # reduction candidate for 1,8 G6: 6 # 29 pairs G6: 1,8 # 19 pairs * PAIR A7: 1,6 BLK 7 B8: 1,6,7 # reduction candidate for 1,6 B8: 7 => CTR * .16794538.476.5219593.2.467.6.357....2...6375735..2...6812497534795.....352...9.4 B8: 1,6 # 23 pairs * PAIR A7: 1,6 ROW 7 G7: 1,6,7 # reduction candidate for 1,6 G7: 7 => CTR * .16794538.476.5219593.2.467.6.357....2...6375735..2...6812497534795.....352...9.4 G7: 1,6 # 23 pairs * PAIR A7: 1,6 COL A A4: 1,6,8,9 # reduction candidate for 1,6 A4: 8,9 # 28 pairs A4: 1,6 # 24 pairs * PAIR C7: 1,7 BLK 7 B8: 1,7,6 # reduction candidate for 1,7 B8: 6 => CTR * 2165947389486735125731284..6913578..82.916375735482...187249653469835.2.352761984 B8: 1,7 # 27 pairs * PAIR C7: 1,7 ROW 7 G7: 1,7,6 # reduction candidate for 1,7 G7: 6 => CTR * 216594738.486.351.5.3..84..6..3578..82.9163757354821..187249653469835.21352761984 G7: 1,7 # 27 pairs * PAIR F9: 1,8 BLK 8 D9: 1,8,7 # reduction candidate for 1,8 D9: 1,8 => CTR * ..6.94.38.4.6...1.5.3.2.496.9.357....2.9.63757354.268968.249.534.9.6382.352.7.964 D9: 7 # 14 pairs * PAIR H9: 6,8 BLK 9 G8: 6,8,1,2,7 # reduction candidate for 6,8 G8: 6,8 # 20 pairs H8: 6,8,2 # reduction candidate for 6,8 H8: 6,8 => CTR * 2.6.94.38.4.6...1.593...426.6.3578.2.2..16375735.826.168.249.534.9...2.7352...9.4 H8: 2 # 19 pairs * PAIR H9: 6,8 COL H H6: 6,8,4,9 # reduction candidate for 6,8 H6: 6,8 => CTR * 2.65947389486...1.5.3...496.91357.42824916375735482169187249653469.35.21352.6.984 H6: 4,9 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060722-absurd-base-pr-000.dot * REASONING * DIS # B3: 1,7 => CTR => B3: 9 * DIS # D1: 1,7 => CTR => D1: 5 * DIS # B8: 6 => CTR => B8: 1,7 * DIS # E2: 3 => CTR => E2: 2,7 * DIS # D3: 7 => CTR => D3: 1,8 * DIS # H6: 6,8 => CTR => H6: 4,9 * DIS # B8: 7 => CTR => B8: 1,6 * DIS # G7: 7 => CTR => G7: 1,6 * DIS # B8: 6 => CTR => B8: 1,7 * DIS # G7: 6 => CTR => G7: 1,7 * DIS # D9: 1,8 => CTR => D9: 7 * DIS # H8: 6,8 => CTR => H8: 2 * DIS # H6: 6,8 => CTR => H6: 4,9 * CNT 13 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B1,C2,C7,D5,D6,D8,E3,E5,E6,E8,E9,F2,F3,F8,F9,H9) * ..6.94.38.4.6...1.5.3...4.....357....2...6375735..2....8.249.534.9......352...9.4 * PAIR B1: 1,7 BLK 1 B3: 1,7,9 # reduction candidate for 1,7 B3: 1,7 => CTR * 2.6594738948673512573.284..69.3578...2.9.63757354.2....87249.53469.35...352.6.984 * PAIR B1: 1,7 COL B B8: 1,7,6 # reduction candidate for 1,7 B8: 6 => CTR * .765942382486.3519593.2.467.14357....2...6375735..2....8.249.534.9......352...9.4 * PAIR RESTART * PAIR E3: 2,7 BLK 2 E2: 2,7,3 # reduction candidate for 2,7 E2: 3 => CTR * ..6.94.38.4.635.19593.2.467.6.357....2...6375735..2...68.249.534.95.....352...9.4 * PAIR E3: 2,7 ROW 3 I3: 2,7,6 # reduction candidate for 2,7 I3: 6 => CTR * ..6594738.47623519593178426.6.357....2...6375735..26.1681249.534.9835...352761984 * PAIR RESTART * PAIR E5: 1,8 ROW 5 A5: 1,8,9 # reduction candidate for 1,8 A5: 1,8 # 17 pairs C5: 1,8,4 # reduction candidate for 1,8 C5: 1,8 # 17 pairs * PAIR E6: 1,8 ROW 6 G6: 1,8,6 # reduction candidate for 1,8 G6: 6 => SOLVED * 176594238248673519593128467961357842824916375735482691687249153419835726352761984 * DURATION: 0:00:11.645927 START: 00:54:48.532605 END: 00:55:00.178532 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060722-absurd-base-pr-001.dot * REASONING * DIS # B3: 1,7 => CTR => B3: 9 * DIS B3: 9 # B8: 6 => CTR => B8: 1,7 * DIS B3: 9 + B8: 1,7 # E2: 3 => CTR => E2: 2,7 * DIS B3: 9 + B8: 1,7 + E2: 2,7 # I3: 6 => CTR => I3: 2,7 * PRF B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # G6: 6 => SOL * STA B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 + G6: 6 * CNT 5 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060722, absurd
Solution
position: 176594238248673519593128467961357842824916375735482691687249153419835726352761984 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 # B3: 1,7 => CTR => B3: 9 * INC # B3: 9 => UNS * DIS # D1: 1,7 => CTR => D1: 5 * INC # D1: 5 => UNS * INC # B8: 1,7 => UNS * DIS # B8: 6 => CTR => B8: 1,7 * INC # E2: 2,7 => UNS * DIS # E2: 3 => CTR => E2: 2,7 * INC # I3: 2,7 => UNS * INC # I3: 6,9 => UNS * INC # D3: 1,8 => UNS * DIS # D3: 7 => CTR => D3: 1,8 * INC # A5: 1,8 => UNS * INC # C5: 1,8 => UNS * INC # H6: 4,9 => UNS * DIS # H6: 6,8 => CTR => H6: 4,9 * INC # G6: 1,8 => UNS * INC # G6: 6 => UNS * INC # B8: 1,6 => UNS * DIS # B8: 7 => CTR => B8: 1,6 * INC # G7: 1,6 => UNS * DIS # G7: 7 => CTR => G7: 1,6 * INC # A4: 1,6 => UNS * INC # A4: 8,9 => UNS * INC # B8: 1,7 => UNS * DIS # B8: 6 => CTR => B8: 1,7 * INC # G7: 1,7 => UNS * DIS # G7: 6 => CTR => G7: 1,7 * DIS # D9: 1,8 => CTR => D9: 7 * INC # D9: 7 => UNS * INC # G8: 6,8 => UNS * DIS # H8: 6,8 => CTR => H8: 2 * INC # H8: 2 => UNS * DIS # H6: 6,8 => CTR => H6: 4,9 * INC # H6: 4,9 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 1,7 => CTR => B3: 9 * INC B3: 9 # B8: 1,7 => UNS * DIS B3: 9 # B8: 6 => CTR => B8: 1,7 * INC B3: 9 + B8: 1,7 # E2: 2,7 => UNS * DIS B3: 9 + B8: 1,7 # E2: 3 => CTR => E2: 2,7 * INC B3: 9 + B8: 1,7 + E2: 2,7 # I3: 2,7 => UNS * DIS B3: 9 + B8: 1,7 + E2: 2,7 # I3: 6 => CTR => I3: 2,7 * INC B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # A5: 1,8 => UNS * INC B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # C5: 1,8 => UNS * INC B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # G6: 1,8 => UNS * PRF B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # G6: 6 => SOL * STA B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 + G6: 6 * CNT 11 HDP CHAINS / 11 HYP OPENED