Analysis of zz-www.sudokuoftheday.co.uk-20060629-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: 9...7..6.4..68..2...6...4.....34.6.....2....13...1..82.73.....929...1...1...9.... initial
Autosolve
position: 9...7..6.4..68..2...6...4.....34.6.....2..3413...1..82.73.....929...1...1...9.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G2: 1,5 => CTR => G2: 7,9 * DIS # C1: 1,5 => CTR => C1: 2,8 * DIS # C1: 5,8 => CTR => C1: 1,2 * DIS # F5: 5,6 => CTR => F5: 7,8,9 * DIS # H4: 5,7 => CTR => H4: 9 * DIS # B9: 5,8 => CTR => B9: 4,6 * CNT 6 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G2: 1,5 => CTR => G2: 7,9 * DIS G2: 7,9 # H3: 7,9 => CTR => H3: 1,5 * DIS G2: 7,9 + H3: 1,5 # G7: 1,5 => CTR => G7: 2,8 * PRF G2: 7,9 + H3: 1,5 + G7: 2,8 => SOL * STA G2: 7,9 + H3: 1,5 + G7: 2,8 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9...7..6.4..68..2...6...4.....34.6.....2....13...1..82.73.....929...1...1...9.... | initial |
| 9...7..6.4..68..2...6...4.....34.6.....2..3413...1..82.73.....929...1...1...9.... | autosolve |
| 952473168417685923836129457721348695689257341345916782573864219294531876168792534 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) G1: 1,5 B4: 1,2 C4: 1,2 E5: 5,6 I4: 5,7 H7: 1,5 I8: 4,6 I9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,D3: 1.. / D1 = 1 => 16 pairs (_) / D3 = 1 => 10 pairs (_) B4,C4: 1.. / B4 = 1 => 7 pairs (_) / C4 = 1 => 7 pairs (_) G7,H7: 1.. / G7 = 1 => 0 pairs (X) / H7 = 1 => 7 pairs (_) H3,H7: 1.. / H3 = 1 => 0 pairs (X) / H7 = 1 => 7 pairs (_) B4,C4: 2.. / B4 = 2 => 7 pairs (_) / C4 = 2 => 7 pairs (_) G7,G9: 2.. / G7 = 2 => 17 pairs (_) / G9 = 2 => 8 pairs (_) F9,G9: 2.. / F9 = 2 => 17 pairs (_) / G9 = 2 => 8 pairs (_) C1,C4: 2.. / C1 = 2 => 7 pairs (_) / C4 = 2 => 7 pairs (_) E3,E7: 2.. / E3 = 2 => 18 pairs (_) / E7 = 2 => 9 pairs (_) E8,F9: 3.. / E8 = 3 => 18 pairs (_) / F9 = 3 => 12 pairs (_) H8,H9: 3.. / H8 = 3 => 12 pairs (_) / H9 = 3 => 18 pairs (_) E8,H8: 3.. / E8 = 3 => 18 pairs (_) / H8 = 3 => 12 pairs (_) F9,H9: 3.. / F9 = 3 => 12 pairs (_) / H9 = 3 => 18 pairs (_) E3,E8: 3.. / E3 = 3 => 12 pairs (_) / E8 = 3 => 18 pairs (_) D1,F1: 4.. / D1 = 4 => 12 pairs (_) / F1 = 4 => 11 pairs (_) B6,C6: 4.. / B6 = 4 => 12 pairs (_) / C6 = 4 => 0 pairs (X) D7,F7: 4.. / D7 = 4 => 11 pairs (_) / F7 = 4 => 12 pairs (_) I8,I9: 4.. / I8 = 4 => 0 pairs (X) / I9 = 4 => 18 pairs (_) C8,I8: 4.. / C8 = 4 => 18 pairs (_) / I8 = 4 => 0 pairs (X) B6,B9: 4.. / B6 = 4 => 12 pairs (_) / B9 = 4 => 0 pairs (X) D1,D7: 4.. / D1 = 4 => 12 pairs (_) / D7 = 4 => 11 pairs (_) F1,F7: 4.. / F1 = 4 => 11 pairs (_) / F7 = 4 => 12 pairs (_) A7,B9: 6.. / A7 = 6 => 12 pairs (_) / B9 = 6 => 18 pairs (_) I8,I9: 6.. / I8 = 6 => 18 pairs (_) / I9 = 6 => 0 pairs (X) B6,F6: 6.. / B6 = 6 => 0 pairs (X) / F6 = 6 => 13 pairs (_) E8,I8: 6.. / E8 = 6 => 0 pairs (X) / I8 = 6 => 18 pairs (_) A5,A7: 6.. / A5 = 6 => 18 pairs (_) / A7 = 6 => 12 pairs (_) C2,A3: 7.. / C2 = 7 => 11 pairs (_) / A3 = 7 => 0 pairs (X) I1,I3: 8.. / I1 = 8 => 8 pairs (_) / I3 = 8 => 10 pairs (_) F4,F5: 8.. / F4 = 8 => 11 pairs (_) / F5 = 8 => 20 pairs (_) A4,F4: 8.. / A4 = 8 => 20 pairs (_) / F4 = 8 => 11 pairs (_) G2,H3: 9.. / G2 = 9 => 10 pairs (_) / H3 = 9 => 0 pairs (X) C5,C6: 9.. / C5 = 9 => 8 pairs (_) / C6 = 9 => 0 pairs (X) H4,G6: 9.. / H4 = 9 => 10 pairs (_) / G6 = 9 => 0 pairs (X) F2,G2: 9.. / F2 = 9 => 0 pairs (X) / G2 = 9 => 10 pairs (_) F4,H4: 9.. / F4 = 9 => 0 pairs (X) / H4 = 9 => 10 pairs (_) C5,F5: 9.. / C5 = 9 => 8 pairs (_) / F5 = 9 => 0 pairs (X) D3,D6: 9.. / D3 = 9 => 0 pairs (X) / D6 = 9 => 11 pairs (_) G2,G6: 9.. / G2 = 9 => 10 pairs (_) / G6 = 9 => 0 pairs (X) H3,H4: 9.. / H3 = 9 => 0 pairs (X) / H4 = 9 => 10 pairs (_) * DURATION: 0:00:46.733093 START: 00:11:19.286591 END: 00:12:06.019684 2019-05-01 * CP COUNT: (40) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C4,E5,G1,H7,I4,I8,I9) * 9...7..6.4..68..2...6...4.....34.6.....2..3413...1..82.73.....929...1...1...9.... * PAIR G1: 1,5 BLK 3 G2: 1,5,7,9 # reduction candidate for 1,5 G2: 1,5 => CTR * 9...7..6.4..689.2...6...49....34.6....92..3413..91..82.73....1929...1...1...9.... G2: 7,9 # 9 pairs H3: 1,5,7,9 # reduction candidate for 1,5 H3: 1,5 # 22 pairs * PAIR G1: 1,5 ROW 1 B1: 1,5,2,3,8 # reduction candidate for 1,5 B1: 1,5 # 20 pairs C1: 1,5,2,8 # reduction candidate for 1,5 C1: 1,5 => CTR * 9..47.16.4.168.9277.61.945..12347695..92.83413.791..82.73..4.1929...1...1...9.... C1: 2,8 # 9 pairs D1: 1,5,4 # reduction candidate for 1,5 D1: 1,5 # 11 pairs * PAIR G1: 1,5 COL G G7: 1,5,2,8 # reduction candidate for 1,5 G7: 1,5 # 20 pairs G7: 2,8 # 8 pairs * PAIR B4: 1,2 COL B B1: 1,2,3,5,8 # reduction candidate for 1,2 B1: 1,2 # 10 pairs B3: 1,2,3,5,8 # reduction candidate for 1,2 B3: 1,2 # 10 pairs * PAIR C4: 1,2 COL C C1: 1,2,5,8 # reduction candidate for 1,2 C1: 5,8 => CTR * 9...7..6.4.168..2.7.6...4...12348697...2..34134..16582.73.....929...1...1...9.... C1: 1,2 # 10 pairs * PAIR E5: 5,6 BLK 5 F5: 5,6,7,8,9 # reduction candidate for 5,6 F5: 5,6 => CTR * 9...7.1684176859238.613947552.3486977892.6341364.1.582673.....929..61.3414..932.6 F5: 7,8,9 # 8 pairs F6: 5,6,7,9 # reduction candidate for 5,6 F6: 5,6 # 10 pairs * PAIR E5: 5,6 ROW 5 A5: 5,6,7,8 # reduction candidate for 5,6 A5: 5,6 # 20 pairs B5: 5,6,8 # reduction candidate for 5,6 B5: 5,6 # 14 pairs * PAIR E5: 5,6 COL E E7: 5,6,2 # reduction candidate for 5,6 E7: 5,6 # 18 pairs E8: 5,6,3 # reduction candidate for 5,6 E8: 5,6 # 12 pairs * PAIR I4: 5,7 BLK 6 H4: 5,7,9 # reduction candidate for 5,7 H4: 5,7 => CTR * 9...7..6.4..68..2...6...49....3496....92.83413...1.982.73....1929...1...1...9.... H4: 9 # 10 pairs G6: 5,7,9 # reduction candidate for 5,7 G6: 5,7 # 10 pairs * PAIR I4: 5,7 ROW 4 A4: 5,7,8 # reduction candidate for 5,7 A4: 5,7 # 11 pairs F4: 5,7,8,9 # reduction candidate for 5,7 F4: 5,7 # 24 pairs * PAIR I4: 5,7 COL I I2: 5,7,3 # reduction candidate for 5,7 I2: 5,7 # 11 pairs I3: 5,7,3,8 # reduction candidate for 5,7 I3: 5,7 # 11 pairs * PAIR H7: 1,5 BLK 9 G7: 1,5,2,8 # reduction candidate for 1,5 G7: 1,5 # 20 pairs G7: 2,8 # 8 pairs * PAIR H7: 1,5 COL H H3: 1,5,7,9 # reduction candidate for 1,5 H3: 1,5 # 22 pairs H3: 7,9 # 8 pairs * PAIR I9: 4,6 ROW 9 B9: 4,6,5,8 # reduction candidate for 4,6 B9: 5,8 => CTR * 9..47216.43168592772613945851234.69..6925.34134.916.82673.24.1929..61.341.4.932.6 B9: 4,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060629-absurd-base-pr-000.dot * REASONING * DIS # G2: 1,5 => CTR => G2: 7,9 * DIS # C1: 1,5 => CTR => C1: 2,8 * DIS # C1: 5,8 => CTR => C1: 1,2 * DIS # F5: 5,6 => CTR => F5: 7,8,9 * DIS # H4: 5,7 => CTR => H4: 9 * DIS # B9: 5,8 => CTR => B9: 4,6 * CNT 6 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C4,E5,G1,H7,I4,I8,I9) * 9...7..6.4..68..2...6...4.....34.6.....2..3413...1..82.73.....929...1...1...9.... * PAIR G1: 1,5 BLK 3 G2: 1,5,7,9 # reduction candidate for 1,5 G2: 1,5 => CTR * 9...7..6.4..689.2...6...49....34.6....92..3413..91..82.73....1929...1...1...9.... H3: 1,5,7,9 # reduction candidate for 1,5 H3: 1,5 # 22 pairs * RESTART * PAIR G1: 1,5 BLK 3 H3: 1,5,7,9 # reduction candidate for 1,5 H3: 7,9 => CTR * 9.2.7.16.41768.92...612947..2134.6977.92.6341364917582673.5..1929...1..414..9...6 * PAIR G1: 1,5 COL G G7: 1,5,2,8 # reduction candidate for 1,5 G7: 1,5 => CTR * 9.2473168417685923.3612.4.7.2134.695..92..3413...1.782.738.4..929...1...1...9.2.. G7: 2,8 => SOLVED * 952473168417685923836129457721348695689257341345916782573864219294531876168792534 * DURATION: 0:00:05.771128 START: 00:12:25.988385 END: 00:12:31.759513 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060629-absurd-base-pr-001.dot * REASONING * DIS # G2: 1,5 => CTR => G2: 7,9 * DIS G2: 7,9 # H3: 7,9 => CTR => H3: 1,5 * DIS G2: 7,9 + H3: 1,5 # G7: 1,5 => CTR => G7: 2,8 * PRF G2: 7,9 + H3: 1,5 + G7: 2,8 => SOL * STA G2: 7,9 + H3: 1,5 + G7: 2,8 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060629, absurd
Solution
position: 952473168417685923836129457721348695689257341345916782573864219294531876168792534 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 # G2: 1,5 => CTR => G2: 7,9 * INC # G2: 7,9 => UNS * INC # H3: 1,5 => UNS * INC # B1: 1,5 => UNS * DIS # C1: 1,5 => CTR => C1: 2,8 * INC # C1: 2,8 => UNS * INC # D1: 1,5 => UNS * INC # G7: 1,5 => UNS * INC # G7: 2,8 => UNS * INC # B1: 1,2 => UNS * INC # B3: 1,2 => UNS * INC # C1: 1,2 => UNS * DIS # C1: 5,8 => CTR => C1: 1,2 * DIS # F5: 5,6 => CTR => F5: 7,8,9 * INC # F5: 7,8,9 => UNS * INC # F6: 5,6 => UNS * INC # A5: 5,6 => UNS * INC # B5: 5,6 => UNS * INC # E7: 5,6 => UNS * INC # E8: 5,6 => UNS * DIS # H4: 5,7 => CTR => H4: 9 * INC # H4: 9 => UNS * INC # G6: 5,7 => UNS * INC # A4: 5,7 => UNS * INC # F4: 5,7 => UNS * INC # I2: 5,7 => UNS * INC # I3: 5,7 => UNS * INC # G7: 1,5 => UNS * INC # G7: 2,8 => UNS * INC # H3: 1,5 => UNS * INC # H3: 7,9 => UNS * INC # B9: 4,6 => UNS * DIS # B9: 5,8 => CTR => B9: 4,6 * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G2: 1,5 => CTR => G2: 7,9 * INC G2: 7,9 # H3: 1,5 => UNS * INC G2: 7,9 # H3: 1,5 => UNS * DIS G2: 7,9 # H3: 7,9 => CTR => H3: 1,5 * DIS G2: 7,9 + H3: 1,5 # G7: 1,5 => CTR => G7: 2,8 * PRF G2: 7,9 + H3: 1,5 + G7: 2,8 => SOL * STA G2: 7,9 + H3: 1,5 + G7: 2,8 * CNT 6 HDP CHAINS / 5 HYP OPENED