Analysis of zz-www.sudokuoftheday.co.uk-20060909-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006
level: medium
position: 41..7...5.....57...........9..7...2...3......1.246..8.....869..3.92....66...1.2.. initial
Autosolve
position: 41..72.952....57..........29..7.8.2.8.3.2....1.246..8..21.869..3.92....66...1.2.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 6,8 => CTR => G1: 3 * DIS # E2: 4 => CTR => E2: 3,9 * PRF # E3: 4 => SOL * DIS # C9: 4 => CTR => C9: 5,7 * PRF # B4: 4,5 => SOL * DIS # G4: 4,5 => CTR => G4: 1,3,6 * DIS # C9: 7 => CTR => C9: 4,5 * PRF # B5: 4,6 => SOL * DIS # G4: 3,5 => CTR => G4: 1,4,6 * DIS # D5: 1,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * DIS # I6: 7 => CTR => I6: 3,9 * DIS # F9: 3,9 => CTR => F9: 4,7 * PRF # F9: 4,7 => SOL * DIS # G4: 3,5 => CTR => G4: 1,4,6 * DIS # C9: 4 => CTR => C9: 5,7 * DIS # D9: 3,5 => CTR => D9: 9 * PRF # B8: 4,5 => SOL * PRF # F9: 4,7 => SOL * DIS # F9: 3,9 => CTR => F9: 4,7 * CNT 20 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G1: 6,8 => CTR => G1: 3 * DIS G1: 3 # E2: 4 => CTR => E2: 3,9 * DIS G1: 3 + E2: 3,9 # D2: 6,8 => CTR => D2: 1 * PRF G1: 3 + E2: 3,9 + D2: 1 => SOL * STA G1: 3 + E2: 3,9 + D2: 1 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 41..7...5.....57...........9..7...2...3......1.246..8.....869..3.92....66...1.2.. | initial |
| 41..72.952....57..........29..7.8.2.8.3.2....1.246..8..21.869..3.92....66...1.2.. | autosolve |
| 418672395236195748597843162954738621863521479172469583721386954349257816685914237 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) C1: 6,8 B2: 3,9 C2: 6,8 A3: 5,7 B3: 3,9 C3: 5,7 C4: 4,5 B6: 5,7 E4: 3,5 F5: 1,9 F6: 3,9 G6: 3,5 A7: 5,7 D7: 3,5 E8: 4,5 F8: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D5,F5: 1.. / D5 = 1 => 0 pairs (X) / F5 = 1 => 26 pairs (_) G4,I4: 1.. / G4 = 1 => 0 pairs (X) / I4 = 1 => 16 pairs (_) G8,H8: 1.. / G8 = 1 => 20 pairs (_) / H8 = 1 => 16 pairs (_) F3,F5: 1.. / F3 = 1 => 0 pairs (X) / F5 = 1 => 26 pairs (_) I2,I4: 1.. / I2 = 1 => 0 pairs (X) / I4 = 1 => 16 pairs (_) B2,B3: 3.. / B2 = 3 => 17 pairs (_) / B3 = 3 => 16 pairs (_) E4,F6: 3.. / E4 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) D1,G1: 3.. / D1 = 3 => 0 pairs (X) / G1 = 3 => 20 pairs (_) H7,I7: 4.. / H7 = 4 => 17 pairs (_) / I7 = 4 => 18 pairs (_) C4,C9: 4.. / C4 = 4 => 20 pairs (_) / C9 = 4 => 0 pairs (X) A3,C3: 5.. / A3 = 5 => 15 pairs (_) / C3 = 5 => 0 pairs (X) E4,D5: 5.. / E4 = 5 => 0 pairs (X) / D5 = 5 => 0 pairs (_) B6,G6: 5.. / B6 = 5 => 0 pairs (X) / G6 = 5 => 17 pairs (_) A3,A7: 5.. / A3 = 5 => 15 pairs (_) / A7 = 5 => 0 pairs (X) E4,E8: 5.. / E4 = 5 => 0 pairs (X) / E8 = 5 => 0 pairs (_) C1,C2: 6.. / C1 = 6 => 18 pairs (_) / C2 = 6 => 16 pairs (_) B4,B5: 6.. / B4 = 6 => 16 pairs (_) / B5 = 6 => 0 pairs (*) B4,G4: 6.. / B4 = 6 => 16 pairs (_) / G4 = 6 => 0 pairs (*) A3,C3: 7.. / A3 = 7 => 0 pairs (X) / C3 = 7 => 15 pairs (_) B5,B6: 7.. / B5 = 7 => 0 pairs (X) / B6 = 7 => 17 pairs (_) A7,C9: 7.. / A7 = 7 => 15 pairs (_) / C9 = 7 => 0 pairs (X) F8,F9: 7.. / F8 = 7 => 16 pairs (_) / F9 = 7 => 0 pairs (X) B6,I6: 7.. / B6 = 7 => 17 pairs (_) / I6 = 7 => 0 pairs (X) F8,H8: 7.. / F8 = 7 => 16 pairs (_) / H8 = 7 => 0 pairs (X) A3,A7: 7.. / A3 = 7 => 0 pairs (X) / A7 = 7 => 15 pairs (_) C3,C9: 7.. / C3 = 7 => 15 pairs (_) / C9 = 7 => 0 pairs (X) C1,C2: 8.. / C1 = 8 => 16 pairs (_) / C2 = 8 => 18 pairs (_) B8,B9: 8.. / B8 = 8 => 18 pairs (_) / B9 = 8 => 0 pairs (*) G8,I9: 8.. / G8 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) D3,G3: 8.. / D3 = 8 => 18 pairs (_) / G3 = 8 => 21 pairs (_) B8,G8: 8.. / B8 = 8 => 18 pairs (_) / G8 = 8 => 0 pairs (*) B9,I9: 8.. / B9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) I2,I9: 8.. / I2 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) B2,B3: 9.. / B2 = 9 => 16 pairs (_) / B3 = 9 => 17 pairs (_) E2,E3: 9.. / E2 = 9 => 17 pairs (_) / E3 = 9 => 16 pairs (_) I5,I6: 9.. / I5 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) D9,F9: 9.. / D9 = 9 => 17 pairs (_) / F9 = 9 => 0 pairs (X) B2,E2: 9.. / B2 = 9 => 16 pairs (_) / E2 = 9 => 17 pairs (_) B3,E3: 9.. / B3 = 9 => 17 pairs (_) / E3 = 9 => 16 pairs (_) F6,I6: 9.. / F6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) D5,D9: 9.. / D5 = 9 => 0 pairs (X) / D9 = 9 => 17 pairs (_) * DURATION: 0:00:52.930875 START: 02:30:20.506034 END: 02:31:13.436909 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,B2,B3,B6,C1,C2,C3,C4,D7,E4,E8,F5,F6,F8,G6) * 41..72.952....57..........29..7.8.2.8.3.2....1.246..8..21.869..3.92....66...1.2.. * PAIR C1: 6,8 ROW 1 D1: 6,8,3 # reduction candidate for 6,8 D1: 6,8 # 20 pairs G1: 6,8,3 # reduction candidate for 6,8 G1: 6,8 => CTR * 41.372.952....57..........29..738.2.8.352....1.246..8..21.869..3.92....66...1.2.. G1: 3 # 20 pairs * PAIR B2: 3,9 ROW 2 E2: 3,9,4 # reduction candidate for 3,9 E2: 4 => CTR * 41..72.9529..457...3..91..29..738.2.8.3.2....1.246..8..21.869..3.92....66...1.2.. E2: 3,9 # 19 pairs * PAIR C2: 6,8 ROW 2 D2: 6,8,1,3 # reduction candidate for 6,8 D2: 1,3 # 22 pairs D2: 6,8 # 19 pairs * PAIR B3: 3,9 ROW 3 E3: 3,9,4 # reduction candidate for 3,9 E3: 4 => SOLVED * 418672395236195748597843162954738621863521479172469583721386954349257816685914237 E3: 3,9 # 18 pairs * PAIR C3: 5,7 COL C C9: 5,7,4 # reduction candidate for 5,7 C9: 4 => CTR * 41..72.952....57....7.....29.5738.2.8.3521..91724695837213869543.925...6654.1.2.. C9: 5,7 # 20 pairs * PAIR C4: 4,5 BLK 4 B4: 4,5,6 # reduction candidate for 4,5 B4: 4,5 => SOLVED * 418672395236195748597843162954738621863521479172469583721386954349257816685914237 B4: 6 # 16 pairs B5: 4,5,6,7 # reduction candidate for 4,5 B5: 4,5 # 18 pairs * PAIR C4: 4,5 ROW 4 G4: 4,5,1,3,6 # reduction candidate for 4,5 G4: 4,5 => CTR * 41..7239523..957.4597.438.29657384218435216791.2469583.213869..3.925...665.91.238 G4: 1,3,6 # 16 pairs * PAIR C4: 4,5 COL C C9: 4,5,7 # reduction candidate for 4,5 C9: 7 => CTR * 41..723952....57..7.5..48.29.475862.8.3.2.4..17246.58.5213869..389247156647519238 C9: 4,5 # 15 pairs * PAIR B6: 5,7 BLK 4 B5: 5,7,4,6 # reduction candidate for 5,7 B5: 4,6 => SOLVED * 418672395236195748597843162954738621863521479172469583721386954349257816685914237 B5: 5,7 # 20 pairs * PAIR E4: 3,5 ROW 4 G4: 3,5,1,4,6 # reduction candidate for 3,5 G4: 3,5 => CTR * 41.372.952....57..........29647385218.352....1.246..8..21.869..3.92....66...1.2.. G4: 1,4,6 # 16 pairs * PAIR F5: 1,9 BLK 5 D5: 1,9,5 # reduction candidate for 1,9 D5: 1,9 => CTR * 41.372.952...957.......4..2964758321853921467172463589.21.869..38924715664..192.8 D5: 5 => SOLVED * 418672395236195748597843162954738621863521479172469583721386954349257816685914237 * PAIR F6: 3,9 ROW 6 I6: 3,9,7 # reduction candidate for 3,9 I6: 7 => CTR * 41.372.952....57..........29..738.2.87352...91.2469387.21.869..3.92....66..91.2.. I6: 3,9 # 17 pairs * PAIR F6: 3,9 COL F F9: 3,9,4,7 # reduction candidate for 3,9 F9: 3,9 => CTR * 41.372.952...957.......4..2964758321853921467172463589.21.869..38924715664..192.8 F9: 4,7 => SOLVED * 418672395236195748597843162954738621863521479172469583721386954349257816685914237 * PAIR G6: 3,5 BLK 6 G4: 3,5,1,4,6 # reduction candidate for 3,5 G4: 3,5 => CTR * 41.372.952....57..........29647385218.352....1.246..8..21.869..3.92....66...1.2.. G4: 1,4,6 # 16 pairs * PAIR A7: 5,7 BLK 7 C9: 5,7,4 # reduction candidate for 5,7 C9: 4 => CTR * 41..72.952....57....7.....29.5738.2.8.3521..91724695837213869543.925...6654.1.2.. C9: 5,7 # 20 pairs * PAIR A7: 5,7 ROW 7 H7: 5,7,3,4 # reduction candidate for 5,7 H7: 5,7 # 28 pairs H7: 3,4 # 17 pairs * PAIR D7: 3,5 BLK 8 D9: 3,5,9 # reduction candidate for 3,5 D9: 3,5 => CTR * 41.372.952...957.......4..2964758321853921467172463589.21.869..38924715664..192.8 D9: 9 # 17 pairs * PAIR D7: 3,5 ROW 7 H7: 3,5,4,7 # reduction candidate for 3,5 H7: 4,7 # 17 pairs H7: 3,5 # 17 pairs * PAIR E8: 4,5 ROW 8 B8: 4,5,8 # reduction candidate for 4,5 B8: 4,5 => SOLVED * 418672395236195748597843162954738621863521479172469583721386954349257816685914237 B8: 8 # 18 pairs * PAIR F8: 4,7 BLK 8 F9: 4,7,3,9 # reduction candidate for 4,7 F9: 4,7 => SOLVED * 418672395236195748597843162954738621863521479172469583721386954349257816685914237 F9: 3,9 => CTR * 41.372.952...957.......4..2964758321853921467172463589.21.869..38924715664..192.8 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060909-absurd-base-pr-000.dot * REASONING * DIS # G1: 6,8 => CTR => G1: 3 * DIS # E2: 4 => CTR => E2: 3,9 * PRF # E3: 4 => SOL * DIS # C9: 4 => CTR => C9: 5,7 * PRF # B4: 4,5 => SOL * DIS # G4: 4,5 => CTR => G4: 1,3,6 * DIS # C9: 7 => CTR => C9: 4,5 * PRF # B5: 4,6 => SOL * DIS # G4: 3,5 => CTR => G4: 1,4,6 * DIS # D5: 1,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * DIS # I6: 7 => CTR => I6: 3,9 * DIS # F9: 3,9 => CTR => F9: 4,7 * PRF # F9: 4,7 => SOL * DIS # G4: 3,5 => CTR => G4: 1,4,6 * DIS # C9: 4 => CTR => C9: 5,7 * DIS # D9: 3,5 => CTR => D9: 9 * PRF # B8: 4,5 => SOL * PRF # F9: 4,7 => SOL * DIS # F9: 3,9 => CTR => F9: 4,7 * CNT 20 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,B2,B3,B6,C1,C2,C3,C4,D7,E4,E8,F5,F6,F8,G6) * 41..72.952....57..........29..7.8.2.8.3.2....1.246..8..21.869..3.92....66...1.2.. * PAIR C1: 6,8 ROW 1 D1: 6,8,3 # reduction candidate for 6,8 D1: 6,8 # 20 pairs G1: 6,8,3 # reduction candidate for 6,8 G1: 6,8 => CTR * 41.372.952....57..........29..738.2.8.352....1.246..8..21.869..3.92....66...1.2.. * RESTART * PAIR RESTART * PAIR B2: 3,9 ROW 2 E2: 3,9,4 # reduction candidate for 3,9 E2: 4 => CTR * 41..7239529.3457...3..91..29..738.2.8.3.2....17246.58..21.869..3.92....66...1.2.. * PAIR RESTART * PAIR C2: 6,8 ROW 2 D2: 6,8,1 # reduction candidate for 6,8 D2: 6,8 => CTR * 41..723952....57........8629..738.218.3521.79172469583.213869..3892.7..66..91.2.. D2: 1 => SOLVED * 418672395236195748597843162954738621863521479172469583721386954349257816685914237 * DURATION: 0:00:05.530064 START: 02:31:45.265830 END: 02:31:50.795894 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060909-absurd-base-pr-001.dot * REASONING * DIS # G1: 6,8 => CTR => G1: 3 * DIS G1: 3 # E2: 4 => CTR => E2: 3,9 * DIS G1: 3 + E2: 3,9 # D2: 6,8 => CTR => D2: 1 * PRF G1: 3 + E2: 3,9 + D2: 1 => SOL * STA G1: 3 + E2: 3,9 + D2: 1 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060909, absurd
Solution
position: 418672395236195748597843162954738621863521479172469583721386954349257816685914237 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 # D1: 6,8 => UNS * DIS # G1: 6,8 => CTR => G1: 3 * INC # G1: 3 => UNS * INC # E2: 3,9 => UNS * DIS # E2: 4 => CTR => E2: 3,9 * INC # D2: 6,8 => UNS * INC # D2: 1,3 => UNS * INC # E3: 3,9 => UNS * PRF # E3: 4 => SOL * INC # C9: 5,7 => UNS * DIS # C9: 4 => CTR => C9: 5,7 * PRF # B4: 4,5 => SOL * INC # B4: 6 => UNS * INC # B5: 4,5 => UNS * DIS # G4: 4,5 => CTR => G4: 1,3,6 * INC # G4: 1,3,6 => UNS * INC # C9: 4,5 => UNS * DIS # C9: 7 => CTR => C9: 4,5 * INC # B5: 5,7 => UNS * PRF # B5: 4,6 => SOL * DIS # G4: 3,5 => CTR => G4: 1,4,6 * INC # G4: 1,4,6 => UNS * DIS # D5: 1,9 => CTR => D5: 5 * PRF # D5: 5 => SOL * INC # I6: 3,9 => UNS * DIS # I6: 7 => CTR => I6: 3,9 * DIS # F9: 3,9 => CTR => F9: 4,7 * PRF # F9: 4,7 => SOL * DIS # G4: 3,5 => CTR => G4: 1,4,6 * INC # G4: 1,4,6 => UNS * INC # C9: 5,7 => UNS * DIS # C9: 4 => CTR => C9: 5,7 * INC # H7: 5,7 => UNS * INC # H7: 3,4 => UNS * DIS # D9: 3,5 => CTR => D9: 9 * INC # D9: 9 => UNS * INC # H7: 3,5 => UNS * INC # H7: 4,7 => UNS * PRF # B8: 4,5 => SOL * INC # B8: 8 => UNS * PRF # F9: 4,7 => SOL * DIS # F9: 3,9 => CTR => F9: 4,7 * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 6,8 => UNS * DIS # G1: 6,8 => CTR => G1: 3 * INC G1: 3 # E2: 3,9 => UNS * DIS G1: 3 # E2: 4 => CTR => E2: 3,9 * DIS G1: 3 + E2: 3,9 # D2: 6,8 => CTR => D2: 1 * PRF G1: 3 + E2: 3,9 + D2: 1 => SOL * STA G1: 3 + E2: 3,9 + D2: 1 * CNT 6 HDP CHAINS / 5 HYP OPENED