Analysis of zz-www.sudokuoftheday.co.uk-20060516-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: ..78.......815.....5..43..8.92....5......1.6....4..2...34...1..1..3.452..2.6...7. initial
Autosolve
position: .178...45.481576.2.5..43718.927...51..3..1.6..614..2...34...18.1..3.452..2561..7. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 3,9 => SOL * DIS # A1: 2 => CTR => A1: 3,9 * DIS # A3: 6,9 => CTR => A3: 2 * PRF # A3: 2 => SOL * DIS # E1: 2,9 => CTR => E1: 6 * PRF # A3: 2,9 => SOL * DIS # A3: 6 => CTR => A3: 2,9 * PRF # D7: 2,9 => SOL * PRF # A1: 3,9 => SOL * DIS # A1: 2 => CTR => A1: 3,9 * DIS # A5: 4,8 => CTR => A5: 5,7 * DIS # G4: 3 => CTR => G4: 4,8 * PRF # A5: 7,8 => SOL * DIS # E4: 6,8 => CTR => E4: 3 * PRF # A5: 4,7 => SOL * DIS # E6: 8 => CTR => E6: 3,9 * PRF # A7: 6,9 => SOL * DIS # A7: 7 => CTR => A7: 6,9 * PRF # F6: 8,9 => SOL * PRF # A7: 6,9 => SOL * DIS # A7: 7 => CTR => A7: 6,9 * DIS # G4: 3,4 => CTR => G4: 8 * CNT 22 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:
* PRF # A1: 3,9 => SOL * STA A1: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..78.......815.....5..43..8.92....5......1.6....4..2...34...1..1..3.452..2.6...7. | initial |
| .178...45.481576.2.5..43718.927...51..3..1.6..614..2...34...18.1..3.452..2561..7. | autosolve |
| 917862345348157692256943718492736851783521964561498237634275189179384526825619473 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) A2: 3,9 C3: 6,9 D3: 2,9 G1: 3,9 H2: 3,9 A4: 4,8 B5: 7,8 F4: 6,8 I5: 4,7 H6: 3,9 I6: 3,7 B8: 7,8 C8: 6,9 A9: 8,9 E8: 7,8 F9: 8,9 I7: 6,9 I8: 6,9 G9: 3,4 I9: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 2.. / A1 = 2 => 0 pairs (X) / A3 = 2 => 0 pairs (_) D5,E5: 2.. / D5 = 2 => 0 pairs (X) / E5 = 2 => 25 pairs (_) A3,D3: 2.. / A3 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) F1,F7: 2.. / F1 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) A1,A2: 3.. / A1 = 3 => 0 pairs (X) / A2 = 3 => 16 pairs (_) G1,H2: 3.. / G1 = 3 => 16 pairs (_) / H2 = 3 => 0 pairs (X) E4,E6: 3.. / E4 = 3 => 22 pairs (_) / E6 = 3 => 0 pairs (X) G9,I9: 3.. / G9 = 3 => 0 pairs (X) / I9 = 3 => 18 pairs (_) A1,G1: 3.. / A1 = 3 => 0 pairs (X) / G1 = 3 => 16 pairs (_) A2,H2: 3.. / A2 = 3 => 16 pairs (_) / H2 = 3 => 0 pairs (X) E4,G4: 3.. / E4 = 3 => 22 pairs (_) / G4 = 3 => 0 pairs (X) H2,H6: 3.. / H2 = 3 => 0 pairs (X) / H6 = 3 => 16 pairs (_) I6,I9: 3.. / I6 = 3 => 0 pairs (X) / I9 = 3 => 18 pairs (_) A4,A5: 4.. / A4 = 4 => 20 pairs (_) / A5 = 4 => 0 pairs (X) G9,I9: 4.. / G9 = 4 => 18 pairs (_) / I9 = 4 => 0 pairs (X) A4,G4: 4.. / A4 = 4 => 20 pairs (_) / G4 = 4 => 0 pairs (X) I5,I9: 4.. / I5 = 4 => 18 pairs (_) / I9 = 4 => 0 pairs (X) A5,A6: 5.. / A5 = 5 => 23 pairs (_) / A6 = 5 => 0 pairs (*) D5,F6: 5.. / D5 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) D7,F7: 5.. / D7 = 5 => 23 pairs (_) / F7 = 5 => 0 pairs (*) A5,D5: 5.. / A5 = 5 => 23 pairs (_) / D5 = 5 => 0 pairs (*) A6,F6: 5.. / A6 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) D5,D7: 5.. / D5 = 5 => 0 pairs (*) / D7 = 5 => 0 pairs (X) F6,F7: 5.. / F6 = 5 => 23 pairs (_) / F7 = 5 => 0 pairs (*) A3,C3: 6.. / A3 = 6 => 0 pairs (X) / C3 = 6 => 0 pairs (_) E1,F1: 6.. / E1 = 6 => 21 pairs (_) / F1 = 6 => 0 pairs (X) E4,F4: 6.. / E4 = 6 => 0 pairs (X) / F4 = 6 => 21 pairs (_) A7,C8: 6.. / A7 = 6 => 0 pairs (*) / C8 = 6 => 0 pairs (X) I7,I8: 6.. / I7 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) A7,I7: 6.. / A7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) C8,I8: 6.. / C8 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) A3,A7: 6.. / A3 = 6 => 0 pairs (X) / A7 = 6 => 0 pairs (_) C3,C8: 6.. / C3 = 6 => 0 pairs (*) / C8 = 6 => 0 pairs (X) E1,E4: 6.. / E1 = 6 => 21 pairs (_) / E4 = 6 => 0 pairs (X) F1,F4: 6.. / F1 = 6 => 0 pairs (X) / F4 = 6 => 21 pairs (_) I5,I6: 7.. / I5 = 7 => 0 pairs (X) / I6 = 7 => 18 pairs (_) A7,B8: 7.. / A7 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) E7,E8: 7.. / E7 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) A6,I6: 7.. / A6 = 7 => 0 pairs (X) / I6 = 7 => 18 pairs (_) A7,E7: 7.. / A7 = 7 => 0 pairs (X) / E7 = 7 => 0 pairs (_) B8,E8: 7.. / B8 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) B5,B8: 7.. / B5 = 7 => 0 pairs (X) / B8 = 7 => 0 pairs (_) G4,G5: 8.. / G4 = 8 => 21 pairs (_) / G5 = 8 => 0 pairs (X) B8,A9: 8.. / B8 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) E8,F9: 8.. / E8 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) B8,E8: 8.. / B8 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) A9,F9: 8.. / A9 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) B5,B8: 8.. / B5 = 8 => 0 pairs (*) / B8 = 8 => 0 pairs (X) G1,H2: 9.. / G1 = 9 => 0 pairs (X) / H2 = 9 => 16 pairs (_) G5,H6: 9.. / G5 = 9 => 16 pairs (_) / H6 = 9 => 0 pairs (X) I7,I8: 9.. / I7 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) A2,H2: 9.. / A2 = 9 => 0 pairs (X) / H2 = 9 => 16 pairs (_) C8,I8: 9.. / C8 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) A9,F9: 9.. / A9 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) C3,C8: 9.. / C3 = 9 => 0 pairs (X) / C8 = 9 => 0 pairs (_) G1,G5: 9.. / G1 = 9 => 0 pairs (X) / G5 = 9 => 16 pairs (_) H2,H6: 9.. / H2 = 9 => 16 pairs (_) / H6 = 9 => 0 pairs (X) * DURATION: 0:01:19.114540 START: 23:11:03.218896 END: 23:12:22.333436 2019-04-30 * CP COUNT: (57) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A9,B5,B8,C3,C8,D3,E8,F4,F9,G1,G9,H2,H6,I5,I6,I7,I8,I9) * .178...45.481576.2.5..43718.927...51..3..1.6..614..2...34...18.1..3.452..2561..7. * PAIR A2: 3,9 BLK 1 A1: 3,9,2 # reduction candidate for 3,9 A1: 3,9 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 A1: 2 => CTR * 2178..345348157692.5.243718.92736.51..3.2196..614..237.3497.18.1..3.452..2561..7. * PAIR C3: 6,9 BLK 1 A3: 6,9,2 # reduction candidate for 6,9 A3: 6,9 => CTR * 2178..345348157692.5.243718.92736.51..3.2196..614..237.3497.18.1..3.452..2561..7. A3: 2 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 * PAIR D3: 2,9 BLK 2 E1: 2,9,6 # reduction candidate for 2,9 E1: 2,9 => CTR * .178.6.45.481576.2.5..43718.92768351..3..1864861435297.345.218.18.37452.92561..7. E1: 6 # 21 pairs F1: 2,9,6 # reduction candidate for 2,9 F1: 2,9 # 21 pairs * PAIR D3: 2,9 ROW 3 A3: 2,9,6 # reduction candidate for 2,9 A3: 2,9 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 A3: 6 => CTR * 2178..345348157692659243718.92736.51..3.2196..614..237.3497.18.1..3.452..2561..7. * PAIR D3: 2,9 COL D D5: 2,9,5 # reduction candidate for 2,9 D5: 2,9 # 23 pairs D7: 2,9,5 # reduction candidate for 2,9 D7: 2,9 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 D7: 5 # 23 pairs * PAIR G1: 3,9 ROW 1 A1: 3,9,2 # reduction candidate for 3,9 A1: 3,9 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 A1: 2 => CTR * 2178..345348157692.5.243718.92736.51..3.2196..614..237.3497.18.1..3.452..2561..7. * PAIR A4: 4,8 BLK 4 A5: 4,8,5,7 # reduction candidate for 4,8 A5: 4,8 => CTR * .178...45.481576.2.5..43718.927...51..352196.5614..237734.95186186374529925618.7. A5: 5,7 # 21 pairs * PAIR A4: 4,8 ROW 4 G4: 4,8,3 # reduction candidate for 4,8 G4: 3 => CTR * .178...45.481576.2.5..437184927..351..3..1864861435297.345..18.18.37452.925618473 G4: 4,8 # 22 pairs * PAIR B5: 7,8 BLK 4 A5: 7,8,4,5 # reduction candidate for 7,8 A5: 7,8 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 A5: 4,5 # 21 pairs A6: 7,8,5 # reduction candidate for 7,8 A6: 7,8 # 23 pairs * PAIR F4: 6,8 BLK 5 E4: 6,8,3 # reduction candidate for 6,8 E4: 6,8 => CTR * .178...45.481576.2.5..43718.927..351..3..1864.6143.297.34...18.18.37452.925618473 E4: 3 # 22 pairs * PAIR I5: 4,7 ROW 5 A5: 4,7,5,8 # reduction candidate for 4,7 A5: 4,7 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 A5: 5,8 # 21 pairs * PAIR H6: 3,9 ROW 6 E6: 3,9,8 # reduction candidate for 3,9 E6: 8 => CTR * .1786..45348157692.59243718.92736.51.73.219645614892...34...18.18.37452.925618.7. E6: 3,9 # 20 pairs * PAIR C8: 6,9 BLK 7 A7: 6,9,7 # reduction candidate for 6,9 A7: 6,9 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 A7: 7 => CTR * 217869345348157692659243718.927...51..3.21.6..614..2..734.92186186374529925618.7. * PAIR F9: 8,9 COL F F6: 8,9,5 # reduction candidate for 8,9 F6: 8,9 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 F6: 5 # 23 pairs * PAIR I7: 6,9 ROW 7 A7: 6,9,7 # reduction candidate for 6,9 A7: 6,9 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 A7: 7 => CTR * 217869345348157692659243718.927...51..3.21.6..614..2..734.92186186374529925618.7. * PAIR G9: 3,4 COL G G4: 3,4,8 # reduction candidate for 3,4 G4: 3,4 => CTR * .178...45.481576.2.5..43718.927...51..3..186..614..29..34...18.18.37452.925618.7. G4: 8 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060516-absurd-base-pr-000.dot * REASONING * PRF # A1: 3,9 => SOL * DIS # A1: 2 => CTR => A1: 3,9 * DIS # A3: 6,9 => CTR => A3: 2 * PRF # A3: 2 => SOL * DIS # E1: 2,9 => CTR => E1: 6 * PRF # A3: 2,9 => SOL * DIS # A3: 6 => CTR => A3: 2,9 * PRF # D7: 2,9 => SOL * PRF # A1: 3,9 => SOL * DIS # A1: 2 => CTR => A1: 3,9 * DIS # A5: 4,8 => CTR => A5: 5,7 * DIS # G4: 3 => CTR => G4: 4,8 * PRF # A5: 7,8 => SOL * DIS # E4: 6,8 => CTR => E4: 3 * PRF # A5: 4,7 => SOL * DIS # E6: 8 => CTR => E6: 3,9 * PRF # A7: 6,9 => SOL * DIS # A7: 7 => CTR => A7: 6,9 * PRF # F6: 8,9 => SOL * PRF # A7: 6,9 => SOL * DIS # A7: 7 => CTR => A7: 6,9 * DIS # G4: 3,4 => CTR => G4: 8 * CNT 22 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,A9,B5,B8,C3,C8,D3,E8,F4,F9,G1,G9,H2,H6,I5,I6,I7,I8,I9) * .178...45.481576.2.5..43718.927...51..3..1.6..614..2...34...18.1..3.452..2561..7. * PAIR A2: 3,9 BLK 1 A1: 3,9,2 # reduction candidate for 3,9 A1: 3,9 => SOLVED * 917862345348157692256943718492736851783521964561498237634275189179384526825619473 * DURATION: 0:00:01.717816 START: 23:12:51.660102 END: 23:12:53.377918 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060516-absurd-base-pr-001.dot * REASONING * PRF # A1: 3,9 => SOL * STA A1: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060516, absurd
Solution
position: 917862345348157692256943718492736851783521964561498237634275189179384526825619473 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:
* PRF # A1: 3,9 => SOL * DIS # A1: 2 => CTR => A1: 3,9 * DIS # A3: 6,9 => CTR => A3: 2 * PRF # A3: 2 => SOL * DIS # E1: 2,9 => CTR => E1: 6 * INC # E1: 6 => UNS * INC # F1: 2,9 => UNS * PRF # A3: 2,9 => SOL * DIS # A3: 6 => CTR => A3: 2,9 * INC # D5: 2,9 => UNS * PRF # D7: 2,9 => SOL * INC # D7: 5 => UNS * PRF # A1: 3,9 => SOL * DIS # A1: 2 => CTR => A1: 3,9 * DIS # A5: 4,8 => CTR => A5: 5,7 * INC # A5: 5,7 => UNS * INC # G4: 4,8 => UNS * DIS # G4: 3 => CTR => G4: 4,8 * PRF # A5: 7,8 => SOL * INC # A5: 4,5 => UNS * INC # A6: 7,8 => UNS * DIS # E4: 6,8 => CTR => E4: 3 * INC # E4: 3 => UNS * PRF # A5: 4,7 => SOL * INC # A5: 5,8 => UNS * INC # E6: 3,9 => UNS * DIS # E6: 8 => CTR => E6: 3,9 * PRF # A7: 6,9 => SOL * DIS # A7: 7 => CTR => A7: 6,9 * PRF # F6: 8,9 => SOL * INC # F6: 5 => UNS * PRF # A7: 6,9 => SOL * DIS # A7: 7 => CTR => A7: 6,9 * DIS # G4: 3,4 => CTR => G4: 8 * INC # G4: 8 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 3,9 => SOL * STA A1: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED