Analysis of zz-www.sudokuoftheday.co.uk-20060826-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: .5.2...7.....4.2..9..5...43.75......2.8......49..2......6.8..9..8..61..75...3...6 initial
Autosolve
position: .542.3.7.....4.2..9..57..43.75......2.8.5....49..2......6.8539.38..61..75...32..6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 6 => CTR => B3: 1,2 * PRF # G1: 1,9 => SOL * DIS # F2: 6,8 => CTR => F2: 9 * DIS # G3: 1 => CTR => G3: 6,8 * PRF # F4: 6,8 => SOL * DIS # F6: 6,8 => CTR => F6: 7 * DIS # B5: 3 => CTR => B5: 1,6 * DIS # D4: 1,6 => CTR => D4: 3,8 * DIS # H4: 1,6 => CTR => H4: 2,3,8 * PRF # A1: 1,6 => SOL * DIS # A2: 1,6 => CTR => A2: 7,8 * PRF # B5: 6 => SOL * DIS # C2: 1,3 => CTR => C2: 7 * PRF # C2: 7 => SOL * DIS # I4: 1,9 => CTR => I4: 2,4,8 * PRF # I4: 4,9 => SOL * DIS # G5: 4,9 => CTR => G5: 7 * DIS # F5: 7 => CTR => F5: 4,9 * PRF # A2: 6,8 => SOL * PRF # B7: 1,4 => SOL * DIS # B7: 2 => CTR => B7: 1,4 * DIS # G9: 4 => CTR => G9: 1,8 * DIS # H4: 1,8 => CTR => H4: 2,3,6 * CNT 23 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 6 => CTR => B3: 1,2 * PRF B3: 1,2 # G1: 1,9 => SOL * STA B3: 1,2 + G1: 1,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.2...7.....4.2..9..5...43.75......2.8......49..2......6.8..9..8..61..75...3...6 | initial |
| .542.3.7.....4.2..9..57..43.75......2.8.5....49..2......6.8539.38..61..75...32..6 | autosolve |
| 654213978837649215921578643175396824268154739493827561716485392382961457549732186 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C3: 1,2 E1: 1,9 F3: 6,8 A4: 1,6 C6: 1,3 E4: 1,9 I5: 4,9 A7: 1,7 C8: 2,9 B9: 1,4 C9: 7,9 D7: 4,7 D8: 4,9 D9: 7,9 G8: 4,5 H8: 2,5 H9: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,D2: 1.. / E1 = 1 => 19 pairs (_) / D2 = 1 => 0 pairs (X) E1,E4: 1.. / E1 = 1 => 19 pairs (_) / E4 = 1 => 0 pairs (X) B3,C3: 2.. / B3 = 2 => 0 pairs (*) / C3 = 2 => 0 pairs (X) H4,I4: 2.. / H4 = 2 => 0 pairs (*) / I4 = 2 => 0 pairs (X) B7,C8: 2.. / B7 = 2 => 0 pairs (X) / C8 = 2 => 0 pairs (_) I7,H8: 2.. / I7 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) B7,I7: 2.. / B7 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) C8,H8: 2.. / C8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) B3,B7: 2.. / B3 = 2 => 0 pairs (*) / B7 = 2 => 0 pairs (X) C3,C8: 2.. / C3 = 2 => 0 pairs (X) / C8 = 2 => 0 pairs (_) H4,H8: 2.. / H4 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) I4,I7: 2.. / I4 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) B2,C2: 3.. / B2 = 3 => 20 pairs (_) / C2 = 3 => 0 pairs (X) B5,C6: 3.. / B5 = 3 => 0 pairs (X) / C6 = 3 => 20 pairs (_) D4,H4: 3.. / D4 = 3 => 18 pairs (_) / H4 = 3 => 0 pairs (X) B2,B5: 3.. / B2 = 3 => 20 pairs (_) / B5 = 3 => 0 pairs (X) C2,C6: 3.. / C2 = 3 => 0 pairs (X) / C6 = 3 => 20 pairs (_) F4,F5: 4.. / F4 = 4 => 18 pairs (_) / F5 = 4 => 0 pairs (*) B7,B9: 4.. / B7 = 4 => 0 pairs (X) / B9 = 4 => 19 pairs (_) D7,D8: 4.. / D7 = 4 => 0 pairs (*) / D8 = 4 => 0 pairs (X) D8,G8: 4.. / D8 = 4 => 0 pairs (X) / G8 = 4 => 0 pairs (_) B9,G9: 4.. / B9 = 4 => 19 pairs (_) / G9 = 4 => 0 pairs (X) H2,I2: 5.. / H2 = 5 => 0 pairs (X) / I2 = 5 => 20 pairs (_) G8,H8: 5.. / G8 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) G6,G8: 5.. / G6 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) I2,I6: 5.. / I2 = 5 => 20 pairs (_) / I6 = 5 => 0 pairs (X) A4,B5: 6.. / A4 = 6 => 21 pairs (_) / B5 = 6 => 0 pairs (*) A1,G1: 6.. / A1 = 6 => 0 pairs (*) / G1 = 6 => 0 pairs (X) A2,C2: 7.. / A2 = 7 => 0 pairs (X) / C2 = 7 => 0 pairs (_) F5,F6: 7.. / F5 = 7 => 0 pairs (X) / F6 = 7 => 18 pairs (_) G5,G6: 7.. / G5 = 7 => 18 pairs (_) / G6 = 7 => 0 pairs (X) A7,C9: 7.. / A7 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) D7,D9: 7.. / D7 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) F5,G5: 7.. / F5 = 7 => 0 pairs (X) / G5 = 7 => 18 pairs (_) F6,G6: 7.. / F6 = 7 => 18 pairs (_) / G6 = 7 => 0 pairs (X) A7,D7: 7.. / A7 = 7 => 0 pairs (*) / D7 = 7 => 0 pairs (X) C9,D9: 7.. / C9 = 7 => 0 pairs (X) / D9 = 7 => 0 pairs (_) A2,A7: 7.. / A2 = 7 => 0 pairs (X) / A7 = 7 => 0 pairs (_) C2,C9: 7.. / C2 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) A1,A2: 8.. / A1 = 8 => 21 pairs (_) / A2 = 8 => 0 pairs (*) G9,H9: 8.. / G9 = 8 => 25 pairs (_) / H9 = 8 => 17 pairs (_) F3,G3: 8.. / F3 = 8 => 21 pairs (_) / G3 = 8 => 0 pairs (X) E1,F2: 9.. / E1 = 9 => 0 pairs (X) / F2 = 9 => 19 pairs (_) C8,C9: 9.. / C8 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) D8,D9: 9.. / D8 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) F2,I2: 9.. / F2 = 9 => 19 pairs (_) / I2 = 9 => 0 pairs (X) C8,D8: 9.. / C8 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) C9,D9: 9.. / C9 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) E1,E4: 9.. / E1 = 9 => 0 pairs (X) / E4 = 9 => 19 pairs (_) * DURATION: 0:01:00.480070 START: 02:05:21.313413 END: 02:06:21.793483 2019-05-01 * CP COUNT: (49) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B9,C3,C6,C8,C9,D7,D8,D9,E1,E4,F3,G8,H8,H9,I5) * .542.3.7.....4.2..9..57..43.75......2.8.5....49..2......6.8539.38..61..75...32..6 * PAIR C3: 1,2 BLK 1 B3: 1,2,6 # reduction candidate for 1,2 B3: 6 => CTR * 8542136797...4.2..962578143675.....22.8.5....49..2.7.1126785394389461527547932816 B3: 1,2 # 23 pairs * PAIR E1: 1,9 ROW 1 G1: 1,9,6,8 # reduction candidate for 1,9 G1: 1,9 => SOLVED * 654213978837649215921578643175396824268154739493827561716485392382961457549732186 G1: 6,8 # 20 pairs I1: 1,9,8 # reduction candidate for 1,9 I1: 1,9 # 22 pairs * PAIR F3: 6,8 BLK 2 D2: 6,8,1 # reduction candidate for 6,8 D2: 6,8 # 19 pairs F2: 6,8,9 # reduction candidate for 6,8 F2: 6,8 => CTR * .54293.7....14.2.99..57..43.75.1....2.8.5...449..2...5..6.8539.38..615275...32486 F2: 9 # 19 pairs * PAIR F3: 6,8 ROW 3 G3: 6,8,1 # reduction candidate for 6,8 G3: 1 => CTR * 8542136797...4.2..962578143675.....22.8.5....49..2.7.1126785394389461527547932816 G3: 6,8 # 23 pairs * PAIR F3: 6,8 COL F F4: 6,8,4,9 # reduction candidate for 6,8 F4: 6,8 => SOLVED * 654213978837649215921578643175396824268154739493827561716485392382961457549732186 F4: 4,9 # 18 pairs F6: 6,8,7 # reduction candidate for 6,8 F6: 6,8 => CTR * 854213.7.7...492..9.257..43.75.94..22.8.574.949..2.7..126785394389461527547932..6 F6: 7 # 18 pairs * PAIR A4: 1,6 BLK 4 B5: 1,6,3 # reduction candidate for 1,6 B5: 3 => CTR * 8542.367.7.3.4.2..9.257..43675.....2238.5...9491.2....126785394389461527547932..6 B5: 1,6 # 20 pairs * PAIR A4: 1,6 ROW 4 D4: 1,6,3,8 # reduction candidate for 1,6 D4: 1,6 => CTR * 8542.367.7...4.2..9.257..4367519..322.8.5.9..49..2....126785394389461527547932..6 D4: 3,8 # 18 pairs G4: 1,6,4,8,9 # reduction candidate for 1,6 G4: 1,6 # 22 pairs H4: 1,6,2,3,8 # reduction candidate for 1,6 H4: 1,6 => CTR * 8542.367.7...4.2..9.257..436753...122.8.5...949..2....126785394389461527547932186 H4: 2,3,8 # 17 pairs * PAIR A4: 1,6 COL A A1: 1,6,8 # reduction candidate for 1,6 A1: 1,6 => SOLVED * 654213978837649215921578643175396824268154739493827561716485392382961457549732186 A1: 8 # 21 pairs A2: 1,6,7,8 # reduction candidate for 1,6 A2: 1,6 => CTR * 8542.367..37.4.2.59.157.843175.9....2.8.5....493.2....7.648539.38.961457549732..6 A2: 7,8 # 18 pairs * PAIR C6: 1,3 BLK 4 B5: 1,3,6 # reduction candidate for 1,3 B5: 6 => SOLVED * 654213978837649215921578643175396824268154739493827561716485392382961457549732186 B5: 1,3 # 21 pairs * PAIR C6: 1,3 ROW 6 D6: 1,3,6,8 # reduction candidate for 1,3 D6: 1,3 # 19 pairs H6: 1,3,5,6,8 # reduction candidate for 1,3 H6: 1,3 # 20 pairs * PAIR C6: 1,3 COL C C2: 1,3,7 # reduction candidate for 1,3 C2: 1,3 => CTR * 8542.367.7...4.2..9.257..43675.....22.8.5...949..2....126785394389461527547932..6 C2: 7 => SOLVED * 654213978837649215921578643175396824268154739493827561716485392382961457549732186 * PAIR E4: 1,9 ROW 4 G4: 1,9,4,6,8 # reduction candidate for 1,9 G4: 1,9 # 24 pairs I4: 1,9,2,4,8 # reduction candidate for 1,9 I4: 1,9 => CTR * .542.3.7...7.4.2.592157..43.753.482.2.8.5...4493.2.5.1716485392382961457549732186 I4: 2,4,8 # 17 pairs * PAIR I5: 4,9 BLK 6 G4: 4,9,1,6,8 # reduction candidate for 4,9 G4: 4,9 # 19 pairs I4: 4,9,1,2,8 # reduction candidate for 4,9 I4: 4,9 => SOLVED * 654213978837649215921578643175396824268154739493827561716485392382961457549732186 I4: 1,2,8 # 17 pairs G5: 4,9,7 # reduction candidate for 4,9 G5: 4,9 => CTR * 854213.7.7...492..9.257..43.75.94..22.8.574.949..2.7..126785394389461527547932..6 G5: 7 # 18 pairs * PAIR I5: 4,9 ROW 5 F5: 4,9,7 # reduction candidate for 4,9 F5: 7 => CTR * 854213.7.7...492..9.257..43.75.94..22.8.574.949..2.7..126785394389461527547932..6 F5: 4,9 # 18 pairs * PAIR A7: 1,7 COL A A2: 1,7,6,8 # reduction candidate for 1,7 A2: 6,8 => SOLVED * 654213978837649215921578643175396824268154739493827561716485392382961457549732186 A2: 1,7 # 22 pairs * PAIR B9: 1,4 BLK 7 B7: 1,4,2 # reduction candidate for 1,4 B7: 1,4 => SOLVED * 654213978837649215921578643175396824268154739493827561716485392382961457549732186 B7: 2 => CTR * 8542.367.7...4.2..9.257..43675.....22.8.5...949..2....126785394389461527547932..6 * PAIR B9: 1,4 ROW 9 G9: 1,4,8 # reduction candidate for 1,4 G9: 8 # 25 pairs G9: 1,4 # 17 pairs * PAIR H9: 1,8 BLK 9 G9: 1,8,4 # reduction candidate for 1,8 G9: 4 => CTR * .542.3.7.....4.2..9..57..43.75......2.8.5....49..2.....4678539.38..61..75...32486 G9: 1,8 # 19 pairs * PAIR H9: 1,8 COL H H2: 1,8,5,6 # reduction candidate for 1,8 H2: 1,8 # 22 pairs H4: 1,8,2,3,6 # reduction candidate for 1,8 H4: 1,8 => CTR * 8542.367.7...4.2..9.257..436753....22.8.5...949..2....126785394389461527547932..6 H4: 2,3,6 # 17 pairs H6: 1,8,3,5,6 # reduction candidate for 1,8 H6: 1,8 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060826-absurd-base-pr-000.dot * REASONING * DIS # B3: 6 => CTR => B3: 1,2 * PRF # G1: 1,9 => SOL * DIS # F2: 6,8 => CTR => F2: 9 * DIS # G3: 1 => CTR => G3: 6,8 * PRF # F4: 6,8 => SOL * DIS # F6: 6,8 => CTR => F6: 7 * DIS # B5: 3 => CTR => B5: 1,6 * DIS # D4: 1,6 => CTR => D4: 3,8 * DIS # H4: 1,6 => CTR => H4: 2,3,8 * PRF # A1: 1,6 => SOL * DIS # A2: 1,6 => CTR => A2: 7,8 * PRF # B5: 6 => SOL * DIS # C2: 1,3 => CTR => C2: 7 * PRF # C2: 7 => SOL * DIS # I4: 1,9 => CTR => I4: 2,4,8 * PRF # I4: 4,9 => SOL * DIS # G5: 4,9 => CTR => G5: 7 * DIS # F5: 7 => CTR => F5: 4,9 * PRF # A2: 6,8 => SOL * PRF # B7: 1,4 => SOL * DIS # B7: 2 => CTR => B7: 1,4 * DIS # G9: 4 => CTR => G9: 1,8 * DIS # H4: 1,8 => CTR => H4: 2,3,6 * CNT 23 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B9,C3,C6,C8,C9,D7,D8,D9,E1,E4,F3,G8,H8,H9,I5) * .542.3.7.....4.2..9..57..43.75......2.8.5....49..2......6.8539.38..61..75...32..6 * PAIR C3: 1,2 BLK 1 B3: 1,2,6 # reduction candidate for 1,2 B3: 6 => CTR * 8542136797...4.2..962578143675.....22.8.5....49..2.7.1126785394389461527547932816 * PAIR E1: 1,9 ROW 1 G1: 1,9,6,8 # reduction candidate for 1,9 G1: 1,9 => SOLVED * 654213978837649215921578643175396824268154739493827561716485392382961457549732186 * DURATION: 0:00:03.077322 START: 02:06:57.205896 END: 02:07:00.283218 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060826-absurd-base-pr-001.dot * REASONING * DIS # B3: 6 => CTR => B3: 1,2 * PRF B3: 1,2 # G1: 1,9 => SOL * STA B3: 1,2 + G1: 1,9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060826, absurd
Solution
position: 654213978837649215921578643175396824268154739493827561716485392382961457549732186 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 # B3: 1,2 => UNS * DIS # B3: 6 => CTR => B3: 1,2 * PRF # G1: 1,9 => SOL * INC # G1: 6,8 => UNS * INC # I1: 1,9 => UNS * INC # D2: 6,8 => UNS * DIS # F2: 6,8 => CTR => F2: 9 * INC # F2: 9 => UNS * INC # G3: 6,8 => UNS * DIS # G3: 1 => CTR => G3: 6,8 * PRF # F4: 6,8 => SOL * INC # F4: 4,9 => UNS * DIS # F6: 6,8 => CTR => F6: 7 * INC # F6: 7 => UNS * INC # B5: 1,6 => UNS * DIS # B5: 3 => CTR => B5: 1,6 * DIS # D4: 1,6 => CTR => D4: 3,8 * INC # D4: 3,8 => UNS * INC # G4: 1,6 => UNS * DIS # H4: 1,6 => CTR => H4: 2,3,8 * INC # H4: 2,3,8 => UNS * PRF # A1: 1,6 => SOL * INC # A1: 8 => UNS * DIS # A2: 1,6 => CTR => A2: 7,8 * INC # A2: 7,8 => UNS * INC # B5: 1,3 => UNS * PRF # B5: 6 => SOL * INC # D6: 1,3 => UNS * INC # H6: 1,3 => UNS * DIS # C2: 1,3 => CTR => C2: 7 * PRF # C2: 7 => SOL * INC # G4: 1,9 => UNS * DIS # I4: 1,9 => CTR => I4: 2,4,8 * INC # I4: 2,4,8 => UNS * INC # G4: 4,9 => UNS * PRF # I4: 4,9 => SOL * INC # I4: 1,2,8 => UNS * DIS # G5: 4,9 => CTR => G5: 7 * INC # G5: 7 => UNS * INC # F5: 4,9 => UNS * DIS # F5: 7 => CTR => F5: 4,9 * INC # A2: 1,7 => UNS * PRF # A2: 6,8 => SOL * PRF # B7: 1,4 => SOL * DIS # B7: 2 => CTR => B7: 1,4 * INC # G9: 1,4 => UNS * INC # G9: 8 => UNS * INC # G9: 1,8 => UNS * DIS # G9: 4 => CTR => G9: 1,8 * INC # H2: 1,8 => UNS * DIS # H4: 1,8 => CTR => H4: 2,3,6 * INC # H4: 2,3,6 => UNS * INC # H6: 1,8 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 1,2 => UNS * DIS # B3: 6 => CTR => B3: 1,2 * PRF B3: 1,2 # G1: 1,9 => SOL * STA B3: 1,2 + G1: 1,9 * CNT 3 HDP CHAINS / 3 HYP OPENED