Analysis of zz-www.sudokuoftheday.co.uk-20060426-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: ..4.1.2..3....7..5.2..9.8.7.3....1....7..6.5.8............5...869.7.1....7.4.3... initial
Autosolve
position: 7.4.182..389..7.15.2..9.8.7.3..7.18...78.6.5.8..1.........5...869.7.1....7.4.3..1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 5,6 => CTR => C3: 1 * DIS # D1: 3 => CTR => D1: 5,6 * DIS # C3: 6 => CTR => C3: 1,5 * DIS # E2: 4 => CTR => E2: 2,6 * DIS # D7: 9 => CTR => D7: 2,6 * DIS # H3: 3 => CTR => H3: 4,6 * DIS # E2: 2 => CTR => E2: 4,6 * DIS # A5: 1 => CTR => A5: 4,9 * DIS # F4: 4,9 => CTR => F4: 2,5 * DIS # I4: 4,9 => CTR => I4: 2,6 * DIS # A5: 1,4 => CTR => A5: 9 * DIS # A7: 2 => CTR => A7: 1,4 * DIS # C8: 3 => CTR => C8: 5,8 * DIS # D7: 2,9 => CTR => D7: 6 * PRF # D7: 6 => SOL * PRF # E9: 2,8 => SOL * DIS # E9: 6 => CTR => E9: 2,8 * CNT 17 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 5,6 => CTR => C3: 1 * PRF C3: 1 # D7: 2,6 => SOL * STA C3: 1 + D7: 2,6 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..4.1.2..3....7..5.2..9.8.7.3....1....7..6.5.8............5...869.7.1....7.4.3... | initial |
| 7.4.182..389..7.15.2..9.8.7.3..7.18...78.6.5.8..1.........5...869.7.1....7.4.3..1 | autosolve |
| 764518239389267415521394867432975186917846352856132974143659728698721543275483691 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B1: 5,6 A3: 1,5 D2: 2,6 F3: 4,5 G2: 4,6 A4: 4,9 B5: 1,4 B6: 5,6 B7: 1,4 C7: 1,3 A9: 2,5 C9: 5,8 F7: 2,9 E8: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,C3: 1.. / A3 = 1 => 0 pairs (X) / C3 = 1 => 26 pairs (_) A5,B5: 1.. / A5 = 1 => 0 pairs (X) / B5 = 1 => 14 pairs (_) B5,B7: 1.. / B5 = 1 => 14 pairs (_) / B7 = 1 => 0 pairs (X) C3,C7: 1.. / C3 = 1 => 26 pairs (_) / C7 = 1 => 0 pairs (X) D2,E2: 2.. / D2 = 2 => 16 pairs (_) / E2 = 2 => 0 pairs (X) C4,C6: 2.. / C4 = 2 => 17 pairs (_) / C6 = 2 => 17 pairs (_) A7,A9: 2.. / A7 = 2 => 0 pairs (X) / A9 = 2 => 26 pairs (_) E5,I5: 2.. / E5 = 2 => 0 pairs (X) / I5 = 2 => 16 pairs (_) D1,D3: 3.. / D1 = 3 => 0 pairs (X) / D3 = 3 => 18 pairs (_) E5,E6: 3.. / E5 = 3 => 17 pairs (_) / E6 = 3 => 15 pairs (_) C7,C8: 3.. / C7 = 3 => 26 pairs (_) / C8 = 3 => 0 pairs (X) D3,H3: 3.. / D3 = 3 => 18 pairs (_) / H3 = 3 => 0 pairs (X) E2,F3: 4.. / E2 = 4 => 0 pairs (X) / F3 = 4 => 22 pairs (_) G2,H3: 4.. / G2 = 4 => 22 pairs (_) / H3 = 4 => 0 pairs (X) A7,B7: 4.. / A7 = 4 => 0 pairs (X) / B7 = 4 => 14 pairs (_) E2,G2: 4.. / E2 = 4 => 0 pairs (X) / G2 = 4 => 22 pairs (_) F3,H3: 4.. / F3 = 4 => 22 pairs (_) / H3 = 4 => 0 pairs (X) B5,B7: 4.. / B5 = 4 => 0 pairs (X) / B7 = 4 => 14 pairs (_) G8,G9: 5.. / G8 = 5 => 16 pairs (_) / G9 = 5 => 0 pairs (X) B1,D1: 5.. / B1 = 5 => 0 pairs (X) / D1 = 5 => 24 pairs (_) C8,G8: 5.. / C8 = 5 => 0 pairs (X) / G8 = 5 => 16 pairs (_) A3,A9: 5.. / A3 = 5 => 26 pairs (_) / A9 = 5 => 0 pairs (X) B1,B6: 5.. / B1 = 5 => 0 pairs (X) / B6 = 5 => 24 pairs (_) B1,C3: 6.. / B1 = 6 => 24 pairs (_) / C3 = 6 => 0 pairs (X) D7,E9: 6.. / D7 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) C4,I4: 6.. / C4 = 6 => 0 pairs (X) / I4 = 6 => 16 pairs (_) B1,B6: 6.. / B1 = 6 => 24 pairs (_) / B6 = 6 => 0 pairs (X) E2,E9: 6.. / E2 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) G6,H6: 7.. / G6 = 7 => 15 pairs (_) / H6 = 7 => 15 pairs (_) G7,H7: 7.. / G7 = 7 => 15 pairs (_) / H7 = 7 => 15 pairs (_) G6,G7: 7.. / G6 = 7 => 15 pairs (_) / G7 = 7 => 15 pairs (_) H6,H7: 7.. / H6 = 7 => 15 pairs (_) / H7 = 7 => 15 pairs (_) C8,C9: 8.. / C8 = 8 => 0 pairs (*) / C9 = 8 => 0 pairs (X) E8,E9: 8.. / E8 = 8 => 15 pairs (_) / E9 = 8 => 0 pairs (*) C8,E8: 8.. / C8 = 8 => 0 pairs (*) / E8 = 8 => 0 pairs (X) C9,E9: 8.. / C9 = 8 => 15 pairs (_) / E9 = 8 => 0 pairs (*) H1,I1: 9.. / H1 = 9 => 18 pairs (_) / I1 = 9 => 16 pairs (_) A4,A5: 9.. / A4 = 9 => 0 pairs (X) / A5 = 9 => 13 pairs (_) D7,F7: 9.. / D7 = 9 => 0 pairs (X) / F7 = 9 => 25 pairs (_) G9,H9: 9.. / G9 = 9 => 17 pairs (_) / H9 = 9 => 17 pairs (_) D4,D7: 9.. / D4 = 9 => 25 pairs (_) / D7 = 9 => 0 pairs (X) * DURATION: 0:00:46.415262 START: 22:40:25.584638 END: 22:41:11.999900 2019-04-30 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A9,B1,B5,B6,B7,C7,C9,D2,E8,F3,F7,G2) * 7.4.182..389..7.15.2..9.8.7.3..7.18...78.6.5.8..1.........5...869.7.1....7.4.3..1 * PAIR B1: 5,6 BLK 1 C3: 5,6,1 # reduction candidate for 5,6 C3: 5,6 => CTR * 7.4.182..38926741512..948.7.3.97.18.9178.63528..13....241659738693781524578423..1 C3: 1 # 26 pairs * PAIR B1: 5,6 ROW 1 D1: 5,6,3 # reduction candidate for 5,6 D1: 3 => CTR * 754318269389..741512659483743..7.1869178.6.5.86.1......41.5.3786937815..5784.3..1 D1: 5,6 # 18 pairs * PAIR A3: 1,5 BLK 1 C3: 1,5,6 # reduction candidate for 1,5 C3: 6 => CTR * 754.182..389267415126.9483743.97.1869178.635286.13....2416597.86937815..578423..1 C3: 1,5 # 24 pairs * PAIR D2: 2,6 BLK 2 E2: 2,6,4 # reduction candidate for 2,6 E2: 4 => CTR * 7.4.182..389247615.2..95847.3.57.18...78.6.5.8..1........952.6869.781....7.4.3..1 E2: 2,6 # 22 pairs * PAIR D2: 2,6 COL D D7: 2,6,9 # reduction candidate for 2,6 D7: 9 => CTR * 764518239389.2741552139486793.275184..78.6952852149.7...3952..8695781...278463591 D7: 2,6 # 25 pairs * PAIR F3: 4,5 COL F F4: 4,5,2,9 # reduction candidate for 4,5 F4: 4,5 # 17 pairs F6: 4,5,2,9 # reduction candidate for 4,5 F6: 4,5 # 16 pairs * PAIR G2: 4,6 BLK 3 H3: 4,6,3 # reduction candidate for 4,6 H3: 3 => CTR * 75431826938926741512659483743.97.1869178.6.5.86.1.....241.593786937815..578423691 H3: 4,6 # 18 pairs * PAIR G2: 4,6 ROW 2 E2: 4,6,2 # reduction candidate for 4,6 E2: 2 => CTR * 7.4.182.938962741552139486743..7.1869178463528..1.........5...869.781.24278463591 E2: 4,6 # 16 pairs * PAIR G2: 4,6 COL G G6: 4,6,3,7,9 # reduction candidate for 4,6 G6: 4,6 # 21 pairs G6: 3,7,9 # 14 pairs * PAIR A4: 4,9 BLK 4 A5: 4,9,1 # reduction candidate for 4,9 A5: 1 => CTR * 7.4.182.9389..7.15521.948.793..751841478.695.85.149..6413952..8695781.42278463591 A5: 4,9 # 14 pairs * PAIR A4: 4,9 ROW 4 F4: 4,9,2,5 # reduction candidate for 4,9 F4: 4,9 => CTR * 7.4.182.9389..7.15521.948.743..7918.9178.6.5.85.1........952..869.781...278463591 F4: 2,5 # 15 pairs I4: 4,9,2,6 # reduction candidate for 4,9 I4: 4,9 => CTR * 764518239389627415521394867936275184..78.6.528521.9..6...95267869.781.2.278463591 I4: 2,6 # 15 pairs * PAIR B5: 1,4 BLK 4 A5: 1,4,9 # reduction candidate for 1,4 A5: 1,4 => CTR * 7.4.182.9389..7.15521.948.793..75184..78.695.85.149..6..3952..8695781.42278463591 A5: 9 # 13 pairs * PAIR B6: 5,6 BLK 4 C4: 5,6,2 # reduction candidate for 5,6 C4: 5,6 # 17 pairs C6: 5,6,2 # reduction candidate for 5,6 C6: 5,6 # 17 pairs * PAIR B7: 1,4 BLK 7 A7: 1,4,2 # reduction candidate for 1,4 A7: 2 => CTR * 7.4.182..38926741512..948.7.3.97.18.9178.63528..13....241659738693781524578423..1 A7: 1,4 # 26 pairs * PAIR C9: 5,8 BLK 7 C8: 5,8,3 # reduction candidate for 5,8 C8: 3 => CTR * 7.4.182..38926741512..948.7.3.97.18.9178.63528..13....241659738693781524578423..1 C8: 5,8 # 26 pairs * PAIR F7: 2,9 BLK 8 D7: 2,9,6 # reduction candidate for 2,9 D7: 2,9 => CTR * 76451823938962741552139486743.97518...78.6.5285.1.......3.5.678695781324278463591 D7: 6 => SOLVED * 764518239389267415521394867432975186917846352856132974143659728698721543275483691 * PAIR F7: 2,9 COL F F4: 2,9,4,5 # reduction candidate for 2,9 F4: 2,9 # 16 pairs F6: 2,9,4,5 # reduction candidate for 2,9 F6: 2,9 # 17 pairs * PAIR E8: 2,8 BLK 8 E9: 2,8,6 # reduction candidate for 2,8 E9: 2,8 => SOLVED * 764518239389267415521394867432975186917846352856132974143659728698721543275483691 E9: 6 => CTR * 76451823938962741552139486743.97518...78.6.5285.1.......3.5.678695781324278463591 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060426-absurd-base-pr-000.dot * REASONING * DIS # C3: 5,6 => CTR => C3: 1 * DIS # D1: 3 => CTR => D1: 5,6 * DIS # C3: 6 => CTR => C3: 1,5 * DIS # E2: 4 => CTR => E2: 2,6 * DIS # D7: 9 => CTR => D7: 2,6 * DIS # H3: 3 => CTR => H3: 4,6 * DIS # E2: 2 => CTR => E2: 4,6 * DIS # A5: 1 => CTR => A5: 4,9 * DIS # F4: 4,9 => CTR => F4: 2,5 * DIS # I4: 4,9 => CTR => I4: 2,6 * DIS # A5: 1,4 => CTR => A5: 9 * DIS # A7: 2 => CTR => A7: 1,4 * DIS # C8: 3 => CTR => C8: 5,8 * DIS # D7: 2,9 => CTR => D7: 6 * PRF # D7: 6 => SOL * PRF # E9: 2,8 => SOL * DIS # E9: 6 => CTR => E9: 2,8 * CNT 17 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A9,B1,B5,B6,B7,C7,C9,D2,E8,F3,F7,G2) * 7.4.182..389..7.15.2..9.8.7.3..7.18...78.6.5.8..1.........5...869.7.1....7.4.3..1 * PAIR B1: 5,6 BLK 1 C3: 5,6,1 # reduction candidate for 5,6 C3: 5,6 => CTR * 7.4.182..38926741512..948.7.3.97.18.9178.63528..13....241659738693781524578423..1 * PAIR D2: 2,6 COL D D7: 2,6,9 # reduction candidate for 2,6 D7: 2,6 => SOLVED * 764518239389267415521394867432975186917846352856132974143659728698721543275483691 * DURATION: 0:00:03.260808 START: 22:41:37.082805 END: 22:41:40.343613 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060426-absurd-base-pr-001.dot * REASONING * DIS # C3: 5,6 => CTR => C3: 1 * PRF C3: 1 # D7: 2,6 => SOL * STA C3: 1 + D7: 2,6 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060426, absurd
Solution
position: 764518239389267415521394867432975186917846352856132974143659728698721543275483691 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 # C3: 5,6 => CTR => C3: 1 * INC # C3: 1 => UNS * INC # D1: 5,6 => UNS * DIS # D1: 3 => CTR => D1: 5,6 * INC # C3: 1,5 => UNS * DIS # C3: 6 => CTR => C3: 1,5 * INC # E2: 2,6 => UNS * DIS # E2: 4 => CTR => E2: 2,6 * INC # D7: 2,6 => UNS * DIS # D7: 9 => CTR => D7: 2,6 * INC # F4: 4,5 => UNS * INC # F6: 4,5 => UNS * INC # H3: 4,6 => UNS * DIS # H3: 3 => CTR => H3: 4,6 * INC # E2: 4,6 => UNS * DIS # E2: 2 => CTR => E2: 4,6 * INC # G6: 4,6 => UNS * INC # G6: 3,7,9 => UNS * INC # A5: 4,9 => UNS * DIS # A5: 1 => CTR => A5: 4,9 * DIS # F4: 4,9 => CTR => F4: 2,5 * INC # F4: 2,5 => UNS * DIS # I4: 4,9 => CTR => I4: 2,6 * INC # I4: 2,6 => UNS * DIS # A5: 1,4 => CTR => A5: 9 * INC # A5: 9 => UNS * INC # C4: 5,6 => UNS * INC # C6: 5,6 => UNS * INC # A7: 1,4 => UNS * DIS # A7: 2 => CTR => A7: 1,4 * INC # C8: 5,8 => UNS * DIS # C8: 3 => CTR => C8: 5,8 * DIS # D7: 2,9 => CTR => D7: 6 * PRF # D7: 6 => SOL * INC # F4: 2,9 => UNS * INC # F6: 2,9 => UNS * PRF # E9: 2,8 => SOL * DIS # E9: 6 => CTR => E9: 2,8 * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C3: 5,6 => CTR => C3: 1 * PRF C3: 1 # D7: 2,6 => SOL * STA C3: 1 + D7: 2,6 * CNT 2 HDP CHAINS / 2 HYP OPENED