Analysis of zz-www.sudokuoftheday.co.uk-20060620-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: ..3...8...1.9...7.8.......6.....4..7765..2.......6.2....489..5.5.......1......792 initial
Autosolve
position: 4.3...8.9.1.9.8.748.......69..584.67765..2948.487692.5..489.6535.....481.8....792 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 5,7 => CTR => B3: 9 * DIS # B3: 5 => CTR => B3: 7,9 * DIS # E3: 3,5 => CTR => E3: 1,2,4,7 * DIS # H3: 1,2 => CTR => H3: 3 * PRF # H3: 3 => SOL * DIS # G3: 3,5 => CTR => G3: 1 * PRF # G3: 1 => SOL * PRF # A9: 1,3 => SOL * DIS # A9: 6 => CTR => A9: 1,3 * DIS # D3: 1,3 => CTR => D3: 2,4 * DIS # E3: 1,3 => CTR => E3: 2,4,5,7 * DIS # E9: 1,3 => CTR => E9: 4,5 * DIS # G3: 5 => CTR => G3: 1,3 * DIS # H3: 2 => CTR => H3: 1,3 * DIS # B8: 7,9 => CTR => B8: 3 * PRF # B8: 3 => SOL * PRF # A9: 1,6 => SOL * DIS # A9: 3 => CTR => A9: 1,6 * CNT 18 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 5,7 => CTR => B3: 9 * DIS B3: 9 # E3: 3,5 => CTR => E3: 1,2,4 * DIS B3: 9 + E3: 1,2,4 # F3: 1 => CTR => F3: 3,5 * DIS B3: 9 + E3: 1,2,4 + F3: 3,5 # E9: 1,4 => CTR => E9: 3,5 * DIS B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 # H3: 1,2 => CTR => H3: 3 * PRF B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3 => SOL * STA B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3 * CNT 6 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..3...8...1.9...7.8.......6.....4..7765..2.......6.2....489..5.5.......1......792 | initial |
| 4.3...8.9.1.9.8.748.......69..584.67765..2948.487692.5..489.6535.....481.8....792 | autosolve |
| 453176829612938574897245136921584367765312948348769215274891653539627481186453792 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B1: 5,7 A2: 2,6 C2: 2,6 C3: 7,9 E2: 3,5 H1: 1,2 G2: 3,5 B4: 2,3 C4: 1,2 A6: 1,3 D5: 1,3 E5: 1,3 G4: 1,3 H6: 1,3 A7: 1,2 B7: 2,7 C8: 7,9 C9: 1,6 F7: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C4,A6: 1.. / C4 = 1 => 0 pairs (*) / A6 = 1 => 0 pairs (X) D5,E5: 1.. / D5 = 1 => 0 pairs (X) / E5 = 1 => 19 pairs (_) G4,H6: 1.. / G4 = 1 => 0 pairs (X) / H6 = 1 => 0 pairs (_) C4,G4: 1.. / C4 = 1 => 0 pairs (*) / G4 = 1 => 0 pairs (X) A6,H6: 1.. / A6 = 1 => 0 pairs (X) / H6 = 1 => 0 pairs (_) A7,F7: 1.. / A7 = 1 => 0 pairs (X) / F7 = 1 => 0 pairs (_) C4,C9: 1.. / C4 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) G3,G4: 1.. / G3 = 1 => 0 pairs (*) / G4 = 1 => 0 pairs (X) A2,C2: 2.. / A2 = 2 => 0 pairs (X) / C2 = 2 => 0 pairs (_) H1,H3: 2.. / H1 = 2 => 22 pairs (_) / H3 = 2 => 0 pairs (X) B4,C4: 2.. / B4 = 2 => 0 pairs (*) / C4 = 2 => 0 pairs (X) A7,B7: 2.. / A7 = 2 => 0 pairs (*) / B7 = 2 => 0 pairs (X) D8,E8: 2.. / D8 = 2 => 20 pairs (_) / E8 = 2 => 20 pairs (_) A2,A7: 2.. / A2 = 2 => 0 pairs (X) / A7 = 2 => 0 pairs (_) B4,B7: 2.. / B4 = 2 => 0 pairs (*) / B7 = 2 => 0 pairs (X) C2,C4: 2.. / C2 = 2 => 0 pairs (*) / C4 = 2 => 0 pairs (X) B4,A6: 3.. / B4 = 3 => 0 pairs (X) / A6 = 3 => 0 pairs (_) D5,E5: 3.. / D5 = 3 => 19 pairs (_) / E5 = 3 => 0 pairs (X) G4,H6: 3.. / G4 = 3 => 0 pairs (*) / H6 = 3 => 0 pairs (X) B8,A9: 3.. / B8 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) E2,G2: 3.. / E2 = 3 => 20 pairs (_) / G2 = 3 => 0 pairs (X) B4,G4: 3.. / B4 = 3 => 0 pairs (X) / G4 = 3 => 0 pairs (_) A6,H6: 3.. / A6 = 3 => 0 pairs (*) / H6 = 3 => 0 pairs (X) A6,A9: 3.. / A6 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) B4,B8: 3.. / B4 = 3 => 0 pairs (X) / B8 = 3 => 0 pairs (_) H3,H6: 3.. / H3 = 3 => 0 pairs (*) / H6 = 3 => 0 pairs (X) D3,E3: 4.. / D3 = 4 => 22 pairs (_) / E3 = 4 => 21 pairs (_) D9,E9: 4.. / D9 = 4 => 21 pairs (_) / E9 = 4 => 22 pairs (_) D3,D9: 4.. / D3 = 4 => 22 pairs (_) / D9 = 4 => 21 pairs (_) E3,E9: 4.. / E3 = 4 => 21 pairs (_) / E9 = 4 => 22 pairs (_) B1,B3: 5.. / B1 = 5 => 19 pairs (_) / B3 = 5 => 0 pairs (X) G2,G3: 5.. / G2 = 5 => 20 pairs (_) / G3 = 5 => 0 pairs (X) E9,F9: 5.. / E9 = 5 => 22 pairs (_) / F9 = 5 => 19 pairs (_) E2,G2: 5.. / E2 = 5 => 0 pairs (X) / G2 = 5 => 20 pairs (_) A2,C2: 6.. / A2 = 6 => 0 pairs (*) / C2 = 6 => 0 pairs (X) D1,F1: 6.. / D1 = 6 => 20 pairs (_) / F1 = 6 => 22 pairs (_) A9,C9: 6.. / A9 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) D8,F8: 6.. / D8 = 6 => 22 pairs (_) / F8 = 6 => 20 pairs (_) A2,A9: 6.. / A2 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) C2,C9: 6.. / C2 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) D1,D8: 6.. / D1 = 6 => 20 pairs (_) / D8 = 6 => 22 pairs (_) F1,F8: 6.. / F1 = 6 => 22 pairs (_) / F8 = 6 => 20 pairs (_) B7,F7: 7.. / B7 = 7 => 0 pairs (*) / F7 = 7 => 0 pairs (X) C3,C8: 7.. / C3 = 7 => 17 pairs (_) / C8 = 7 => 0 pairs (X) B3,C3: 9.. / B3 = 9 => 17 pairs (_) / C3 = 9 => 0 pairs (X) B8,C8: 9.. / B8 = 9 => 0 pairs (X) / C8 = 9 => 17 pairs (_) B3,B8: 9.. / B3 = 9 => 17 pairs (_) / B8 = 9 => 0 pairs (X) C3,C8: 9.. / C3 = 9 => 0 pairs (X) / C8 = 9 => 17 pairs (_) * DURATION: 0:00:58.020811 START: 23:58:22.352147 END: 23:59:20.372958 2019-04-30 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,B1,B4,B7,C2,C3,C4,C8,C9,D5,E2,E5,F7,G2,G4,H1,H6) * 4.3...8.9.1.9.8.748.......69..584.67765..2948.487692.5..489.6535.....481.8....792 * PAIR B1: 5,7 BLK 1 B3: 5,7,9 # reduction candidate for 5,7 B3: 5,7 => CTR * 4.3...8.96129.8.748.9.....69..584.67765..2948.487692.5..489.653597...481386...792 B3: 9 # 17 pairs * PAIR B1: 5,7 ROW 1 E1: 5,7,1,2 # reduction candidate for 5,7 E1: 5,7 # 21 pairs F1: 5,7,1,6 # reduction candidate for 5,7 F1: 5,7 # 22 pairs * PAIR C3: 7,9 BLK 1 B3: 7,9,5 # reduction candidate for 7,9 B3: 5 => CTR * 473...8.96129.8574859.7...69..584.67765..2948.487692.5..489.653597...481386...792 B3: 7,9 # 19 pairs * PAIR E2: 3,5 BLK 2 E3: 3,5,1,2,4,7 # reduction candidate for 3,5 E3: 3,5 => CTR * 4.3...8196129.8.748..4.1.269..584.67765..2948.48769235..489.6535.....481386145792 E3: 1,2,4,7 # 19 pairs F3: 3,5,1,7 # reduction candidate for 3,5 F3: 3,5 # 20 pairs * PAIR E2: 3,5 COL E E9: 3,5,1,4 # reduction candidate for 3,5 E9: 3,5 # 22 pairs E9: 1,4 # 20 pairs * PAIR H1: 1,2 BLK 3 H3: 1,2,3 # reduction candidate for 1,2 H3: 1,2 => CTR * 4.3...8.96129.8.748.......69..584.67765..2948.48769235..489.6535.....481386...792 H3: 3 => SOLVED * 453176829612938574897245136921584367765312948348769215274891653539627481186453792 * PAIR H1: 1,2 ROW 1 D1: 1,2,6 # reduction candidate for 1,2 D1: 1,2 # 22 pairs E1: 1,2,5,7 # reduction candidate for 1,2 E1: 1,2 # 22 pairs * PAIR G2: 3,5 BLK 3 G3: 3,5,1 # reduction candidate for 3,5 G3: 3,5 => CTR * 4.3...8.9.1.9.8.748.......69..584167765..294814876923527489.6535.....481.8....792 G3: 1 => SOLVED * 453176829612938574897245136921584367765312948348769215274891653539627481186453792 * PAIR A6: 1,3 COL A A9: 1,3,6 # reduction candidate for 1,3 A9: 1,3 => SOLVED * 453176829612938574897245136921584367765312948348769215274891653539627481186453792 A9: 6 => CTR * 4.3...8.9.1.9.8.748.......69..584.67765..294834876921512489.6535.....481.8....792 * PAIR D5: 1,3 COL D D3: 1,3,2,4 # reduction candidate for 1,3 D3: 1,3 => CTR * 4.3...8196129.8.748...4..269..584.67765..2948.48769235..489.6535.....4813864..792 D3: 2,4 # 20 pairs D9: 1,3,4 # reduction candidate for 1,3 D9: 1,3 # 22 pairs * PAIR E5: 1,3 COL E E3: 1,3,2,4,5,7 # reduction candidate for 1,3 E3: 1,3 => CTR * 4.3...8196129.8.748..4.1.269..584.67765..2948.48769235..489.6535.....481386145792 E3: 2,4,5,7 # 19 pairs E9: 1,3,4,5 # reduction candidate for 1,3 E9: 1,3 => CTR * 453...8.9.1.9583748...4.5.6932584167765..294814876923527489165359....481.8.4.5792 E9: 4,5 # 20 pairs * PAIR G4: 1,3 COL G G3: 1,3,5 # reduction candidate for 1,3 G3: 5 => CTR * 4.3...8.9.1.9.8.748.....5.69..584167765..294814876923527489.6535.....481.8....792 G3: 1,3 # 20 pairs * PAIR H6: 1,3 COL H H3: 1,3,2 # reduction candidate for 1,3 H3: 2 => CTR * 4.3...8196129.8.748......269..584.67765..2948.48769235..489.6535.....481386...792 H3: 1,3 # 22 pairs * PAIR C8: 7,9 BLK 7 B8: 7,9,3 # reduction candidate for 7,9 B8: 7,9 => CTR * 4.3...8.9.1.9.8.748.......6932584167765..294814876923527489165359....481.8....792 B8: 3 => SOLVED * 453176829612938574897245136921584367765312948348769215274891653539627481186453792 * PAIR C9: 1,6 BLK 7 A9: 1,6,3 # reduction candidate for 1,6 A9: 1,6 => SOLVED * 453176829612938574897245136921584367765312948348769215274891653539627481186453792 A9: 3 => CTR * 4.3...8.96129.8.748.......6921584367765..29483487692.5..489.6535.....481.8....792 * PAIR F7: 1,7 COL F F1: 1,7,5,6 # reduction candidate for 1,7 F1: 1,7 # 23 pairs F3: 1,7,3,5 # reduction candidate for 1,7 F3: 1,7 # 26 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060620-absurd-base-pr-000.dot * REASONING * DIS # B3: 5,7 => CTR => B3: 9 * DIS # B3: 5 => CTR => B3: 7,9 * DIS # E3: 3,5 => CTR => E3: 1,2,4,7 * DIS # H3: 1,2 => CTR => H3: 3 * PRF # H3: 3 => SOL * DIS # G3: 3,5 => CTR => G3: 1 * PRF # G3: 1 => SOL * PRF # A9: 1,3 => SOL * DIS # A9: 6 => CTR => A9: 1,3 * DIS # D3: 1,3 => CTR => D3: 2,4 * DIS # E3: 1,3 => CTR => E3: 2,4,5,7 * DIS # E9: 1,3 => CTR => E9: 4,5 * DIS # G3: 5 => CTR => G3: 1,3 * DIS # H3: 2 => CTR => H3: 1,3 * DIS # B8: 7,9 => CTR => B8: 3 * PRF # B8: 3 => SOL * PRF # A9: 1,6 => SOL * DIS # A9: 3 => CTR => A9: 1,6 * CNT 18 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,B1,B4,B7,C2,C3,C4,C8,C9,D5,E2,E5,F7,G2,G4,H1,H6) * 4.3...8.9.1.9.8.748.......69..584.67765..2948.487692.5..489.6535.....481.8....792 * PAIR B1: 5,7 BLK 1 B3: 5,7,9 # reduction candidate for 5,7 B3: 5,7 => CTR * 4.3...8.96129.8.748.9.....69..584.67765..2948.487692.5..489.653597...481386...792 * PAIR E2: 3,5 BLK 2 E3: 3,5,1,2,4 # reduction candidate for 3,5 E3: 3,5 => CTR * 453...8196129.8.748974.1.269..584.67765..2948.48769235..489.6535.9...481386145792 F3: 3,5,1 # reduction candidate for 3,5 F3: 3,5 # 18 pairs * RESTART * PAIR E2: 3,5 BLK 2 F3: 3,5,1 # reduction candidate for 3,5 F3: 1 => CTR * 453...8.9.1.95837489734152693258416776513294814876923527489.6535.9...481.8....792 * PAIR E2: 3,5 COL E E9: 3,5,1,4 # reduction candidate for 3,5 E9: 1,4 => CTR * 453...8.9.1.958374897..35.6932584167765..294814876923527489.6535.9...481.8....792 * PAIR RESTART * PAIR H1: 1,2 BLK 3 H3: 1,2,3 # reduction candidate for 1,2 H3: 1,2 => CTR * 453...8.9612938574897.453.69..584.67765312948.48769235..489.6535.9...481386451792 H3: 3 => SOLVED * 453176829612938574897245136921584367765312948348769215274891653539627481186453792 * DURATION: 0:00:08.687359 START: 23:59:46.087632 END: 23:59:54.774991 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060620-absurd-base-pr-001.dot * REASONING * DIS # B3: 5,7 => CTR => B3: 9 * DIS B3: 9 # E3: 3,5 => CTR => E3: 1,2,4 * DIS B3: 9 + E3: 1,2,4 # F3: 1 => CTR => F3: 3,5 * DIS B3: 9 + E3: 1,2,4 + F3: 3,5 # E9: 1,4 => CTR => E9: 3,5 * DIS B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 # H3: 1,2 => CTR => H3: 3 * PRF B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3 => SOL * STA B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3 * CNT 6 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060620, absurd
Solution
position: 453176829612938574897245136921584367765312948348769215274891653539627481186453792 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 # B3: 5,7 => CTR => B3: 9 * INC # B3: 9 => UNS * INC # E1: 5,7 => UNS * INC # F1: 5,7 => UNS * INC # B3: 7,9 => UNS * DIS # B3: 5 => CTR => B3: 7,9 * DIS # E3: 3,5 => CTR => E3: 1,2,4,7 * INC # E3: 1,2,4,7 => UNS * INC # F3: 3,5 => UNS * INC # E9: 3,5 => UNS * INC # E9: 1,4 => UNS * DIS # H3: 1,2 => CTR => H3: 3 * PRF # H3: 3 => SOL * INC # D1: 1,2 => UNS * INC # E1: 1,2 => UNS * DIS # G3: 3,5 => CTR => G3: 1 * PRF # G3: 1 => SOL * PRF # A9: 1,3 => SOL * DIS # A9: 6 => CTR => A9: 1,3 * DIS # D3: 1,3 => CTR => D3: 2,4 * INC # D3: 2,4 => UNS * INC # D9: 1,3 => UNS * DIS # E3: 1,3 => CTR => E3: 2,4,5,7 * INC # E3: 2,4,5,7 => UNS * DIS # E9: 1,3 => CTR => E9: 4,5 * INC # E9: 4,5 => UNS * INC # G3: 1,3 => UNS * DIS # G3: 5 => CTR => G3: 1,3 * INC # H3: 1,3 => UNS * DIS # H3: 2 => CTR => H3: 1,3 * DIS # B8: 7,9 => CTR => B8: 3 * PRF # B8: 3 => SOL * PRF # A9: 1,6 => SOL * DIS # A9: 3 => CTR => A9: 1,6 * INC # F1: 1,7 => UNS * INC # F3: 1,7 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 5,7 => CTR => B3: 9 * DIS B3: 9 # E3: 3,5 => CTR => E3: 1,2,4 * INC B3: 9 + E3: 1,2,4 # F3: 3,5 => UNS * INC B3: 9 + E3: 1,2,4 # F3: 3,5 => UNS * DIS B3: 9 + E3: 1,2,4 # F3: 1 => CTR => F3: 3,5 * INC B3: 9 + E3: 1,2,4 + F3: 3,5 # E9: 3,5 => UNS * DIS B3: 9 + E3: 1,2,4 + F3: 3,5 # E9: 1,4 => CTR => E9: 3,5 * DIS B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 # H3: 1,2 => CTR => H3: 3 * PRF B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3 => SOL * STA B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3 * CNT 9 HDP CHAINS / 8 HYP OPENED