Analysis of zz-www.sudokuoftheday.co.uk-20060419-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: .56.4..124..1...6...3.6.8.4..7.5....9..3..1.......6..8..4..32..5.9.....32...9...1 initial
Autosolve
position: .56.493124.213..6...3.6.8.4..7.51.3.9.53..1..3.1..6..8..4..32..5.9.....3238.9...1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 9 => CTR => B2: 7,8 * DIS # B3: 1,7 => CTR => B3: 9 * DIS # A7: 1,7 => CTR => A7: 6 * PRF # F2: 5 => SOL * DIS # B4: 6,8 => CTR => B4: 2,4 * DIS # B5: 2,4 => CTR => B5: 6,8 * DIS # D6: 2,4 => CTR => D6: 7,9 * DIS # F5: 2,7 => CTR => F5: 4,8 * DIS # D6: 2,7 => CTR => D6: 4,9 * PRF # G4: 6,9 => SOL * DIS # I7: 6,9 => CTR => I7: 5,7 * CNT 11 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 9 => CTR => B2: 7,8 * PRF B2: 7,8 # F2: 5 => SOL * STA B2: 7,8 + F2: 5 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .56.4..124..1...6...3.6.8.4..7.5....9..3..1.......6..8..4..32..5.9.....32...9...1 | initial |
| .56.493124.213..6...3.6.8.4..7.51.3.9.53..1..3.1..6..8..4..32..5.9.....3238.9...1 | autosolve |
| 756849312482135769193267854827451936965328147341976528614783295579612483238594671 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A1: 7,8 A3: 1,7 D1: 7,8 A4: 6,8 B6: 2,4 E6: 2,7 I4: 6,9 I5: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,B3: 1.. / A3 = 1 => 9 pairs (_) / B3 = 1 => 0 pairs (X) E7,E8: 1.. / E7 = 1 => 13 pairs (_) / E8 = 1 => 11 pairs (_) B8,E8: 1.. / B8 = 1 => 13 pairs (_) / E8 = 1 => 11 pairs (_) A3,A7: 1.. / A3 = 1 => 9 pairs (_) / A7 = 1 => 0 pairs (X) D3,F3: 2.. / D3 = 2 => 11 pairs (_) / F3 = 2 => 9 pairs (_) H5,H6: 2.. / H5 = 2 => 9 pairs (_) / H6 = 2 => 10 pairs (_) B4,D4: 2.. / B4 = 2 => 8 pairs (_) / D4 = 2 => 21 pairs (_) G6,H6: 5.. / G6 = 5 => 9 pairs (_) / H6 = 5 => 15 pairs (_) I2,I7: 5.. / I2 = 5 => 13 pairs (_) / I7 = 5 => 13 pairs (_) B5,I5: 6.. / B5 = 6 => 13 pairs (_) / I5 = 6 => 0 pairs (X) D9,G9: 6.. / D9 = 6 => 8 pairs (_) / G9 = 6 => 10 pairs (_) A4,A7: 6.. / A4 = 6 => 0 pairs (X) / A7 = 6 => 10 pairs (_) A1,D1: 7.. / A1 = 7 => 10 pairs (_) / D1 = 7 => 0 pairs (X) A1,B2: 8.. / A1 = 8 => 0 pairs (X) / B2 = 8 => 10 pairs (_) D1,F2: 8.. / D1 = 8 => 10 pairs (_) / F2 = 8 => 0 pairs (X) H7,H8: 8.. / H7 = 8 => 0 pairs (X) / H8 = 8 => 8 pairs (_) A1,D1: 8.. / A1 = 8 => 0 pairs (X) / D1 = 8 => 10 pairs (_) B2,F2: 8.. / B2 = 8 => 10 pairs (_) / F2 = 8 => 0 pairs (X) A1,A4: 8.. / A1 = 8 => 0 pairs (X) / A4 = 8 => 10 pairs (_) B2,B3: 9.. / B2 = 9 => 0 pairs (X) / B3 = 9 => 10 pairs (_) D4,D6: 9.. / D4 = 9 => 0 pairs (X) / D6 = 9 => 8 pairs (_) H7,I7: 9.. / H7 = 9 => 10 pairs (_) / I7 = 9 => 0 pairs (X) B3,H3: 9.. / B3 = 9 => 10 pairs (_) / H3 = 9 => 0 pairs (X) * DURATION: 0:00:23.828857 START: 22:30:02.177550 END: 22:30:26.006407 2019-04-30 * CP COUNT: (23) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A4,B6,D1,E6,I4,I5) * .56.493124.213..6...3.6.8.4..7.51.3.9.53..1..3.1..6..8..4..32..5.9.....3238.9...1 * PAIR A1: 7,8 BLK 1 B2: 7,8,9 # reduction candidate for 7,8 B2: 9 => CTR * 856749312492138.6...3.6.8946.7.51.399.53..1.63.19.6..8..4..32..5.9.....3238.9...1 B2: 7,8 # 10 pairs * PAIR A3: 1,7 BLK 1 B3: 1,7,9 # reduction candidate for 1,7 B3: 1,7 => CTR * 856749312492138.65..3.6.8946.7.51.3.9.53..1..3.1..6..8..4..32.95.9.....3238.9...1 B3: 9 # 10 pairs * PAIR A3: 1,7 COL A A7: 1,7,6 # reduction candidate for 1,7 A7: 1,7 => CTR * 8567493124.2138965.93.6.8746.7.514399.53.41263419267587.4..329.5.9....83238.9...1 A7: 6 # 10 pairs * PAIR D1: 7,8 BLK 2 F2: 7,8,5 # reduction candidate for 7,8 F2: 5 => SOLVED * 756849312482135769193267854827451936965328147341976528614783295579612483238594671 F2: 7,8 # 12 pairs * PAIR D1: 7,8 COL D D7: 7,8,5,6 # reduction candidate for 7,8 D7: 7,8 # 15 pairs D8: 7,8,2,4,6 # reduction candidate for 7,8 D8: 7,8 # 11 pairs * PAIR A4: 6,8 BLK 4 B4: 6,8,2,4 # reduction candidate for 6,8 B4: 6,8 => CTR * .56.493124.213.96..93.62854..72514399253841.63.1976528..4..329.5.9.2..83238.9..41 B4: 2,4 # 10 pairs B5: 6,8,2,4 # reduction candidate for 6,8 B5: 6,8 # 10 pairs * PAIR B6: 2,4 BLK 4 B4: 2,4,6,8 # reduction candidate for 2,4 B4: 2,4 # 10 pairs B5: 2,4,6,8 # reduction candidate for 2,4 B5: 2,4 => CTR * .56.493124.2138965193.6.874.872514399.53.41.63419.6..8..4..329.5.94...83238.9..41 B5: 6,8 # 10 pairs * PAIR B6: 2,4 ROW 6 D6: 2,4,7,9 # reduction candidate for 2,4 D6: 2,4 => CTR * 75684931248213.965193562874827951436965384127341276598674.13289519.28..3238.9...1 D6: 7,9 # 9 pairs H6: 2,4,5,7,9 # reduction candidate for 2,4 H6: 2,4 # 11 pairs * PAIR E6: 2,7 BLK 5 E5: 2,7,8 # reduction candidate for 2,7 E5: 2,7 # 14 pairs F5: 2,7,4,8 # reduction candidate for 2,7 F5: 2,7 => CTR * .56.4931248213..6..93.6.8.4827451.3.96538.1473419765286.4.13295519.28473238.9...1 F5: 4,8 # 9 pairs D6: 2,7,4,9 # reduction candidate for 2,7 D6: 2,7 => CTR * 75684931248213.965193.62874827951436965384127341..65986.45.32895.9..8..3238.9...1 D6: 4,9 # 9 pairs * PAIR E6: 2,7 ROW 6 H6: 2,7,4,5,9 # reduction candidate for 2,7 H6: 4,5,9 # 9 pairs H6: 2,7 # 9 pairs * PAIR E6: 2,7 COL E E8: 2,7,1,8 # reduction candidate for 2,7 E8: 2,7 # 14 pairs E8: 1,8 # 10 pairs * PAIR I4: 6,9 BLK 6 G4: 6,9,4 # reduction candidate for 6,9 G4: 6,9 => SOLVED * 756849312482135769193267854827451936965328147341976528614783295579612483238594671 G4: 4 # 10 pairs * PAIR I4: 6,9 COL I I7: 6,9,5,7 # reduction candidate for 6,9 I7: 6,9 => CTR * 756849312482137965193.6.8748.79514369653.4127341..65986.4..32.95.9..8.43238495..1 I7: 5,7 # 12 pairs * PAIR I5: 6,7 COL I I7: 6,7,5,9 # reduction candidate for 6,7 I7: 6,7 # 20 pairs I7: 5,9 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060419-absurd-base-pr-000.dot * REASONING * DIS # B2: 9 => CTR => B2: 7,8 * DIS # B3: 1,7 => CTR => B3: 9 * DIS # A7: 1,7 => CTR => A7: 6 * PRF # F2: 5 => SOL * DIS # B4: 6,8 => CTR => B4: 2,4 * DIS # B5: 2,4 => CTR => B5: 6,8 * DIS # D6: 2,4 => CTR => D6: 7,9 * DIS # F5: 2,7 => CTR => F5: 4,8 * DIS # D6: 2,7 => CTR => D6: 4,9 * PRF # G4: 6,9 => SOL * DIS # I7: 6,9 => CTR => I7: 5,7 * CNT 11 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A4,B6,D1,E6,I4,I5) * .56.493124.213..6...3.6.8.4..7.51.3.9.53..1..3.1..6..8..4..32..5.9.....3238.9...1 * PAIR A1: 7,8 BLK 1 B2: 7,8,9 # reduction candidate for 7,8 B2: 9 => CTR * 856749312492138.6...3.6.8946.7.51.399.53..1.63.19.6..8..4..32..5.9.....3238.9...1 * PAIR D1: 7,8 BLK 2 F2: 7,8,5 # reduction candidate for 7,8 F2: 5 => SOLVED * 756849312482135769193267854827451936965328147341976528614783295579612483238594671 * DURATION: 0:00:03.327231 START: 22:30:46.165748 END: 22:30:49.492979 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060419-absurd-base-pr-001.dot * REASONING * DIS # B2: 9 => CTR => B2: 7,8 * PRF B2: 7,8 # F2: 5 => SOL * STA B2: 7,8 + F2: 5 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060419, absurd
Solution
position: 756849312482135769193267854827451936965328147341976528614783295579612483238594671 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 # B2: 7,8 => UNS * DIS # B2: 9 => CTR => B2: 7,8 * DIS # B3: 1,7 => CTR => B3: 9 * INC # B3: 9 => UNS * DIS # A7: 1,7 => CTR => A7: 6 * INC # A7: 6 => UNS * INC # F2: 7,8 => UNS * PRF # F2: 5 => SOL * INC # D7: 7,8 => UNS * INC # D8: 7,8 => UNS * DIS # B4: 6,8 => CTR => B4: 2,4 * INC # B4: 2,4 => UNS * INC # B5: 6,8 => UNS * INC # B4: 2,4 => UNS * DIS # B5: 2,4 => CTR => B5: 6,8 * INC # B5: 6,8 => UNS * DIS # D6: 2,4 => CTR => D6: 7,9 * INC # D6: 7,9 => UNS * INC # H6: 2,4 => UNS * INC # E5: 2,7 => UNS * DIS # F5: 2,7 => CTR => F5: 4,8 * INC # F5: 4,8 => UNS * DIS # D6: 2,7 => CTR => D6: 4,9 * INC # D6: 4,9 => UNS * INC # H6: 2,7 => UNS * INC # H6: 4,5,9 => UNS * INC # E8: 2,7 => UNS * INC # E8: 1,8 => UNS * PRF # G4: 6,9 => SOL * INC # G4: 4 => UNS * DIS # I7: 6,9 => CTR => I7: 5,7 * INC # I7: 5,7 => UNS * INC # I7: 6,7 => UNS * INC # I7: 5,9 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 7,8 => UNS * DIS # B2: 9 => CTR => B2: 7,8 * INC B2: 7,8 # F2: 7,8 => UNS * PRF B2: 7,8 # F2: 5 => SOL * STA B2: 7,8 + F2: 5 * CNT 4 HDP CHAINS / 4 HYP OPENED