Analysis of zz-www.sudokuoftheday.co.uk-20060619-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: .6..1...5..8...1.2..........12..789..94..8...5.......6.....592...63...5.3....4... initial
Autosolve
position: .6..1...5..8...1.2........9612537894794..8531583...276.....5923..63..45.3....461. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D1: 7,9 => SOL * DIS # C9: 5 => CTR => C9: 7,9 * PRF # A1: 4,9 => SOL * DIS # E2: 4,9 => CTR => E2: 5,7 * PRF # H3: 6 => SOL * PRF # D1: 2,7,9 => SOL * PRF # B3: 2,4,5 => SOL * DIS # D6: 4,9 => CTR => D6: 1 * DIS # E2: 4,9 => CTR => E2: 5,7 * DIS # D6: 4 => CTR => D6: 1,9 * DIS # F8: 2 => CTR => F8: 1,9 * DIS # B2: 4,7 => CTR => B2: 3,5 * DIS # B3: 4,7 => CTR => B3: 2,3,5 * DIS # C3: 1,7 => CTR => C3: 5 * DIS # B9: 2,7 => CTR => B9: 5 * PRF # B3: 2,7 => SOL * CNT 16 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D1: 7,9 => SOL * STA D1: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6..1...5..8...1.2..........12..789..94..8...5.......6.....592...63...5.3....4... | initial |
| .6..1...5..8...1.2........9612537894794..8531583...276.....5923..63..45.3....461. | autosolve |
| 467912385938756142125483769612537894794268531583149276841675923276391458359824617 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 7,9 A2: 4,9 G1: 3,7 H1: 4,8 H2: 4,6 G3: 3,7 D5: 2,6 E5: 2,6 E6: 4,9 F6: 1,9 B7: 4,7 C7: 1,7 B8: 2,7 I8: 7,8 I9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,C3: 1.. / A3 = 1 => 16 pairs (_) / C3 = 1 => 0 pairs (X) D6,F6: 1.. / D6 = 1 => 15 pairs (_) / F6 = 1 => 0 pairs (X) D7,F8: 1.. / D7 = 1 => 0 pairs (X) / F8 = 1 => 15 pairs (_) A8,F8: 1.. / A8 = 1 => 0 pairs (X) / F8 = 1 => 15 pairs (_) C3,C7: 1.. / C3 = 1 => 0 pairs (X) / C7 = 1 => 16 pairs (_) D6,D7: 1.. / D6 = 1 => 15 pairs (_) / D7 = 1 => 0 pairs (X) F6,F8: 1.. / F6 = 1 => 0 pairs (X) / F8 = 1 => 15 pairs (_) D5,E5: 2.. / D5 = 2 => 14 pairs (_) / E5 = 2 => 13 pairs (_) B2,B3: 3.. / B2 = 3 => 16 pairs (_) / B3 = 3 => 15 pairs (_) G1,G3: 3.. / G1 = 3 => 17 pairs (_) / G3 = 3 => 0 pairs (X) F1,G1: 3.. / F1 = 3 => 0 pairs (X) / G1 = 3 => 17 pairs (_) B2,F2: 3.. / B2 = 3 => 16 pairs (_) / F2 = 3 => 15 pairs (_) D6,E6: 4.. / D6 = 4 => 0 pairs (X) / E6 = 4 => 15 pairs (_) A7,B7: 4.. / A7 = 4 => 0 pairs (X) / B7 = 4 => 15 pairs (_) E2,E3: 5.. / E2 = 5 => 15 pairs (_) / E3 = 5 => 0 pairs (X) B9,C9: 5.. / B9 = 5 => 17 pairs (_) / C9 = 5 => 0 pairs (X) B2,E2: 5.. / B2 = 5 => 0 pairs (X) / E2 = 5 => 15 pairs (_) C3,C9: 5.. / C3 = 5 => 17 pairs (_) / C9 = 5 => 0 pairs (X) F2,F3: 6.. / F2 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) H2,H3: 6.. / H2 = 6 => 16 pairs (_) / H3 = 6 => 0 pairs (*) D5,E5: 6.. / D5 = 6 => 13 pairs (_) / E5 = 6 => 14 pairs (_) D7,E7: 6.. / D7 = 6 => 14 pairs (_) / E7 = 6 => 13 pairs (_) F2,H2: 6.. / F2 = 6 => 0 pairs (*) / H2 = 6 => 0 pairs (X) F3,H3: 6.. / F3 = 6 => 16 pairs (_) / H3 = 6 => 0 pairs (*) D5,D7: 6.. / D5 = 6 => 13 pairs (_) / D7 = 6 => 14 pairs (_) E5,E7: 6.. / E5 = 6 => 14 pairs (_) / E7 = 6 => 13 pairs (_) G1,G3: 7.. / G1 = 7 => 0 pairs (X) / G3 = 7 => 17 pairs (_) I8,I9: 7.. / I8 = 7 => 17 pairs (_) / I9 = 7 => 15 pairs (_) H1,H3: 8.. / H1 = 8 => 15 pairs (_) / H3 = 8 => 15 pairs (_) A7,A8: 8.. / A7 = 8 => 15 pairs (_) / A8 = 8 => 0 pairs (X) I8,I9: 8.. / I8 = 8 => 15 pairs (_) / I9 = 8 => 17 pairs (_) D1,H1: 8.. / D1 = 8 => 15 pairs (_) / H1 = 8 => 15 pairs (_) A8,C9: 9.. / A8 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) C1,C9: 9.. / C1 = 9 => 0 pairs (X) / C9 = 9 => 0 pairs (_) * DURATION: 0:00:37.095734 START: 23:57:07.662513 END: 23:57:44.758247 2019-04-30 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B7,B8,C1,C7,D5,E5,E6,F6,G1,G3,H1,H2,I8,I9) * .6..1...5..8...1.2........9612537894794..8531583...276.....5923..63..45.3....461. * PAIR C1: 7,9 ROW 1 D1: 7,9,2,4,8 # reduction candidate for 7,9 D1: 7,9 => SOLVED * 467912385938756142125483769612537894794268531583149276841675923276391458359824617 D1: 2,4,8 # 15 pairs * PAIR C1: 7,9 COL C C9: 7,9,5 # reduction candidate for 7,9 C9: 5 => CTR * 269.137.5438.59162.....6..9612537894794..8531583...276.4...59239.63.145.3.5..461. C9: 7,9 # 17 pairs * PAIR A2: 4,9 BLK 1 A1: 4,9,2 # reduction candidate for 4,9 A1: 4,9 => SOLVED * 467912385938756142125483769612537894794268531583149276841675923276391458359824617 A1: 2 # 18 pairs * PAIR A2: 4,9 ROW 2 D2: 4,9,7 # reduction candidate for 4,9 D2: 4,9 # 18 pairs E2: 4,9,5,7 # reduction candidate for 4,9 E2: 4,9 => CTR * .6..1...5.587.3162.3..567.9612537894794..8531583...276.4...5923..63..45.3.5..461. E2: 5,7 # 16 pairs * PAIR H1: 4,8 BLK 3 H3: 4,8,6 # reduction candidate for 4,8 H3: 6 => SOLVED * 467912385938756142125483769612537894794268531583149276841675923276391458359824617 H3: 4,8 # 16 pairs * PAIR H1: 4,8 ROW 1 D1: 4,8,2,7,9 # reduction candidate for 4,8 D1: 2,7,9 => SOLVED * 467912385938756142125483769612537894794268531583149276841675923276391458359824617 D1: 4,8 # 17 pairs * PAIR H2: 4,6 BLK 3 H3: 4,6,8 # reduction candidate for 4,6 H3: 8 # 15 pairs H3: 4,6 # 15 pairs * PAIR G3: 3,7 ROW 3 B3: 3,7,2,4,5 # reduction candidate for 3,7 B3: 2,4,5 => SOLVED * 467912385938756142125483769612537894794268531583149276841675923276391458359824617 B3: 3,7 # 18 pairs * PAIR E6: 4,9 BLK 5 D6: 4,9,1 # reduction candidate for 4,9 D6: 4,9 => CTR * .6..1...5..8...1.2........9612537894794..8531583..1276...1659231.63..45.3.9..461. D6: 1 # 15 pairs * PAIR E6: 4,9 COL E E2: 4,9,5,7 # reduction candidate for 4,9 E2: 4,9 => CTR * .6..1...5.587.3162.3..567.9612537894794..8531583...276.4...5923..63..45.3.5..461. E2: 5,7 # 16 pairs * PAIR F6: 1,9 BLK 5 D6: 1,9,4 # reduction candidate for 1,9 D6: 4 => CTR * .6..1...5..8...1.2........9612537894794..8531583491276...1659231.63.945.3.9..461. D6: 1,9 # 15 pairs * PAIR F6: 1,9 COL F F8: 1,9,2 # reduction candidate for 1,9 F8: 2 => CTR * .6..1...5..8...1.2........9612537894794..8531583..1276...1659231.639245832...461. F8: 1,9 # 18 pairs * PAIR B7: 4,7 COL B B2: 4,7,3,5 # reduction candidate for 4,7 B2: 4,7 => CTR * .6..123.5..8.53162.35..67.9612537894794..8531583...276..1..5923..63.145.35...461. B2: 3,5 # 16 pairs B3: 4,7,2,3,5 # reduction candidate for 4,7 B3: 4,7 => CTR * 26.913..5.3875.1.21.5.....9612537894794..8531583149276..1..5923.263.145.35...461. B3: 2,3,5 # 15 pairs * PAIR C7: 1,7 ROW 7 D7: 1,7,6,8 # reduction candidate for 1,7 D7: 6,8 # 16 pairs D7: 1,7 # 13 pairs * PAIR C7: 1,7 COL C C3: 1,7,5 # reduction candidate for 1,7 C3: 1,7 => CTR * 269.137.5438.59162.....6..9612537894794..8531583...276.4...59239.63.145.3.5..461. C3: 5 # 17 pairs * PAIR B8: 2,7 BLK 7 B9: 2,7,5 # reduction candidate for 2,7 B9: 2,7 => CTR * 269.137.5438.59162.....6..9612537894794..8531583...276.4...59239.63.145.3.5..461. B9: 5 # 17 pairs * PAIR B8: 2,7 ROW 8 E8: 2,7,8,9 # reduction candidate for 2,7 E8: 2,7 # 20 pairs E8: 8,9 # 16 pairs * PAIR B8: 2,7 COL B B3: 2,7,3,4,5 # reduction candidate for 2,7 B3: 2,7 => SOLVED * 467912385938756142125483769612537894794268531583149276841675923276391458359824617 B3: 3,4,5 # 15 pairs * PAIR I8: 7,8 ROW 8 E8: 7,8,2,9 # reduction candidate for 7,8 E8: 7,8 # 20 pairs E8: 2,9 # 16 pairs * PAIR I9: 7,8 ROW 9 D9: 7,8,2,9 # reduction candidate for 7,8 D9: 7,8 # 19 pairs E9: 7,8,2,9 # reduction candidate for 7,8 E9: 7,8 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060619-absurd-base-pr-000.dot * REASONING * PRF # D1: 7,9 => SOL * DIS # C9: 5 => CTR => C9: 7,9 * PRF # A1: 4,9 => SOL * DIS # E2: 4,9 => CTR => E2: 5,7 * PRF # H3: 6 => SOL * PRF # D1: 2,7,9 => SOL * PRF # B3: 2,4,5 => SOL * DIS # D6: 4,9 => CTR => D6: 1 * DIS # E2: 4,9 => CTR => E2: 5,7 * DIS # D6: 4 => CTR => D6: 1,9 * DIS # F8: 2 => CTR => F8: 1,9 * DIS # B2: 4,7 => CTR => B2: 3,5 * DIS # B3: 4,7 => CTR => B3: 2,3,5 * DIS # C3: 1,7 => CTR => C3: 5 * DIS # B9: 2,7 => CTR => B9: 5 * PRF # B3: 2,7 => SOL * CNT 16 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B7,B8,C1,C7,D5,E5,E6,F6,G1,G3,H1,H2,I8,I9) * .6..1...5..8...1.2........9612537894794..8531583...276.....5923..63..45.3....461. * PAIR C1: 7,9 ROW 1 D1: 7,9,2,4,8 # reduction candidate for 7,9 D1: 7,9 => SOLVED * 467912385938756142125483769612537894794268531583149276841675923276391458359824617 * DURATION: 0:00:01.834720 START: 23:58:11.582731 END: 23:58:13.417451 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060619-absurd-base-pr-001.dot * REASONING * PRF # D1: 7,9 => SOL * STA D1: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060619, absurd
Solution
position: 467912385938756142125483769612537894794268531583149276841675923276391458359824617 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 # D1: 7,9 => SOL * INC # D1: 2,4,8 => UNS * INC # C9: 7,9 => UNS * DIS # C9: 5 => CTR => C9: 7,9 * PRF # A1: 4,9 => SOL * INC # A1: 2 => UNS * INC # D2: 4,9 => UNS * DIS # E2: 4,9 => CTR => E2: 5,7 * INC # E2: 5,7 => UNS * INC # H3: 4,8 => UNS * PRF # H3: 6 => SOL * INC # D1: 4,8 => UNS * PRF # D1: 2,7,9 => SOL * INC # H3: 4,6 => UNS * INC # H3: 8 => UNS * INC # B3: 3,7 => UNS * PRF # B3: 2,4,5 => SOL * DIS # D6: 4,9 => CTR => D6: 1 * INC # D6: 1 => UNS * DIS # E2: 4,9 => CTR => E2: 5,7 * INC # E2: 5,7 => UNS * INC # D6: 1,9 => UNS * DIS # D6: 4 => CTR => D6: 1,9 * INC # F8: 1,9 => UNS * DIS # F8: 2 => CTR => F8: 1,9 * DIS # B2: 4,7 => CTR => B2: 3,5 * INC # B2: 3,5 => UNS * DIS # B3: 4,7 => CTR => B3: 2,3,5 * INC # B3: 2,3,5 => UNS * INC # D7: 1,7 => UNS * INC # D7: 6,8 => UNS * DIS # C3: 1,7 => CTR => C3: 5 * INC # C3: 5 => UNS * DIS # B9: 2,7 => CTR => B9: 5 * INC # B9: 5 => UNS * INC # E8: 2,7 => UNS * INC # E8: 8,9 => UNS * PRF # B3: 2,7 => SOL * INC # B3: 3,4,5 => UNS * INC # E8: 7,8 => UNS * INC # E8: 2,9 => UNS * INC # D9: 7,8 => UNS * INC # E9: 7,8 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D1: 7,9 => SOL * STA D1: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED