Analysis of zz-www.sudokuoftheday.co.uk-20060412-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: ...948...16..2........1.23947...3.8..52...4..8..4..1.7.85.6..........92.........8 initial
Autosolve
position: ...948...16932.8...48.16239471693582.52...4.38..4521.7.85.6..........92.........8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B9: 2,3 => SOL * DIS # A1: 3,7 => CTR => A1: 2,5 * DIS # C9: 3,7 => CTR => C9: 4,6 * DIS # H2: 4 => CTR => H2: 5,7 * DIS # G9: 3 => CTR => G9: 6,7 * DIS # I8: 4,5 => CTR => I8: 1,6 * PRF # B9: 1,2 => SOL * DIS # C8: 3,6 => CTR => C8: 4,7 * PRF # C9: 3,6 => SOL * DIS # D5: 1 => CTR => D5: 7,8 * DIS # F7: 1,7 => CTR => F7: 4,9 * PRF # F8: 1,7 => SOL * DIS # F9: 1,7 => CTR => F9: 4,5,9 * DIS # B9: 1,3 => CTR => B9: 2,9 * DIS # A9: 3,7 => CTR => A9: 2,6,9 * DIS # C9: 3,7 => CTR => C9: 4,6 * DIS # G9: 6 => CTR => G9: 3,7 * DIS # I8: 1,4 => CTR => I8: 5,6 * DIS # H9: 1,4 => CTR => H9: 5,7 * DIS # F7: 1,4 => CTR => F7: 7,9 * CNT 20 HDP CHAINS / 63 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B9: 2,3 => SOL * STA B9: 2,3 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...948...16..2........1.23947...3.8..52...4..8..4..1.7.85.6..........92.........8 | initial |
| ...948...16932.8...48.16239471693582.52...4.38..4521.7.85.6..........92.........8 | autosolve |
| 237948615169325874548716239471693582652871493893452167785269341314587926926134758 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B1: 2,3 C1: 3,7 A3: 5,7 F2: 5,7 D3: 5,7 G1: 6,7 I2: 4,5 A5: 6,9 B6: 3,9 C6: 3,6 E5: 7,8 F5: 1,7 H5: 6,9 H6: 6,9 B8: 1,3 E9: 3,7 G7: 3,7 I7: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,I1: 1.. / H1 = 1 => 20 pairs (_) / I1 = 1 => 0 pairs (X) D5,F5: 1.. / D5 = 1 => 0 pairs (X) / F5 = 1 => 18 pairs (_) B8,B9: 1.. / B8 = 1 => 17 pairs (_) / B9 = 1 => 0 pairs (X) A1,B1: 2.. / A1 = 2 => 0 pairs (*) / B1 = 2 => 0 pairs (X) D7,D9: 2.. / D7 = 2 => 18 pairs (_) / D9 = 2 => 18 pairs (_) A7,D7: 2.. / A7 = 2 => 18 pairs (_) / D7 = 2 => 18 pairs (_) B1,B9: 2.. / B1 = 2 => 17 pairs (_) / B9 = 2 => 0 pairs (*) B6,C6: 3.. / B6 = 3 => 12 pairs (_) / C6 = 3 => 0 pairs (*) E8,E9: 3.. / E8 = 3 => 20 pairs (_) / E9 = 3 => 18 pairs (_) G7,G9: 3.. / G7 = 3 => 18 pairs (_) / G9 = 3 => 0 pairs (X) A7,G7: 3.. / A7 = 3 => 0 pairs (X) / G7 = 3 => 18 pairs (_) H2,I2: 4.. / H2 = 4 => 0 pairs (X) / I2 = 4 => 21 pairs (_) C8,C9: 4.. / C8 = 4 => 20 pairs (_) / C9 = 4 => 18 pairs (_) A1,A3: 5.. / A1 = 5 => 22 pairs (_) / A3 = 5 => 14 pairs (_) F2,D3: 5.. / F2 = 5 => 14 pairs (_) / D3 = 5 => 22 pairs (_) I8,H9: 5.. / I8 = 5 => 0 pairs (X) / H9 = 5 => 20 pairs (_) A3,D3: 5.. / A3 = 5 => 14 pairs (_) / D3 = 5 => 22 pairs (_) G1,I1: 6.. / G1 = 6 => 27 pairs (_) / I1 = 6 => 0 pairs (X) A5,C6: 6.. / A5 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) H5,H6: 6.. / H5 = 6 => 12 pairs (_) / H6 = 6 => 0 pairs (*) I8,G9: 6.. / I8 = 6 => 27 pairs (_) / G9 = 6 => 0 pairs (X) A5,H5: 6.. / A5 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) C6,H6: 6.. / C6 = 6 => 12 pairs (_) / H6 = 6 => 0 pairs (*) G1,G9: 6.. / G1 = 6 => 27 pairs (_) / G9 = 6 => 0 pairs (X) I1,I8: 6.. / I1 = 6 => 0 pairs (X) / I8 = 6 => 27 pairs (_) F2,D3: 7.. / F2 = 7 => 22 pairs (_) / D3 = 7 => 14 pairs (_) F2,H2: 7.. / F2 = 7 => 22 pairs (_) / H2 = 7 => 14 pairs (_) A3,D3: 7.. / A3 = 7 => 22 pairs (_) / D3 = 7 => 14 pairs (_) D5,E5: 8.. / D5 = 8 => 15 pairs (_) / E5 = 8 => 20 pairs (_) D8,E8: 8.. / D8 = 8 => 20 pairs (_) / E8 = 8 => 15 pairs (_) D5,D8: 8.. / D5 = 8 => 15 pairs (_) / D8 = 8 => 20 pairs (_) E5,E8: 8.. / E5 = 8 => 20 pairs (_) / E8 = 8 => 15 pairs (_) A5,B6: 9.. / A5 = 9 => 12 pairs (_) / B6 = 9 => 0 pairs (*) H5,H6: 9.. / H5 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) F7,F9: 9.. / F7 = 9 => 18 pairs (_) / F9 = 9 => 0 pairs (X) A5,H5: 9.. / A5 = 9 => 12 pairs (_) / H5 = 9 => 0 pairs (*) B6,H6: 9.. / B6 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) A7,F7: 9.. / A7 = 9 => 0 pairs (X) / F7 = 9 => 18 pairs (_) B6,B9: 9.. / B6 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) * DURATION: 0:00:43.476173 START: 22:19:53.135625 END: 22:20:36.611798 2019-04-30 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B1,B6,B8,C1,C6,D3,E5,E9,F2,F5,G1,G7,H5,H6,I2,I7) * ...948...16932.8...48.16239471693582.52...4.38..4521.7.85.6..........92.........8 * PAIR B1: 2,3 BLK 1 A1: 2,3,5,7 # reduction candidate for 2,3 A1: 5,7 # 16 pairs A1: 2,3 # 15 pairs * PAIR B1: 2,3 COL B B9: 2,3,1,9 # reduction candidate for 2,3 B9: 2,3 => SOLVED * 237948615169325874548716239471693582652871493893452167785269341314587926926134758 B9: 1,9 # 18 pairs * PAIR C1: 3,7 BLK 1 A1: 3,7,2,5 # reduction candidate for 3,7 A1: 3,7 => CTR * .2.94861516932587454871623947169358265287149389.4521.7.8526..41...58.9262.6134758 A1: 2,5 # 19 pairs * PAIR C1: 3,7 COL C C8: 3,7,4,6 # reduction candidate for 3,7 C8: 3,7 # 13 pairs C9: 3,7,4,6 # reduction candidate for 3,7 C9: 3,7 => CTR * .2.948...16932.8...48.16239471693582952..1463836452197.85.69374.14...92..9...46.8 C9: 4,6 # 19 pairs * PAIR A3: 5,7 BLK 1 A1: 5,7,2,3 # reduction candidate for 5,7 A1: 5,7 # 16 pairs A1: 2,3 # 15 pairs * PAIR F2: 5,7 ROW 2 H2: 5,7,4 # reduction candidate for 5,7 H2: 4 => CTR * 523948...169327845748516239471693582952..1463836452197.85269..4.14..5926.9.1.4.58 H2: 5,7 # 21 pairs * PAIR F2: 5,7 COL F F8: 5,7,1,4 # reduction candidate for 5,7 F8: 5,7 # 21 pairs F9: 5,7,1,4,9 # reduction candidate for 5,7 F9: 5,7 # 19 pairs * PAIR D3: 5,7 COL D D8: 5,7,1,8 # reduction candidate for 5,7 D8: 5,7 # 18 pairs D9: 5,7,1,2 # reduction candidate for 5,7 D9: 5,7 # 21 pairs * PAIR G1: 6,7 COL G G9: 6,7,3 # reduction candidate for 6,7 G9: 3 => CTR * ...9486..16932.8...48.16239471693582.52...4.38..4521.73852697..714.35926..6.74358 G9: 6,7 # 18 pairs * PAIR I2: 4,5 BLK 3 H2: 4,5,7 # reduction candidate for 4,5 H2: 4,5 # 22 pairs H2: 7 # 14 pairs * PAIR I2: 4,5 COL I I8: 4,5,1,6 # reduction candidate for 4,5 I8: 4,5 => CTR * 5239487161693278..748516239471693582.52..14.3836452197.85.6.3.161..3.92.39....6.8 I8: 1,6 # 21 pairs * PAIR A5: 6,9 COL A A9: 6,9,2,3,7 # reduction candidate for 6,9 A9: 6,9 # 20 pairs A9: 2,3,7 # 18 pairs * PAIR B6: 3,9 COL B B9: 3,9,1,2 # reduction candidate for 3,9 B9: 1,2 => SOLVED * 237948615169325874548716239471693582652871493893452167785269341314587926926134758 B9: 3,9 # 17 pairs * PAIR C6: 3,6 COL C C8: 3,6,4,7 # reduction candidate for 3,6 C8: 3,6 => CTR * ..7948615169325874548716239471693582952...463836452197.85269.41.1...49266.4....58 C8: 4,7 # 19 pairs C9: 3,6,4,7 # reduction candidate for 3,6 C9: 3,6 => SOLVED * 237948615169325874548716239471693582652871493893452167785269341314587926926134758 C9: 4,7 # 19 pairs * PAIR E5: 7,8 BLK 5 D5: 7,8,1 # reduction candidate for 7,8 D5: 1 => CTR * ...948...169325874548716239471693582.521874.38..4521.7.8526...1...8..925...5..6.8 D5: 7,8 # 18 pairs * PAIR E5: 7,8 COL E E8: 7,8,3 # reduction candidate for 7,8 E8: 3 # 20 pairs E8: 7,8 # 18 pairs * PAIR F5: 1,7 BLK 5 D5: 1,7,8 # reduction candidate for 1,7 D5: 1,7 # 20 pairs D5: 8 # 15 pairs * PAIR F5: 1,7 COL F F7: 1,7,4,9 # reduction candidate for 1,7 F7: 1,7 => CTR * ...948...16932.8...48.16239471693582652...49389345216798526.3.......492...4..96.8 F7: 4,9 # 19 pairs F8: 1,7,4,5 # reduction candidate for 1,7 F8: 1,7 => SOLVED * 237948615169325874548716239471693582652871493893452167785269341314587926926134758 F8: 4,5 # 19 pairs F9: 1,7,4,5,9 # reduction candidate for 1,7 F9: 1,7 => CTR * ...948615169325874548716239471693582.52...4.38..4521.7.85269.41...5849266.4....58 F9: 4,5,9 # 18 pairs * PAIR B8: 1,3 BLK 7 B9: 1,3,2,9 # reduction candidate for 1,3 B9: 1,3 => CTR * 327948615169325874548716239471693582652.71493893452167.852673417.4...926..6...758 B9: 2,9 # 18 pairs * PAIR E9: 3,7 BLK 8 E8: 3,7,8 # reduction candidate for 3,7 E8: 3,7 # 20 pairs E8: 8 # 15 pairs * PAIR E9: 3,7 ROW 9 A9: 3,7,2,6,9 # reduction candidate for 3,7 A9: 3,7 => CTR * 52.9487.6169327845748516239471693582.52..14.38..4521.7.85.6.371.178359243.4179658 A9: 2,6,9 # 18 pairs C9: 3,7,4,6 # reduction candidate for 3,7 C9: 3,7 => CTR * .2.948...16932.8...48.16239471693582952..1463836452197.85.69374.14...92..9...46.8 C9: 4,6 # 19 pairs G9: 3,7,6 # reduction candidate for 3,7 G9: 3,7 # 27 pairs * PAIR G7: 3,7 BLK 9 G9: 3,7,6 # reduction candidate for 3,7 G9: 6 => CTR * 5239487161693278..748516239471693582.52..14.3836452197.85.6.3..61..3.92.39....6.8 G9: 3,7 # 27 pairs * PAIR G7: 3,7 ROW 7 A7: 3,7,2,9 # reduction candidate for 3,7 A7: 3,7 # 23 pairs A7: 2,9 # 19 pairs * PAIR I7: 1,4 BLK 9 H7: 1,4,7 # reduction candidate for 1,4 H7: 1,4 # 23 pairs I8: 1,4,5,6 # reduction candidate for 1,4 I8: 1,4 => CTR * 523948716169327845748516239471693582.52..14.3836452197.85.6.37.61..3592439....658 I8: 5,6 # 19 pairs H9: 1,4,5,7 # reduction candidate for 1,4 H9: 1,4 => CTR * ...9487.6169327854748516239471693582.52..14.38..4521.7.85.6.371.....4925..4...6.8 H9: 5,7 # 19 pairs * PAIR I7: 1,4 ROW 7 F7: 1,4,7,9 # reduction candidate for 1,4 F7: 1,4 => CTR * ...9487.61693278..748516239471693582652..14938934521.798526.37.......92......96.8 F7: 7,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060412-absurd-base-pr-000.dot * REASONING * PRF # B9: 2,3 => SOL * DIS # A1: 3,7 => CTR => A1: 2,5 * DIS # C9: 3,7 => CTR => C9: 4,6 * DIS # H2: 4 => CTR => H2: 5,7 * DIS # G9: 3 => CTR => G9: 6,7 * DIS # I8: 4,5 => CTR => I8: 1,6 * PRF # B9: 1,2 => SOL * DIS # C8: 3,6 => CTR => C8: 4,7 * PRF # C9: 3,6 => SOL * DIS # D5: 1 => CTR => D5: 7,8 * DIS # F7: 1,7 => CTR => F7: 4,9 * PRF # F8: 1,7 => SOL * DIS # F9: 1,7 => CTR => F9: 4,5,9 * DIS # B9: 1,3 => CTR => B9: 2,9 * DIS # A9: 3,7 => CTR => A9: 2,6,9 * DIS # C9: 3,7 => CTR => C9: 4,6 * DIS # G9: 6 => CTR => G9: 3,7 * DIS # I8: 1,4 => CTR => I8: 5,6 * DIS # H9: 1,4 => CTR => H9: 5,7 * DIS # F7: 1,4 => CTR => F7: 7,9 * CNT 20 HDP CHAINS / 63 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B1,B6,B8,C1,C6,D3,E5,E9,F2,F5,G1,G7,H5,H6,I2,I7) * ...948...16932.8...48.16239471693582.52...4.38..4521.7.85.6..........92.........8 * PAIR B1: 2,3 BLK 1 A1: 2,3,5,7 # reduction candidate for 2,3 A1: 5,7 # 16 pairs A1: 2,3 # 15 pairs * PAIR B1: 2,3 COL B B9: 2,3,1,9 # reduction candidate for 2,3 B9: 2,3 => SOLVED * 237948615169325874548716239471693582652871493893452167785269341314587926926134758 * DURATION: 0:00:02.903610 START: 22:21:14.183407 END: 22:21:17.087017 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060412-absurd-base-pr-001.dot * REASONING * PRF # B9: 2,3 => SOL * STA B9: 2,3 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060412, absurd
Solution
position: 237948615169325874548716239471693582652871493893452167785269341314587926926134758 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 # A1: 2,3 => UNS * INC # A1: 5,7 => UNS * PRF # B9: 2,3 => SOL * INC # B9: 1,9 => UNS * DIS # A1: 3,7 => CTR => A1: 2,5 * INC # A1: 2,5 => UNS * INC # C8: 3,7 => UNS * DIS # C9: 3,7 => CTR => C9: 4,6 * INC # C9: 4,6 => UNS * INC # A1: 5,7 => UNS * INC # A1: 2,3 => UNS * INC # H2: 5,7 => UNS * DIS # H2: 4 => CTR => H2: 5,7 * INC # F8: 5,7 => UNS * INC # F9: 5,7 => UNS * INC # D8: 5,7 => UNS * INC # D9: 5,7 => UNS * INC # G9: 6,7 => UNS * DIS # G9: 3 => CTR => G9: 6,7 * INC # H2: 4,5 => UNS * INC # H2: 7 => UNS * DIS # I8: 4,5 => CTR => I8: 1,6 * INC # I8: 1,6 => UNS * INC # A9: 6,9 => UNS * INC # A9: 2,3,7 => UNS * INC # B9: 3,9 => UNS * PRF # B9: 1,2 => SOL * DIS # C8: 3,6 => CTR => C8: 4,7 * INC # C8: 4,7 => UNS * PRF # C9: 3,6 => SOL * INC # C9: 4,7 => UNS * INC # D5: 7,8 => UNS * DIS # D5: 1 => CTR => D5: 7,8 * INC # E8: 7,8 => UNS * INC # E8: 3 => UNS * INC # D5: 1,7 => UNS * INC # D5: 8 => UNS * DIS # F7: 1,7 => CTR => F7: 4,9 * INC # F7: 4,9 => UNS * PRF # F8: 1,7 => SOL * INC # F8: 4,5 => UNS * DIS # F9: 1,7 => CTR => F9: 4,5,9 * INC # F9: 4,5,9 => UNS * DIS # B9: 1,3 => CTR => B9: 2,9 * INC # B9: 2,9 => UNS * INC # E8: 3,7 => UNS * INC # E8: 8 => UNS * DIS # A9: 3,7 => CTR => A9: 2,6,9 * INC # A9: 2,6,9 => UNS * DIS # C9: 3,7 => CTR => C9: 4,6 * INC # C9: 4,6 => UNS * INC # G9: 3,7 => UNS * INC # G9: 3,7 => UNS * DIS # G9: 6 => CTR => G9: 3,7 * INC # A7: 3,7 => UNS * INC # A7: 2,9 => UNS * INC # H7: 1,4 => UNS * DIS # I8: 1,4 => CTR => I8: 5,6 * INC # I8: 5,6 => UNS * DIS # H9: 1,4 => CTR => H9: 5,7 * INC # H9: 5,7 => UNS * DIS # F7: 1,4 => CTR => F7: 7,9 * INC # F7: 7,9 => UNS * CNT 63 HDP CHAINS / 63 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 2,3 => UNS * INC # A1: 5,7 => UNS * PRF # B9: 2,3 => SOL * STA B9: 2,3 * CNT 3 HDP CHAINS / 3 HYP OPENED