Analysis of zz-www.sudokuoftheday.co.uk-20060814-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: ..32......2.89..47....41.5..4......6..8....2.....3.5.896...28..2..7......8...97.. initial
Autosolve
position: 4.32...8..2.89..4787..4125..4..28..6..8....2...2.3.5.8967..28..2..78.....8...97.2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 1,5 => CTR => C2: 6 * DIS # A4: 1,5 => CTR => A4: 3,7 * PRF # A9: 1,5 => SOL * DIS # F2: 5 => CTR => F2: 3,6 * DIS # G1: 1,9 => CTR => G1: 6 * DIS # B1: 5 => CTR => B1: 1,9 * DIS # I8: 1,9 => CTR => I8: 3,4,5 * DIS # I8: 3,9 => CTR => I8: 1,4,5 * DIS # B5: 1,9 => CTR => B5: 3,5 * DIS # B1: 5 => CTR => B1: 1,9 * DIS # I7: 1,3 => CTR => I7: 4,5 * DIS # G8: 1,3 => CTR => G8: 4,9 * PRF # H8: 1,3 => SOL * DIS # I8: 1,3 => CTR => I8: 4,5,9 * CNT 14 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 1,5 => CTR => C2: 6 * DIS C2: 6 # D7: 1,5 => CTR => D7: 3,4 * DIS C2: 6 + D7: 3,4 # D9: 1,5 => CTR => D9: 3,4 * DIS C2: 6 + D7: 3,4 + D9: 3,4 # E9: 6 => CTR => E9: 1,5 * PRF C2: 6 + D7: 3,4 + D9: 3,4 + E9: 1,5 # I7: 1,5 => SOL * STA C2: 6 + D7: 3,4 + D9: 3,4 + E9: 1,5 + I7: 1,5 * CNT 5 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..32......2.89..47....41.5..4......6..8....2.....3.5.896...28..2..7......8...97.. | initial |
| 4.32...8..2.89..4787..4125..4..28..6..8....2...2.3.5.8967..28..2..78.....8...97.2 | autosolve |
| 413275689526893147879641253741528396358967421692134578967412835235786914184359762 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A2: 1,5 C3: 6,9 D3: 3,6 I1: 1,9 I3: 3,9 B6: 1,9 E7: 1,5 H7: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,D3: 3.. / F2 = 3 => 12 pairs (_) / D3 = 3 => 0 pairs (X) G2,I3: 3.. / G2 = 3 => 0 pairs (X) / I3 = 3 => 12 pairs (_) B8,A9: 3.. / B8 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) F2,G2: 3.. / F2 = 3 => 12 pairs (_) / G2 = 3 => 0 pairs (X) D3,I3: 3.. / D3 = 3 => 0 pairs (X) / I3 = 3 => 12 pairs (_) B5,B8: 3.. / B5 = 3 => 10 pairs (_) / B8 = 3 => 0 pairs (*) F2,F8: 3.. / F2 = 3 => 12 pairs (_) / F8 = 3 => 0 pairs (X) D6,F6: 4.. / D6 = 4 => 0 pairs (X) / F6 = 4 => 8 pairs (_) G5,I5: 4.. / G5 = 4 => 10 pairs (_) / I5 = 4 => 10 pairs (_) C8,C9: 4.. / C8 = 4 => 12 pairs (_) / C9 = 4 => 9 pairs (_) D7,I7: 4.. / D7 = 4 => 10 pairs (_) / I7 = 4 => 11 pairs (_) C9,D9: 4.. / C9 = 4 => 9 pairs (_) / D9 = 4 => 12 pairs (_) F6,F8: 4.. / F6 = 4 => 8 pairs (_) / F8 = 4 => 0 pairs (X) G5,G8: 4.. / G5 = 4 => 10 pairs (_) / G8 = 4 => 10 pairs (_) I7,I8: 5.. / I7 = 5 => 9 pairs (_) / I8 = 5 => 11 pairs (_) C2,C3: 6.. / C2 = 6 => 12 pairs (_) / C3 = 6 => 0 pairs (X) G1,G2: 6.. / G1 = 6 => 15 pairs (_) / G2 = 6 => 0 pairs (X) A5,A6: 6.. / A5 = 6 => 12 pairs (_) / A6 = 6 => 9 pairs (_) H8,H9: 6.. / H8 = 6 => 16 pairs (_) / H9 = 6 => 15 pairs (_) C3,D3: 6.. / C3 = 6 => 0 pairs (X) / D3 = 6 => 12 pairs (_) F8,H8: 6.. / F8 = 6 => 15 pairs (_) / H8 = 6 => 16 pairs (_) E1,F1: 7.. / E1 = 7 => 10 pairs (_) / F1 = 7 => 11 pairs (_) H4,H6: 7.. / H4 = 7 => 12 pairs (_) / H6 = 7 => 10 pairs (_) A4,H4: 7.. / A4 = 7 => 10 pairs (_) / H4 = 7 => 12 pairs (_) E1,E5: 7.. / E1 = 7 => 10 pairs (_) / E5 = 7 => 11 pairs (_) B1,C3: 9.. / B1 = 9 => 0 pairs (X) / C3 = 9 => 12 pairs (_) C3,I3: 9.. / C3 = 9 => 12 pairs (_) / I3 = 9 => 0 pairs (X) C3,C4: 9.. / C3 = 9 => 12 pairs (_) / C4 = 9 => 0 pairs (X) * DURATION: 0:00:28.966483 START: 01:47:11.081719 END: 01:47:40.048202 2019-05-01 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B6,C3,D3,E7,H7,I1,I3) * 4.32...8..2.89..4787..4125..4..28..6..8....2...2.3.5.8967..28..2..78.....8...97.2 * PAIR A2: 1,5 BLK 1 B1: 1,5,9 # reduction candidate for 1,5 B1: 1,5 # 12 pairs C2: 1,5,6 # reduction candidate for 1,5 C2: 1,5 => CTR * 4932...81125896347876341259.49.28136..8....2..12.3.5.8967..28..2..783.6.38...9712 C2: 6 # 12 pairs * PAIR A2: 1,5 COL A A4: 1,5,3,7 # reduction candidate for 1,5 A4: 1,5 => CTR * 4132..689526893147879641253145928376..8....2..92.3.518967..283.2..78.....8...97.2 A4: 3,7 # 9 pairs A5: 1,5,3,6,7 # reduction candidate for 1,5 A5: 1,5 # 12 pairs A9: 1,5,3 # reduction candidate for 1,5 A9: 1,5 => SOLVED * 413275689526893147879641253741528396358967421692134578967412835235786914184359762 A9: 3 # 10 pairs * PAIR D3: 3,6 BLK 2 F2: 3,6,5 # reduction candidate for 3,6 F2: 5 => CTR * 4.32...8..2.89534787.341259.49.281.6..8....2..12.3.5.8967..28..2..78.....8...97.2 F2: 3,6 # 15 pairs * PAIR D3: 3,6 COL D D9: 3,6,1,4,5 # reduction candidate for 3,6 D9: 3,6 # 11 pairs D9: 1,4,5 # 8 pairs * PAIR I1: 1,9 BLK 3 G1: 1,9,6 # reduction candidate for 1,9 G1: 1,9 => CTR * 4.32...8..2.89.64787634125..4..28..6..8....2...2.3.5.8967..28..2..78.....8...97.2 G1: 6 # 15 pairs * PAIR I1: 1,9 ROW 1 B1: 1,9,5 # reduction candidate for 1,9 B1: 5 => CTR * 4532...8.126895347879.4125..4..28..6..8....2...2.3.5.8967..28..2..78.....8...97.2 B1: 1,9 # 15 pairs * PAIR I1: 1,9 COL I I5: 1,9,3,4 # reduction candidate for 1,9 I5: 1,9 # 18 pairs I8: 1,9,3,4,5 # reduction candidate for 1,9 I8: 1,9 => CTR * 4.32..689.2689314787964125374..283163.8...92469213457896741283523178.4...843.97.2 I8: 3,4,5 # 8 pairs * PAIR I3: 3,9 COL I I5: 3,9,1,4 # reduction candidate for 3,9 I5: 3,9 # 13 pairs I8: 3,9,1,4,5 # reduction candidate for 3,9 I8: 3,9 => CTR * 4.32..981.2.89.64787..4125..4..28..6..8....24..2.345.89674128352..78.4.9.84..97.2 I8: 1,4,5 # 8 pairs * PAIR B6: 1,9 BLK 4 C4: 1,9,5 # reduction candidate for 1,9 C4: 1,9 # 11 pairs B5: 1,9,3,5 # reduction candidate for 1,9 B5: 1,9 => CTR * 4532...8.12.89..4787..4125..4..28..6..8....2...2.3.5.8967..28..23.78.....8...97.2 B5: 3,5 # 9 pairs * PAIR B6: 1,9 ROW 6 D6: 1,9,4,6 # reduction candidate for 1,9 D6: 1,9 # 9 pairs H6: 1,9,7 # reduction candidate for 1,9 H6: 1,9 # 12 pairs * PAIR B6: 1,9 COL B B1: 1,9,5 # reduction candidate for 1,9 B1: 5 => CTR * 4532...8.126895347879.4125..4..28..6..8....2...2.3.5.8967..28..2..78.....8...97.2 B1: 1,9 # 15 pairs * PAIR E7: 1,5 BLK 8 D7: 1,5,3,4 # reduction candidate for 1,5 D7: 1,5 # 20 pairs D9: 1,5,3,4,6 # reduction candidate for 1,5 D9: 1,5 # 20 pairs E9: 1,5,6 # reduction candidate for 1,5 E9: 1,5 # 15 pairs * PAIR E7: 1,5 ROW 7 I7: 1,5,3,4 # reduction candidate for 1,5 I7: 3,4 # 12 pairs I7: 1,5 # 10 pairs * PAIR E7: 1,5 COL E E5: 1,5,6,7 # reduction candidate for 1,5 E5: 1,5 # 20 pairs E5: 6,7 # 9 pairs * PAIR H7: 1,3 BLK 9 I7: 1,3,4,5 # reduction candidate for 1,3 I7: 1,3 => CTR * 4.32...8.12.893647876.4125..4..28..6..8....24..2.345.89674528..231786495584319762 I7: 4,5 # 9 pairs G8: 1,3,4,9 # reduction candidate for 1,3 G8: 1,3 => CTR * 4.3275689.2689314787964125374..28936..8.674216.2.345789673.28142.4786.9..8...9762 G8: 4,9 # 9 pairs H8: 1,3,6,9 # reduction candidate for 1,3 H8: 1,3 => SOLVED * 413275689526893147879641253741528396358967421692134578967412835235786914184359762 H8: 6,9 # 9 pairs I8: 1,3,4,5,9 # reduction candidate for 1,3 I8: 1,3 => CTR * 4.32...8952.893.47879641253.4..28..6..8.67.246.2.34578967412835235786491184359762 I8: 4,5,9 # 8 pairs H9: 1,3,6 # reduction candidate for 1,3 H9: 1,3 # 16 pairs * PAIR H7: 1,3 ROW 7 D7: 1,3,4,5 # reduction candidate for 1,3 D7: 1,3 # 13 pairs D7: 4,5 # 10 pairs * PAIR H7: 1,3 COL H H4: 1,3,7,9 # reduction candidate for 1,3 H4: 1,3 # 17 pairs H4: 7,9 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060814-absurd-base-pr-000.dot * REASONING * DIS # C2: 1,5 => CTR => C2: 6 * DIS # A4: 1,5 => CTR => A4: 3,7 * PRF # A9: 1,5 => SOL * DIS # F2: 5 => CTR => F2: 3,6 * DIS # G1: 1,9 => CTR => G1: 6 * DIS # B1: 5 => CTR => B1: 1,9 * DIS # I8: 1,9 => CTR => I8: 3,4,5 * DIS # I8: 3,9 => CTR => I8: 1,4,5 * DIS # B5: 1,9 => CTR => B5: 3,5 * DIS # B1: 5 => CTR => B1: 1,9 * DIS # I7: 1,3 => CTR => I7: 4,5 * DIS # G8: 1,3 => CTR => G8: 4,9 * PRF # H8: 1,3 => SOL * DIS # I8: 1,3 => CTR => I8: 4,5,9 * CNT 14 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B6,C3,D3,E7,H7,I1,I3) * 4.32...8..2.89..4787..4125..4..28..6..8....2...2.3.5.8967..28..2..78.....8...97.2 * PAIR A2: 1,5 BLK 1 B1: 1,5,9 # reduction candidate for 1,5 B1: 1,5 # 12 pairs C2: 1,5,6 # reduction candidate for 1,5 C2: 1,5 => CTR * 4932...81125896347876341259.49.28136..8....2..12.3.5.8967..28..2..783.6.38...9712 * PAIR RESTART * PAIR E7: 1,5 BLK 8 D7: 1,5,3,4 # reduction candidate for 1,5 D7: 1,5 => CTR * 4132..689526893147879641253.4..28..6..8....2..92.3.5.8967..283423.78.9.5185..97.2 D9: 1,5,3,4 # reduction candidate for 1,5 D9: 1,5 => CTR * 4132..689526893147879641253.4..28..6..8....2..92.3.5.89673.28142.1784.6538...97.2 E9: 1,5,6 # reduction candidate for 1,5 E9: 1,5 # 15 pairs * RESTART * PAIR E7: 1,5 BLK 8 E9: 1,5,6 # reduction candidate for 1,5 E9: 6 => CTR * 4132..68952689314787964125374..28..6..8....2.692134578967.1283523.785.6.18...97.2 * PAIR E7: 1,5 ROW 7 I7: 1,5,4 # reduction candidate for 1,5 I7: 1,5 => SOLVED * 413275689526893147879641253741528396358967421692134578967412835235786914184359762 * DURATION: 0:00:07.295343 START: 01:48:08.071468 END: 01:48:15.366811 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060814-absurd-base-pr-001.dot * REASONING * DIS # C2: 1,5 => CTR => C2: 6 * DIS C2: 6 # D7: 1,5 => CTR => D7: 3,4 * DIS C2: 6 + D7: 3,4 # D9: 1,5 => CTR => D9: 3,4 * DIS C2: 6 + D7: 3,4 + D9: 3,4 # E9: 6 => CTR => E9: 1,5 * PRF C2: 6 + D7: 3,4 + D9: 3,4 + E9: 1,5 # I7: 1,5 => SOL * STA C2: 6 + D7: 3,4 + D9: 3,4 + E9: 1,5 + I7: 1,5 * CNT 5 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060814, absurd
Solution
position: 413275689526893147879641253741528396358967421692134578967412835235786914184359762 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 # B1: 1,5 => UNS * DIS # C2: 1,5 => CTR => C2: 6 * INC # C2: 6 => UNS * DIS # A4: 1,5 => CTR => A4: 3,7 * INC # A4: 3,7 => UNS * INC # A5: 1,5 => UNS * PRF # A9: 1,5 => SOL * INC # A9: 3 => UNS * INC # F2: 3,6 => UNS * DIS # F2: 5 => CTR => F2: 3,6 * INC # D9: 3,6 => UNS * INC # D9: 1,4,5 => UNS * DIS # G1: 1,9 => CTR => G1: 6 * INC # G1: 6 => UNS * INC # B1: 1,9 => UNS * DIS # B1: 5 => CTR => B1: 1,9 * INC # I5: 1,9 => UNS * DIS # I8: 1,9 => CTR => I8: 3,4,5 * INC # I8: 3,4,5 => UNS * INC # I5: 3,9 => UNS * DIS # I8: 3,9 => CTR => I8: 1,4,5 * INC # I8: 1,4,5 => UNS * INC # C4: 1,9 => UNS * DIS # B5: 1,9 => CTR => B5: 3,5 * INC # B5: 3,5 => UNS * INC # D6: 1,9 => UNS * INC # H6: 1,9 => UNS * INC # B1: 1,9 => UNS * DIS # B1: 5 => CTR => B1: 1,9 * INC # D7: 1,5 => UNS * INC # D9: 1,5 => UNS * INC # E9: 1,5 => UNS * INC # I7: 1,5 => UNS * INC # I7: 3,4 => UNS * INC # E5: 1,5 => UNS * INC # E5: 6,7 => UNS * DIS # I7: 1,3 => CTR => I7: 4,5 * INC # I7: 4,5 => UNS * DIS # G8: 1,3 => CTR => G8: 4,9 * INC # G8: 4,9 => UNS * PRF # H8: 1,3 => SOL * INC # H8: 6,9 => UNS * DIS # I8: 1,3 => CTR => I8: 4,5,9 * INC # I8: 4,5,9 => UNS * INC # H9: 1,3 => UNS * INC # D7: 1,3 => UNS * INC # D7: 4,5 => UNS * INC # H4: 1,3 => UNS * INC # H4: 7,9 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 1,5 => UNS * DIS # C2: 1,5 => CTR => C2: 6 * DIS C2: 6 # D7: 1,5 => CTR => D7: 3,4 * DIS C2: 6 + D7: 3,4 # D9: 1,5 => CTR => D9: 3,4 * INC C2: 6 + D7: 3,4 + D9: 3,4 # E9: 1,5 => UNS * INC C2: 6 + D7: 3,4 + D9: 3,4 # E9: 1,5 => UNS * DIS C2: 6 + D7: 3,4 + D9: 3,4 # E9: 6 => CTR => E9: 1,5 * PRF C2: 6 + D7: 3,4 + D9: 3,4 + E9: 1,5 # I7: 1,5 => SOL * STA C2: 6 + D7: 3,4 + D9: 3,4 + E9: 1,5 + I7: 1,5 * CNT 8 HDP CHAINS / 8 HYP OPENED