Analysis of zz-www.sudokuoftheday.co.uk-20060816-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: ....4...1.1....63.7.2.......572...83.8179...4..........7..861...43.7...........9. initial
Autosolve
position: ....4..71.1...763.7.2...45..572..983.8179...4......71..7.38614..43.7..........397 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E9: 1 => SOL * DIS # G8: 5 => CTR => G8: 2,8 * DIS # I2: 2 => CTR => I2: 8,9 * DIS # A6: 4,6 => CTR => A6: 2,3,9 * DIS # C6: 4,6 => CTR => C6: 9 * PRF # C6: 9 => SOL * DIS # E3: 1,6 => CTR => E3: 3 * DIS # F6: 3,5 => CTR => F6: 4,8 * DIS # I6: 2,5 => CTR => I6: 6 * PRF # I6: 6 => SOL * DIS # G8: 2,5 => CTR => G8: 8 * DIS # I6: 5 => CTR => I6: 2,6 * DIS # A5: 3 => CTR => A5: 2,6 * PRF # A7: 5,9 => SOL * DIS # A7: 2 => CTR => A7: 5,9 * DIS # C1: 5,9 => CTR => C1: 6,8 * DIS # C2: 5,9 => CTR => C2: 4,8 * DIS # A9: 2,6 => CTR => A9: 1,5,8 * PRF # B6: 3,9 => SOL * DIS # G8: 2,5 => CTR => G8: 8 * PRF # I8: 2,5 => SOL * DIS # A7: 2,5 => CTR => A7: 9 * PRF # A7: 9 => SOL * DIS # I6: 2,5 => CTR => I6: 6 * PRF # I6: 6 => SOL * DIS # I8: 2,6 => CTR => I8: 5,8 * PRF # I8: 5,8 => SOL * CNT 27 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E9: 1 => SOL * STA E9: 1 * CNT 1 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....4...1.1....63.7.2.......572...83.8179...4..........7..861...43.7...........9. | initial |
| ....4..71.1...763.7.2...45..572..983.8179...4......71..7.38614..43.7..........397 | autosolve |
| 398645271514827639762139458457261983681793524239458716975386142143972865826514397 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) E2: 2,5 G1: 2,8 I3: 8,9 A4: 4,6 E4: 1,6 F4: 1,4 F5: 3,5 G5: 2,5 H5: 2,6 C7: 5,9 B9: 2,6 I7: 2,5 H8: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,F4: 1.. / E4 = 1 => 0 pairs (X) / F4 = 1 => 15 pairs (_) A8,A9: 1.. / A8 = 1 => 14 pairs (_) / A9 = 1 => 24 pairs (_) F1,E2: 2.. / F1 = 2 => 0 pairs (X) / E2 = 2 => 15 pairs (_) G1,I2: 2.. / G1 = 2 => 15 pairs (_) / I2 = 2 => 0 pairs (X) F1,G1: 2.. / F1 = 2 => 0 pairs (X) / G1 = 2 => 15 pairs (_) E2,I2: 2.. / E2 = 2 => 15 pairs (_) / I2 = 2 => 0 pairs (X) A7,I7: 2.. / A7 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) B6,B9: 2.. / B6 = 2 => 17 pairs (_) / B9 = 2 => 0 pairs (*) E2,E9: 2.. / E2 = 2 => 15 pairs (_) / E9 = 2 => 0 pairs (X) H5,H8: 2.. / H5 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) A5,F5: 3.. / A5 = 3 => 0 pairs (X) / F5 = 3 => 16 pairs (_) E3,E6: 3.. / E3 = 3 => 15 pairs (_) / E6 = 3 => 0 pairs (X) A2,C2: 4.. / A2 = 4 => 0 pairs (X) / C2 = 4 => 14 pairs (_) D9,F9: 4.. / D9 = 4 => 13 pairs (_) / F9 = 4 => 15 pairs (_) A4,F4: 4.. / A4 = 4 => 15 pairs (_) / F4 = 4 => 0 pairs (X) C2,C6: 4.. / C2 = 4 => 14 pairs (_) / C6 = 4 => 0 pairs (X) D6,D9: 4.. / D6 = 4 => 15 pairs (_) / D9 = 4 => 13 pairs (_) G5,I6: 5.. / G5 = 5 => 16 pairs (_) / I6 = 5 => 0 pairs (X) F5,G5: 5.. / F5 = 5 => 0 pairs (X) / G5 = 5 => 16 pairs (_) G5,G8: 5.. / G5 = 5 => 16 pairs (_) / G8 = 5 => 0 pairs (X) H5,I6: 6.. / H5 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) H8,I8: 6.. / H8 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) A4,E4: 6.. / A4 = 6 => 0 pairs (X) / E4 = 6 => 15 pairs (_) A5,H5: 6.. / A5 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) H5,H8: 6.. / H5 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) I6,I8: 6.. / I6 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) D6,F6: 8.. / D6 = 8 => 15 pairs (_) / F6 = 8 => 13 pairs (_) A9,C9: 8.. / A9 = 8 => 15 pairs (_) / C9 = 8 => 13 pairs (_) G8,I8: 8.. / G8 = 8 => 15 pairs (_) / I8 = 8 => 0 pairs (X) G1,G8: 8.. / G1 = 8 => 0 pairs (X) / G8 = 8 => 15 pairs (_) I2,I3: 9.. / I2 = 9 => 15 pairs (_) / I3 = 9 => 15 pairs (_) A7,C7: 9.. / A7 = 9 => 0 pairs (*) / C7 = 9 => 0 pairs (X) D8,F8: 9.. / D8 = 9 => 14 pairs (_) / F8 = 9 => 18 pairs (_) * DURATION: 0:00:33.751323 START: 01:49:43.935072 END: 01:50:17.686395 2019-05-01 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B9,C7,E2,E4,F4,F5,G1,G5,H5,H8,I3,I7) * ....4..71.1...763.7.2...45..572..983.8179...4......71..7.38614..43.7..........397 * PAIR E2: 2,5 BLK 2 F1: 2,5,3,8,9 # reduction candidate for 2,5 F1: 3,8,9 # 19 pairs F1: 2,5 # 16 pairs * PAIR E2: 2,5 COL E E9: 2,5,1 # reduction candidate for 2,5 E9: 1 => SOLVED * 398645271514827639762139458457261983681793524239458716975386142143972865826514397 E9: 2,5 # 15 pairs * PAIR G1: 2,8 BLK 3 I2: 2,8,9 # reduction candidate for 2,8 I2: 9 # 15 pairs I2: 2,8 # 15 pairs * PAIR G1: 2,8 ROW 1 F1: 2,8,3,5,9 # reduction candidate for 2,8 F1: 2,8 # 20 pairs F1: 3,5,9 # 16 pairs * PAIR G1: 2,8 COL G G8: 2,8,5 # reduction candidate for 2,8 G8: 5 => CTR * ....4.871.1...76327.2...459.572..983.8179.264......715.7.38614..43.7..........397 G8: 2,8 # 16 pairs * PAIR I3: 8,9 BLK 3 I2: 8,9,2 # reduction candidate for 8,9 I2: 2 => CTR * ....42871.1..57632732...459.572..983.8179.524.2..3.71.279386145.43.7...8.6..2.397 I2: 8,9 # 15 pairs * PAIR I3: 8,9 ROW 3 D3: 8,9,1,6 # reduction candidate for 8,9 D3: 8,9 # 18 pairs F3: 8,9,1,3 # reduction candidate for 8,9 F3: 8,9 # 16 pairs * PAIR A4: 4,6 BLK 4 A6: 4,6,2,3,9 # reduction candidate for 4,6 A6: 4,6 => CTR * ....4..71.14..763.7.2...45..572..983.8179..64..9...71.975386142.43.7..........397 A6: 2,3,9 # 13 pairs C6: 4,6,9 # reduction candidate for 4,6 C6: 4,6 => CTR * ....4..71.1...763.7.2...45..572..983.8179..64......71.279386145.43.7.826......397 C6: 9 => SOLVED * 398645271514827639762139458457261983681793524239458716975386142143972865826514397 * PAIR E4: 1,6 COL E E3: 1,6,3 # reduction candidate for 1,6 E3: 1,6 => CTR * ....4..71.1...763.7.2...45..572..983381795264....3.715.7.386142.43.7..........397 E3: 3 # 15 pairs * PAIR F4: 1,4 COL F F9: 1,4,2,5 # reduction candidate for 1,4 F9: 2,5 # 14 pairs F9: 1,4 # 14 pairs * PAIR F5: 3,5 BLK 5 E6: 3,5,6 # reduction candidate for 3,5 E6: 3,5 # 15 pairs F6: 3,5,4,8 # reduction candidate for 3,5 F6: 3,5 => CTR * ....4..71.1...763.7.2.3.45.657214983.8179..64...86.71.279386145.43.7.826...4..397 F6: 4,8 # 14 pairs * PAIR F5: 3,5 COL F F1: 3,5,2,8,9 # reduction candidate for 3,5 F1: 3,5 # 20 pairs F1: 2,8,9 # 14 pairs * PAIR G5: 2,5 BLK 6 I6: 2,5,6 # reduction candidate for 2,5 I6: 2,5 => CTR * ....4..71.1...763.7.2...45..572..983.8179..64......71.279386145.43.7.826......397 I6: 6 => SOLVED * 398645271514827639762139458457261983681793524239458716975386142143972865826514397 * PAIR G5: 2,5 COL G G8: 2,5,8 # reduction candidate for 2,5 G8: 2,5 => CTR * ....42871.1..57632732...459.572..9836817935243.....71.279386145.43.7.268.6..2.397 G8: 8 # 15 pairs * PAIR H5: 2,6 BLK 6 I6: 2,6,5 # reduction candidate for 2,6 I6: 5 => CTR * ....4..71.1...763.7.2...45..572..983.8179..64......715.7.386142.43.7..........397 I6: 2,6 # 16 pairs * PAIR H5: 2,6 ROW 5 A5: 2,6,3 # reduction candidate for 2,6 A5: 3 => CTR * ....4..71.1...763.7.2...45..572..983381795264......715.7.386142.43.7..........397 A5: 2,6 # 16 pairs * PAIR C7: 5,9 BLK 7 A7: 5,9,2 # reduction candidate for 5,9 A7: 5,9 => SOLVED * 398645271514827639762139458457261983681793524239458716975386142143972865826514397 A7: 2 => CTR * ..6.4..71.1...763.7.26..45..57261983681793524.2....716279386145.43.7..6..6....397 * PAIR C7: 5,9 COL C C1: 5,9,6,8 # reduction candidate for 5,9 C1: 5,9 => CTR * ....4..71.1...763.7.2...45..572..983.8179..64......71.279386145.43.7.826......397 C1: 6,8 # 14 pairs C2: 5,9,4,8 # reduction candidate for 5,9 C2: 5,9 => CTR * ....4..7141...763.7.2...45.657214983.8179..64..4...71.279386145.43.7.826...4..397 C2: 4,8 # 14 pairs * PAIR B9: 2,6 BLK 7 A9: 2,6,1,5,8 # reduction candidate for 2,6 A9: 2,6 => CTR * ..6.4.271.1..2763.7.26314584572..983681793524......716.7.386142143972865268...397 A9: 1,5,8 # 13 pairs * PAIR B9: 2,6 COL B B6: 2,6,3,9 # reduction candidate for 2,6 B6: 3,9 => SOLVED * 398645271514827639762139458457261983681793524239458716975386142143972865826514397 B6: 2,6 # 16 pairs * PAIR I7: 2,5 BLK 9 G8: 2,5,8 # reduction candidate for 2,5 G8: 2,5 => CTR * ....42871.1..57632732...459.572..9836817935243.....71.279386145.43.7.268.6..2.397 G8: 8 # 15 pairs I8: 2,5,6,8 # reduction candidate for 2,5 I8: 2,5 => SOLVED * 398645271514827639762139458457261983681793524239458716975386142143972865826514397 I8: 6,8 # 14 pairs * PAIR I7: 2,5 ROW 7 A7: 2,5,9 # reduction candidate for 2,5 A7: 2,5 => CTR * ....4..71.1...763.7.2...45..572..983.8179..64......71.279386145.43.7.826......397 A7: 9 => SOLVED * 398645271514827639762139458457261983681793524239458716975386142143972865826514397 * PAIR I7: 2,5 COL I I6: 2,5,6 # reduction candidate for 2,5 I6: 2,5 => CTR * ....4..71.1...763.7.2...45..572..983.8179..64......71.279386145.43.7.826......397 I6: 6 => SOLVED * 398645271514827639762139458457261983681793524239458716975386142143972865826514397 * PAIR H8: 2,6 BLK 9 I8: 2,6,5,8 # reduction candidate for 2,6 I8: 2,6 => CTR * ....4.271.1..2763.7.2.3.45..572..983681793524.24...71.279386145.43.7.8...6...2397 I8: 5,8 => SOLVED * 398645271514827639762139458457261983681793524239458716975386142143972865826514397 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060816-absurd-base-pr-000.dot * REASONING * PRF # E9: 1 => SOL * DIS # G8: 5 => CTR => G8: 2,8 * DIS # I2: 2 => CTR => I2: 8,9 * DIS # A6: 4,6 => CTR => A6: 2,3,9 * DIS # C6: 4,6 => CTR => C6: 9 * PRF # C6: 9 => SOL * DIS # E3: 1,6 => CTR => E3: 3 * DIS # F6: 3,5 => CTR => F6: 4,8 * DIS # I6: 2,5 => CTR => I6: 6 * PRF # I6: 6 => SOL * DIS # G8: 2,5 => CTR => G8: 8 * DIS # I6: 5 => CTR => I6: 2,6 * DIS # A5: 3 => CTR => A5: 2,6 * PRF # A7: 5,9 => SOL * DIS # A7: 2 => CTR => A7: 5,9 * DIS # C1: 5,9 => CTR => C1: 6,8 * DIS # C2: 5,9 => CTR => C2: 4,8 * DIS # A9: 2,6 => CTR => A9: 1,5,8 * PRF # B6: 3,9 => SOL * DIS # G8: 2,5 => CTR => G8: 8 * PRF # I8: 2,5 => SOL * DIS # A7: 2,5 => CTR => A7: 9 * PRF # A7: 9 => SOL * DIS # I6: 2,5 => CTR => I6: 6 * PRF # I6: 6 => SOL * DIS # I8: 2,6 => CTR => I8: 5,8 * PRF # I8: 5,8 => SOL * CNT 27 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B9,C7,E2,E4,F4,F5,G1,G5,H5,H8,I3,I7) * ....4..71.1...763.7.2...45..572..983.8179...4......71..7.38614..43.7..........397 * PAIR E2: 2,5 BLK 2 F1: 2,5,3,8,9 # reduction candidate for 2,5 F1: 3,8,9 # 19 pairs F1: 2,5 # 16 pairs * PAIR E2: 2,5 COL E E9: 2,5,1 # reduction candidate for 2,5 E9: 1 => SOLVED * 398645271514827639762139458457261983681793524239458716975386142143972865826514397 * DURATION: 0:00:03.332469 START: 01:50:51.817052 END: 01:50:55.149521 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060816-absurd-base-pr-001.dot * REASONING * PRF # E9: 1 => SOL * STA E9: 1 * CNT 1 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060816, absurd
Solution
position: 398645271514827639762139458457261983681793524239458716975386142143972865826514397 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 # F1: 2,5 => UNS * INC # F1: 3,8,9 => UNS * INC # E9: 2,5 => UNS * PRF # E9: 1 => SOL * INC # I2: 2,8 => UNS * INC # I2: 9 => UNS * INC # F1: 2,8 => UNS * INC # F1: 3,5,9 => UNS * INC # G8: 2,8 => UNS * DIS # G8: 5 => CTR => G8: 2,8 * INC # I2: 8,9 => UNS * DIS # I2: 2 => CTR => I2: 8,9 * INC # D3: 8,9 => UNS * INC # F3: 8,9 => UNS * DIS # A6: 4,6 => CTR => A6: 2,3,9 * INC # A6: 2,3,9 => UNS * DIS # C6: 4,6 => CTR => C6: 9 * PRF # C6: 9 => SOL * DIS # E3: 1,6 => CTR => E3: 3 * INC # E3: 3 => UNS * INC # F9: 1,4 => UNS * INC # F9: 2,5 => UNS * INC # E6: 3,5 => UNS * DIS # F6: 3,5 => CTR => F6: 4,8 * INC # F6: 4,8 => UNS * INC # F1: 3,5 => UNS * INC # F1: 2,8,9 => UNS * DIS # I6: 2,5 => CTR => I6: 6 * PRF # I6: 6 => SOL * DIS # G8: 2,5 => CTR => G8: 8 * INC # G8: 8 => UNS * INC # I6: 2,6 => UNS * DIS # I6: 5 => CTR => I6: 2,6 * INC # A5: 2,6 => UNS * DIS # A5: 3 => CTR => A5: 2,6 * PRF # A7: 5,9 => SOL * DIS # A7: 2 => CTR => A7: 5,9 * DIS # C1: 5,9 => CTR => C1: 6,8 * INC # C1: 6,8 => UNS * DIS # C2: 5,9 => CTR => C2: 4,8 * INC # C2: 4,8 => UNS * DIS # A9: 2,6 => CTR => A9: 1,5,8 * INC # A9: 1,5,8 => UNS * INC # B6: 2,6 => UNS * PRF # B6: 3,9 => SOL * DIS # G8: 2,5 => CTR => G8: 8 * INC # G8: 8 => UNS * PRF # I8: 2,5 => SOL * INC # I8: 6,8 => UNS * DIS # A7: 2,5 => CTR => A7: 9 * PRF # A7: 9 => SOL * DIS # I6: 2,5 => CTR => I6: 6 * PRF # I6: 6 => SOL * DIS # I8: 2,6 => CTR => I8: 5,8 * PRF # I8: 5,8 => SOL * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 2,5 => UNS * INC # F1: 3,8,9 => UNS * INC # E9: 2,5 => UNS * PRF # E9: 1 => SOL * STA E9: 1 * CNT 4 HDP CHAINS / 4 HYP OPENED