Analysis of zz-www.sudokuoftheday.co.uk-20060508-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: .1.....5.8...67.....34..8..5.82...969..78.5....1..5.8.1......37.8....9...37...... initial
Autosolve
position: 71....65.8...67.....34..87.5.82...969..78.5..3.1..5.8.1......37.8..7.9.5.37.....8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I5: 2,4 => CTR => I5: 1,3 * DIS # C5: 4 => CTR => C5: 2,6 * PRF # E9: 2,4 => SOL * DIS # H9: 2,4 => CTR => H9: 1,6 * DIS # G2: 2,4 => CTR => G2: 1,3 * CNT 5 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:
* DIS # I5: 2,4 => CTR => I5: 1,3 * DIS I5: 1,3 # C5: 4 => CTR => C5: 2,6 * DIS I5: 1,3 + C5: 2,6 # F8: 2,4 => CTR => F8: 1,3 * PRF I5: 1,3 + C5: 2,6 + F8: 1,3 # E9: 2,4 => SOL * STA I5: 1,3 + C5: 2,6 + F8: 1,3 + E9: 2,4 * CNT 4 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1.....5.8...67.....34..8..5.82...969..78.5....1..5.8.1......37.8....9...37...... | initial |
| 71....65.8...67.....34..87.5.82...969..78.5..3.1..5.8.1......37.8..7.9.5.37.....8 | autosolve |
| 714938652825167349693452871548213796962784513371695284159826437486371925237549168 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A3: 2,6 B4: 4,7 D6: 6,9 E6: 4,9 I6: 2,4 B7: 5,9 C7: 5,9 C8: 2,6 D7: 6,8 E7: 2,4 F7: 6,8 D8: 1,3 G7: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E7,G7: 2.. / E7 = 2 => 14 pairs (_) / G7 = 2 => 12 pairs (_) G4,I5: 3.. / G4 = 3 => 18 pairs (_) / I5 = 3 => 14 pairs (_) D8,F8: 3.. / D8 = 3 => 15 pairs (_) / F8 = 3 => 0 pairs (X) F5,I5: 3.. / F5 = 3 => 18 pairs (_) / I5 = 3 => 14 pairs (_) E1,E4: 3.. / E1 = 3 => 16 pairs (_) / E4 = 3 => 22 pairs (_) G2,G4: 3.. / G2 = 3 => 14 pairs (_) / G4 = 3 => 18 pairs (_) A8,A9: 4.. / A8 = 4 => 14 pairs (_) / A9 = 4 => 17 pairs (_) C1,I1: 4.. / C1 = 4 => 15 pairs (_) / I1 = 4 => 18 pairs (_) E7,G7: 4.. / E7 = 4 => 12 pairs (_) / G7 = 4 => 14 pairs (_) D2,E3: 5.. / D2 = 5 => 18 pairs (_) / E3 = 5 => 13 pairs (_) B7,C7: 5.. / B7 = 5 => 12 pairs (_) / C7 = 5 => 11 pairs (_) D9,E9: 5.. / D9 = 5 => 13 pairs (_) / E9 = 5 => 18 pairs (_) B3,E3: 5.. / B3 = 5 => 18 pairs (_) / E3 = 5 => 13 pairs (_) C2,C7: 5.. / C2 = 5 => 12 pairs (_) / C7 = 5 => 11 pairs (_) D2,D9: 5.. / D2 = 5 => 18 pairs (_) / D9 = 5 => 13 pairs (_) E3,E9: 5.. / E3 = 5 => 13 pairs (_) / E9 = 5 => 18 pairs (_) A3,B3: 6.. / A3 = 6 => 14 pairs (_) / B3 = 6 => 0 pairs (X) F5,D6: 6.. / F5 = 6 => 0 pairs (X) / D6 = 6 => 11 pairs (_) D7,F7: 6.. / D7 = 6 => 0 pairs (X) / F7 = 6 => 11 pairs (_) H8,H9: 6.. / H8 = 6 => 0 pairs (X) / H9 = 6 => 14 pairs (_) B6,D6: 6.. / B6 = 6 => 0 pairs (X) / D6 = 6 => 11 pairs (_) A9,H9: 6.. / A9 = 6 => 0 pairs (X) / H9 = 6 => 14 pairs (_) C5,C8: 6.. / C5 = 6 => 0 pairs (X) / C8 = 6 => 14 pairs (_) D6,D7: 6.. / D6 = 6 => 11 pairs (_) / D7 = 6 => 0 pairs (X) F5,F7: 6.. / F5 = 6 => 0 pairs (X) / F7 = 6 => 11 pairs (_) B4,B6: 7.. / B4 = 7 => 12 pairs (_) / B6 = 7 => 23 pairs (_) G4,G6: 7.. / G4 = 7 => 23 pairs (_) / G6 = 7 => 12 pairs (_) B4,G4: 7.. / B4 = 7 => 12 pairs (_) / G4 = 7 => 23 pairs (_) B6,G6: 7.. / B6 = 7 => 23 pairs (_) / G6 = 7 => 12 pairs (_) D1,F1: 8.. / D1 = 8 => 0 pairs (X) / F1 = 8 => 11 pairs (_) D7,F7: 8.. / D7 = 8 => 11 pairs (_) / F7 = 8 => 0 pairs (X) D1,D7: 8.. / D1 = 8 => 0 pairs (X) / D7 = 8 => 11 pairs (_) F1,F7: 8.. / F1 = 8 => 11 pairs (_) / F7 = 8 => 0 pairs (X) D6,E6: 9.. / D6 = 9 => 0 pairs (X) / E6 = 9 => 11 pairs (_) B7,C7: 9.. / B7 = 9 => 11 pairs (_) / C7 = 9 => 12 pairs (_) * DURATION: 0:00:39.402386 START: 22:59:47.519710 END: 23:00:26.922096 2019-04-30 * CP COUNT: (35) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B4,B7,C7,C8,D6,D7,D8,E6,E7,F7,G7,I6) * 71....65.8...67.....34..87.5.82...969..78.5..3.1..5.8.1......37.8..7.9.5.37.....8 * PAIR A3: 2,6 BLK 1 B3: 2,6,5,9 # reduction candidate for 2,6 B3: 2,6 # 19 pairs B3: 5,9 # 16 pairs * PAIR A3: 2,6 COL A A8: 2,6,4 # reduction candidate for 2,6 A8: 2,6 # 17 pairs A9: 2,6,4 # reduction candidate for 2,6 A9: 2,6 # 14 pairs * PAIR B4: 4,7 BLK 4 B6: 4,7,2,6 # reduction candidate for 4,7 B6: 4,7 # 16 pairs B6: 2,6 # 14 pairs * PAIR B4: 4,7 ROW 4 G4: 4,7,1,3 # reduction candidate for 4,7 G4: 4,7 # 23 pairs G4: 1,3 # 13 pairs * PAIR E6: 4,9 COL E E9: 4,9,1,2,5 # reduction candidate for 4,9 E9: 4,9 # 24 pairs E9: 1,2,5 # 13 pairs * PAIR I6: 2,4 BLK 6 H5: 2,4,1 # reduction candidate for 2,4 H5: 2,4 # 15 pairs I5: 2,4,1,3 # reduction candidate for 2,4 I5: 2,4 => CTR * 71.93865.8..167..3..345.87.5.82..3969..78351.3.169578.1..8.6.37.8.3719.5.37...1.8 I5: 1,3 # 14 pairs G6: 2,4,7 # reduction candidate for 2,4 G6: 2,4 # 23 pairs * PAIR I6: 2,4 ROW 6 B6: 2,4,6,7 # reduction candidate for 2,4 B6: 6,7 # 15 pairs B6: 2,4 # 11 pairs * PAIR I6: 2,4 COL I I1: 2,4,3,9 # reduction candidate for 2,4 I1: 2,4 # 16 pairs I2: 2,4,1,3,9 # reduction candidate for 2,4 I2: 2,4 # 24 pairs * PAIR B7: 5,9 COL B B2: 5,9,2,4 # reduction candidate for 5,9 B2: 5,9 # 19 pairs B3: 5,9,2,6 # reduction candidate for 5,9 B3: 5,9 # 16 pairs * PAIR C7: 5,9 COL C C2: 5,9,2,4 # reduction candidate for 5,9 C2: 2,4 # 21 pairs C2: 5,9 # 15 pairs * PAIR C8: 2,6 BLK 7 A8: 2,6,4 # reduction candidate for 2,6 A8: 2,6 # 17 pairs A9: 2,6,4 # reduction candidate for 2,6 A9: 2,6 # 14 pairs * PAIR C8: 2,6 ROW 8 H8: 2,6,1,4 # reduction candidate for 2,6 H8: 2,6 # 17 pairs H8: 1,4 # 16 pairs * PAIR C8: 2,6 COL C C5: 2,6,4 # reduction candidate for 2,6 C5: 4 => CTR * 71....65484..67.2.6.34..87.5782.43969.478.5..3.1..57821......37.86.7.945437...168 C5: 2,6 # 15 pairs * PAIR E7: 2,4 BLK 8 F8: 2,4,1,3 # reduction candidate for 2,4 F8: 2,4 # 28 pairs E9: 2,4,1,5,9 # reduction candidate for 2,4 E9: 2,4 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486371925237549168 E9: 1,5,9 # 13 pairs F9: 2,4,1,9 # reduction candidate for 2,4 F9: 2,4 # 19 pairs * PAIR D8: 1,3 BLK 8 F8: 1,3,2,4 # reduction candidate for 1,3 F8: 2,4 # 28 pairs F8: 1,3 # 15 pairs * PAIR D8: 1,3 COL D D2: 1,3,5,9 # reduction candidate for 1,3 D2: 5,9 # 17 pairs D2: 1,3 # 15 pairs * PAIR G7: 2,4 BLK 9 H8: 2,4,1,6 # reduction candidate for 2,4 H8: 2,4 # 17 pairs G9: 2,4,1 # reduction candidate for 2,4 G9: 2,4 # 20 pairs H9: 2,4,1,6 # reduction candidate for 2,4 H9: 2,4 => CTR * 71....65.8...67...26345.87.5.821..969.678.5..3.1695.8.1..8.6.37482.7.9656375.91.8 H9: 1,6 # 14 pairs * PAIR G7: 2,4 COL G G2: 2,4,1,3 # reduction candidate for 2,4 G2: 2,4 => CTR * 71.93865.8..167..3..345.87.5.82..3969..7835..3.169578.1..8.6.37.8.37.9.5.37...1.8 G2: 1,3 # 14 pairs G6: 2,4,7 # reduction candidate for 2,4 G6: 2,4 # 23 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060508-absurd-base-pr-000.dot * REASONING * DIS # I5: 2,4 => CTR => I5: 1,3 * DIS # C5: 4 => CTR => C5: 2,6 * PRF # E9: 2,4 => SOL * DIS # H9: 2,4 => CTR => H9: 1,6 * DIS # G2: 2,4 => CTR => G2: 1,3 * CNT 5 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B4,B7,C7,C8,D6,D7,D8,E6,E7,F7,G7,I6) * 71....65.8...67.....34..87.5.82...969..78.5..3.1..5.8.1......37.8..7.9.5.37.....8 * PAIR A3: 2,6 BLK 1 B3: 2,6,5,9 # reduction candidate for 2,6 B3: 2,6 # 19 pairs B3: 5,9 # 16 pairs * PAIR A3: 2,6 COL A A8: 2,6,4 # reduction candidate for 2,6 A8: 2,6 # 17 pairs A9: 2,6,4 # reduction candidate for 2,6 A9: 2,6 # 14 pairs * PAIR B4: 4,7 BLK 4 B6: 4,7,2,6 # reduction candidate for 4,7 B6: 4,7 # 16 pairs B6: 2,6 # 14 pairs * PAIR B4: 4,7 ROW 4 G4: 4,7,1,3 # reduction candidate for 4,7 G4: 4,7 # 23 pairs G4: 1,3 # 13 pairs * PAIR E6: 4,9 COL E E9: 4,9,1,2,5 # reduction candidate for 4,9 E9: 4,9 # 24 pairs E9: 1,2,5 # 13 pairs * PAIR I6: 2,4 BLK 6 H5: 2,4,1 # reduction candidate for 2,4 H5: 2,4 # 15 pairs I5: 2,4,1,3 # reduction candidate for 2,4 I5: 2,4 => CTR * 71.93865.8..167..3..345.87.5.82..3969..78351.3.169578.1..8.6.37.8.3719.5.37...1.8 G6: 2,4,7 # reduction candidate for 2,4 G6: 2,4 # 23 pairs * PAIR I6: 2,4 ROW 6 B6: 2,4,6,7 # reduction candidate for 2,4 B6: 6,7 # 16 pairs B6: 2,4 # 12 pairs * PAIR I6: 2,4 COL I I1: 2,4,3,9 # reduction candidate for 2,4 I1: 2,4 # 16 pairs I2: 2,4,1,3,9 # reduction candidate for 2,4 I2: 2,4 # 24 pairs * PAIR RESTART * PAIR I6: 2,4 BLK 6 H5: 2,4,1 # reduction candidate for 2,4 H5: 2,4 # 15 pairs G6: 2,4,7 # reduction candidate for 2,4 G6: 2,4 # 23 pairs * PAIR I6: 2,4 ROW 6 B6: 2,4,6,7 # reduction candidate for 2,4 B6: 6,7 # 16 pairs B6: 2,4 # 12 pairs * PAIR I6: 2,4 COL I I1: 2,4,3,9 # reduction candidate for 2,4 I1: 2,4 # 16 pairs I2: 2,4,1,3,9 # reduction candidate for 2,4 I2: 2,4 # 24 pairs * PAIR B7: 5,9 COL B B2: 5,9,2,4 # reduction candidate for 5,9 B2: 5,9 # 20 pairs B3: 5,9,2,6 # reduction candidate for 5,9 B3: 5,9 # 17 pairs * PAIR C7: 5,9 COL C C2: 5,9,2,4 # reduction candidate for 5,9 C2: 2,4 # 21 pairs C2: 5,9 # 16 pairs * PAIR C8: 2,6 BLK 7 A8: 2,6,4 # reduction candidate for 2,6 A8: 2,6 # 18 pairs A9: 2,6,4 # reduction candidate for 2,6 A9: 2,6 # 15 pairs * PAIR C8: 2,6 ROW 8 H8: 2,6,1,4 # reduction candidate for 2,6 H8: 2,6 # 18 pairs H8: 1,4 # 17 pairs * PAIR C8: 2,6 COL C C5: 2,6,4 # reduction candidate for 2,6 C5: 4 => CTR * 71....65484..67.2.6.34..87.5782.43969.478.5..3.1..57821......37.86.7.945437...168 * PAIR RESTART * PAIR C8: 2,6 BLK 7 A8: 2,6,4 # reduction candidate for 2,6 A8: 2,6 # 20 pairs A9: 2,6,4 # reduction candidate for 2,6 A9: 2,6 # 17 pairs * PAIR C8: 2,6 ROW 8 H8: 2,6,1,4 # reduction candidate for 2,6 H8: 2,6 # 20 pairs H8: 1,4 # 19 pairs * PAIR E7: 2,4 BLK 8 F8: 2,4,1,3 # reduction candidate for 2,4 F8: 2,4 => CTR * 71493865282..67.4.6.34..87.5782...969..78.5..3.169578.1..8.6.37.8.37.915.37..9.68 E9: 2,4,5,9 # reduction candidate for 2,4 E9: 2,4 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486371925237549168 * DURATION: 0:00:25.013795 START: 23:00:54.047387 END: 23:01:19.061182 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060508-absurd-base-pr-001.dot * REASONING * DIS # I5: 2,4 => CTR => I5: 1,3 * DIS I5: 1,3 # C5: 4 => CTR => C5: 2,6 * DIS I5: 1,3 + C5: 2,6 # F8: 2,4 => CTR => F8: 1,3 * PRF I5: 1,3 + C5: 2,6 + F8: 1,3 # E9: 2,4 => SOL * STA I5: 1,3 + C5: 2,6 + F8: 1,3 + E9: 2,4 * CNT 4 HDP CHAINS / 39 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060508, absurd
Solution
position: 714938652825167349693452871548213796962784513371695284159826437486371925237549168 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 # B3: 2,6 => UNS * INC # B3: 5,9 => UNS * INC # A8: 2,6 => UNS * INC # A9: 2,6 => UNS * INC # B6: 4,7 => UNS * INC # B6: 2,6 => UNS * INC # G4: 4,7 => UNS * INC # G4: 1,3 => UNS * INC # E9: 4,9 => UNS * INC # E9: 1,2,5 => UNS * INC # H5: 2,4 => UNS * DIS # I5: 2,4 => CTR => I5: 1,3 * INC # I5: 1,3 => UNS * INC # G6: 2,4 => UNS * INC # B6: 2,4 => UNS * INC # B6: 6,7 => UNS * INC # I1: 2,4 => UNS * INC # I2: 2,4 => UNS * INC # B2: 5,9 => UNS * INC # B3: 5,9 => UNS * INC # C2: 5,9 => UNS * INC # C2: 2,4 => UNS * INC # A8: 2,6 => UNS * INC # A9: 2,6 => UNS * INC # H8: 2,6 => UNS * INC # H8: 1,4 => UNS * INC # C5: 2,6 => UNS * DIS # C5: 4 => CTR => C5: 2,6 * INC # F8: 2,4 => UNS * PRF # E9: 2,4 => SOL * INC # E9: 1,5,9 => UNS * INC # F9: 2,4 => UNS * INC # F8: 1,3 => UNS * INC # F8: 2,4 => UNS * INC # D2: 1,3 => UNS * INC # D2: 5,9 => UNS * INC # H8: 2,4 => UNS * INC # G9: 2,4 => UNS * DIS # H9: 2,4 => CTR => H9: 1,6 * INC # H9: 1,6 => UNS * DIS # G2: 2,4 => CTR => G2: 1,3 * INC # G2: 1,3 => UNS * INC # G6: 2,4 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 2,6 => UNS * INC # B3: 5,9 => UNS * INC # A8: 2,6 => UNS * INC # A9: 2,6 => UNS * INC # B6: 4,7 => UNS * INC # B6: 2,6 => UNS * INC # G4: 4,7 => UNS * INC # G4: 1,3 => UNS * INC # E9: 4,9 => UNS * INC # E9: 1,2,5 => UNS * INC # H5: 2,4 => UNS * DIS # I5: 2,4 => CTR => I5: 1,3 * INC I5: 1,3 # G6: 2,4 => UNS * INC I5: 1,3 # B6: 2,4 => UNS * INC I5: 1,3 # B6: 6,7 => UNS * INC I5: 1,3 # I1: 2,4 => UNS * INC I5: 1,3 # I2: 2,4 => UNS * INC I5: 1,3 # H5: 2,4 => UNS * INC I5: 1,3 # G6: 2,4 => UNS * INC I5: 1,3 # B6: 2,4 => UNS * INC I5: 1,3 # B6: 6,7 => UNS * INC I5: 1,3 # I1: 2,4 => UNS * INC I5: 1,3 # I2: 2,4 => UNS * INC I5: 1,3 # B2: 5,9 => UNS * INC I5: 1,3 # B3: 5,9 => UNS * INC I5: 1,3 # C2: 5,9 => UNS * INC I5: 1,3 # C2: 2,4 => UNS * INC I5: 1,3 # A8: 2,6 => UNS * INC I5: 1,3 # A9: 2,6 => UNS * INC I5: 1,3 # H8: 2,6 => UNS * INC I5: 1,3 # H8: 1,4 => UNS * INC I5: 1,3 # C5: 2,6 => UNS * DIS I5: 1,3 # C5: 4 => CTR => C5: 2,6 * INC I5: 1,3 + C5: 2,6 # A8: 2,6 => UNS * INC I5: 1,3 + C5: 2,6 # A9: 2,6 => UNS * INC I5: 1,3 + C5: 2,6 # H8: 2,6 => UNS * INC I5: 1,3 + C5: 2,6 # H8: 1,4 => UNS * DIS I5: 1,3 + C5: 2,6 # F8: 2,4 => CTR => F8: 1,3 * PRF I5: 1,3 + C5: 2,6 + F8: 1,3 # E9: 2,4 => SOL * STA I5: 1,3 + C5: 2,6 + F8: 1,3 + E9: 2,4 * CNT 39 HDP CHAINS / 39 HYP OPENED