Analysis of zz-www.sudokuoftheday.co.uk-20190120-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: .....9.2.9..47.....512.........1..8..7..94.3...8..597.6.....4.31...4389..3......2 initial
Autosolve
position: .....9.2.9.247.3...512...49....1..8..7.894.3..18..597.6.....4.312..4389..3......2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 6,8 => CTR => B1: 4 * PRF # F2: 6,8 => SOL * DIS # I2: 6,8 => CTR => I2: 1,5 * PRF # F2: 6,8 => SOL * DIS # E3: 6,8 => CTR => E3: 3 * DIS # I1: 6,7 => CTR => I1: 1,8 * DIS # G5: 1,6 => CTR => G5: 2,5 * DIS # C4: 5,6 => CTR => C4: 3,4,9 * DIS # I5: 5,6 => CTR => I5: 1 * DIS # D4: 3,6 => CTR => D4: 7 * DIS # D1: 3,6 => CTR => D1: 1,5 * DIS # I4: 5 => CTR => I4: 4,6 * DIS # D8: 5,7 => CTR => D8: 6 * DIS # H9: 1,5 => CTR => H9: 6 * DIS # H2: 6 => CTR => H2: 1,5 * CNT 15 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 6,8 => CTR => B1: 4 * PRF B1: 4 # F2: 6,8 => SOL * STA B1: 4 + F2: 6,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....9.2.9..47.....512.........1..8..7..94.3...8..597.6.....4.31...4389..3......2 | initial |
| .....9.2.9.247.3...512...49....1..8..7.894.3..18..597.6.....4.312..4389..3......2 | autosolve |
| 743159628962478315851236749394712586576894231218365974687921453125643897439587162 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B2: 6,8 F3: 6,8 G3: 6,7 A5: 2,5 C5: 5,6 D6: 3,6 I6: 4,6 B7: 8,9 C8: 5,7 H7: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,F2: 1.. / D1 = 1 => 0 pairs (*) / F2 = 1 => 0 pairs (X) G5,I5: 1.. / G5 = 1 => 0 pairs (X) / I5 = 1 => 10 pairs (_) F4,E6: 2.. / F4 = 2 => 13 pairs (_) / E6 = 2 => 13 pairs (_) G4,G5: 2.. / G4 = 2 => 12 pairs (_) / G5 = 2 => 10 pairs (_) E7,F7: 2.. / E7 = 2 => 13 pairs (_) / F7 = 2 => 13 pairs (_) A5,G5: 2.. / A5 = 2 => 12 pairs (_) / G5 = 2 => 10 pairs (_) A6,E6: 2.. / A6 = 2 => 13 pairs (_) / E6 = 2 => 13 pairs (_) E6,E7: 2.. / E6 = 2 => 13 pairs (_) / E7 = 2 => 13 pairs (_) F4,F7: 2.. / F4 = 2 => 13 pairs (_) / F7 = 2 => 13 pairs (_) A3,E3: 3.. / A3 = 3 => 0 pairs (X) / E3 = 3 => 12 pairs (_) C1,C4: 3.. / C1 = 3 => 13 pairs (_) / C4 = 3 => 16 pairs (_) I4,I6: 4.. / I4 = 4 => 0 pairs (X) / I6 = 4 => 13 pairs (_) A9,C9: 4.. / A9 = 4 => 15 pairs (_) / C9 = 4 => 10 pairs (_) A6,I6: 4.. / A6 = 4 => 0 pairs (X) / I6 = 4 => 13 pairs (_) B1,B4: 4.. / B1 = 4 => 11 pairs (_) / B4 = 4 => 0 pairs (X) D1,E1: 5.. / D1 = 5 => 15 pairs (_) / E1 = 5 => 12 pairs (_) H2,I2: 5.. / H2 = 5 => 16 pairs (_) / I2 = 5 => 20 pairs (_) D8,I8: 6.. / D8 = 6 => 15 pairs (_) / I8 = 6 => 0 pairs (X) H2,H9: 6.. / H2 = 6 => 0 pairs (X) / H9 = 6 => 16 pairs (_) D4,F4: 7.. / D4 = 7 => 13 pairs (_) / F4 = 7 => 0 pairs (X) I8,G9: 7.. / I8 = 7 => 15 pairs (_) / G9 = 7 => 0 pairs (X) A3,G3: 7.. / A3 = 7 => 19 pairs (_) / G3 = 7 => 17 pairs (_) I1,I8: 7.. / I1 = 7 => 0 pairs (X) / I8 = 7 => 15 pairs (_) I1,I2: 8.. / I1 = 8 => 16 pairs (_) / I2 = 8 => 0 pairs (X) B7,A9: 8.. / B7 = 8 => 17 pairs (_) / A9 = 8 => 0 pairs (X) B4,C4: 9.. / B4 = 9 => 17 pairs (_) / C4 = 9 => 0 pairs (X) D7,D9: 9.. / D7 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) C9,D9: 9.. / C9 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) B4,B7: 9.. / B4 = 9 => 17 pairs (_) / B7 = 9 => 0 pairs (X) * DURATION: 0:00:27.216595 START: 03:05:21.787706 END: 03:05:49.004301 2019-05-01 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B2,B7,C5,C8,D6,F3,G3,H7,I6) * .....9.2.9.247.3...512...49....1..8..7.894.3..18..597.6.....4.312..4389..3......2 * PAIR B2: 6,8 BLK 1 B1: 6,8,4 # reduction candidate for 6,8 B1: 6,8 => CTR * 4.3..9.2.9.247.3..751238649.49.1..86.76894.3..18..597469..824.312.64389.83495...2 B1: 4 # 11 pairs * PAIR B2: 6,8 ROW 2 F2: 6,8,1 # reduction candidate for 6,8 F2: 6,8 => SOLVED * 743159628962478315851236749394712586576894231218365974687921453125643897439587162 F2: 1 # 13 pairs I2: 6,8,1,5 # reduction candidate for 6,8 I2: 6,8 => CTR * .4.5.9.2.962471358.512...49.9471..8..76894.3.21836597468.927413127643895439158762 I2: 1,5 # 19 pairs * PAIR F3: 6,8 BLK 2 E1: 6,8,3,5 # reduction candidate for 6,8 E1: 6,8 # 17 pairs F2: 6,8,1 # reduction candidate for 6,8 F2: 6,8 => SOLVED * 743159628962478315851236749394712586576894231218365974687921453125643897439587162 F2: 1 # 13 pairs E3: 6,8,3 # reduction candidate for 6,8 E3: 6,8 => CTR * 847.39.2.9624713583512..749.93712.8..7689423..183.597.689..74.31256438977349...62 E3: 3 # 12 pairs * PAIR F3: 6,8 COL F F9: 6,8,1,7 # reduction candidate for 6,8 F9: 6,8 # 16 pairs F9: 1,7 # 11 pairs * PAIR G3: 6,7 BLK 3 G1: 6,7,1 # reduction candidate for 6,7 G1: 6,7 # 21 pairs I1: 6,7,1,8 # reduction candidate for 6,7 I1: 6,7 => CTR * .4.5.912.962471358.512...49.9471..8..76894.3121836597468.9274131276438954391...62 I1: 1,8 # 16 pairs * PAIR G3: 6,7 COL G G9: 6,7,1,5 # reduction candidate for 6,7 G9: 6,7 # 24 pairs G9: 1,5 # 17 pairs * PAIR A5: 2,5 BLK 4 A4: 2,5,3,4 # reduction candidate for 2,5 A4: 2,5 # 15 pairs A4: 3,4 # 11 pairs * PAIR A5: 2,5 ROW 5 G5: 2,5,1,6 # reduction candidate for 2,5 G5: 1,6 => CTR * .....9.2.9.247.35..512...495...1628427689413541832597668..52413125643897734981562 G5: 2,5 # 11 pairs * PAIR C5: 5,6 BLK 4 C4: 5,6,3,4,9 # reduction candidate for 5,6 C4: 5,6 => CTR * .43..9.2796247.3.8751238649.9..16.8.276894.31.18325976689.5.4.3127.4389.5349..762 C4: 3,4,9 # 10 pairs * PAIR C5: 5,6 ROW 5 G5: 5,6,1,2 # reduction candidate for 5,6 G5: 5,6 # 13 pairs I5: 5,6,1 # reduction candidate for 5,6 I5: 5,6 => CTR * .....9.2.9.247.35..512...495...1628427689413541832597668..52413125643897734981562 I5: 1 # 10 pairs * PAIR D6: 3,6 BLK 5 D4: 3,6,7 # reduction candidate for 3,6 D4: 3,6 => CTR * .....9.279.247.36..512...49....17.8..7.894.3..18.2597.6....24.312..43896.3....7.2 D4: 7 # 13 pairs E6: 3,6,2 # reduction candidate for 3,6 E6: 3,6 # 13 pairs * PAIR D6: 3,6 COL D D1: 3,6,1,5 # reduction candidate for 3,6 D1: 3,6 => CTR * ....59.279.247136..512...49...71..8..7.894.3..18..597.6.....4.312.543896.3....7.2 D1: 1,5 # 12 pairs * PAIR I6: 4,6 BLK 6 I4: 4,6,5 # reduction candidate for 4,6 I4: 5 => CTR * .....912.9.247135..512..749....1.685576894231.18..59746.....413125643897.3.187562 I4: 4,6 # 18 pairs * PAIR C8: 5,7 BLK 7 C7: 5,7,9 # reduction candidate for 5,7 C7: 5,7 # 15 pairs A9: 5,7,4,8 # reduction candidate for 5,7 A9: 5,7 # 16 pairs C9: 5,7,4,9 # reduction candidate for 5,7 C9: 5,7 # 14 pairs * PAIR C8: 5,7 ROW 8 D8: 5,7,6 # reduction candidate for 5,7 D8: 5,7 => CTR * .....9.279.247.36..512...49....1..8..7.894.3..18..597.6.....4.312..43896.3....7.2 D8: 6 # 15 pairs I8: 5,7,6 # reduction candidate for 5,7 I8: 5,7 # 15 pairs * PAIR H7: 1,5 BLK 9 G9: 1,5,6,7 # reduction candidate for 1,5 G9: 1,5 # 17 pairs H9: 1,5,6 # reduction candidate for 1,5 H9: 1,5 => CTR * .....91289824713653512..749..3.1..8..7.894.31.18..597.69....4.3125643897834957612 H9: 6 # 16 pairs * PAIR H7: 1,5 ROW 7 D7: 1,5,7,9 # reduction candidate for 1,5 D7: 1,5 # 13 pairs D7: 7,9 # 11 pairs * PAIR H7: 1,5 COL H H2: 1,5,6 # reduction candidate for 1,5 H2: 6 => CTR * .....91289824713653512..749..3.1..8..7.894.31.18..597.69....4.3125643897834957612 H2: 1,5 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190120-absurd-base-pr-000.dot * REASONING * DIS # B1: 6,8 => CTR => B1: 4 * PRF # F2: 6,8 => SOL * DIS # I2: 6,8 => CTR => I2: 1,5 * PRF # F2: 6,8 => SOL * DIS # E3: 6,8 => CTR => E3: 3 * DIS # I1: 6,7 => CTR => I1: 1,8 * DIS # G5: 1,6 => CTR => G5: 2,5 * DIS # C4: 5,6 => CTR => C4: 3,4,9 * DIS # I5: 5,6 => CTR => I5: 1 * DIS # D4: 3,6 => CTR => D4: 7 * DIS # D1: 3,6 => CTR => D1: 1,5 * DIS # I4: 5 => CTR => I4: 4,6 * DIS # D8: 5,7 => CTR => D8: 6 * DIS # H9: 1,5 => CTR => H9: 6 * DIS # H2: 6 => CTR => H2: 1,5 * CNT 15 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B2,B7,C5,C8,D6,F3,G3,H7,I6) * .....9.2.9.247.3...512...49....1..8..7.894.3..18..597.6.....4.312..4389..3......2 * PAIR B2: 6,8 BLK 1 B1: 6,8,4 # reduction candidate for 6,8 B1: 6,8 => CTR * 4.3..9.2.9.247.3..751238649.49.1..86.76894.3..18..597469..824.312.64389.83495...2 * PAIR B2: 6,8 ROW 2 F2: 6,8,1 # reduction candidate for 6,8 F2: 6,8 => SOLVED * 743159628962478315851236749394712586576894231218365974687921453125643897439587162 * DURATION: 0:00:02.855775 START: 03:06:14.426729 END: 03:06:17.282504 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190120-absurd-base-pr-001.dot * REASONING * DIS # B1: 6,8 => CTR => B1: 4 * PRF B1: 4 # F2: 6,8 => SOL * STA B1: 4 + F2: 6,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190120, absurd
Solution
position: 743159628962478315851236749394712586576894231218365974687921453125643897439587162 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:
* DIS # B1: 6,8 => CTR => B1: 4 * INC # B1: 4 => UNS * PRF # F2: 6,8 => SOL * INC # F2: 1 => UNS * DIS # I2: 6,8 => CTR => I2: 1,5 * INC # I2: 1,5 => UNS * INC # E1: 6,8 => UNS * PRF # F2: 6,8 => SOL * INC # F2: 1 => UNS * DIS # E3: 6,8 => CTR => E3: 3 * INC # E3: 3 => UNS * INC # F9: 6,8 => UNS * INC # F9: 1,7 => UNS * INC # G1: 6,7 => UNS * DIS # I1: 6,7 => CTR => I1: 1,8 * INC # I1: 1,8 => UNS * INC # G9: 6,7 => UNS * INC # G9: 1,5 => UNS * INC # A4: 2,5 => UNS * INC # A4: 3,4 => UNS * INC # G5: 2,5 => UNS * DIS # G5: 1,6 => CTR => G5: 2,5 * DIS # C4: 5,6 => CTR => C4: 3,4,9 * INC # C4: 3,4,9 => UNS * INC # G5: 5,6 => UNS * DIS # I5: 5,6 => CTR => I5: 1 * INC # I5: 1 => UNS * DIS # D4: 3,6 => CTR => D4: 7 * INC # D4: 7 => UNS * INC # E6: 3,6 => UNS * DIS # D1: 3,6 => CTR => D1: 1,5 * INC # D1: 1,5 => UNS * INC # I4: 4,6 => UNS * DIS # I4: 5 => CTR => I4: 4,6 * INC # C7: 5,7 => UNS * INC # A9: 5,7 => UNS * INC # C9: 5,7 => UNS * DIS # D8: 5,7 => CTR => D8: 6 * INC # D8: 6 => UNS * INC # I8: 5,7 => UNS * INC # G9: 1,5 => UNS * DIS # H9: 1,5 => CTR => H9: 6 * INC # H9: 6 => UNS * INC # D7: 1,5 => UNS * INC # D7: 7,9 => UNS * INC # H2: 1,5 => UNS * DIS # H2: 6 => CTR => H2: 1,5 * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 6,8 => CTR => B1: 4 * PRF B1: 4 # F2: 6,8 => SOL * STA B1: 4 + F2: 6,8 * CNT 2 HDP CHAINS / 2 HYP OPENED