Analysis of zz-www.sudokuoftheday.co.uk-20190110-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..4.....8...2.5...5...9.8.....4.1....2.8..7..497....8.....6.1..2.5.7..36......2. initial
Autosolve
position: 9..458...8...2.5..25..79.8.....4.1....2.8..7..4976...8...2.6.1..2.5.7..36..8.4.2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 1,3 => CTR => C2: 4,6,7 * DIS # G1: 3,6 => CTR => G1: 2,7 * DIS # H2: 3,6 => CTR => H2: 4,9 * DIS # D5: 1 => CTR => D5: 3,9 * DIS # F6: 3,5 => CTR => F6: 1,2 * DIS # E9: 3,9 => CTR => E9: 1 * DIS # E9: 3 => CTR => E9: 1,9 * DIS # G7: 7,9 => CTR => G7: 4,8 * CNT 8 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 1,3 => CTR => C2: 4,6,7 * DIS C2: 4,6,7 # G1: 3,6 => CTR => G1: 2,7 * DIS C2: 4,6,7 + G1: 2,7 # H2: 3,6 => CTR => H2: 4,9 * DIS C2: 4,6,7 + G1: 2,7 + H2: 4,9 # G3: 4 => CTR => G3: 3,6 * DIS C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 # D5: 1 => CTR => D5: 3,9 * PRF C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 + D5: 3,9 # H4: 5 => SOL * STA C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 + D5: 3,9 + H4: 5 * CNT 6 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9..4.....8...2.5...5...9.8.....4.1....2.8..7..497....8.....6.1..2.5.7..36......2. | initial |
| 9..458...8...2.5..25..79.8.....4.1....2.8..7..4976...8...2.6.1..2.5.7..36..8.4.2. | autosolve |
| 931458762867123594254679381786342159312985476549761238495236817128597643673814925 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) F2: 1,3 H1: 3,6 D4: 3,9 G6: 2,3 H6: 3,5 A8: 1,4 C8: 1,8 E7: 3,9 E8: 1,9 G9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E8,E9: 1.. / E8 = 1 => 0 pairs (X) / E9 = 1 => 10 pairs (_) A6,F6: 1.. / A6 = 1 => 19 pairs (_) / F6 = 1 => 15 pairs (_) G1,I1: 2.. / G1 = 2 => 0 pairs (X) / I1 = 2 => 10 pairs (_) F4,F6: 2.. / F4 = 2 => 10 pairs (_) / F6 = 2 => 0 pairs (X) I4,G6: 2.. / I4 = 2 => 0 pairs (X) / G6 = 2 => 10 pairs (_) F4,I4: 2.. / F4 = 2 => 10 pairs (_) / I4 = 2 => 0 pairs (X) F6,G6: 2.. / F6 = 2 => 0 pairs (X) / G6 = 2 => 10 pairs (_) G1,G6: 2.. / G1 = 2 => 0 pairs (X) / G6 = 2 => 10 pairs (_) I1,I4: 2.. / I1 = 2 => 10 pairs (_) / I4 = 2 => 0 pairs (X) E7,E9: 3.. / E7 = 3 => 11 pairs (_) / E9 = 3 => 0 pairs (X) C2,C3: 4.. / C2 = 4 => 0 pairs (X) / C3 = 4 => 16 pairs (_) G5,I5: 4.. / G5 = 4 => 17 pairs (_) / I5 = 4 => 12 pairs (_) A7,A8: 4.. / A7 = 4 => 0 pairs (*) / A8 = 4 => 0 pairs (X) H2,H8: 4.. / H2 = 4 => 18 pairs (_) / H8 = 4 => 0 pairs (*) H4,H6: 5.. / H4 = 5 => 16 pairs (_) / H6 = 5 => 10 pairs (_) I7,I9: 5.. / I7 = 5 => 15 pairs (_) / I9 = 5 => 10 pairs (_) A5,F5: 5.. / A5 = 5 => 25 pairs (_) / F5 = 5 => 12 pairs (_) C9,I9: 5.. / C9 = 5 => 15 pairs (_) / I9 = 5 => 10 pairs (_) D2,D3: 6.. / D2 = 6 => 11 pairs (_) / D3 = 6 => 14 pairs (_) G8,H8: 6.. / G8 = 6 => 11 pairs (_) / H8 = 6 => 0 pairs (X) A4,A7: 7.. / A4 = 7 => 10 pairs (_) / A7 = 7 => 0 pairs (X) B4,C4: 8.. / B4 = 8 => 10 pairs (_) / C4 = 8 => 0 pairs (X) G7,G8: 8.. / G7 = 8 => 9 pairs (_) / G8 = 8 => 0 pairs (X) C8,G8: 8.. / C8 = 8 => 9 pairs (_) / G8 = 8 => 0 pairs (X) B4,B7: 8.. / B4 = 8 => 10 pairs (_) / B7 = 8 => 0 pairs (X) H2,I2: 9.. / H2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) D4,D5: 9.. / D4 = 9 => 0 pairs (X) / D5 = 9 => 16 pairs (_) B7,B9: 9.. / B7 = 9 => 11 pairs (_) / B9 = 9 => 12 pairs (_) * DURATION: 0:00:26.515534 START: 02:50:45.412393 END: 02:51:11.927927 2019-05-01 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C8,D4,E7,E8,F2,G6,G9,H1,H6) * 9..458...8...2.5..25..79.8.....4.1....2.8..7..4976...8...2.6.1..2.5.7..36..8.4.2. * PAIR F2: 1,3 BLK 2 D2: 1,3,6 # reduction candidate for 1,3 D2: 1,3 # 14 pairs D3: 1,3,6 # reduction candidate for 1,3 D3: 1,3 # 11 pairs * PAIR F2: 1,3 ROW 2 B2: 1,3,6,7 # reduction candidate for 1,3 B2: 1,3 # 14 pairs C2: 1,3,4,6,7 # reduction candidate for 1,3 C2: 1,3 => CTR * 9..458.3.873621549254379681...94.15...218..7.14976...8...2.6.1.42.5.7.636..8.4.2. C2: 4,6,7 # 10 pairs * PAIR F2: 1,3 COL F F5: 1,3,5 # reduction candidate for 1,3 F5: 1,3 # 25 pairs F6: 1,3,2,5 # reduction candidate for 1,3 F6: 1,3 # 12 pairs * PAIR H1: 3,6 BLK 3 G1: 3,6,2,7 # reduction candidate for 3,6 G1: 3,6 => CTR * 9..458..28...2.59725..79481....421....2.8..74.4976.2.84..2.6.1.1285976436..814.2. G1: 2,7 # 11 pairs H2: 3,6,4,9 # reduction candidate for 3,6 H2: 3,6 => CTR * 9..458...874.2.5.925..79.8.78.34.19.51298..7..4976..584..2.6.1.1285976436..814.2. H2: 4,9 # 11 pairs G3: 3,6,4 # reduction candidate for 3,6 G3: 3,6 # 14 pairs * PAIR H1: 3,6 ROW 1 B1: 3,6,1,7 # reduction candidate for 3,6 B1: 3,6 # 13 pairs C1: 3,6,1,7 # reduction candidate for 3,6 C1: 3,6 # 13 pairs * PAIR H1: 3,6 COL H H4: 3,6,5,9 # reduction candidate for 3,6 H4: 3,6 # 13 pairs H4: 5,9 # 11 pairs * PAIR D4: 3,9 BLK 5 D5: 3,9,1 # reduction candidate for 3,9 D5: 1 => CTR * 9..458...8...21549254.79.81...94.1....218.97414976...8...2.641.42.5.78.36..8.4.2. D5: 3,9 # 14 pairs * PAIR D4: 3,9 ROW 4 H4: 3,9,5,6 # reduction candidate for 3,9 H4: 3,9 # 14 pairs H4: 5,6 # 13 pairs * PAIR G6: 2,3 ROW 6 F6: 2,3,1,5 # reduction candidate for 2,3 F6: 2,3 # 25 pairs F6: 1,5 # 11 pairs * PAIR G6: 2,3 COL G G1: 2,3,6,7 # reduction candidate for 2,3 G1: 2,3 # 13 pairs G1: 6,7 # 11 pairs * PAIR H6: 3,5 BLK 6 H4: 3,5,6,9 # reduction candidate for 3,5 H4: 3,5 # 15 pairs H4: 6,9 # 12 pairs * PAIR H6: 3,5 ROW 6 A6: 3,5,1 # reduction candidate for 3,5 A6: 3,5 # 15 pairs F6: 3,5,1,2 # reduction candidate for 3,5 F6: 3,5 => CTR * 9..4587328...2.549254379681...942156.62.8..7414976.2.8...2.641.42.5.78636..8.492. F6: 1,2 # 11 pairs * PAIR E7: 3,9 BLK 8 E9: 3,9,1 # reduction candidate for 3,9 E9: 3,9 => CTR * 9..4582378...2.549254379681.8694.1.2..2.8.476.49762358...2.6814428517..36..8.4725 E9: 1 # 10 pairs * PAIR E7: 3,9 ROW 7 B7: 3,9,7,8 # reduction candidate for 3,9 B7: 7,8 # 13 pairs B7: 3,9 # 12 pairs * PAIR E8: 1,9 BLK 8 E9: 1,9,3 # reduction candidate for 1,9 E9: 3 => CTR * 91.45823786..2.549254.79.81.8..4.1.2..2.8.476.49762358...296814428517963691834725 E9: 1,9 # 11 pairs * PAIR G9: 7,9 BLK 9 G7: 7,9,4,8 # reduction candidate for 7,9 G7: 7,9 => CTR * 9..458.3.8...2.549254379681...94.15...2.8..7..4976...8...2.6.1..2.5.78636..8.4.2. G7: 4,8 # 11 pairs I7: 7,9,4,5 # reduction candidate for 7,9 I7: 7,9 # 13 pairs I9: 7,9,5 # reduction candidate for 7,9 I9: 7,9 # 15 pairs * PAIR G9: 7,9 ROW 9 B9: 7,9,1,3 # reduction candidate for 7,9 B9: 7,9 # 13 pairs B9: 1,3 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190110-absurd-base-pr-000.dot * REASONING * DIS # C2: 1,3 => CTR => C2: 4,6,7 * DIS # G1: 3,6 => CTR => G1: 2,7 * DIS # H2: 3,6 => CTR => H2: 4,9 * DIS # D5: 1 => CTR => D5: 3,9 * DIS # F6: 3,5 => CTR => F6: 1,2 * DIS # E9: 3,9 => CTR => E9: 1 * DIS # E9: 3 => CTR => E9: 1,9 * DIS # G7: 7,9 => CTR => G7: 4,8 * CNT 8 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C8,D4,E7,E8,F2,G6,G9,H1,H6) * 9..458...8...2.5..25..79.8.....4.1....2.8..7..4976...8...2.6.1..2.5.7..36..8.4.2. * PAIR F2: 1,3 BLK 2 D2: 1,3,6 # reduction candidate for 1,3 D2: 1,3 # 14 pairs D3: 1,3,6 # reduction candidate for 1,3 D3: 1,3 # 11 pairs * PAIR F2: 1,3 ROW 2 B2: 1,3,6,7 # reduction candidate for 1,3 B2: 1,3 # 14 pairs C2: 1,3,4,6,7 # reduction candidate for 1,3 C2: 1,3 => CTR * 9..458.3.873621549254379681...94.15...218..7.14976...8...2.6.1.42.5.7.636..8.4.2. * RESTART * PAIR F2: 1,3 ROW 2 B2: 1,3,6,7 # reduction candidate for 1,3 B2: 1,3 # 14 pairs B2: 6,7 # 11 pairs * PAIR F2: 1,3 COL F F5: 1,3,5 # reduction candidate for 1,3 F5: 1,3 # 26 pairs F6: 1,3,2,5 # reduction candidate for 1,3 F6: 1,3 # 12 pairs * PAIR RESTART * PAIR F2: 1,3 BLK 2 D2: 1,3,6 # reduction candidate for 1,3 D2: 1,3 # 14 pairs D3: 1,3,6 # reduction candidate for 1,3 D3: 1,3 # 12 pairs * PAIR F2: 1,3 ROW 2 B2: 1,3,6,7 # reduction candidate for 1,3 B2: 1,3 # 14 pairs B2: 6,7 # 11 pairs * PAIR F2: 1,3 COL F F5: 1,3,5 # reduction candidate for 1,3 F5: 1,3 # 26 pairs F6: 1,3,2,5 # reduction candidate for 1,3 F6: 1,3 # 12 pairs * PAIR H1: 3,6 BLK 3 G1: 3,6,2,7 # reduction candidate for 3,6 G1: 3,6 => CTR * 9..458..28...2.59725..79481....421....2.8..74.4976.2.84..2.6.1.1285976436..814.2. H2: 3,6,4,9 # reduction candidate for 3,6 H2: 3,6 => CTR * 9..458...874.2.5.925..79.8.78.34.19.51298..7..4976..584..2.6.1.1285976436..814.2. G3: 3,6,4 # reduction candidate for 3,6 G3: 3,6 # 14 pairs * RESTART * PAIR H1: 3,6 BLK 3 G3: 3,6,4 # reduction candidate for 3,6 G3: 4 => CTR * 9..458.3.8...2.5..25..7948.....4.1....2.8..74.4976..584..2.6.1.1285976436..814.2. * PAIR H1: 3,6 ROW 1 B1: 3,6,1,7 # reduction candidate for 3,6 B1: 3,6 # 16 pairs C1: 3,6,1,7 # reduction candidate for 3,6 C1: 3,6 # 16 pairs * PAIR D4: 3,9 BLK 5 D5: 3,9,1 # reduction candidate for 3,9 D5: 1 => CTR * 9..458...8...21549254.79.81...94.1....218.97414976...8...2.641.42.5.78.36..8.4.2. * PAIR D4: 3,9 ROW 4 H4: 3,9,5 # reduction candidate for 3,9 H4: 5 => SOLVED * 931458762867123594254679381786342159312985476549761238495236817128597643673814925 * DURATION: 0:00:14.149176 START: 02:51:32.417049 END: 02:51:46.566225 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190110-absurd-base-pr-001.dot * REASONING * DIS # C2: 1,3 => CTR => C2: 4,6,7 * DIS C2: 4,6,7 # G1: 3,6 => CTR => G1: 2,7 * DIS C2: 4,6,7 + G1: 2,7 # H2: 3,6 => CTR => H2: 4,9 * DIS C2: 4,6,7 + G1: 2,7 + H2: 4,9 # G3: 4 => CTR => G3: 3,6 * DIS C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 # D5: 1 => CTR => D5: 3,9 * PRF C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 + D5: 3,9 # H4: 5 => SOL * STA C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 + D5: 3,9 + H4: 5 * CNT 6 HDP CHAINS / 25 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190110, absurd
Solution
position: 931458762867123594254679381786342159312985476549761238495236817128597643673814925 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 # D2: 1,3 => UNS * INC # D3: 1,3 => UNS * INC # B2: 1,3 => UNS * DIS # C2: 1,3 => CTR => C2: 4,6,7 * INC # C2: 4,6,7 => UNS * INC # F5: 1,3 => UNS * INC # F6: 1,3 => UNS * DIS # G1: 3,6 => CTR => G1: 2,7 * INC # G1: 2,7 => UNS * DIS # H2: 3,6 => CTR => H2: 4,9 * INC # H2: 4,9 => UNS * INC # G3: 3,6 => UNS * INC # B1: 3,6 => UNS * INC # C1: 3,6 => UNS * INC # H4: 3,6 => UNS * INC # H4: 5,9 => UNS * INC # D5: 3,9 => UNS * DIS # D5: 1 => CTR => D5: 3,9 * INC # H4: 3,9 => UNS * INC # H4: 5,6 => UNS * INC # F6: 2,3 => UNS * INC # F6: 1,5 => UNS * INC # G1: 2,3 => UNS * INC # G1: 6,7 => UNS * INC # H4: 3,5 => UNS * INC # H4: 6,9 => UNS * INC # A6: 3,5 => UNS * DIS # F6: 3,5 => CTR => F6: 1,2 * INC # F6: 1,2 => UNS * DIS # E9: 3,9 => CTR => E9: 1 * INC # E9: 1 => UNS * INC # B7: 3,9 => UNS * INC # B7: 7,8 => UNS * INC # E9: 1,9 => UNS * DIS # E9: 3 => CTR => E9: 1,9 * DIS # G7: 7,9 => CTR => G7: 4,8 * INC # G7: 4,8 => UNS * INC # I7: 7,9 => UNS * INC # I9: 7,9 => UNS * INC # B9: 7,9 => UNS * INC # B9: 1,3 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 1,3 => UNS * INC # D3: 1,3 => UNS * INC # B2: 1,3 => UNS * DIS # C2: 1,3 => CTR => C2: 4,6,7 * INC C2: 4,6,7 # B2: 1,3 => UNS * INC C2: 4,6,7 # B2: 6,7 => UNS * INC C2: 4,6,7 # F5: 1,3 => UNS * INC C2: 4,6,7 # F6: 1,3 => UNS * INC C2: 4,6,7 # D2: 1,3 => UNS * INC C2: 4,6,7 # D3: 1,3 => UNS * INC C2: 4,6,7 # B2: 1,3 => UNS * INC C2: 4,6,7 # B2: 6,7 => UNS * INC C2: 4,6,7 # F5: 1,3 => UNS * INC C2: 4,6,7 # F6: 1,3 => UNS * DIS C2: 4,6,7 # G1: 3,6 => CTR => G1: 2,7 * DIS C2: 4,6,7 + G1: 2,7 # H2: 3,6 => CTR => H2: 4,9 * INC C2: 4,6,7 + G1: 2,7 + H2: 4,9 # G3: 3,6 => UNS * INC C2: 4,6,7 + G1: 2,7 + H2: 4,9 # G3: 3,6 => UNS * DIS C2: 4,6,7 + G1: 2,7 + H2: 4,9 # G3: 4 => CTR => G3: 3,6 * INC C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 # B1: 3,6 => UNS * INC C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 # C1: 3,6 => UNS * INC C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 # D5: 3,9 => UNS * DIS C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 # D5: 1 => CTR => D5: 3,9 * INC C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 + D5: 3,9 # H4: 3,9 => UNS * PRF C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 + D5: 3,9 # H4: 5 => SOL * STA C2: 4,6,7 + G1: 2,7 + H2: 4,9 + G3: 3,6 + D5: 3,9 + H4: 5 * CNT 25 HDP CHAINS / 25 HYP OPENED