Analysis of zz-www.sudokuoftheday.co.uk-20190301-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: 85...1.2...7.3.....9.74.......8.....32.......14...9.3..85....4763......8........9 initial
Autosolve
position: 853..1724467.3....29174...357.8.34..32.....7.14..79.3.985....4763...7..871..8...9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 2,5 => CTR => F2: 8 * DIS # D8: 2,5 => CTR => D8: 1,4,9 * PRF # D9: 2,5 => SOL * DIS # F2: 2 => CTR => F2: 5,8 * DIS # H3: 6 => CTR => H3: 5,8 * DIS # G2: 1,5 => CTR => G2: 9 * PRF # G2: 9 => SOL * PRF # H2: 1,5 => SOL * DIS # H3: 5,6 => CTR => H3: 8 * DIS # G9: 5,6 => CTR => G9: 2,3 * PRF # H2: 1,9 => SOL * DIS # H2: 5,8 => CTR => H2: 1,9 * DIS # D7: 2,6 => CTR => D7: 1,3 * DIS # D9: 2,6 => CTR => D9: 3,4,5 * PRF # H2: 1,5 => SOL * DIS # G9: 5,6 => CTR => G9: 2,3 * PRF # D9: 5,6 => SOL * DIS # H3: 5,6 => CTR => H3: 8 * CNT 18 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 2,5 => CTR => F2: 8 * DIS F2: 8 # G2: 1,5 => CTR => G2: 9 * PRF F2: 8 + G2: 9 => SOL * STA F2: 8 + G2: 9 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 85...1.2...7.3.....9.74.......8.....32.......14...9.3..85....4763......8........9 | initial |
| 853..1724467.3....29174...357.8.34..32.....7.14..79.3.985....4763...7..871..8...9 | autosolve |
| 853961724467238915291745683576823491329154876148679532985316247632497158714582369 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) D1: 6,9 E1: 6,9 D2: 2,5 F3: 5,8 I2: 1,5 G3: 5,6 C4: 6,9 C5: 8,9 C6: 6,8 H4: 1,9 G5: 8,9 G6: 5,8 C8: 2,4 C9: 2,4 F7: 2,6 H8: 1,5 H9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,F2: 2.. / D2 = 2 => 22 pairs (_) / F2 = 2 => 0 pairs (X) E4,D6: 2.. / E4 = 2 => 21 pairs (_) / D6 = 2 => 0 pairs (X) I4,I6: 2.. / I4 = 2 => 0 pairs (X) / I6 = 2 => 21 pairs (_) C8,C9: 2.. / C8 = 2 => 20 pairs (_) / C9 = 2 => 15 pairs (_) E4,I4: 2.. / E4 = 2 => 21 pairs (_) / I4 = 2 => 0 pairs (X) D6,I6: 2.. / D6 = 2 => 0 pairs (X) / I6 = 2 => 21 pairs (_) D7,D9: 3.. / D7 = 3 => 17 pairs (_) / D9 = 3 => 19 pairs (_) G7,G9: 3.. / G7 = 3 => 19 pairs (_) / G9 = 3 => 17 pairs (_) D7,G7: 3.. / D7 = 3 => 17 pairs (_) / G7 = 3 => 19 pairs (_) D9,G9: 3.. / D9 = 3 => 19 pairs (_) / G9 = 3 => 17 pairs (_) D5,F5: 4.. / D5 = 4 => 21 pairs (_) / F5 = 4 => 18 pairs (_) C8,C9: 4.. / C8 = 4 => 15 pairs (_) / C9 = 4 => 20 pairs (_) C8,D8: 4.. / C8 = 4 => 15 pairs (_) / D8 = 4 => 20 pairs (_) F5,F9: 4.. / F5 = 4 => 18 pairs (_) / F9 = 4 => 21 pairs (_) E5,E8: 5.. / E5 = 5 => 20 pairs (_) / E8 = 5 => 0 pairs (X) D1,E1: 6.. / D1 = 6 => 17 pairs (_) / E1 = 6 => 20 pairs (_) G3,H3: 6.. / G3 = 6 => 16 pairs (_) / H3 = 6 => 0 pairs (X) C4,C6: 6.. / C4 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) H3,H9: 6.. / H3 = 6 => 0 pairs (X) / H9 = 6 => 16 pairs (_) F2,F3: 8.. / F2 = 8 => 21 pairs (_) / F3 = 8 => 0 pairs (X) H2,H3: 8.. / H2 = 8 => 0 pairs (X) / H3 = 8 => 21 pairs (_) C5,C6: 8.. / C5 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) G5,G6: 8.. / G5 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) F2,H2: 8.. / F2 = 8 => 21 pairs (_) / H2 = 8 => 0 pairs (X) F3,H3: 8.. / F3 = 8 => 0 pairs (X) / H3 = 8 => 21 pairs (_) C5,G5: 8.. / C5 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) C6,G6: 8.. / C6 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) D1,E1: 9.. / D1 = 9 => 20 pairs (_) / E1 = 9 => 17 pairs (_) G2,H2: 9.. / G2 = 9 => 0 pairs (*) / H2 = 9 => 0 pairs (X) C4,C5: 9.. / C4 = 9 => 0 pairs (X) / C5 = 9 => 0 pairs (_) H4,G5: 9.. / H4 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) D8,E8: 9.. / D8 = 9 => 17 pairs (_) / E8 = 9 => 20 pairs (_) C4,H4: 9.. / C4 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) C5,G5: 9.. / C5 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) D1,D8: 9.. / D1 = 9 => 20 pairs (_) / D8 = 9 => 17 pairs (_) E1,E8: 9.. / E1 = 9 => 17 pairs (_) / E8 = 9 => 20 pairs (_) G2,G5: 9.. / G2 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) H2,H4: 9.. / H2 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) * DURATION: 0:00:56.599965 START: 04:08:02.947450 END: 04:08:59.547415 2019-05-01 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,C5,C6,C8,C9,D1,D2,E1,F3,F7,G3,G5,G6,H4,H8,H9,I2) * 853..1724467.3....29174...357.8.34..32.....7.14..79.3.985....4763...7..871..8...9 * PAIR D2: 2,5 BLK 2 F2: 2,5,8 # reduction candidate for 2,5 F2: 2,5 => CTR * 853..1724467.3..8.291748..357.8.349.329...87.148.7953.985....4763...7.1871..8..59 F2: 8 # 21 pairs * PAIR D2: 2,5 COL D D6: 2,5,6 # reduction candidate for 2,5 D6: 2,5 # 18 pairs D8: 2,5,1,4,9 # reduction candidate for 2,5 D8: 2,5 => CTR * 853961724467.3...529174568357.8234..32.154.7614.679.3298531..47634.97..871248.3.9 D8: 1,4,9 # 17 pairs D9: 2,5,3,4,6 # reduction candidate for 2,5 D9: 2,5 => SOLVED * 853961724467238915291745683576823491329154876148679532985316247632497158714582369 D9: 3,4,6 # 17 pairs * PAIR F3: 5,8 BLK 2 F2: 5,8,2 # reduction candidate for 5,8 F2: 2 => CTR * 853..1724467.32.8.291748..357.8.349.329...87.148.7953.985..6.4763...7.1871..8..59 F2: 5,8 # 22 pairs * PAIR F3: 5,8 ROW 3 H3: 5,8,6 # reduction candidate for 5,8 H3: 6 => CTR * 853..1724467.3..8.29174856357.8.349.329...87.14..79.3.985....4763...7..871..8...9 H3: 5,8 # 16 pairs * PAIR I2: 1,5 BLK 3 G2: 1,5,9 # reduction candidate for 1,5 G2: 1,5 => CTR * 853..1724467.38.912917456835798.341.328.5.97614627983.985....4763...7.5871..8..69 G2: 9 => SOLVED * 853961724467238915291745683576823491329154876148679532985316247632497158714582369 H2: 1,5,8,9 # reduction candidate for 1,5 H2: 1,5 => SOLVED * 853961724467238915291745683576823491329154876148679532985316247632497158714582369 H2: 8,9 # 18 pairs * PAIR I2: 1,5 COL I I5: 1,5,6 # reduction candidate for 1,5 I5: 6 # 24 pairs I5: 1,5 # 22 pairs * PAIR G3: 5,6 BLK 3 H3: 5,6,8 # reduction candidate for 5,6 H3: 5,6 => CTR * 853..1724467.3..8.291748..357.8.349.329...87.148.7953.985....4763...7.1871..8..59 H3: 8 # 21 pairs * PAIR G3: 5,6 COL G G9: 5,6,2,3 # reduction candidate for 5,6 G9: 5,6 => CTR * 853..1724467.3.19.29174...357.8.34..32.....7.14..79.3.985...34763...7218712384..9 G9: 2,3 # 18 pairs * PAIR H4: 1,9 COL H H2: 1,9,5,8 # reduction candidate for 1,9 H2: 1,9 => SOLVED * 853961724467238915291745683576823491329154876148679532985316247632497158714582369 H2: 5,8 => CTR * 853..1724467.3.9.129174...357.8.34..32.....7.14..79.3.985....4763...7..871..8...9 * PAIR C8: 2,4 ROW 8 D8: 2,4,1,5,9 # reduction candidate for 2,4 D8: 2,4 # 23 pairs D8: 1,5,9 # 15 pairs * PAIR C9: 2,4 ROW 9 D9: 2,4,3,5,6 # reduction candidate for 2,4 D9: 2,4 # 20 pairs F9: 2,4,5,6 # reduction candidate for 2,4 F9: 2,4 # 18 pairs * PAIR F7: 2,6 BLK 8 D7: 2,6,1,3 # reduction candidate for 2,6 D7: 2,6 => CTR * 853961724467532.8129174865357.8.34..32.1.4.7.14..79.3.985.1.34763.497..8714385269 D7: 1,3 # 18 pairs E7: 2,6,1 # reduction candidate for 2,6 E7: 2,6 # 21 pairs D9: 2,6,3,4,5 # reduction candidate for 2,6 D9: 2,6 => CTR * 853961724467532.8129174...357.8234..32.1.4.7.14..79.32985316247632497..8714285369 D9: 3,4,5 # 17 pairs F9: 2,6,4,5 # reduction candidate for 2,6 F9: 2,6 # 25 pairs * PAIR F7: 2,6 ROW 7 G7: 2,6,1,3 # reduction candidate for 2,6 G7: 2,6 # 21 pairs G7: 1,3 # 19 pairs * PAIR H8: 1,5 BLK 9 G8: 1,5,2 # reduction candidate for 1,5 G8: 1,5 # 23 pairs G8: 2 # 15 pairs * PAIR H8: 1,5 ROW 8 D8: 1,5,2,4,9 # reduction candidate for 1,5 D8: 1,5 # 19 pairs E8: 1,5,2,9 # reduction candidate for 1,5 E8: 1,5 # 18 pairs * PAIR H8: 1,5 COL H H2: 1,5,8,9 # reduction candidate for 1,5 H2: 1,5 => SOLVED * 853961724467238915291745683576823491329154876148679532985316247632497158714582369 H2: 8,9 # 18 pairs * PAIR H9: 5,6 BLK 9 G9: 5,6,2,3 # reduction candidate for 5,6 G9: 5,6 => CTR * 853..1724467.3.19.29174...357.8.34..32.....7.14..79.3.985...34763...7218712384..9 G9: 2,3 # 18 pairs * PAIR H9: 5,6 ROW 9 D9: 5,6,2,3,4 # reduction candidate for 5,6 D9: 5,6 => SOLVED * 853961724467238915291745683576823491329154876148679532985316247632497158714582369 D9: 2,3,4 # 17 pairs F9: 5,6,2,4 # reduction candidate for 5,6 F9: 5,6 # 20 pairs * PAIR H9: 5,6 COL H H3: 5,6,8 # reduction candidate for 5,6 H3: 5,6 => CTR * 853..1724467.3..8.291748..357.8.349.329...87.148.7953.985....4763...7.1871..8..59 H3: 8 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190301-absurd-base-pr-000.dot * REASONING * DIS # F2: 2,5 => CTR => F2: 8 * DIS # D8: 2,5 => CTR => D8: 1,4,9 * PRF # D9: 2,5 => SOL * DIS # F2: 2 => CTR => F2: 5,8 * DIS # H3: 6 => CTR => H3: 5,8 * DIS # G2: 1,5 => CTR => G2: 9 * PRF # G2: 9 => SOL * PRF # H2: 1,5 => SOL * DIS # H3: 5,6 => CTR => H3: 8 * DIS # G9: 5,6 => CTR => G9: 2,3 * PRF # H2: 1,9 => SOL * DIS # H2: 5,8 => CTR => H2: 1,9 * DIS # D7: 2,6 => CTR => D7: 1,3 * DIS # D9: 2,6 => CTR => D9: 3,4,5 * PRF # H2: 1,5 => SOL * DIS # G9: 5,6 => CTR => G9: 2,3 * PRF # D9: 5,6 => SOL * DIS # H3: 5,6 => CTR => H3: 8 * CNT 18 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,C5,C6,C8,C9,D1,D2,E1,F3,F7,G3,G5,G6,H4,H8,H9,I2) * 853..1724467.3....29174...357.8.34..32.....7.14..79.3.985....4763...7..871..8...9 * PAIR D2: 2,5 BLK 2 F2: 2,5,8 # reduction candidate for 2,5 F2: 2,5 => CTR * 853..1724467.3..8.291748..357.8.349.329...87.148.7953.985....4763...7.1871..8..59 * PAIR I2: 1,5 BLK 3 G2: 1,5,9 # reduction candidate for 1,5 G2: 1,5 => CTR * 853..1724467238.9.291745683579823416328...975146579832985....4763..57..871..8..69 G2: 9 => SOLVED * 853961724467238915291745683576823491329154876148679532985316247632497158714582369 * DURATION: 0:00:03.833882 START: 04:09:40.788995 END: 04:09:44.622877 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190301-absurd-base-pr-001.dot * REASONING * DIS # F2: 2,5 => CTR => F2: 8 * DIS F2: 8 # G2: 1,5 => CTR => G2: 9 * PRF F2: 8 + G2: 9 => SOL * STA F2: 8 + G2: 9 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190301, absurd
Solution
position: 853961724467238915291745683576823491329154876148679532985316247632497158714582369 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 # F2: 2,5 => CTR => F2: 8 * INC # F2: 8 => UNS * INC # D6: 2,5 => UNS * DIS # D8: 2,5 => CTR => D8: 1,4,9 * INC # D8: 1,4,9 => UNS * PRF # D9: 2,5 => SOL * INC # D9: 3,4,6 => UNS * INC # F2: 5,8 => UNS * DIS # F2: 2 => CTR => F2: 5,8 * INC # H3: 5,8 => UNS * DIS # H3: 6 => CTR => H3: 5,8 * DIS # G2: 1,5 => CTR => G2: 9 * PRF # G2: 9 => SOL * PRF # H2: 1,5 => SOL * INC # H2: 8,9 => UNS * INC # I5: 1,5 => UNS * INC # I5: 6 => UNS * DIS # H3: 5,6 => CTR => H3: 8 * INC # H3: 8 => UNS * DIS # G9: 5,6 => CTR => G9: 2,3 * INC # G9: 2,3 => UNS * PRF # H2: 1,9 => SOL * DIS # H2: 5,8 => CTR => H2: 1,9 * INC # D8: 2,4 => UNS * INC # D8: 1,5,9 => UNS * INC # D9: 2,4 => UNS * INC # F9: 2,4 => UNS * DIS # D7: 2,6 => CTR => D7: 1,3 * INC # D7: 1,3 => UNS * INC # E7: 2,6 => UNS * DIS # D9: 2,6 => CTR => D9: 3,4,5 * INC # D9: 3,4,5 => UNS * INC # F9: 2,6 => UNS * INC # G7: 2,6 => UNS * INC # G7: 1,3 => UNS * INC # G8: 1,5 => UNS * INC # G8: 2 => UNS * INC # D8: 1,5 => UNS * INC # E8: 1,5 => UNS * PRF # H2: 1,5 => SOL * INC # H2: 8,9 => UNS * DIS # G9: 5,6 => CTR => G9: 2,3 * INC # G9: 2,3 => UNS * PRF # D9: 5,6 => SOL * INC # D9: 2,3,4 => UNS * INC # F9: 5,6 => UNS * DIS # H3: 5,6 => CTR => H3: 8 * INC # H3: 8 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F2: 2,5 => CTR => F2: 8 * DIS F2: 8 # G2: 1,5 => CTR => G2: 9 * PRF F2: 8 + G2: 9 => SOL * STA F2: 8 + G2: 9 * CNT 3 HDP CHAINS / 2 HYP OPENED