Analysis of zz-www.sudokuoftheday.co.uk-20190326-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: 1...2.........3.8.4.9.........1..6..68...54....1.3...8..32...4..9.4.7..2.5..6.... initial
Autosolve
position: 13852....5679.328.42987...53.51..6..6827954139.163...87132...468964.7..225436.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H1: 7,9 => SOL * DIS # H1: 6 => CTR => H1: 7,9 * DIS # I1: 7,9 => CTR => I1: 4 * PRF # I1: 4 => SOL * DIS # G9: 7,9 => CTR => G9: 1,8 * PRF # G8: 5 => SOL * DIS # F4: 2 => CTR => F4: 4,8 * PRF # F4: 2,4 => SOL * DIS # F4: 8 => CTR => F4: 2,4 * DIS # H4: 7,9 => CTR => H4: 2 * DIS # I1: 7,9 => CTR => I1: 4 * PRF # I1: 4 => SOL * PRF # I9: 7,9 => SOL * DIS # I9: 1 => CTR => I9: 7,9 * DIS # H6: 2 => CTR => H6: 5,7 * DIS # G7: 9 => CTR => G7: 5,8 * PRF # F9: 8,9 => SOL * DIS # F9: 1 => CTR => F9: 8,9 * PRF # G7: 8,9 => SOL * DIS # G7: 5 => CTR => G7: 8,9 * PRF # G8: 1,5 => SOL * DIS # G8: 3 => CTR => G8: 1,5 * PRF # G8: 3,5 => SOL * DIS # G8: 1 => CTR => G8: 3,5 * DIS # G9: 7,9 => CTR => G9: 1,8 * PRF # I9: 7,9 => SOL * DIS # I9: 1 => CTR => I9: 7,9 * PRF # H1: 7,9 => SOL * DIS # H1: 6 => CTR => H1: 7,9 * DIS # H4: 7,9 => CTR => H4: 2 * CNT 30 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H1: 7,9 => SOL * STA H1: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1...2.........3.8.4.9.........1..6..68...54....1.3...8..32...4..9.4.7..2.5..6.... | initial |
| 13852....5679.328.42987...53.51..6..6827954139.163...87132...468964.7..225436.... | autosolve |
| 138526974567943281429871365375184629682795413941632758713259846896417532254368197 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) F1: 4,6 E2: 1,4 F3: 1,6 G1: 7,9 I2: 1,4 G3: 1,3 H3: 3,6 B4: 4,7 B6: 4,7 E4: 4,8 F6: 2,4 I4: 7,9 G6: 5,7 E7: 5,8 F7: 8,9 E8: 1,5 H8: 3,5 H9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F3: 1.. / E2 = 1 => 0 pairs (X) / F3 = 1 => 0 pairs (_) I2,G3: 1.. / I2 = 1 => 0 pairs (*) / G3 = 1 => 0 pairs (X) E8,F9: 1.. / E8 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) E2,I2: 1.. / E2 = 1 => 0 pairs (X) / I2 = 1 => 0 pairs (_) F3,G3: 1.. / F3 = 1 => 0 pairs (*) / G3 = 1 => 0 pairs (X) E8,G8: 1.. / E8 = 1 => 0 pairs (*) / G8 = 1 => 0 pairs (X) E2,E8: 1.. / E2 = 1 => 0 pairs (X) / E8 = 1 => 0 pairs (_) F3,F9: 1.. / F3 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) I2,I9: 1.. / I2 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) F4,F6: 2.. / F4 = 2 => 0 pairs (X) / F6 = 2 => 18 pairs (_) H4,H6: 2.. / H4 = 2 => 18 pairs (_) / H6 = 2 => 0 pairs (X) F4,H4: 2.. / F4 = 2 => 0 pairs (X) / H4 = 2 => 18 pairs (_) F6,H6: 2.. / F6 = 2 => 18 pairs (_) / H6 = 2 => 0 pairs (X) G3,H3: 3.. / G3 = 3 => 0 pairs (*) / H3 = 3 => 0 pairs (X) G8,H8: 3.. / G8 = 3 => 0 pairs (X) / H8 = 3 => 0 pairs (_) G3,G8: 3.. / G3 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) H3,H8: 3.. / H3 = 3 => 0 pairs (X) / H8 = 3 => 0 pairs (_) F1,E2: 4.. / F1 = 4 => 0 pairs (X) / E2 = 4 => 0 pairs (_) I1,I2: 4.. / I1 = 4 => 0 pairs (*) / I2 = 4 => 0 pairs (X) B4,B6: 4.. / B4 = 4 => 0 pairs (X) / B6 = 4 => 18 pairs (_) F1,I1: 4.. / F1 = 4 => 0 pairs (X) / I1 = 4 => 0 pairs (_) E2,I2: 4.. / E2 = 4 => 0 pairs (*) / I2 = 4 => 0 pairs (X) B6,F6: 4.. / B6 = 4 => 18 pairs (_) / F6 = 4 => 0 pairs (X) E2,E4: 4.. / E2 = 4 => 0 pairs (*) / E4 = 4 => 0 pairs (X) G6,H6: 5.. / G6 = 5 => 0 pairs (X) / H6 = 5 => 0 pairs (_) E7,E8: 5.. / E7 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) E7,G7: 5.. / E7 = 5 => 0 pairs (*) / G7 = 5 => 0 pairs (X) H6,H8: 5.. / H6 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) F1,F3: 6.. / F1 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) H1,H3: 6.. / H1 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) F1,H1: 6.. / F1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) F3,H3: 6.. / F3 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) B4,B6: 7.. / B4 = 7 => 18 pairs (_) / B6 = 7 => 0 pairs (X) E4,F4: 8.. / E4 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) G7,G9: 8.. / G7 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) F9,G9: 8.. / F9 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) E4,E7: 8.. / E4 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) H4,I4: 9.. / H4 = 9 => 0 pairs (X) / I4 = 9 => 20 pairs (_) F7,F9: 9.. / F7 = 9 => 19 pairs (_) / F9 = 9 => 0 pairs (X) F7,G7: 9.. / F7 = 9 => 19 pairs (_) / G7 = 9 => 0 pairs (X) * DURATION: 0:00:48.959904 START: 04:48:49.723433 END: 04:49:38.683337 2019-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,E2,E4,E7,E8,F1,F3,F6,F7,G1,G3,G6,H3,H8,H9,I2,I4) * 13852....5679.328.42987...53.51..6..6827954139.163...87132...468964.7..225436.... * PAIR G1: 7,9 BLK 3 H1: 7,9,6 # reduction candidate for 7,9 H1: 7,9 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 H1: 6 => CTR * 13852..6.5679.328.4298761353.51..6..6827954139.163...87132...4689641735225436...1 I1: 7,9,4 # reduction candidate for 7,9 I1: 7,9 => CTR * 138524.6.5679132844298761353.5148629682795413941632..87132895468964.7..225436.... I1: 4 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 * PAIR G1: 7,9 COL G G9: 7,9,1,8 # reduction candidate for 7,9 G9: 7,9 => CTR * 13852....5679132844298761353.51..6..6827954139.163...87132..8468964.7..2254368..1 G9: 1,8 # 19 pairs * PAIR G3: 1,3 COL G G8: 1,3,5 # reduction candidate for 1,3 G8: 5 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 G8: 1,3 # 19 pairs * PAIR E4: 4,8 BLK 5 F4: 4,8,2 # reduction candidate for 4,8 F4: 2 => CTR * 138526..45679.328.42987...53.51826..6827954139.1634.2871325..46896417.5225436.... F4: 4,8 # 18 pairs * PAIR F6: 2,4 BLK 5 F4: 2,4,8 # reduction candidate for 2,4 F4: 2,4 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 F4: 8 => CTR * 13852....5679.328.42987...53.51.86296827954139.1632..8713289546896457132254361897 * PAIR I4: 7,9 BLK 6 H4: 7,9,2 # reduction candidate for 7,9 H4: 7,9 => CTR * 138526..45679.328.42987...53.51.26..6827954139.1634.287132...468964.7.5225436.... H4: 2 # 18 pairs * PAIR I4: 7,9 COL I I1: 7,9,4 # reduction candidate for 7,9 I1: 7,9 => CTR * 138524.6.5679132844298761353.5148629682795413941632..87132895468964.7..225436.... I1: 4 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 I9: 7,9,1 # reduction candidate for 7,9 I9: 7,9 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 I9: 1 => CTR * 13852....5679132844298761353.5148629682795413941632..8713289.468964.7..225436...1 * PAIR G6: 5,7 BLK 6 H6: 5,7,2 # reduction candidate for 5,7 H6: 2 => CTR * 13852....56794328142987...53.51..6..6827954139.163.52871325..4689641735225436.... H6: 5,7 # 18 pairs * PAIR E7: 5,8 ROW 7 G7: 5,8,9 # reduction candidate for 5,8 G7: 9 => CTR * 13852....5679.328.42987...53.51..6..6827954139.163...8713258946896417..2254369871 G7: 5,8 # 19 pairs * PAIR F7: 8,9 BLK 8 F9: 8,9,1 # reduction candidate for 8,9 F9: 8,9 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 F9: 1 => CTR * 13852.9..5679132844298761353.51486296827954139416327587132.9.468964.7..22543618.. * PAIR F7: 8,9 ROW 7 G7: 8,9,5 # reduction candidate for 8,9 G7: 8,9 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 G7: 5 => CTR * 13852....5679.328.42987...53.51..6..6827954139.163...87132.95468964571322543618.. * PAIR E8: 1,5 ROW 8 G8: 1,5,3 # reduction candidate for 1,5 G8: 1,5 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 G8: 3 => CTR * 13852....56794328142987...53.51..6..6827954139.163...87132...4689641735225436.... * PAIR H8: 3,5 BLK 9 G8: 3,5,1 # reduction candidate for 3,5 G8: 3,5 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 G8: 1 => CTR * 13852....5679.328.42987.3653.51..6..6827954139.163...87132...468964.7132254361... * PAIR H9: 7,9 BLK 9 G9: 7,9,1,8 # reduction candidate for 7,9 G9: 7,9 => CTR * 13852....5679132844298761353.51..6..6827954139.163...87132..8468964.7..2254368..1 G9: 1,8 # 19 pairs I9: 7,9,1 # reduction candidate for 7,9 I9: 7,9 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 I9: 1 => CTR * 13852....5679132844298761353.5148629682795413941632..8713289.468964.7..225436...1 * PAIR H9: 7,9 COL H H1: 7,9,6 # reduction candidate for 7,9 H1: 7,9 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 H1: 6 => CTR * 13852..6.5679.328.4298761353.51..6..6827954139.163...87132...4689641735225436...1 H4: 7,9,2 # reduction candidate for 7,9 H4: 7,9 => CTR * 138526..45679.328.42987...53.51.26..6827954139.1634.287132...468964.7.5225436.... H4: 2 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190326-absurd-base-pr-000.dot * REASONING * PRF # H1: 7,9 => SOL * DIS # H1: 6 => CTR => H1: 7,9 * DIS # I1: 7,9 => CTR => I1: 4 * PRF # I1: 4 => SOL * DIS # G9: 7,9 => CTR => G9: 1,8 * PRF # G8: 5 => SOL * DIS # F4: 2 => CTR => F4: 4,8 * PRF # F4: 2,4 => SOL * DIS # F4: 8 => CTR => F4: 2,4 * DIS # H4: 7,9 => CTR => H4: 2 * DIS # I1: 7,9 => CTR => I1: 4 * PRF # I1: 4 => SOL * PRF # I9: 7,9 => SOL * DIS # I9: 1 => CTR => I9: 7,9 * DIS # H6: 2 => CTR => H6: 5,7 * DIS # G7: 9 => CTR => G7: 5,8 * PRF # F9: 8,9 => SOL * DIS # F9: 1 => CTR => F9: 8,9 * PRF # G7: 8,9 => SOL * DIS # G7: 5 => CTR => G7: 8,9 * PRF # G8: 1,5 => SOL * DIS # G8: 3 => CTR => G8: 1,5 * PRF # G8: 3,5 => SOL * DIS # G8: 1 => CTR => G8: 3,5 * DIS # G9: 7,9 => CTR => G9: 1,8 * PRF # I9: 7,9 => SOL * DIS # I9: 1 => CTR => I9: 7,9 * PRF # H1: 7,9 => SOL * DIS # H1: 6 => CTR => H1: 7,9 * DIS # H4: 7,9 => CTR => H4: 2 * CNT 30 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,E2,E4,E7,E8,F1,F3,F6,F7,G1,G3,G6,H3,H8,H9,I2,I4) * 13852....5679.328.42987...53.51..6..6827954139.163...87132...468964.7..225436.... * PAIR G1: 7,9 BLK 3 H1: 7,9,6 # reduction candidate for 7,9 H1: 7,9 => SOLVED * 138526974567943281429871365375184629682795413941632758713259846896417532254368197 * DURATION: 0:00:01.612482 START: 04:50:09.233908 END: 04:50:10.846390 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190326-absurd-base-pr-001.dot * REASONING * PRF # H1: 7,9 => SOL * STA H1: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190326, absurd
Solution
position: 138526974567943281429871365375184629682795413941632758713259846896417532254368197 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:
* PRF # H1: 7,9 => SOL * DIS # H1: 6 => CTR => H1: 7,9 * DIS # I1: 7,9 => CTR => I1: 4 * PRF # I1: 4 => SOL * DIS # G9: 7,9 => CTR => G9: 1,8 * INC # G9: 1,8 => UNS * INC # G8: 1,3 => UNS * PRF # G8: 5 => SOL * INC # F4: 4,8 => UNS * DIS # F4: 2 => CTR => F4: 4,8 * PRF # F4: 2,4 => SOL * DIS # F4: 8 => CTR => F4: 2,4 * DIS # H4: 7,9 => CTR => H4: 2 * INC # H4: 2 => UNS * DIS # I1: 7,9 => CTR => I1: 4 * PRF # I1: 4 => SOL * PRF # I9: 7,9 => SOL * DIS # I9: 1 => CTR => I9: 7,9 * INC # H6: 5,7 => UNS * DIS # H6: 2 => CTR => H6: 5,7 * INC # G7: 5,8 => UNS * DIS # G7: 9 => CTR => G7: 5,8 * PRF # F9: 8,9 => SOL * DIS # F9: 1 => CTR => F9: 8,9 * PRF # G7: 8,9 => SOL * DIS # G7: 5 => CTR => G7: 8,9 * PRF # G8: 1,5 => SOL * DIS # G8: 3 => CTR => G8: 1,5 * PRF # G8: 3,5 => SOL * DIS # G8: 1 => CTR => G8: 3,5 * DIS # G9: 7,9 => CTR => G9: 1,8 * INC # G9: 1,8 => UNS * PRF # I9: 7,9 => SOL * DIS # I9: 1 => CTR => I9: 7,9 * PRF # H1: 7,9 => SOL * DIS # H1: 6 => CTR => H1: 7,9 * DIS # H4: 7,9 => CTR => H4: 2 * INC # H4: 2 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # H1: 7,9 => SOL * STA H1: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED