Analysis of zz-www.sudokuoftheday.co.uk-20060424-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: ....57....4.32.....8..1.2..2...3.4....1...3.5......712..26.31.97.45.....396.....7 initial
Autosolve
position: .2..57....4.32.....8..1.2..2...3.4....1...3.5.3..6.7128526731497145.....396.....7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D1: 4,9 => SOL * DIS # D1: 8 => CTR => D1: 4,9 * DIS # F3: 4,9 => CTR => F3: 6 * DIS # D6: 4,9 => CTR => D6: 8 * PRF # D6: 8 => SOL * DIS # A6: 5 => CTR => A6: 4,9 * DIS # F5: 4,9 => CTR => F5: 2,8 * DIS # H4: 6,8 => CTR => H4: 9 * PRF # I1: 6,8 => SOL * DIS # I2: 6,8 => CTR => I2: 1 * DIS # I8: 6,8 => CTR => I8: 3 * DIS # F8: 2 => CTR => F8: 8,9 * DIS # E5: 4 => CTR => E5: 8,9 * DIS # F9: 4,8 => CTR => F9: 1,2 * DIS # F9: 4,8 => CTR => F9: 1,2 * DIS # H8: 6,8 => CTR => H8: 2,3 * DIS # I8: 6,8 => CTR => I8: 3 * DIS # G2: 6,8 => CTR => G2: 5,9 * DIS # H9: 2 => CTR => H9: 5,8 * CNT 19 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:
* PRF # D1: 4,9 => SOL * STA D1: 4,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....57....4.32.....8..1.2..2...3.4....1...3.5......712..26.31.97.45.....396.....7 | initial |
| .2..57....4.32.....8..1.2..2...3.4....1...3.5.3..6.7128526731497145.....396.....7 | autosolve |
| 123457968649328571587916234278135496461792385935864712852673149714589623396241857 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C1: 3,9 D3: 4,9 B4: 6,7 A5: 4,9 B5: 6,7 D4: 1,7 D5: 2,7 I4: 6,8 E8: 8,9 D9: 1,2 E9: 4,8 G8: 6,8 G9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A2: 1.. / A1 = 1 => 14 pairs (_) / A2 = 1 => 0 pairs (X) I1,I2: 1.. / I1 = 1 => 0 pairs (X) / I2 = 1 => 14 pairs (_) D4,F4: 1.. / D4 = 1 => 23 pairs (_) / F4 = 1 => 0 pairs (X) D9,F9: 1.. / D9 = 1 => 0 pairs (X) / F9 = 1 => 23 pairs (_) A1,I1: 1.. / A1 = 1 => 14 pairs (_) / I1 = 1 => 0 pairs (X) A2,I2: 1.. / A2 = 1 => 0 pairs (X) / I2 = 1 => 14 pairs (_) D4,D9: 1.. / D4 = 1 => 23 pairs (_) / D9 = 1 => 0 pairs (X) F4,F9: 1.. / F4 = 1 => 0 pairs (X) / F9 = 1 => 23 pairs (_) D5,F5: 2.. / D5 = 2 => 0 pairs (X) / F5 = 2 => 23 pairs (_) H8,H9: 2.. / H8 = 2 => 29 pairs (_) / H9 = 2 => 0 pairs (X) F8,H8: 2.. / F8 = 2 => 0 pairs (X) / H8 = 2 => 29 pairs (_) D5,D9: 2.. / D5 = 2 => 0 pairs (X) / D9 = 2 => 23 pairs (_) C1,C3: 3.. / C1 = 3 => 16 pairs (_) / C3 = 3 => 21 pairs (_) H8,I8: 3.. / H8 = 3 => 0 pairs (X) / I8 = 3 => 26 pairs (_) I1,I3: 4.. / I1 = 4 => 0 pairs (X) / I3 = 4 => 0 pairs (_) A5,A6: 4.. / A5 = 4 => 13 pairs (_) / A6 = 4 => 21 pairs (_) E9,F9: 4.. / E9 = 4 => 13 pairs (_) / F9 = 4 => 0 pairs (X) D1,I1: 4.. / D1 = 4 => 0 pairs (*) / I1 = 4 => 0 pairs (X) E5,E9: 4.. / E5 = 4 => 0 pairs (X) / E9 = 4 => 13 pairs (_) F4,F6: 5.. / F4 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) G9,H9: 5.. / G9 = 5 => 15 pairs (_) / H9 = 5 => 21 pairs (_) C4,F4: 5.. / C4 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) G2,G9: 5.. / G2 = 5 => 21 pairs (_) / G9 = 5 => 15 pairs (_) F2,F3: 6.. / F2 = 6 => 0 pairs (X) / F3 = 6 => 19 pairs (_) B4,B5: 6.. / B4 = 6 => 0 pairs (X) / B5 = 6 => 23 pairs (_) B5,H5: 6.. / B5 = 6 => 23 pairs (_) / H5 = 6 => 0 pairs (X) C2,C3: 7.. / C2 = 7 => 13 pairs (_) / C3 = 7 => 17 pairs (_) H2,H3: 7.. / H2 = 7 => 17 pairs (_) / H3 = 7 => 13 pairs (_) B4,B5: 7.. / B4 = 7 => 23 pairs (_) / B5 = 7 => 0 pairs (X) D4,D5: 7.. / D4 = 7 => 0 pairs (X) / D5 = 7 => 23 pairs (_) C2,H2: 7.. / C2 = 7 => 13 pairs (_) / H2 = 7 => 17 pairs (_) C3,H3: 7.. / C3 = 7 => 17 pairs (_) / H3 = 7 => 13 pairs (_) B4,D4: 7.. / B4 = 7 => 23 pairs (_) / D4 = 7 => 0 pairs (X) B5,D5: 7.. / B5 = 7 => 0 pairs (X) / D5 = 7 => 23 pairs (_) D1,F2: 8.. / D1 = 8 => 0 pairs (X) / F2 = 8 => 0 pairs (_) C4,C6: 8.. / C4 = 8 => 0 pairs (*) / C6 = 8 => 0 pairs (X) D1,D6: 8.. / D1 = 8 => 0 pairs (X) / D6 = 8 => 0 pairs (_) G1,G2: 9.. / G1 = 9 => 18 pairs (_) / G2 = 9 => 19 pairs (_) H4,H5: 9.. / H4 = 9 => 15 pairs (_) / H5 = 9 => 0 pairs (X) E8,F8: 9.. / E8 = 9 => 14 pairs (_) / F8 = 9 => 27 pairs (_) E5,E8: 9.. / E5 = 9 => 27 pairs (_) / E8 = 9 => 14 pairs (_) * DURATION: 0:00:53.169354 START: 22:37:37.638982 END: 22:38:30.808336 2019-04-30 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B4,B5,C1,D3,D4,D5,D9,E8,E9,G8,G9,I4) * .2..57....4.32.....8..1.2..2...3.4....1...3.5.3..6.7128526731497145.....396.....7 * PAIR C1: 3,9 BLK 1 C3: 3,9,5,7 # reduction candidate for 3,9 C3: 3,9 # 19 pairs C3: 5,7 # 17 pairs * PAIR D3: 4,9 BLK 2 D1: 4,9,8 # reduction candidate for 4,9 D1: 4,9 => SOLVED * 123457968649328571587916234278135496461792385935864712852673149714589623396241857 D1: 8 => CTR * 123857964.4.32...1.8..1.2.32...3.4.6.61...3.5.3..6.7128526731497145...3.396....27 F3: 4,9,6 # reduction candidate for 4,9 F3: 4,9 => CTR * 123857964.4.326..168..1.2.32...3.4.6.61...3.5.3..6.7128526731497145...3.396....27 F3: 6 # 19 pairs * PAIR D3: 4,9 COL D D6: 4,9,8 # reduction candidate for 4,9 D6: 4,9 => CTR * 123857964.4.32...1.8..1.2.32...3.4.6.61...3.5.3..6.7128526731497145...3.396....27 D6: 8 => SOLVED * 123457968649328571587916234278135496461792385935864712852673149714589623396241857 * PAIR A5: 4,9 BLK 4 A6: 4,9,5 # reduction candidate for 4,9 A6: 5 => CTR * .23.57....4.32.....8..1.23.27.1354..4617.23.553..6.7128526731497145..623396241..7 A6: 4,9 # 19 pairs * PAIR A5: 4,9 ROW 5 E5: 4,9,8 # reduction candidate for 4,9 E5: 4,9 # 18 pairs F5: 4,9,2,8 # reduction candidate for 4,9 F5: 4,9 => CTR * .2.857.34.4.32...1.83.1.276265731498.7128.365.38.6571285267314971459.6.339614...7 F5: 2,8 # 14 pairs * PAIR I4: 6,8 BLK 6 H4: 6,8,9 # reduction candidate for 6,8 H4: 6,8 => CTR * .2.8579.4.4.32...1.8..1.2.627.13.468461782395.38.6.712852673149714598623396241..7 H4: 9 # 15 pairs H5: 6,8,9 # reduction candidate for 6,8 H5: 6,8 # 15 pairs * PAIR I4: 6,8 COL I I1: 6,8,1,3,4 # reduction candidate for 6,8 I1: 6,8 => SOLVED * 123457968649328571587916234278135496461792385935864712852673149714589623396241857 I1: 1,3,4 # 13 pairs I2: 6,8,1 # reduction candidate for 6,8 I2: 6,8 => CTR * .2.457..114.328..6.8.9162.42...3.4.8..1.8.3.5.3..6.7128526731497145....3396.....7 I2: 1 # 14 pairs I8: 6,8,3 # reduction candidate for 6,8 I8: 6,8 => CTR * .2..57.8..4.328....8..162..265731498.71289365.3846571285267314971459283639614.527 I8: 3 # 26 pairs * PAIR E8: 8,9 BLK 8 F8: 8,9,2 # reduction candidate for 8,9 F8: 2 => CTR * .2.857.34.4.32...1.83.1.276265731498.712..365.38.657128526731497145926833961..527 F8: 8,9 # 29 pairs * PAIR E8: 8,9 COL E E5: 8,9,4 # reduction candidate for 8,9 E5: 4 => CTR * .2.857.34.4.32...1.83419276265731498971248365438965712852673149714592683396184527 E5: 8,9 # 13 pairs * PAIR D9: 1,2 BLK 8 F9: 1,2,4,8 # reduction candidate for 1,2 F9: 4,8 => CTR * .2.857.34.4.32...1.83.1.276265731498.712..365.38.657128526731497145926833961..527 F9: 1,2 # 29 pairs * PAIR E9: 4,8 BLK 8 F9: 4,8,1,2 # reduction candidate for 4,8 F9: 4,8 => CTR * .2.857.34.4.32...1.83.1.276265731498.712..365.38.657128526731497145926833961..527 F9: 1,2 # 29 pairs * PAIR E9: 4,8 COL E E5: 4,8,9 # reduction candidate for 4,8 E5: 9 # 27 pairs E5: 4,8 # 14 pairs * PAIR G8: 6,8 BLK 9 H8: 6,8,2,3 # reduction candidate for 6,8 H8: 6,8 => CTR * .29857.3..4.32.....83.1.27.265731498.712..365.38.657128526731497145926833961..527 H8: 2,3 # 14 pairs I8: 6,8,3 # reduction candidate for 6,8 I8: 6,8 => CTR * .2..57.8..4.328....8..162..265731498.71289365.3846571285267314971459283639614.527 I8: 3 # 26 pairs * PAIR G8: 6,8 COL G G1: 6,8,9 # reduction candidate for 6,8 G1: 6,8 # 19 pairs G2: 6,8,5,9 # reduction candidate for 6,8 G2: 6,8 => CTR * 123.57964.4.32.8.1.8..1.2.32...3.4.6.617.23.5.3..6.7128526731497145..6..396...5.7 G2: 5,9 # 14 pairs * PAIR G9: 5,8 BLK 9 H9: 5,8,2 # reduction candidate for 5,8 H9: 2 => CTR * .2.857.34.4.32...1.83.1.276265731498.712..365.38.657128526731497145926833961..527 H9: 5,8 # 29 pairs * PAIR G9: 5,8 COL G G2: 5,8,6,9 # reduction candidate for 5,8 G2: 5,8 # 19 pairs G2: 6,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060424-absurd-base-pr-000.dot * REASONING * PRF # D1: 4,9 => SOL * DIS # D1: 8 => CTR => D1: 4,9 * DIS # F3: 4,9 => CTR => F3: 6 * DIS # D6: 4,9 => CTR => D6: 8 * PRF # D6: 8 => SOL * DIS # A6: 5 => CTR => A6: 4,9 * DIS # F5: 4,9 => CTR => F5: 2,8 * DIS # H4: 6,8 => CTR => H4: 9 * PRF # I1: 6,8 => SOL * DIS # I2: 6,8 => CTR => I2: 1 * DIS # I8: 6,8 => CTR => I8: 3 * DIS # F8: 2 => CTR => F8: 8,9 * DIS # E5: 4 => CTR => E5: 8,9 * DIS # F9: 4,8 => CTR => F9: 1,2 * DIS # F9: 4,8 => CTR => F9: 1,2 * DIS # H8: 6,8 => CTR => H8: 2,3 * DIS # I8: 6,8 => CTR => I8: 3 * DIS # G2: 6,8 => CTR => G2: 5,9 * DIS # H9: 2 => CTR => H9: 5,8 * CNT 19 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B4,B5,C1,D3,D4,D5,D9,E8,E9,G8,G9,I4) * .2..57....4.32.....8..1.2..2...3.4....1...3.5.3..6.7128526731497145.....396.....7 * PAIR C1: 3,9 BLK 1 C3: 3,9,5,7 # reduction candidate for 3,9 C3: 3,9 # 19 pairs C3: 5,7 # 17 pairs * PAIR D3: 4,9 BLK 2 D1: 4,9,8 # reduction candidate for 4,9 D1: 4,9 => SOLVED * 123457968649328571587916234278135496461792385935864712852673149714589623396241857 * DURATION: 0:00:03.106643 START: 22:39:01.110178 END: 22:39:04.216821 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060424-absurd-base-pr-001.dot * REASONING * PRF # D1: 4,9 => SOL * STA D1: 4,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060424, absurd
Solution
position: 123457968649328571587916234278135496461792385935864712852673149714589623396241857 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 # C3: 3,9 => UNS * INC # C3: 5,7 => UNS * PRF # D1: 4,9 => SOL * DIS # D1: 8 => CTR => D1: 4,9 * DIS # F3: 4,9 => CTR => F3: 6 * INC # F3: 6 => UNS * DIS # D6: 4,9 => CTR => D6: 8 * PRF # D6: 8 => SOL * INC # A6: 4,9 => UNS * DIS # A6: 5 => CTR => A6: 4,9 * INC # E5: 4,9 => UNS * DIS # F5: 4,9 => CTR => F5: 2,8 * INC # F5: 2,8 => UNS * DIS # H4: 6,8 => CTR => H4: 9 * INC # H4: 9 => UNS * INC # H5: 6,8 => UNS * PRF # I1: 6,8 => SOL * INC # I1: 1,3,4 => UNS * DIS # I2: 6,8 => CTR => I2: 1 * INC # I2: 1 => UNS * DIS # I8: 6,8 => CTR => I8: 3 * INC # I8: 3 => UNS * INC # F8: 8,9 => UNS * DIS # F8: 2 => CTR => F8: 8,9 * INC # E5: 8,9 => UNS * DIS # E5: 4 => CTR => E5: 8,9 * INC # F9: 1,2 => UNS * DIS # F9: 4,8 => CTR => F9: 1,2 * DIS # F9: 4,8 => CTR => F9: 1,2 * INC # F9: 1,2 => UNS * INC # E5: 4,8 => UNS * INC # E5: 9 => UNS * DIS # H8: 6,8 => CTR => H8: 2,3 * INC # H8: 2,3 => UNS * DIS # I8: 6,8 => CTR => I8: 3 * INC # I8: 3 => UNS * INC # G1: 6,8 => UNS * DIS # G2: 6,8 => CTR => G2: 5,9 * INC # G2: 5,9 => UNS * INC # H9: 5,8 => UNS * DIS # H9: 2 => CTR => H9: 5,8 * INC # G2: 5,8 => UNS * INC # G2: 6,9 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 3,9 => UNS * INC # C3: 5,7 => UNS * PRF # D1: 4,9 => SOL * STA D1: 4,9 * CNT 3 HDP CHAINS / 3 HYP OPENED