Analysis of zz-www.sudokuoftheday.co.uk-20060821-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: .894...5.3..69..2....3..............5..7.4.3.2.3....97.68...1..7.......5.2.1..96. initial
Autosolve
position: .894..35.3..69..2...23....98........5967.4.3.2.3....97968...17.731.....54251..96. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 4,7 => CTR => B2: 5 * DIS # G2: 8 => CTR => G2: 4,7 * PRF # I4: 1,6 => SOL * DIS # I4: 2,4 => CTR => I4: 1,6 * PRF # B4: 4,7 => SOL * DIS # B4: 1 => CTR => B4: 4,7 * PRF # B4: 1,4 => SOL * DIS # B4: 7 => CTR => B4: 1,4 * DIS # G6: 5,8 => CTR => G6: 4,6 * DIS # I4: 1,4 => CTR => I4: 2,6 * PRF # B4: 1,4 => SOL * DIS # B4: 7 => CTR => B4: 1,4 * DIS # H3: 8 => CTR => H3: 1,4 * PRF # I5: 2,8 => SOL * DIS # I5: 1 => CTR => I5: 2,8 * DIS # E5: 2,8 => CTR => E5: 1 * PRF # E5: 1 => SOL * DIS # G8: 4 => CTR => G8: 2,8 * PRF # E7: 2,5 => SOL * DIS # D4: 9 => CTR => D4: 2,5 * DIS # G8: 4,8 => CTR => G8: 2 * PRF # E8: 4,8 => SOL * PRF # H3: 4,8 => SOL * DIS # H3: 1 => CTR => H3: 4,8 * DIS # F9: 3,8 => CTR => F9: 7 * CNT 25 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 # B2: 4,7 => CTR => B2: 5 * DIS B2: 5 # G2: 8 => CTR => G2: 4,7 * PRF B2: 5 + G2: 4,7 # I4: 1,6 => SOL * STA B2: 5 + G2: 4,7 + I4: 1,6 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .894...5.3..69..2....3..............5..7.4.3.2.3....97.68...1..7.......5.2.1..96. | initial |
| .894..35.3..69..2...23....98........5967.4.3.2.3....97968...17.731.....54251..96. | autosolve |
| 689472351354691728172358649847239516596714832213865497968523174731946285425187963 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A1: 1,6 C2: 4,7 A3: 1,6 E1: 2,7 F1: 2,7 I1: 1,6 C4: 4,7 B6: 1,4 D6: 5,8 H4: 1,4 G5: 2,8 D7: 2,5 H8: 4,8 I9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 0 pairs (X) / A3 = 1 => 0 pairs (_) B4,B6: 1.. / B4 = 1 => 0 pairs (X) / B6 = 1 => 0 pairs (_) A1,I1: 1.. / A1 = 1 => 0 pairs (X) / I1 = 1 => 0 pairs (_) F2,I2: 1.. / F2 = 1 => 23 pairs (_) / I2 = 1 => 0 pairs (X) E5,I5: 1.. / E5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) H3,H4: 1.. / H3 = 1 => 0 pairs (X) / H4 = 1 => 0 pairs (_) E1,F1: 2.. / E1 = 2 => 0 pairs (X) / F1 = 2 => 14 pairs (_) I7,G8: 2.. / I7 = 2 => 0 pairs (X) / G8 = 2 => 21 pairs (_) E4,F4: 3.. / E4 = 3 => 16 pairs (_) / F4 = 3 => 0 pairs (X) I7,I9: 3.. / I7 = 3 => 0 pairs (X) / I9 = 3 => 17 pairs (_) E7,E8: 4.. / E7 = 4 => 15 pairs (_) / E8 = 4 => 0 pairs (*) B6,G6: 4.. / B6 = 4 => 0 pairs (X) / G6 = 4 => 0 pairs (_) E7,I7: 4.. / E7 = 4 => 15 pairs (_) / I7 = 4 => 0 pairs (*) C2,C4: 4.. / C2 = 4 => 0 pairs (*) / C4 = 4 => 0 pairs (X) B2,B3: 5.. / B2 = 5 => 16 pairs (_) / B3 = 5 => 0 pairs (X) G4,G6: 5.. / G4 = 5 => 16 pairs (_) / G6 = 5 => 0 pairs (X) B2,F2: 5.. / B2 = 5 => 16 pairs (_) / F2 = 5 => 0 pairs (X) A1,A3: 6.. / A1 = 6 => 0 pairs (*) / A3 = 6 => 0 pairs (X) I1,G3: 6.. / I1 = 6 => 0 pairs (X) / G3 = 6 => 0 pairs (_) E8,F8: 6.. / E8 = 6 => 15 pairs (_) / F8 = 6 => 22 pairs (_) A1,I1: 6.. / A1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) A3,G3: 6.. / A3 = 6 => 0 pairs (X) / G3 = 6 => 0 pairs (_) I1,I4: 6.. / I1 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) E1,F1: 7.. / E1 = 7 => 14 pairs (_) / F1 = 7 => 0 pairs (X) G2,G3: 7.. / G2 = 7 => 0 pairs (*) / G3 = 7 => 0 pairs (X) B4,C4: 7.. / B4 = 7 => 0 pairs (X) / C4 = 7 => 0 pairs (_) E9,F9: 7.. / E9 = 7 => 0 pairs (X) / F9 = 7 => 14 pairs (_) B3,G3: 7.. / B3 = 7 => 0 pairs (*) / G3 = 7 => 0 pairs (X) C2,C4: 7.. / C2 = 7 => 0 pairs (X) / C4 = 7 => 0 pairs (_) E1,E9: 7.. / E1 = 7 => 14 pairs (_) / E9 = 7 => 0 pairs (X) F1,F9: 7.. / F1 = 7 => 0 pairs (X) / F9 = 7 => 14 pairs (_) D6,D8: 8.. / D6 = 8 => 15 pairs (_) / D8 = 8 => 0 pairs (X) H3,H8: 8.. / H3 = 8 => 0 pairs (X) / H8 = 8 => 18 pairs (_) D4,F4: 9.. / D4 = 9 => 0 pairs (X) / F4 = 9 => 18 pairs (_) D8,F8: 9.. / D8 = 9 => 18 pairs (_) / F8 = 9 => 0 pairs (X) D4,D8: 9.. / D4 = 9 => 0 pairs (X) / D8 = 9 => 18 pairs (_) F4,F8: 9.. / F4 = 9 => 18 pairs (_) / F8 = 9 => 0 pairs (X) * DURATION: 0:00:46.723585 START: 01:57:38.738692 END: 01:58:25.462277 2019-05-01 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B6,C2,C4,D6,D7,E1,F1,G5,H4,H8,I1,I9) * .894..35.3..69..2...23....98........5967.4.3.2.3....97968...17.731.....54251..96. * PAIR C2: 4,7 BLK 1 B2: 4,7,5 # reduction candidate for 4,7 B2: 4,7 => CTR * .894..35.3..695.21.523..7498......1.596714.3.213...497968...174731.462.54251..96. B2: 5 # 16 pairs B3: 4,7,5 # reduction candidate for 4,7 B3: 4,7 # 16 pairs * PAIR C2: 4,7 ROW 2 G2: 4,7,8 # reduction candidate for 4,7 G2: 8 => CTR * .894..3563..69.82.6.23..7.98........5967142382.3....97968...172731...4854251..963 G2: 4,7 # 18 pairs * PAIR I1: 1,6 COL I I4: 1,6,2,4 # reduction candidate for 1,6 I4: 1,6 => SOLVED * 689472351354691728172358649847239516596714832213865497968523174731946285425187963 I4: 2,4 => CTR * 1894723563.46917286723..419817..9.42596724831243815.97968...174731.462854251..963 * PAIR C4: 4,7 BLK 4 B4: 4,7,1 # reduction candidate for 4,7 B4: 4,7 => SOLVED * 689472351354691728172358649847239516596714832213865497968523174731946285425187963 B4: 1 => CTR * 1894723563546917286723..419817.6..4259672483124381..97968...174731.462854251..963 * PAIR B6: 1,4 BLK 4 B4: 1,4,7 # reduction candidate for 1,4 B4: 1,4 => SOLVED * 689472351354691728172358649847239516596714832213865497968523174731946285425187963 B4: 7 => CTR * .894..35.3.769.82...23..749874....1.596714.3.213...497968...17.731.....54251..96. * PAIR D6: 5,8 BLK 5 E6: 5,8,1,6 # reduction candidate for 5,8 E6: 5,8 # 20 pairs F6: 5,8,1,6 # reduction candidate for 5,8 F6: 5,8 # 26 pairs * PAIR D6: 5,8 ROW 6 G6: 5,8,4,6 # reduction candidate for 5,8 G6: 5,8 => CTR * 1894..3563.4691.286.23..419817..9.4.5967.4.31243....97968...174731.462854251..963 G6: 4,6 # 18 pairs * PAIR H4: 1,4 BLK 6 I4: 1,4,2,6 # reduction candidate for 1,4 I4: 1,4 => CTR * 1894..3563..69..2.6.23....98........5967.4.3.2.3....97968...17.731.....54251..96. I4: 2,6 # 15 pairs * PAIR H4: 1,4 ROW 4 B4: 1,4,7 # reduction candidate for 1,4 B4: 1,4 => SOLVED * 689472351354691728172358649847239516596714832213865497968523174731946285425187963 B4: 7 => CTR * .894..35.3.769.82...23..749874....1.596714.3.213...497968...17.731.....54251..96. * PAIR H4: 1,4 COL H H3: 1,4,8 # reduction candidate for 1,4 H3: 8 => CTR * .894..35.3..69872...23...898......1.596714.3.213...497968...17.731....454251..96. H3: 1,4 # 18 pairs * PAIR G5: 2,8 BLK 6 I5: 2,8,1 # reduction candidate for 2,8 I5: 2,8 => SOLVED * 689472351354691728172358649847239516596714832213865497968523174731946285425187963 I5: 1 => CTR * 1894723563546917286723..419817....4259672483124381..979682..174731946285425187963 * PAIR G5: 2,8 ROW 5 E5: 2,8,1 # reduction candidate for 2,8 E5: 2,8 => CTR * 1894723563546917286723..419817....4259672483124381..979682..174731946285425187963 E5: 1 => SOLVED * 689472351354691728172358649847239516596714832213865497968523174731946285425187963 * PAIR G5: 2,8 COL G G8: 2,8,4 # reduction candidate for 2,8 G8: 4 => CTR * .894..35.3.469..2...23...4981.......5967.4.3.2438...97968543172731...4854251..963 G8: 2,8 # 20 pairs * PAIR D7: 2,5 BLK 8 E7: 2,5,3,4 # reduction candidate for 2,5 E7: 2,5 => SOLVED * 689472351354691728172358649847239516596714832213865497968523174731946285425187963 E7: 3,4 # 15 pairs F7: 2,5,3 # reduction candidate for 2,5 F7: 2,5 # 23 pairs * PAIR D7: 2,5 COL D D4: 2,5,9 # reduction candidate for 2,5 D4: 9 => CTR * .894..35.3..69..24.423..7.98.49...1.596714.3.213...497968.4.17.731.69.454251..96. D4: 2,5 # 18 pairs * PAIR H8: 4,8 BLK 9 G8: 4,8,2 # reduction candidate for 4,8 G8: 4,8 => CTR * .894..35.3..69..24.423..7.98.4.3..1.5967.4.3.2.38...97968543172731.....54251..963 G8: 2 # 21 pairs * PAIR H8: 4,8 ROW 8 E8: 4,8,2,6 # reduction candidate for 4,8 E8: 4,8 => SOLVED * 689472351354691728172358649847239516596714832213865497968523174731946285425187963 E8: 2,6 # 16 pairs * PAIR H8: 4,8 COL H H3: 4,8,1 # reduction candidate for 4,8 H3: 4,8 => SOLVED * 689472351354691728172358649847239516596714832213865497968523174731946285425187963 H3: 1 => CTR * 1894723563546917286723..419817.6..4259672483124381..97968...174731.462854251..963 * PAIR I9: 3,8 ROW 9 E9: 3,8,7 # reduction candidate for 3,8 E9: 3,8 # 14 pairs F9: 3,8,7 # reduction candidate for 3,8 F9: 3,8 => CTR * 68942735135.6917281723..649847.3.516596714832213...497968...174731.46285425178963 F9: 7 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060821-absurd-base-pr-000.dot * REASONING * DIS # B2: 4,7 => CTR => B2: 5 * DIS # G2: 8 => CTR => G2: 4,7 * PRF # I4: 1,6 => SOL * DIS # I4: 2,4 => CTR => I4: 1,6 * PRF # B4: 4,7 => SOL * DIS # B4: 1 => CTR => B4: 4,7 * PRF # B4: 1,4 => SOL * DIS # B4: 7 => CTR => B4: 1,4 * DIS # G6: 5,8 => CTR => G6: 4,6 * DIS # I4: 1,4 => CTR => I4: 2,6 * PRF # B4: 1,4 => SOL * DIS # B4: 7 => CTR => B4: 1,4 * DIS # H3: 8 => CTR => H3: 1,4 * PRF # I5: 2,8 => SOL * DIS # I5: 1 => CTR => I5: 2,8 * DIS # E5: 2,8 => CTR => E5: 1 * PRF # E5: 1 => SOL * DIS # G8: 4 => CTR => G8: 2,8 * PRF # E7: 2,5 => SOL * DIS # D4: 9 => CTR => D4: 2,5 * DIS # G8: 4,8 => CTR => G8: 2 * PRF # E8: 4,8 => SOL * PRF # H3: 4,8 => SOL * DIS # H3: 1 => CTR => H3: 4,8 * DIS # F9: 3,8 => CTR => F9: 7 * CNT 25 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B6,C2,C4,D6,D7,E1,F1,G5,H4,H8,I1,I9) * .894..35.3..69..2...23....98........5967.4.3.2.3....97968...17.731.....54251..96. * PAIR C2: 4,7 BLK 1 B2: 4,7,5 # reduction candidate for 4,7 B2: 4,7 => CTR * .894..35.3..695.21.523..7498......1.596714.3.213...497968...174731.462.54251..96. * RESTART * PAIR C2: 4,7 ROW 2 G2: 4,7,8 # reduction candidate for 4,7 G2: 8 => CTR * .894..35.35769.824.423..719874......5967.4.3.2.3....97968...17.731.....54251..96. * PAIR RESTART * PAIR I1: 1,6 COL I I4: 1,6,2,4 # reduction candidate for 1,6 I4: 1,6 => SOLVED * 689472351354691728172358649847239516596714832213865497968523174731946285425187963 * DURATION: 0:00:03.740850 START: 01:58:55.322031 END: 01:58:59.062881 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060821-absurd-base-pr-001.dot * REASONING * DIS # B2: 4,7 => CTR => B2: 5 * DIS B2: 5 # G2: 8 => CTR => G2: 4,7 * PRF B2: 5 + G2: 4,7 # I4: 1,6 => SOL * STA B2: 5 + G2: 4,7 + I4: 1,6 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060821, absurd
Solution
position: 689472351354691728172358649847239516596714832213865497968523174731946285425187963 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 # B2: 4,7 => CTR => B2: 5 * INC # B2: 5 => UNS * INC # B3: 4,7 => UNS * INC # G2: 4,7 => UNS * DIS # G2: 8 => CTR => G2: 4,7 * PRF # I4: 1,6 => SOL * DIS # I4: 2,4 => CTR => I4: 1,6 * PRF # B4: 4,7 => SOL * DIS # B4: 1 => CTR => B4: 4,7 * PRF # B4: 1,4 => SOL * DIS # B4: 7 => CTR => B4: 1,4 * INC # E6: 5,8 => UNS * INC # F6: 5,8 => UNS * DIS # G6: 5,8 => CTR => G6: 4,6 * INC # G6: 4,6 => UNS * DIS # I4: 1,4 => CTR => I4: 2,6 * INC # I4: 2,6 => UNS * PRF # B4: 1,4 => SOL * DIS # B4: 7 => CTR => B4: 1,4 * INC # H3: 1,4 => UNS * DIS # H3: 8 => CTR => H3: 1,4 * PRF # I5: 2,8 => SOL * DIS # I5: 1 => CTR => I5: 2,8 * DIS # E5: 2,8 => CTR => E5: 1 * PRF # E5: 1 => SOL * INC # G8: 2,8 => UNS * DIS # G8: 4 => CTR => G8: 2,8 * PRF # E7: 2,5 => SOL * INC # E7: 3,4 => UNS * INC # F7: 2,5 => UNS * INC # D4: 2,5 => UNS * DIS # D4: 9 => CTR => D4: 2,5 * DIS # G8: 4,8 => CTR => G8: 2 * INC # G8: 2 => UNS * PRF # E8: 4,8 => SOL * INC # E8: 2,6 => UNS * PRF # H3: 4,8 => SOL * DIS # H3: 1 => CTR => H3: 4,8 * INC # E9: 3,8 => UNS * DIS # F9: 3,8 => CTR => F9: 7 * INC # F9: 7 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 4,7 => CTR => B2: 5 * INC B2: 5 # G2: 4,7 => UNS * DIS B2: 5 # G2: 8 => CTR => G2: 4,7 * PRF B2: 5 + G2: 4,7 # I4: 1,6 => SOL * STA B2: 5 + G2: 4,7 + I4: 1,6 * CNT 4 HDP CHAINS / 4 HYP OPENED