Analysis of zz-www.sudokuoftheday.co.uk-20190412-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: ..87..6...61.........14.....5...73.93..9....7.9.....2.7..6....49.5...8...1...3... initial
Autosolve
position: .387..6.1.61.......79146....5...73.93..9....7.97....2.7.36....49.5.718...1...3... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 2,5 => CTR => A1: 4 * DIS # H2: 4,9 => CTR => H2: 7 * DIS # D2: 2,5 => CTR => D2: 3,8 * DIS # E2: 2,5 => CTR => E2: 3,8,9 * DIS # F2: 2,5 => CTR => F2: 8,9 * DIS # G7: 2,5 => CTR => G7: 1,9 * DIS # G9: 2,5 => CTR => G9: 7,9 * DIS # D2: 2,8 => CTR => D2: 3,5 * DIS # D9: 2,8 => CTR => D9: 4,5 * DIS # H4: 6,8 => CTR => H4: 1,4 * DIS # B5: 4 => CTR => B5: 2,8 * DIS # D9: 5,8 => CTR => D9: 2,4 * DIS # G7: 2,5 => CTR => G7: 1,9 * DIS # G9: 2,5 => CTR => G9: 7,9 * DIS # D9: 2,5 => CTR => D9: 4,8 * DIS # E9: 2,5 => CTR => E9: 8,9 * CNT 16 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 2,5 => CTR => A1: 4 * DIS A1: 4 # G7: 2,5 => CTR => G7: 1,9 * DIS A1: 4 + G7: 1,9 # G9: 2,5 => CTR => G9: 7,9 * DIS A1: 4 + G7: 1,9 + G9: 7,9 # E4: 2,8 => CTR => E4: 1,6 * DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 # E5: 2,8 => CTR => E5: 1,5,6 * DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 # F5: 4,5 => CTR => F5: 2,8 * DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 # H4: 6,8 => CTR => H4: 1,4 * PRF A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4 => SOL * STA A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4 * CNT 8 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..87..6...61.........14.....5...73.93..9....7.9.....2.7..6....49.5...8...1...3... | initial |
| .387..6.1.61.......79146....5...73.93..9....7.97....2.7.36....49.5.718...1...3... | autosolve |
| 438725691261389475579146283152867349384912567697534128723658914945271836816493752 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A3: 2,5 H1: 4,9 I2: 2,5 G3: 2,5 H3: 3,8 I3: 3,8 D4: 2,8 I6: 6,8 B7: 2,8 B8: 2,4 A9: 6,8 D8: 2,4 H8: 3,6 I8: 3,6 I9: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,A6: 1.. / A4 = 1 => 18 pairs (_) / A6 = 1 => 17 pairs (_) G7,H7: 1.. / G7 = 1 => 0 pairs (X) / H7 = 1 => 15 pairs (_) I2,G3: 2.. / I2 = 2 => 0 pairs (X) / G3 = 2 => 15 pairs (_) A3,G3: 2.. / A3 = 2 => 0 pairs (X) / G3 = 2 => 15 pairs (_) B8,D8: 2.. / B8 = 2 => 0 pairs (X) / D8 = 2 => 18 pairs (_) I2,I9: 2.. / I2 = 2 => 0 pairs (X) / I9 = 2 => 15 pairs (_) D2,E2: 3.. / D2 = 3 => 18 pairs (_) / E2 = 3 => 15 pairs (_) H3,I3: 3.. / H3 = 3 => 11 pairs (_) / I3 = 3 => 13 pairs (_) D6,E6: 3.. / D6 = 3 => 15 pairs (_) / E6 = 3 => 18 pairs (_) H8,I8: 3.. / H8 = 3 => 13 pairs (_) / I8 = 3 => 11 pairs (_) D2,D6: 3.. / D2 = 3 => 18 pairs (_) / D6 = 3 => 15 pairs (_) E2,E6: 3.. / E2 = 3 => 15 pairs (_) / E6 = 3 => 18 pairs (_) H3,H8: 3.. / H3 = 3 => 11 pairs (_) / H8 = 3 => 13 pairs (_) I3,I8: 3.. / I3 = 3 => 13 pairs (_) / I8 = 3 => 11 pairs (_) A1,A2: 4.. / A1 = 4 => 23 pairs (_) / A2 = 4 => 0 pairs (X) F5,F6: 4.. / F5 = 4 => 0 pairs (X) / F6 = 4 => 16 pairs (_) B8,C9: 4.. / B8 = 4 => 18 pairs (_) / C9 = 4 => 0 pairs (X) D8,D9: 4.. / D8 = 4 => 0 pairs (X) / D9 = 4 => 18 pairs (_) A1,H1: 4.. / A1 = 4 => 23 pairs (_) / H1 = 4 => 0 pairs (X) C4,H4: 4.. / C4 = 4 => 0 pairs (X) / H4 = 4 => 0 pairs (_) F6,G6: 4.. / F6 = 4 => 16 pairs (_) / G6 = 4 => 0 pairs (X) B8,D8: 4.. / B8 = 4 => 18 pairs (_) / D8 = 4 => 0 pairs (X) C9,D9: 4.. / C9 = 4 => 0 pairs (X) / D9 = 4 => 18 pairs (_) B5,B8: 4.. / B5 = 4 => 0 pairs (X) / B8 = 4 => 18 pairs (_) I2,G3: 5.. / I2 = 5 => 15 pairs (_) / G3 = 5 => 0 pairs (X) A3,G3: 5.. / A3 = 5 => 15 pairs (_) / G3 = 5 => 0 pairs (X) I2,I9: 5.. / I2 = 5 => 15 pairs (_) / I9 = 5 => 0 pairs (X) A9,C9: 6.. / A9 = 6 => 17 pairs (_) / C9 = 6 => 13 pairs (_) H8,I8: 6.. / H8 = 6 => 11 pairs (_) / I8 = 6 => 13 pairs (_) I6,I8: 6.. / I6 = 6 => 11 pairs (_) / I8 = 6 => 13 pairs (_) G2,H2: 7.. / G2 = 7 => 0 pairs (X) / H2 = 7 => 17 pairs (_) G9,H9: 7.. / G9 = 7 => 17 pairs (_) / H9 = 7 => 0 pairs (X) G2,G9: 7.. / G2 = 7 => 0 pairs (X) / G9 = 7 => 17 pairs (_) H2,H9: 7.. / H2 = 7 => 17 pairs (_) / H9 = 7 => 0 pairs (X) H3,I3: 8.. / H3 = 8 => 13 pairs (_) / I3 = 8 => 11 pairs (_) B7,A9: 8.. / B7 = 8 => 17 pairs (_) / A9 = 8 => 13 pairs (_) B5,B7: 8.. / B5 = 8 => 13 pairs (_) / B7 = 8 => 17 pairs (_) I3,I6: 8.. / I3 = 8 => 11 pairs (_) / I6 = 8 => 13 pairs (_) * DURATION: 0:00:50.389912 START: 05:14:20.085091 END: 05:15:10.475003 2019-05-01 * CP COUNT: (38) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B7,B8,D4,D8,G3,H1,H3,H8,I2,I3,I6,I8,I9) * .387..6.1.61.......79146....5...73.93..9....7.97....2.7.36....49.5.718...1...3... * PAIR A3: 2,5 BLK 1 A1: 2,5,4 # reduction candidate for 2,5 A1: 2,5 => CTR * .387..641461538..22791465...548273.93..9...57.973.54287.3659.149452718.681.4.3... A1: 4 # 23 pairs A2: 2,5,4 # reduction candidate for 2,5 A2: 2,5 # 23 pairs * PAIR H1: 4,9 BLK 3 G2: 4,9,7 # reduction candidate for 4,9 G2: 4,9 # 17 pairs H2: 4,9,7 # reduction candidate for 4,9 H2: 4,9 => CTR * .387..6.1.615387922791465...548273.93..9...57.973.54287.3659.149452718.681.4.3.7. H2: 7 # 17 pairs * PAIR I2: 2,5 ROW 2 A2: 2,5,4 # reduction candidate for 2,5 A2: 2,5 # 23 pairs D2: 2,5,3,8 # reduction candidate for 2,5 D2: 2,5 => CTR * .387..641461538..22791465...548273.93..9...57.973...287.36....49452718.68164.3275 D2: 3,8 # 16 pairs E2: 2,5,3,8,9 # reduction candidate for 2,5 E2: 2,5 => CTR * .387..6414613.8....79146....548273.93..9....7.97.3..2.7.36....49452718...1.4.3... E2: 3,8,9 # 15 pairs F2: 2,5,8,9 # reduction candidate for 2,5 F2: 2,5 => CTR * .387..641461.......79146....548273.93..9....7.97534.2.7.36....49452718...1.4.3... F2: 8,9 # 16 pairs * PAIR G3: 2,5 COL G G7: 2,5,1,9 # reduction candidate for 2,5 G7: 2,5 => CTR * 538792641.61.......79146....54827369382964157697.154287236..514945271836816453..2 G7: 1,9 # 18 pairs G9: 2,5,7,9 # reduction candidate for 2,5 G9: 2,5 => CTR * .387..6.1.61...7...79146....54827369382964157697.1542872365.9149452718..816493.7. G9: 7,9 # 16 pairs * PAIR D4: 2,8 BLK 5 E4: 2,8,1,6 # reduction candidate for 2,8 E4: 2,8 # 24 pairs E5: 2,8,1,5,6 # reduction candidate for 2,8 E5: 2,8 # 22 pairs F5: 2,8,4,5 # reduction candidate for 2,8 F5: 2,8 # 19 pairs * PAIR D4: 2,8 COL D D2: 2,8,3,5 # reduction candidate for 2,8 D2: 2,8 => CTR * 4387..6912618394755791462...5...734934.9....7.973.4.2.7836....49254718..614583..2 D2: 3,5 # 16 pairs D9: 2,8,4,5 # reduction candidate for 2,8 D9: 2,8 => CTR * 4387..691261389475579146238.5...734934.9....7.975341267836..914925471863614893752 D9: 4,5 # 16 pairs * PAIR I6: 6,8 BLK 6 H4: 6,8,1,4 # reduction candidate for 6,8 H4: 6,8 => CTR * .387.26.1.61538..227914658315482736938296..57697315.2872368...49452718368164.3... H4: 1,4 # 19 pairs H5: 6,8,1,4,5 # reduction candidate for 6,8 H5: 6,8 # 19 pairs * PAIR I6: 6,8 ROW 6 A6: 6,8,1 # reduction candidate for 6,8 A6: 6,8 # 18 pairs E6: 6,8,1,3,5 # reduction candidate for 6,8 E6: 6,8 # 19 pairs * PAIR B7: 2,8 ROW 7 E7: 2,8,5,9 # reduction candidate for 2,8 E7: 2,8 # 19 pairs F7: 2,8,5,9 # reduction candidate for 2,8 F7: 2,8 # 20 pairs * PAIR B7: 2,8 COL B B5: 2,8,4 # reduction candidate for 2,8 B5: 4 => CTR * 4387..691.61..94755791462...5...734934.9.8.67.975.4.2.7836..9149254718..614.93752 B5: 2,8 # 18 pairs * PAIR B8: 2,4 BLK 7 C9: 2,4,6 # reduction candidate for 2,4 C9: 2,4 # 17 pairs C9: 6 # 13 pairs * PAIR B8: 2,4 COL B B5: 2,4,8 # reduction candidate for 2,4 B5: 2,4 # 17 pairs B5: 8 # 13 pairs * PAIR A9: 6,8 COL A A4: 6,8,1 # reduction candidate for 6,8 A4: 6,8 # 17 pairs A6: 6,8,1 # reduction candidate for 6,8 A6: 6,8 # 18 pairs * PAIR D8: 2,4 BLK 8 D9: 2,4,5,8 # reduction candidate for 2,4 D9: 5,8 => CTR * 4387..691261389475579146238.5...734934.9....7.975341267836..914925471863614893752 D9: 2,4 # 19 pairs * PAIR I9: 2,5 BLK 9 G7: 2,5,1,9 # reduction candidate for 2,5 G7: 2,5 => CTR * 538792641.61.......79146....54827369382964157697.154287236..514945271836816453..2 G7: 1,9 # 18 pairs G9: 2,5,7,9 # reduction candidate for 2,5 G9: 2,5 => CTR * .387..6.1.61...7...79146....54827369382964157697.1542872365.9149452718..816493.7. G9: 7,9 # 16 pairs * PAIR I9: 2,5 ROW 9 D9: 2,5,4,8 # reduction candidate for 2,5 D9: 2,5 => CTR * 4387..691.61...47..79146....5...734934.9....7.97..4.2.7836....49254718..614.83... D9: 4,8 # 18 pairs E9: 2,5,8,9 # reduction candidate for 2,5 E9: 2,5 => CTR * .387..6.1.61.....55791462...548273.93829....7.97534.2.7236....49452718..816453..2 E9: 8,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190412-absurd-base-pr-000.dot * REASONING * DIS # A1: 2,5 => CTR => A1: 4 * DIS # H2: 4,9 => CTR => H2: 7 * DIS # D2: 2,5 => CTR => D2: 3,8 * DIS # E2: 2,5 => CTR => E2: 3,8,9 * DIS # F2: 2,5 => CTR => F2: 8,9 * DIS # G7: 2,5 => CTR => G7: 1,9 * DIS # G9: 2,5 => CTR => G9: 7,9 * DIS # D2: 2,8 => CTR => D2: 3,5 * DIS # D9: 2,8 => CTR => D9: 4,5 * DIS # H4: 6,8 => CTR => H4: 1,4 * DIS # B5: 4 => CTR => B5: 2,8 * DIS # D9: 5,8 => CTR => D9: 2,4 * DIS # G7: 2,5 => CTR => G7: 1,9 * DIS # G9: 2,5 => CTR => G9: 7,9 * DIS # D9: 2,5 => CTR => D9: 4,8 * DIS # E9: 2,5 => CTR => E9: 8,9 * CNT 16 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B7,B8,D4,D8,G3,H1,H3,H8,I2,I3,I6,I8,I9) * .387..6.1.61.......79146....5...73.93..9....7.97....2.7.36....49.5.718...1...3... * PAIR A3: 2,5 BLK 1 A1: 2,5,4 # reduction candidate for 2,5 A1: 2,5 => CTR * .387..641461538..22791465...548273.93..9...57.973.54287.3659.149452718.681.4.3... * RESTART * PAIR G3: 2,5 COL G G7: 2,5,1,9 # reduction candidate for 2,5 G7: 2,5 => CTR * 4387..691.61...74..79146....548273693829641576975...2.7.36...149452718...1.4.397. G9: 2,5,7,9 # reduction candidate for 2,5 G9: 2,5 => CTR * 4387.2691.61..974..79146....5482736938296.1576975...2.7236..9149452718..816493.7. * PAIR RESTART * PAIR D4: 2,8 BLK 5 E4: 2,8,1,6 # reduction candidate for 2,8 E4: 2,8 => CTR * 438752691261.39..55791462...5...73.93.29....7.973...2.7.36.8.549.5.718..816..3..2 E5: 2,8,1,5,6 # reduction candidate for 2,8 E5: 2,8 => CTR * 438752691261.39..55791462...5...73.93..9....7.973...2.7.36.8.549.5.718..816..3..2 F5: 2,8,4,5 # reduction candidate for 2,8 F5: 2,8 # 26 pairs * RESTART * PAIR D4: 2,8 BLK 5 F5: 2,8,4,5 # reduction candidate for 2,8 F5: 4,5 => CTR * 4387..691261.....55791462...562173493429.5187197..45267836..9149254718636145.3..2 * PAIR I6: 6,8 BLK 6 H4: 6,8,1,4 # reduction candidate for 6,8 H4: 6,8 => CTR * 4387..691261.....55791462...542.73.938.9....7.97..4.2.7.36....49.5.718...1...3..2 H4: 1,4 => SOLVED * 438725691261389475579146283152867349384912567697534128723658914945271836816493752 * DURATION: 0:00:09.247265 START: 05:15:44.940227 END: 05:15:54.187492 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190412-absurd-base-pr-001.dot * REASONING * DIS # A1: 2,5 => CTR => A1: 4 * DIS A1: 4 # G7: 2,5 => CTR => G7: 1,9 * DIS A1: 4 + G7: 1,9 # G9: 2,5 => CTR => G9: 7,9 * DIS A1: 4 + G7: 1,9 + G9: 7,9 # E4: 2,8 => CTR => E4: 1,6 * DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 # E5: 2,8 => CTR => E5: 1,5,6 * DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 # F5: 4,5 => CTR => F5: 2,8 * DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 # H4: 6,8 => CTR => H4: 1,4 * PRF A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4 => SOL * STA A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4 * CNT 8 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190412, absurd
Solution
position: 438725691261389475579146283152867349384912567697534128723658914945271836816493752 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 # A1: 2,5 => CTR => A1: 4 * INC # A1: 4 => UNS * INC # A2: 2,5 => UNS * INC # G2: 4,9 => UNS * DIS # H2: 4,9 => CTR => H2: 7 * INC # H2: 7 => UNS * INC # A2: 2,5 => UNS * DIS # D2: 2,5 => CTR => D2: 3,8 * INC # D2: 3,8 => UNS * DIS # E2: 2,5 => CTR => E2: 3,8,9 * INC # E2: 3,8,9 => UNS * DIS # F2: 2,5 => CTR => F2: 8,9 * INC # F2: 8,9 => UNS * DIS # G7: 2,5 => CTR => G7: 1,9 * INC # G7: 1,9 => UNS * DIS # G9: 2,5 => CTR => G9: 7,9 * INC # G9: 7,9 => UNS * INC # E4: 2,8 => UNS * INC # E5: 2,8 => UNS * INC # F5: 2,8 => UNS * DIS # D2: 2,8 => CTR => D2: 3,5 * INC # D2: 3,5 => UNS * DIS # D9: 2,8 => CTR => D9: 4,5 * INC # D9: 4,5 => UNS * DIS # H4: 6,8 => CTR => H4: 1,4 * INC # H4: 1,4 => UNS * INC # H5: 6,8 => UNS * INC # A6: 6,8 => UNS * INC # E6: 6,8 => UNS * INC # E7: 2,8 => UNS * INC # F7: 2,8 => UNS * INC # B5: 2,8 => UNS * DIS # B5: 4 => CTR => B5: 2,8 * INC # C9: 2,4 => UNS * INC # C9: 6 => UNS * INC # B5: 2,4 => UNS * INC # B5: 8 => UNS * INC # A4: 6,8 => UNS * INC # A6: 6,8 => UNS * INC # D9: 2,4 => UNS * DIS # D9: 5,8 => CTR => D9: 2,4 * DIS # G7: 2,5 => CTR => G7: 1,9 * INC # G7: 1,9 => UNS * DIS # G9: 2,5 => CTR => G9: 7,9 * INC # G9: 7,9 => UNS * DIS # D9: 2,5 => CTR => D9: 4,8 * INC # D9: 4,8 => UNS * DIS # E9: 2,5 => CTR => E9: 8,9 * INC # E9: 8,9 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 2,5 => CTR => A1: 4 * DIS A1: 4 # G7: 2,5 => CTR => G7: 1,9 * DIS A1: 4 + G7: 1,9 # G9: 2,5 => CTR => G9: 7,9 * DIS A1: 4 + G7: 1,9 + G9: 7,9 # E4: 2,8 => CTR => E4: 1,6 * DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 # E5: 2,8 => CTR => E5: 1,5,6 * INC A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 # F5: 2,8 => UNS * INC A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 # F5: 2,8 => UNS * DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 # F5: 4,5 => CTR => F5: 2,8 * DIS A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 # H4: 6,8 => CTR => H4: 1,4 * PRF A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4 => SOL * STA A1: 4 + G7: 1,9 + G9: 7,9 + E4: 1,6 + E5: 1,5,6 + F5: 2,8 + H4: 1,4 * CNT 10 HDP CHAINS / 9 HYP OPENED