Analysis of zz-www.sudokuoftheday.co.uk-20190105-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: ....17.9...6....5...9..64.1.9.4..1...547...89.8...5....73.54.....5..972....6..5.. initial
Autosolve
position: ....17.9...694..5...9..64.1.9.4..1.5.547...89.8..95....73.549...65..972.9..67.5.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 2,8 => CTR => A1: 4,5 * DIS # A2: 2,8 => CTR => A2: 1,7 * DIS # A3: 2,8 => CTR => A3: 5,7 * DIS # D1: 2,8 => CTR => D1: 3,5 * DIS # G1: 2,8 => CTR => G1: 3,6 * PRF # C9: 2,8 => SOL * DIS # C9: 1 => CTR => C9: 2,8 * DIS # B2: 2,3 => CTR => B2: 1 * DIS # H6: 3,7 => CTR => H6: 4,6 * DIS # C6: 2,7 => CTR => C6: 1 * PRF # C6: 1 => SOL * DIS # D8: 3,8 => CTR => D8: 1 * CNT 12 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 2,8 => CTR => A1: 4,5 * DIS A1: 4,5 # A2: 2,8 => CTR => A2: 1,7 * DIS A1: 4,5 + A2: 1,7 # A3: 2,8 => CTR => A3: 5,7 * DIS A1: 4,5 + A2: 1,7 + A3: 5,7 # B2: 2,3 => CTR => B2: 1 * DIS A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 # D8: 3,8 => CTR => D8: 1 * DIS A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 + D8: 1 # I1: 2,3 => CTR => I1: 6 * PRF A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 + D8: 1 + I1: 6 => SOL * STA A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 + D8: 1 + I1: 6 * CNT 7 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....17.9...6....5...9..64.1.9.4..1...547...89.8...5....73.54.....5..972....6..5.. | initial |
| ....17.9...694..5...9..64.1.9.4..1.5.547...89.8..95....73.549...65..972.9..67.5.. | autosolve |
| 428517396716943852539826471697482135354761289281395647173254968865139724942678513 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) C1: 2,8 B3: 2,3 H3: 3,7 C4: 2,7 E8: 3,8 H7: 1,6 I7: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,B2: 1.. / A2 = 1 => 0 pairs (X) / B2 = 1 => 8 pairs (_) F5,D6: 1.. / F5 = 1 => 8 pairs (_) / D6 = 1 => 0 pairs (X) H7,H9: 1.. / H7 = 1 => 14 pairs (_) / H9 = 1 => 0 pairs (*) A5,F5: 1.. / A5 = 1 => 0 pairs (X) / F5 = 1 => 8 pairs (_) A8,D8: 1.. / A8 = 1 => 0 pairs (X) / D8 = 1 => 10 pairs (_) B2,B9: 1.. / B2 = 1 => 8 pairs (_) / B9 = 1 => 0 pairs (X) C6,C9: 1.. / C6 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) F5,F9: 1.. / F5 = 1 => 8 pairs (_) / F9 = 1 => 0 pairs (X) D7,F9: 2.. / D7 = 2 => 9 pairs (_) / F9 = 2 => 0 pairs (X) A7,D7: 2.. / A7 = 2 => 0 pairs (X) / D7 = 2 => 9 pairs (_) A1,B1: 4.. / A1 = 4 => 14 pairs (_) / B1 = 4 => 11 pairs (_) H6,I6: 4.. / H6 = 4 => 8 pairs (_) / I6 = 4 => 0 pairs (X) A8,B9: 4.. / A8 = 4 => 11 pairs (_) / B9 = 4 => 14 pairs (_) A8,I8: 4.. / A8 = 4 => 11 pairs (_) / I8 = 4 => 14 pairs (_) A1,A8: 4.. / A1 = 4 => 14 pairs (_) / A8 = 4 => 11 pairs (_) B1,B9: 4.. / B1 = 4 => 11 pairs (_) / B9 = 4 => 14 pairs (_) H6,H9: 4.. / H6 = 4 => 8 pairs (_) / H9 = 4 => 0 pairs (X) A1,A3: 5.. / A1 = 5 => 11 pairs (_) / A3 = 5 => 12 pairs (_) D1,D3: 5.. / D1 = 5 => 12 pairs (_) / D3 = 5 => 11 pairs (_) A1,D1: 5.. / A1 = 5 => 11 pairs (_) / D1 = 5 => 12 pairs (_) A3,D3: 5.. / A3 = 5 => 12 pairs (_) / D3 = 5 => 11 pairs (_) G1,I1: 6.. / G1 = 6 => 12 pairs (_) / I1 = 6 => 0 pairs (*) E4,E5: 6.. / E4 = 6 => 16 pairs (_) / E5 = 6 => 8 pairs (_) H7,I7: 6.. / H7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) A2,A3: 7.. / A2 = 7 => 11 pairs (_) / A3 = 7 => 0 pairs (X) I2,H3: 7.. / I2 = 7 => 0 pairs (X) / H3 = 7 => 11 pairs (_) C4,C6: 7.. / C4 = 7 => 11 pairs (_) / C6 = 7 => 0 pairs (X) A2,I2: 7.. / A2 = 7 => 11 pairs (_) / I2 = 7 => 0 pairs (X) A3,H3: 7.. / A3 = 7 => 0 pairs (X) / H3 = 7 => 11 pairs (_) C4,H4: 7.. / C4 = 7 => 11 pairs (_) / H4 = 7 => 0 pairs (X) I2,I6: 7.. / I2 = 7 => 0 pairs (X) / I6 = 7 => 11 pairs (_) G1,G2: 8.. / G1 = 8 => 0 pairs (X) / G2 = 8 => 8 pairs (_) E4,F4: 8.. / E4 = 8 => 17 pairs (_) / F4 = 8 => 8 pairs (_) C1,C9: 8.. / C1 = 8 => 8 pairs (_) / C9 = 8 => 0 pairs (X) * DURATION: 0:00:35.574492 START: 02:44:03.239287 END: 02:44:38.813779 2019-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,C1,C4,E8,H3,H7,I7) * ....17.9...694..5...9..64.1.9.4..1.5.547...89.8..95....73.549...65..972.9..67.5.. * PAIR C1: 2,8 BLK 1 A1: 2,8,4,5 # reduction candidate for 2,8 A1: 2,8 => CTR * .48517.9.716943852539826471397482165.5476138968.395.47.73.549..46513972892.678534 A1: 4,5 # 8 pairs A2: 2,8,1,7 # reduction candidate for 2,8 A2: 2,8 => CTR * 5...17.9..1694..577.9586431.9.4.81.5.547...89.8..95....73.549...65.3972.9..67.5.3 A2: 1,7 # 8 pairs A3: 2,8,5,7 # reduction candidate for 2,8 A3: 2,8 => CTR * 54.817.9.716943852839526471.974.21.5.547.1.89.8.395.4717325496.4651.972.92.67.5.4 A3: 5,7 # 9 pairs * PAIR C1: 2,8 ROW 1 D1: 2,8,3,5 # reduction candidate for 2,8 D1: 2,8 => CTR * 548217.9.716943852.395.6471.974..1.5.547.1.89.8.395.47.73.549..46513972892.678534 D1: 3,5 # 8 pairs G1: 2,8,3,6 # reduction candidate for 2,8 G1: 2,8 => CTR * ....178967169483528.95.6471.97482135.54761289281395647173254968.65..972.9..67.51. G1: 3,6 # 9 pairs * PAIR C1: 2,8 COL C C9: 2,8,1 # reduction candidate for 2,8 C9: 2,8 => SOLVED * 428517396716943852539826471697482135354761289281395647173254968865139724942678513 C9: 1 => CTR * .48.1769..1694.857739..64.1.9.4..1.5.547.1.8918..95.64.73.549164651.972.92167.54. * PAIR B3: 2,3 BLK 1 B1: 2,3,4 # reduction candidate for 2,3 B1: 2,3 # 14 pairs B2: 2,3,1 # reduction candidate for 2,3 B2: 2,3 => CTR * ....17.9.1.694..577.9586431.9.4.81.5.547.1.89.81.95.74.73.549..465139728918672543 B2: 1 # 8 pairs * PAIR B3: 2,3 ROW 3 D3: 2,3,5,8 # reduction candidate for 2,3 D3: 2,3 # 19 pairs E3: 2,3,8 # reduction candidate for 2,3 E3: 2,3 # 14 pairs * PAIR H3: 3,7 BLK 3 I2: 3,7,2 # reduction candidate for 3,7 I2: 3,7 # 14 pairs I2: 2 # 12 pairs * PAIR H3: 3,7 COL H H4: 3,7,6 # reduction candidate for 3,7 H4: 3,7 # 12 pairs H6: 3,7,4,6 # reduction candidate for 3,7 H6: 3,7 => CTR * .4..17.9...694..577.9586431.9.4.81.5.547.1.89.8..95.74.738549164651397289.8672543 H6: 4,6 # 8 pairs * PAIR C4: 2,7 BLK 4 C6: 2,7,1 # reduction candidate for 2,7 C6: 2,7 => CTR * .48.1769..1694.857739..64.1.9.4..1.5.547.1.8918..95.64.73.549164651.972.92167.54. C6: 1 => SOLVED * 428517396716943852539826471697482135354761289281395647173254968865139724942678513 * PAIR E8: 3,8 BLK 8 D8: 3,8,1 # reduction candidate for 3,8 D8: 3,8 => CTR * 4..517.9..1694..5.5.9..6471.974..1.5.547.1.89.81.95.47.73154968165..9724948672513 D8: 1 # 10 pairs F9: 3,8,1,2 # reduction candidate for 3,8 F9: 3,8 # 22 pairs * PAIR E8: 3,8 ROW 8 I8: 3,8,4 # reduction candidate for 3,8 I8: 4 # 14 pairs I8: 3,8 # 11 pairs * PAIR E8: 3,8 COL E E3: 3,8,2 # reduction candidate for 3,8 E3: 3,8 # 13 pairs E4: 3,8,2,6 # reduction candidate for 3,8 E4: 3,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190105-absurd-base-pr-000.dot * REASONING * DIS # A1: 2,8 => CTR => A1: 4,5 * DIS # A2: 2,8 => CTR => A2: 1,7 * DIS # A3: 2,8 => CTR => A3: 5,7 * DIS # D1: 2,8 => CTR => D1: 3,5 * DIS # G1: 2,8 => CTR => G1: 3,6 * PRF # C9: 2,8 => SOL * DIS # C9: 1 => CTR => C9: 2,8 * DIS # B2: 2,3 => CTR => B2: 1 * DIS # H6: 3,7 => CTR => H6: 4,6 * DIS # C6: 2,7 => CTR => C6: 1 * PRF # C6: 1 => SOL * DIS # D8: 3,8 => CTR => D8: 1 * CNT 12 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,C1,C4,E8,H3,H7,I7) * ....17.9...694..5...9..64.1.9.4..1.5.547...89.8..95....73.549...65..972.9..67.5.. * PAIR C1: 2,8 BLK 1 A1: 2,8,4,5 # reduction candidate for 2,8 A1: 2,8 => CTR * .48517.9.716943852539826471397482165.5476138968.395.47.73.549..46513972892.678534 A2: 2,8,1,7 # reduction candidate for 2,8 A2: 2,8 => CTR * 5...17.9..1694..577.9586431.9.4.81.5.547...89.8..95....73.549...65.3972.9..67.5.3 A3: 2,8,5,7 # reduction candidate for 2,8 A3: 2,8 => CTR * 54.817.9.716943852839526471.974.21.5.547.1.89.8.395.4717325496.4651.972.92.67.5.4 * PAIR B3: 2,3 BLK 1 B1: 2,3,4 # reduction candidate for 2,3 B1: 2,3 # 14 pairs B2: 2,3,1 # reduction candidate for 2,3 B2: 2,3 => CTR * ..8.17.9.1.694.8577.9586431.9.4.81.5.547.1.89.81.95.74.73.549..4651397289..67.5.. * RESTART * PAIR B3: 2,3 ROW 3 D3: 2,3,8 # reduction candidate for 2,3 D3: 2,3 # 18 pairs E3: 2,3,8 # reduction candidate for 2,3 E3: 2,3 # 17 pairs * PAIR E8: 3,8 BLK 8 D8: 3,8,1 # reduction candidate for 3,8 D8: 3,8 => CTR * 4.8517.9.71694.85.5.9..6471.974..1.5.547.1.89.81.95.47873.549..165..972494267.5.. * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A7,B1,B3,C6,C9,D6,D7,E3,E5,F2,F9,G1,H4,H7,H9,I2,I7,I9) * 4.8517.9.71694.85.5.9..6471.974..1.5.547.1.89.8..95.47.73.549..86513972494.67.5.. * PAIR B1: 2,3 ROW 1 I1: 2,3,6 # reduction candidate for 2,3 I1: 2,3 => CTR * 4.851769.71694.85.5.9..6471.974..165.54761.89681.95.47173.549..86513972494.67.5.. I1: 6 => SOLVED * 428517396716943852539826471697482135354761289281395647173254968865139724942678513 * DURATION: 0:00:09.375287 START: 02:44:58.073199 END: 02:45:07.448486 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190105-absurd-base-pr-001.dot * REASONING * DIS # A1: 2,8 => CTR => A1: 4,5 * DIS A1: 4,5 # A2: 2,8 => CTR => A2: 1,7 * DIS A1: 4,5 + A2: 1,7 # A3: 2,8 => CTR => A3: 5,7 * DIS A1: 4,5 + A2: 1,7 + A3: 5,7 # B2: 2,3 => CTR => B2: 1 * DIS A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 # D8: 3,8 => CTR => D8: 1 * DIS A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 + D8: 1 # I1: 2,3 => CTR => I1: 6 * PRF A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 + D8: 1 + I1: 6 => SOL * STA A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 + D8: 1 + I1: 6 * CNT 7 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190105, absurd
Solution
position: 428517396716943852539826471697482135354761289281395647173254968865139724942678513 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: 2,8 => CTR => A1: 4,5 * INC # A1: 4,5 => UNS * DIS # A2: 2,8 => CTR => A2: 1,7 * INC # A2: 1,7 => UNS * DIS # A3: 2,8 => CTR => A3: 5,7 * INC # A3: 5,7 => UNS * DIS # D1: 2,8 => CTR => D1: 3,5 * INC # D1: 3,5 => UNS * DIS # G1: 2,8 => CTR => G1: 3,6 * INC # G1: 3,6 => UNS * PRF # C9: 2,8 => SOL * DIS # C9: 1 => CTR => C9: 2,8 * INC # B1: 2,3 => UNS * DIS # B2: 2,3 => CTR => B2: 1 * INC # B2: 1 => UNS * INC # D3: 2,3 => UNS * INC # E3: 2,3 => UNS * INC # I2: 3,7 => UNS * INC # I2: 2 => UNS * INC # H4: 3,7 => UNS * DIS # H6: 3,7 => CTR => H6: 4,6 * INC # H6: 4,6 => UNS * DIS # C6: 2,7 => CTR => C6: 1 * PRF # C6: 1 => SOL * DIS # D8: 3,8 => CTR => D8: 1 * INC # D8: 1 => UNS * INC # F9: 3,8 => UNS * INC # I8: 3,8 => UNS * INC # I8: 4 => UNS * INC # E3: 3,8 => UNS * INC # E4: 3,8 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 2,8 => CTR => A1: 4,5 * DIS A1: 4,5 # A2: 2,8 => CTR => A2: 1,7 * DIS A1: 4,5 + A2: 1,7 # A3: 2,8 => CTR => A3: 5,7 * INC A1: 4,5 + A2: 1,7 + A3: 5,7 # B1: 2,3 => UNS * DIS A1: 4,5 + A2: 1,7 + A3: 5,7 # B2: 2,3 => CTR => B2: 1 * INC A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 # D3: 2,3 => UNS * INC A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 # E3: 2,3 => UNS * DIS A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 # D8: 3,8 => CTR => D8: 1 * DIS A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 + D8: 1 # I1: 2,3 => CTR => I1: 6 * PRF A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 + D8: 1 + I1: 6 => SOL * STA A1: 4,5 + A2: 1,7 + A3: 5,7 + B2: 1 + D8: 1 + I1: 6 * CNT 10 HDP CHAINS / 9 HYP OPENED