Analysis of zz-www.sudokuoftheday.co.uk-20060602-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: ..8.....1..4..76...6...9.5.........668.79.52.2..4..78..7.386....4...2..........9. initial
Autosolve
position: ..86...71..4..763.76...9.5.4.7..8.1668.79.5242..46.78..7.386.4..4.9.2.6...6....9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 2,8 => CTR => I2: 9 * DIS # G3: 2,8 => CTR => G3: 4 * DIS # D3: 2,8 => CTR => D3: 1 * DIS # C6: 1,3 => CTR => C6: 5,9 * PRF # C8: 1,3 => SOL * DIS # E4: 3 => CTR => E4: 2,5 * DIS # D2: 2,5 => CTR => D2: 1,8 * DIS # F6: 5 => CTR => F6: 1,3 * DIS # B4: 5 => CTR => B4: 3,9 * DIS # B6: 3,9 => CTR => B6: 1,5 * DIS # B9: 1,5 => CTR => B9: 2,3 * DIS # D2: 1,5 => CTR => D2: 2,8 * DIS # E9: 4,5 => CTR => E9: 1,7 * DIS # F1: 3 => CTR => F1: 4,5 * PRF # C7: 5,9 => SOL * DIS # C7: 1,9 => CTR => C7: 2,5 * CNT 16 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I2: 2,8 => CTR => I2: 9 * DIS I2: 9 # G3: 2,8 => CTR => G3: 4 * DIS I2: 9 + G3: 4 # C3: 1,3 => CTR => C3: 2 * PRF I2: 9 + G3: 4 + C3: 2 => SOL * STA I2: 9 + G3: 4 + C3: 2 * CNT 4 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..8.....1..4..76...6...9.5.........668.79.52.2..4..78..7.386....4...2..........9. | initial |
| ..86...71..4..763.76...9.5.4.7..8.1668.79.5242..46.78..7.386.4..4.9.2.6...6....9. | autosolve |
| 398645271514827639762139458437258916681793524259461783975386142143972865826514397 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) I3: 2,8 C5: 1,3 D4: 2,5 F5: 1,3 G4: 3,9 I6: 3,9 D9: 1,5 F9: 4,5 G7: 1,2 I7: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F5,F6: 1.. / F5 = 1 => 0 pairs (X) / F6 = 1 => 16 pairs (_) C5,F5: 1.. / C5 = 1 => 16 pairs (_) / F5 = 1 => 0 pairs (X) D4,E4: 2.. / D4 = 2 => 11 pairs (_) / E4 = 2 => 0 pairs (X) C7,B9: 2.. / C7 = 2 => 19 pairs (_) / B9 = 2 => 0 pairs (*) C3,C7: 2.. / C3 = 2 => 0 pairs (*) / C7 = 2 => 0 pairs (X) G4,I6: 3.. / G4 = 3 => 0 pairs (X) / I6 = 3 => 13 pairs (_) C3,E3: 3.. / C3 = 3 => 0 pairs (X) / E3 = 3 => 16 pairs (_) C5,F5: 3.. / C5 = 3 => 0 pairs (X) / F5 = 3 => 16 pairs (_) G1,G3: 4.. / G1 = 4 => 0 pairs (X) / G3 = 4 => 11 pairs (_) E9,F9: 4.. / E9 = 4 => 0 pairs (X) / F9 = 4 => 10 pairs (_) E3,G3: 4.. / E3 = 4 => 0 pairs (X) / G3 = 4 => 11 pairs (_) F1,F9: 4.. / F1 = 4 => 0 pairs (X) / F9 = 4 => 10 pairs (_) E8,E9: 7.. / E8 = 7 => 12 pairs (_) / E9 = 7 => 11 pairs (_) I8,I9: 7.. / I8 = 7 => 11 pairs (_) / I9 = 7 => 12 pairs (_) E8,I8: 7.. / E8 = 7 => 12 pairs (_) / I8 = 7 => 11 pairs (_) E9,I9: 7.. / E9 = 7 => 11 pairs (_) / I9 = 7 => 12 pairs (_) D2,D3: 8.. / D2 = 8 => 12 pairs (_) / D3 = 8 => 0 pairs (X) A8,A9: 8.. / A8 = 8 => 11 pairs (_) / A9 = 8 => 10 pairs (_) D2,I2: 8.. / D2 = 8 => 12 pairs (_) / I2 = 8 => 0 pairs (X) G1,I2: 9.. / G1 = 9 => 0 pairs (X) / I2 = 9 => 13 pairs (_) G4,I6: 9.. / G4 = 9 => 13 pairs (_) / I6 = 9 => 0 pairs (X) A7,C7: 9.. / A7 = 9 => 16 pairs (_) / C7 = 9 => 0 pairs (X) B4,G4: 9.. / B4 = 9 => 0 pairs (X) / G4 = 9 => 13 pairs (_) C6,C7: 9.. / C6 = 9 => 16 pairs (_) / C7 = 9 => 0 pairs (X) G1,G4: 9.. / G1 = 9 => 0 pairs (X) / G4 = 9 => 13 pairs (_) I2,I6: 9.. / I2 = 9 => 13 pairs (_) / I6 = 9 => 0 pairs (X) * DURATION: 0:00:27.213074 START: 23:34:27.270408 END: 23:34:54.483482 2019-04-30 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,D4,D9,F5,F9,G4,G7,I3,I6,I7) * ..86...71..4..763.76...9.5.4.7..8.1668.79.5242..46.78..7.386.4..4.9.2.6...6....9. * PAIR I3: 2,8 BLK 3 I2: 2,8,9 # reduction candidate for 2,8 I2: 2,8 => CTR * ..86249719.4..7632762.3945849725831668.79.5242..46.789.79386245.4.9.2.6..26.45.97 I2: 9 # 13 pairs G3: 2,8,4 # reduction candidate for 2,8 G3: 2,8 => CTR * ..8635471..48.7639763149.5.4372589166817935242..461783.72386145.459.2.6..16574.9. G3: 4 # 11 pairs * PAIR I3: 2,8 ROW 3 D3: 2,8,1 # reduction candidate for 2,8 D3: 2,8 => CTR * .9864.271.248.763976.2.94584.7..891668.79.5242.946.783972386145.459.2.67..6.74.92 D3: 1 # 14 pairs * PAIR I3: 2,8 COL I I9: 2,8,3,5,7 # reduction candidate for 2,8 I9: 2,8 # 15 pairs I9: 3,5,7 # 10 pairs * PAIR C5: 1,3 BLK 4 B6: 1,3,5,9 # reduction candidate for 1,3 B6: 1,3 # 13 pairs C6: 1,3,5,9 # reduction candidate for 1,3 C6: 1,3 => CTR * ..862497191485763.762.394584.7..8.1668.79.5242..46.78.179386245.459.2.6..26....9. C6: 5,9 # 11 pairs * PAIR C5: 1,3 COL C C3: 1,3,2 # reduction candidate for 1,3 C3: 1,3 # 19 pairs C8: 1,3,5 # reduction candidate for 1,3 C8: 1,3 => SOLVED * 398645271514827639762139458437258916681793524259461783975386142143972865826514397 C8: 5 # 11 pairs * PAIR D4: 2,5 BLK 5 E4: 2,5,3 # reduction candidate for 2,5 E4: 3 => CTR * ..86...71..4..763.76...9.5.4.72389166837915242..465783.7.386.4..4.9.2.6...6..4.9. E4: 2,5 # 14 pairs * PAIR D4: 2,5 COL D D2: 2,5,1,8 # reduction candidate for 2,5 D2: 2,5 => CTR * ..86...71..4..763876.8.9.524.7..8.1668.79.5242..46.789.7.386.4..4.9.2.6...6....9. D2: 1,8 # 11 pairs * PAIR F5: 1,3 BLK 5 F6: 1,3,5 # reduction candidate for 1,3 F6: 5 => CTR * ..86.3.71..4..763.763..9.5.4.7..8.1668.7915242..46578..7.386.4..4.9.2.6...6..4.9. F6: 1,3 # 14 pairs * PAIR G4: 3,9 ROW 4 B4: 3,9,5 # reduction candidate for 3,9 B4: 5 => CTR * ..86...71..4..763.76...9.5.4572389166837915242..465783.7.386.4..4.9.2.6...6..4.9. B4: 3,9 # 14 pairs * PAIR I6: 3,9 ROW 6 B6: 3,9,1,5 # reduction candidate for 3,9 B6: 3,9 => CTR * 3.86...719148576327621394584.7..8.1668.7935242..46178..79386.4..439.2.6..26....9. B6: 1,5 # 11 pairs C6: 3,9,1,5 # reduction candidate for 3,9 C6: 3,9 # 14 pairs * PAIR D9: 1,5 BLK 8 E8: 1,5,7 # reduction candidate for 1,5 E8: 1,5 # 11 pairs E9: 1,5,4,7 # reduction candidate for 1,5 E9: 1,5 # 13 pairs * PAIR D9: 1,5 ROW 9 A9: 1,5,3,8 # reduction candidate for 1,5 A9: 1,5 # 23 pairs B9: 1,5,2,3 # reduction candidate for 1,5 B9: 1,5 => CTR * ..86...711.4..76397631.9.5.437258916681793524259461783972386145.45912.67.16574.9. B9: 2,3 # 11 pairs * PAIR D9: 1,5 COL D D2: 1,5,2,8 # reduction candidate for 1,5 D2: 1,5 => CTR * ..86...71..4..763876.8.9.524.72.8.1668.79.5242..46.789.7.386.4..4.9.2.6...6....9. D2: 2,8 # 11 pairs * PAIR F9: 4,5 BLK 8 E9: 4,5,1,7 # reduction candidate for 4,5 E9: 4,5 => CTR * 3.86..971594.1763.761.3945.4572.8.1668.79.5242..46.78..72386145145972.6.8361..297 E9: 1,7 # 11 pairs * PAIR F9: 4,5 COL F F1: 4,5,3 # reduction candidate for 4,5 F1: 3 => CTR * ..86.3.71..4..763.763..9.5.4.7.3891668179.5242..46.78..7.386.4..4.9.2.6...6....9. F1: 4,5 # 14 pairs * PAIR G7: 1,2 BLK 9 G9: 1,2,3,8 # reduction candidate for 1,2 G9: 1,2 # 14 pairs G9: 3,8 # 11 pairs * PAIR G7: 1,2 ROW 7 C7: 1,2,5,9 # reduction candidate for 1,2 C7: 5,9 => SOLVED * 398645271514827639762139458437258916681793524259461783975386142143972865826514397 C7: 1,2 # 18 pairs * PAIR I7: 2,5 BLK 9 I9: 2,5,3,7,8 # reduction candidate for 2,5 I9: 2,5 # 17 pairs I9: 3,7,8 # 10 pairs * PAIR I7: 2,5 ROW 7 C7: 2,5,1,9 # reduction candidate for 2,5 C7: 1,9 => CTR * ..8645271..48276397621394584372589166817935242.5461783579386142.439728658265.4.97 C7: 2,5 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060602-absurd-base-pr-000.dot * REASONING * DIS # I2: 2,8 => CTR => I2: 9 * DIS # G3: 2,8 => CTR => G3: 4 * DIS # D3: 2,8 => CTR => D3: 1 * DIS # C6: 1,3 => CTR => C6: 5,9 * PRF # C8: 1,3 => SOL * DIS # E4: 3 => CTR => E4: 2,5 * DIS # D2: 2,5 => CTR => D2: 1,8 * DIS # F6: 5 => CTR => F6: 1,3 * DIS # B4: 5 => CTR => B4: 3,9 * DIS # B6: 3,9 => CTR => B6: 1,5 * DIS # B9: 1,5 => CTR => B9: 2,3 * DIS # D2: 1,5 => CTR => D2: 2,8 * DIS # E9: 4,5 => CTR => E9: 1,7 * DIS # F1: 3 => CTR => F1: 4,5 * PRF # C7: 5,9 => SOL * DIS # C7: 1,9 => CTR => C7: 2,5 * CNT 16 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,D4,D9,F5,F9,G4,G7,I3,I6,I7) * ..86...71..4..763.76...9.5.4.7..8.1668.79.5242..46.78..7.386.4..4.9.2.6...6....9. * PAIR I3: 2,8 BLK 3 I2: 2,8,9 # reduction candidate for 2,8 I2: 2,8 => CTR * ..86249719.4..7632762.3945849725831668.79.5242..46.789.79386245.4.9.2.6..26.45.97 G3: 2,8,4 # reduction candidate for 2,8 G3: 2,8 => CTR * ..8635471..48.7639763149.5.4372589166817935242..461783.72386145.459.2.6..16574.9. * PAIR C5: 1,3 COL C C3: 1,3,2 # reduction candidate for 1,3 C3: 1,3 => CTR * .9864.2711248576397631294584.7..891668.79.5242.946.783972386145.45912.67..6574.92 C3: 2 => SOLVED * 398645271514827639762139458437258916681793524259461783975386142143972865826514397 * DURATION: 0:00:02.896115 START: 23:35:19.185572 END: 23:35:22.081687 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060602-absurd-base-pr-001.dot * REASONING * DIS # I2: 2,8 => CTR => I2: 9 * DIS I2: 9 # G3: 2,8 => CTR => G3: 4 * DIS I2: 9 + G3: 4 # C3: 1,3 => CTR => C3: 2 * PRF I2: 9 + G3: 4 + C3: 2 => SOL * STA I2: 9 + G3: 4 + C3: 2 * CNT 4 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060602, absurd
Solution
position: 398645271514827639762139458437258916681793524259461783975386142143972865826514397 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 # I2: 2,8 => CTR => I2: 9 * INC # I2: 9 => UNS * DIS # G3: 2,8 => CTR => G3: 4 * INC # G3: 4 => UNS * DIS # D3: 2,8 => CTR => D3: 1 * INC # D3: 1 => UNS * INC # I9: 2,8 => UNS * INC # I9: 3,5,7 => UNS * INC # B6: 1,3 => UNS * DIS # C6: 1,3 => CTR => C6: 5,9 * INC # C6: 5,9 => UNS * INC # C3: 1,3 => UNS * PRF # C8: 1,3 => SOL * INC # C8: 5 => UNS * INC # E4: 2,5 => UNS * DIS # E4: 3 => CTR => E4: 2,5 * DIS # D2: 2,5 => CTR => D2: 1,8 * INC # D2: 1,8 => UNS * INC # F6: 1,3 => UNS * DIS # F6: 5 => CTR => F6: 1,3 * INC # B4: 3,9 => UNS * DIS # B4: 5 => CTR => B4: 3,9 * DIS # B6: 3,9 => CTR => B6: 1,5 * INC # B6: 1,5 => UNS * INC # C6: 3,9 => UNS * INC # E8: 1,5 => UNS * INC # E9: 1,5 => UNS * INC # A9: 1,5 => UNS * DIS # B9: 1,5 => CTR => B9: 2,3 * INC # B9: 2,3 => UNS * DIS # D2: 1,5 => CTR => D2: 2,8 * INC # D2: 2,8 => UNS * DIS # E9: 4,5 => CTR => E9: 1,7 * INC # E9: 1,7 => UNS * INC # F1: 4,5 => UNS * DIS # F1: 3 => CTR => F1: 4,5 * INC # G9: 1,2 => UNS * INC # G9: 3,8 => UNS * INC # C7: 1,2 => UNS * PRF # C7: 5,9 => SOL * INC # I9: 2,5 => UNS * INC # I9: 3,7,8 => UNS * INC # C7: 2,5 => UNS * DIS # C7: 1,9 => CTR => C7: 2,5 * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I2: 2,8 => CTR => I2: 9 * DIS I2: 9 # G3: 2,8 => CTR => G3: 4 * DIS I2: 9 + G3: 4 # C3: 1,3 => CTR => C3: 2 * PRF I2: 9 + G3: 4 + C3: 2 => SOL * STA I2: 9 + G3: 4 + C3: 2 * CNT 4 HDP CHAINS / 3 HYP OPENED