Analysis of zz-www.sudokuoftheday.co.uk-20190324-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: ..7...6.1.....3......8..4.9.4...182.29..4......3.....6....29...65......8...75.... initial
Autosolve
position: ..7.9.6.1.....3......8..4.9.469.182.298.46.....3.8.946...629...652..4798...758.6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 1,3 => CTR => B3: 2,6 * DIS # A9: 1,3 => CTR => A9: 4,9 * DIS # C2: 1,5 => CTR => C2: 4,9 * DIS # I2: 7 => CTR => I2: 2,5 * DIS # A6: 1 => CTR => A6: 5,7 * DIS # I5: 3,5 => CTR => I5: 7 * DIS # I5: 3,5 => CTR => I5: 7 * DIS # I7: 4 => CTR => I7: 3,5 * DIS # A9: 1,3 => CTR => A9: 4,9 * DIS # B3: 1,3 => CTR => B3: 2,6 * PRF # G7: 1,5 => SOL * DIS # H5: 7 => CTR => H5: 1,5 * CNT 12 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 1,3 => CTR => B3: 2,6 * DIS B3: 2,6 # A9: 1,3 => CTR => A9: 4,9 * DIS B3: 2,6 + A9: 4,9 # D1: 2,5 => CTR => D1: 4 * PRF B3: 2,6 + A9: 4,9 + D1: 4 # I2: 2,5 => SOL * STA B3: 2,6 + A9: 4,9 + D1: 4 + I2: 2,5 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..7...6.1.....3......8..4.9.4...182.29..4......3.....6....29...65......8...75.... | initial |
| ..7.9.6.1.....3......8..4.9.469.182.298.46.....3.8.946...629...652..4798...758.6. | autosolve |
| 327495681489163572165872439746931825298546317513287946874629153652314798931758264 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A3: 1,3 C3: 1,5 F1: 2,5 G2: 2,5 A4: 5,7 B6: 1,7 E4: 3,7 D5: 3,5 D6: 2,5 I4: 3,5 A7: 7,8 B7: 7,8 C7: 1,4 B9: 1,3 D8: 1,3 E8: 1,3 H7: 1,5 G9: 1,2 I9: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A6,B6: 1.. / A6 = 1 => 0 pairs (X) / B6 = 1 => 20 pairs (_) G5,H5: 1.. / G5 = 1 => 0 pairs (X) / H5 = 1 => 26 pairs (_) D8,E8: 1.. / D8 = 1 => 21 pairs (_) / E8 = 1 => 14 pairs (_) D2,D8: 1.. / D2 = 1 => 14 pairs (_) / D8 = 1 => 21 pairs (_) H5,H7: 1.. / H5 = 1 => 26 pairs (_) / H7 = 1 => 0 pairs (X) B1,B3: 2.. / B1 = 2 => 14 pairs (_) / B3 = 2 => 22 pairs (_) G2,I2: 2.. / G2 = 2 => 0 pairs (X) / I2 = 2 => 25 pairs (_) D6,F6: 2.. / D6 = 2 => 20 pairs (_) / F6 = 2 => 20 pairs (_) G9,I9: 2.. / G9 = 2 => 25 pairs (_) / I9 = 2 => 0 pairs (X) B3,F3: 2.. / B3 = 2 => 22 pairs (_) / F3 = 2 => 14 pairs (_) D1,D6: 2.. / D1 = 2 => 20 pairs (_) / D6 = 2 => 20 pairs (_) G2,G9: 2.. / G2 = 2 => 0 pairs (X) / G9 = 2 => 25 pairs (_) I2,I9: 2.. / I2 = 2 => 25 pairs (_) / I9 = 2 => 0 pairs (X) H1,H3: 3.. / H1 = 3 => 25 pairs (_) / H3 = 3 => 25 pairs (_) E4,D5: 3.. / E4 = 3 => 14 pairs (_) / D5 = 3 => 21 pairs (_) A9,B9: 3.. / A9 = 3 => 0 pairs (X) / B9 = 3 => 19 pairs (_) D8,E8: 3.. / D8 = 3 => 14 pairs (_) / E8 = 3 => 21 pairs (_) G7,I7: 3.. / G7 = 3 => 21 pairs (_) / I7 = 3 => 0 pairs (*) E4,I4: 3.. / E4 = 3 => 14 pairs (_) / I4 = 3 => 21 pairs (_) D5,D8: 3.. / D5 = 3 => 21 pairs (_) / D8 = 3 => 14 pairs (_) E4,E8: 3.. / E4 = 3 => 14 pairs (_) / E8 = 3 => 21 pairs (_) G5,G7: 3.. / G5 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) D1,D2: 4.. / D1 = 4 => 25 pairs (_) / D2 = 4 => 24 pairs (_) I7,I9: 4.. / I7 = 4 => 0 pairs (X) / I9 = 4 => 25 pairs (_) A1,D1: 4.. / A1 = 4 => 24 pairs (_) / D1 = 4 => 25 pairs (_) C7,I7: 4.. / C7 = 4 => 25 pairs (_) / I7 = 4 => 0 pairs (X) C2,C3: 5.. / C2 = 5 => 0 pairs (X) / C3 = 5 => 20 pairs (_) A4,A6: 5.. / A4 = 5 => 21 pairs (_) / A6 = 5 => 14 pairs (_) A4,I4: 5.. / A4 = 5 => 21 pairs (_) / I4 = 5 => 14 pairs (_) B2,B3: 6.. / B2 = 6 => 20 pairs (_) / B3 = 6 => 14 pairs (_) E2,E3: 6.. / E2 = 6 => 14 pairs (_) / E3 = 6 => 20 pairs (_) B2,E2: 6.. / B2 = 6 => 20 pairs (_) / E2 = 6 => 14 pairs (_) B3,E3: 6.. / B3 = 6 => 14 pairs (_) / E3 = 6 => 20 pairs (_) E4,F6: 7.. / E4 = 7 => 21 pairs (_) / F6 = 7 => 14 pairs (_) H5,I5: 7.. / H5 = 7 => 0 pairs (X) / I5 = 7 => 25 pairs (_) A7,B7: 7.. / A7 = 7 => 0 pairs (X) / B7 = 7 => 20 pairs (_) A4,E4: 7.. / A4 = 7 => 14 pairs (_) / E4 = 7 => 21 pairs (_) B6,B7: 7.. / B6 = 7 => 0 pairs (X) / B7 = 7 => 20 pairs (_) F3,F6: 7.. / F3 = 7 => 21 pairs (_) / F6 = 7 => 14 pairs (_) I2,I5: 7.. / I2 = 7 => 0 pairs (X) / I5 = 7 => 25 pairs (_) H1,H2: 8.. / H1 = 8 => 14 pairs (_) / H2 = 8 => 21 pairs (_) A7,B7: 8.. / A7 = 8 => 20 pairs (_) / B7 = 8 => 0 pairs (X) A2,C2: 9.. / A2 = 9 => 19 pairs (_) / C2 = 9 => 21 pairs (_) A9,C9: 9.. / A9 = 9 => 21 pairs (_) / C9 = 9 => 19 pairs (_) A2,A9: 9.. / A2 = 9 => 19 pairs (_) / A9 = 9 => 21 pairs (_) C2,C9: 9.. / C2 = 9 => 21 pairs (_) / C9 = 9 => 19 pairs (_) * DURATION: 0:00:58.613330 START: 04:46:03.253643 END: 04:47:01.866973 2019-05-01 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A7,B6,B7,B9,C3,C7,D5,D6,D8,E4,E8,F1,G2,G9,H7,I4,I9) * ..7.9.6.1.....3......8..4.9.469.182.298.46.....3.8.946...629...652..4798...758.6. * PAIR A3: 1,3 BLK 1 B3: 1,3,2,6 # reduction candidate for 1,3 B3: 1,3 => CTR * .27.956.1.6...3......862479.469.182.298.46..7..3287946...629...652..4798...758.6. B3: 2,6 # 20 pairs * PAIR A3: 1,3 COL A A9: 1,3,4,9 # reduction candidate for 1,3 A9: 1,3 => CTR * 4.7.9.6319.14.35.2..58..4.9.46971823298346157713.8.946874629315652134798139758264 A9: 4,9 # 22 pairs * PAIR C3: 1,5 BLK 1 C2: 1,5,4,9 # reduction candidate for 1,5 C2: 1,5 => CTR * 4.7.9.6.19..4.35.2..58.7439546971823298346157713.8.946874629315652134798..9758264 C2: 4,9 # 22 pairs * PAIR F1: 2,5 BLK 2 D1: 2,5,4 # reduction candidate for 2,5 D1: 2,5 # 24 pairs F3: 2,5,7 # reduction candidate for 2,5 F3: 2,5 # 14 pairs * PAIR F1: 2,5 COL F F6: 2,5,7 # reduction candidate for 2,5 F6: 2,5 # 21 pairs F6: 7 # 14 pairs * PAIR G2: 2,5 BLK 3 I2: 2,5,7 # reduction candidate for 2,5 I2: 7 => CTR * ..7.9.6.1.....32.7...8..4.9.469.182.298.46.7...3.8.946...629.1.652..4798...758.6. I2: 2,5 # 25 pairs * PAIR A4: 5,7 BLK 4 A6: 5,7,1 # reduction candidate for 5,7 A6: 1 => CTR * ..7.9.6.1.....3...3..8.745954697182329834651.173.8.94678.6293..652134798...758.6. A6: 5,7 # 20 pairs * PAIR B6: 1,7 BLK 4 A6: 1,7,5 # reduction candidate for 1,7 A6: 1,7 # 21 pairs A6: 5 # 14 pairs * PAIR D5: 3,5 ROW 5 G5: 3,5,1 # reduction candidate for 3,5 G5: 3,5 # 26 pairs I5: 3,5,7 # reduction candidate for 3,5 I5: 3,5 => CTR * ..7.9.6.1.....3..7...8..4.9.469.182.298.46.7...3.8.946...629.1.652..4798...758264 I5: 7 # 25 pairs * PAIR D6: 2,5 BLK 5 F6: 2,5,7 # reduction candidate for 2,5 F6: 2,5 # 21 pairs F6: 7 # 14 pairs * PAIR D6: 2,5 COL D D1: 2,5,4 # reduction candidate for 2,5 D1: 4 # 25 pairs D1: 2,5 # 24 pairs * PAIR I4: 3,5 BLK 6 G5: 3,5,1 # reduction candidate for 3,5 G5: 3,5 # 26 pairs I5: 3,5,7 # reduction candidate for 3,5 I5: 3,5 => CTR * ..7.9.6.1.....3..7...8..4.9.469.182.298.46.7...3.8.946...629.1.652..4798...758264 I5: 7 # 25 pairs * PAIR I4: 3,5 COL I I7: 3,5,4 # reduction candidate for 3,5 I7: 4 => CTR * ..7.9.6.1...4.3275..58.7439546971823298346517..3.8.946..1629354652134798.34758162 I7: 3,5 # 25 pairs * PAIR C7: 1,4 BLK 7 A9: 1,4,3,9 # reduction candidate for 1,4 A9: 1,4 # 20 pairs C9: 1,4,9 # reduction candidate for 1,4 C9: 1,4 # 21 pairs * PAIR C7: 1,4 COL C C2: 1,4,5,9 # reduction candidate for 1,4 C2: 1,4 # 21 pairs C2: 5,9 # 20 pairs * PAIR B9: 1,3 BLK 7 A9: 1,3,4,9 # reduction candidate for 1,3 A9: 1,3 => CTR * 4.7.9.6319.14.35.2..58..4.9.46971823298346157713.8.946874629315652134798139758264 A9: 4,9 # 22 pairs * PAIR B9: 1,3 COL B B3: 1,3,2,6 # reduction candidate for 1,3 B3: 1,3 => CTR * .27.956.1.6...3......862479.469.182.298.46..7..3287946...629...652..4798...758.6. B3: 2,6 # 20 pairs * PAIR H7: 1,5 BLK 9 G7: 1,5,3 # reduction candidate for 1,5 G7: 1,5 => SOLVED * 327495681489163572165872439746931825298546317513287946874629153652314798931758264 G7: 3 # 21 pairs * PAIR H7: 1,5 COL H H5: 1,5,7 # reduction candidate for 1,5 H5: 7 => CTR * ..7.9.6.1.....3......8..4.9.469.182.298.4617...3.8.946...629315652..4798...758264 H5: 1,5 # 25 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190324-absurd-base-pr-000.dot * REASONING * DIS # B3: 1,3 => CTR => B3: 2,6 * DIS # A9: 1,3 => CTR => A9: 4,9 * DIS # C2: 1,5 => CTR => C2: 4,9 * DIS # I2: 7 => CTR => I2: 2,5 * DIS # A6: 1 => CTR => A6: 5,7 * DIS # I5: 3,5 => CTR => I5: 7 * DIS # I5: 3,5 => CTR => I5: 7 * DIS # I7: 4 => CTR => I7: 3,5 * DIS # A9: 1,3 => CTR => A9: 4,9 * DIS # B3: 1,3 => CTR => B3: 2,6 * PRF # G7: 1,5 => SOL * DIS # H5: 7 => CTR => H5: 1,5 * CNT 12 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A7,B6,B7,B9,C3,C7,D5,D6,D8,E4,E8,F1,G2,G9,H7,I4,I9) * ..7.9.6.1.....3......8..4.9.469.182.298.46.....3.8.946...629...652..4798...758.6. * PAIR A3: 1,3 BLK 1 B3: 1,3,2,6 # reduction candidate for 1,3 B3: 1,3 => CTR * .27.956.1.6...3......862479.469.182.298.46..7..3287946...629...652..4798...758.6. * PAIR A3: 1,3 COL A A9: 1,3,4,9 # reduction candidate for 1,3 A9: 1,3 => CTR * 4.7.9.6319.14.35.2..58..4.9.46971823298346157713.8.946874629315652134798139758264 * PAIR RESTART * PAIR F1: 2,5 BLK 2 D1: 2,5,4 # reduction candidate for 2,5 D1: 2,5 => CTR * 4.7.9.631..94.3.8.3.581.479.469.182.298.46..7..3.8794687.629...652134798.3.758.6. * PAIR G2: 2,5 BLK 3 I2: 2,5,7 # reduction candidate for 2,5 I2: 2,5 => SOLVED * 327495681489163572165872439746931825298546317513287946874629153652314798931758264 * DURATION: 0:00:06.068306 START: 04:47:28.312941 END: 04:47:34.381247 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190324-absurd-base-pr-001.dot * REASONING * DIS # B3: 1,3 => CTR => B3: 2,6 * DIS B3: 2,6 # A9: 1,3 => CTR => A9: 4,9 * DIS B3: 2,6 + A9: 4,9 # D1: 2,5 => CTR => D1: 4 * PRF B3: 2,6 + A9: 4,9 + D1: 4 # I2: 2,5 => SOL * STA B3: 2,6 + A9: 4,9 + D1: 4 + I2: 2,5 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190324, absurd
Solution
position: 327495681489163572165872439746931825298546317513287946874629153652314798931758264 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 # B3: 1,3 => CTR => B3: 2,6 * INC # B3: 2,6 => UNS * DIS # A9: 1,3 => CTR => A9: 4,9 * INC # A9: 4,9 => UNS * DIS # C2: 1,5 => CTR => C2: 4,9 * INC # C2: 4,9 => UNS * INC # D1: 2,5 => UNS * INC # F3: 2,5 => UNS * INC # F6: 2,5 => UNS * INC # F6: 7 => UNS * INC # I2: 2,5 => UNS * DIS # I2: 7 => CTR => I2: 2,5 * INC # A6: 5,7 => UNS * DIS # A6: 1 => CTR => A6: 5,7 * INC # A6: 1,7 => UNS * INC # A6: 5 => UNS * INC # G5: 3,5 => UNS * DIS # I5: 3,5 => CTR => I5: 7 * INC # I5: 7 => UNS * INC # F6: 2,5 => UNS * INC # F6: 7 => UNS * INC # D1: 2,5 => UNS * INC # D1: 4 => UNS * INC # G5: 3,5 => UNS * DIS # I5: 3,5 => CTR => I5: 7 * INC # I5: 7 => UNS * INC # I7: 3,5 => UNS * DIS # I7: 4 => CTR => I7: 3,5 * INC # A9: 1,4 => UNS * INC # C9: 1,4 => UNS * INC # C2: 1,4 => UNS * INC # C2: 5,9 => UNS * DIS # A9: 1,3 => CTR => A9: 4,9 * INC # A9: 4,9 => UNS * DIS # B3: 1,3 => CTR => B3: 2,6 * INC # B3: 2,6 => UNS * PRF # G7: 1,5 => SOL * INC # G7: 3 => UNS * INC # H5: 1,5 => UNS * DIS # H5: 7 => CTR => H5: 1,5 * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B3: 1,3 => CTR => B3: 2,6 * DIS B3: 2,6 # A9: 1,3 => CTR => A9: 4,9 * DIS B3: 2,6 + A9: 4,9 # D1: 2,5 => CTR => D1: 4 * PRF B3: 2,6 + A9: 4,9 + D1: 4 # I2: 2,5 => SOL * STA B3: 2,6 + A9: 4,9 + D1: 4 + I2: 2,5 * CNT 4 HDP CHAINS / 4 HYP OPENED