Analysis of zz-www.sudokuoftheday.co.uk-20190318-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: ..427..1..3.1.4.8.7....6..4....6...83.98...4......1.....6...8.7.1.3.........2.... initial
Autosolve
position: ..427..1..3.19478.7.15.6..41...6...8379852.4...8..1.....6.1.837.173...6...3627... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 2,5 => CTR => A2: 6 * DIS # I2: 6 => CTR => I2: 2,5 * PRF # G3: 2,9 => SOL * DIS # G3: 3 => CTR => G3: 2,9 * DIS # B3: 2,9 => CTR => B3: 8 * PRF # B3: 8 => SOL * DIS # B4: 2,5 => CTR => B4: 4 * DIS # B6: 2,5 => CTR => B6: 4,6 * PRF # G4: 2,5 => SOL * PRF # G4: 2,5 => SOL * PRF # F8: 5,9 => SOL * DIS # F8: 8 => CTR => F8: 5,9 * PRF # A7: 5,9 => SOL * DIS # B7: 5,9 => CTR => B7: 2,4 * DIS # G9: 5,9 => CTR => G9: 1,4 * DIS # I9: 5,9 => CTR => I9: 1 * DIS # A9: 5,9 => CTR => A9: 4,8 * CNT 17 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 # A2: 2,5 => CTR => A2: 6 * PRF A2: 6 # G3: 2,9 => SOL * STA A2: 6 + G3: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..427..1..3.1.4.8.7....6..4....6...83.98...4......1.....6...8.7.1.3.........2.... | initial |
| ..427..1..3.19478.7.15.6..41...6...8379852.4...8..1.....6.1.837.173...6...3627... | autosolve |
| 594278613632194785781536924145963278379852146268741359926415837417389562853627491 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C2: 2,5 F1: 3,8 E3: 3,8 H3: 2,9 C4: 2,5 F4: 3,9 E6: 3,4 G5: 1,6 I5: 1,6 D7: 4,9 F7: 5,9 E8: 4,8 H9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G5,I5: 1.. / G5 = 1 => 13 pairs (_) / I5 = 1 => 0 pairs (X) G9,I9: 1.. / G9 = 1 => 0 pairs (X) / I9 = 1 => 13 pairs (_) G5,G9: 1.. / G5 = 1 => 13 pairs (_) / G9 = 1 => 0 pairs (X) I5,I9: 1.. / I5 = 1 => 0 pairs (X) / I9 = 1 => 13 pairs (_) A7,B7: 2.. / A7 = 2 => 14 pairs (_) / B7 = 2 => 16 pairs (_) G8,I8: 2.. / G8 = 2 => 20 pairs (_) / I8 = 2 => 15 pairs (_) C2,C4: 2.. / C2 = 2 => 15 pairs (_) / C4 = 2 => 14 pairs (_) F1,E3: 3.. / F1 = 3 => 0 pairs (X) / E3 = 3 => 0 pairs (_) F4,E6: 3.. / F4 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) E3,G3: 3.. / E3 = 3 => 0 pairs (*) / G3 = 3 => 0 pairs (X) F4,G4: 3.. / F4 = 3 => 0 pairs (*) / G4 = 3 => 0 pairs (X) E3,E6: 3.. / E3 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) F1,F4: 3.. / F1 = 3 => 0 pairs (X) / F4 = 3 => 0 pairs (_) I1,I6: 3.. / I1 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) D7,E8: 4.. / D7 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) G8,G9: 4.. / G8 = 4 => 0 pairs (X) / G9 = 4 => 13 pairs (_) B4,D4: 4.. / B4 = 4 => 14 pairs (_) / D4 = 4 => 0 pairs (X) E6,E8: 4.. / E6 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) F7,F8: 5.. / F7 = 5 => 13 pairs (_) / F8 = 5 => 0 pairs (X) C2,C4: 5.. / C2 = 5 => 14 pairs (_) / C4 = 5 => 15 pairs (_) A6,B6: 6.. / A6 = 6 => 0 pairs (X) / B6 = 6 => 13 pairs (_) G5,I5: 6.. / G5 = 6 => 0 pairs (X) / I5 = 6 => 13 pairs (_) A2,I2: 6.. / A2 = 6 => 14 pairs (_) / I2 = 6 => 0 pairs (X) B1,B6: 6.. / B1 = 6 => 0 pairs (X) / B6 = 6 => 13 pairs (_) G1,G5: 6.. / G1 = 6 => 13 pairs (_) / G5 = 6 => 0 pairs (X) D4,D6: 7.. / D4 = 7 => 14 pairs (_) / D6 = 7 => 14 pairs (_) H4,H6: 7.. / H4 = 7 => 14 pairs (_) / H6 = 7 => 14 pairs (_) D4,H4: 7.. / D4 = 7 => 14 pairs (_) / H4 = 7 => 14 pairs (_) D6,H6: 7.. / D6 = 7 => 14 pairs (_) / H6 = 7 => 14 pairs (_) F1,E3: 8.. / F1 = 8 => 0 pairs (*) / E3 = 8 => 0 pairs (X) A9,B9: 8.. / A9 = 8 => 13 pairs (_) / B9 = 8 => 0 pairs (X) E8,F8: 8.. / E8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) B3,E3: 8.. / B3 = 8 => 0 pairs (*) / E3 = 8 => 0 pairs (X) A1,A9: 8.. / A1 = 8 => 0 pairs (X) / A9 = 8 => 13 pairs (_) E3,E8: 8.. / E3 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) F1,F8: 8.. / F1 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) * DURATION: 0:00:38.542114 START: 04:37:09.586650 END: 04:37:48.128764 2019-05-01 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C4,D7,E3,E6,E8,F1,F4,F7,G5,H3,H9,I5) * ..427..1..3.19478.7.15.6..41...6...8379852.4...8..1.....6.1.837.173...6...3627... * PAIR C2: 2,5 BLK 1 A2: 2,5,6 # reduction candidate for 2,5 A2: 2,5 => CTR * ..427..1..3.1947867.15.6..41...6...8379852641..8.41.....641.837.1738.4624836271.. A2: 6 # 14 pairs * PAIR C2: 2,5 ROW 2 I2: 2,5,6 # reduction candidate for 2,5 I2: 6 => CTR * ..427..1..3.1947867.15.6..41...6...8379852641..8.41.....641.837.1738.4624836271.. I2: 2,5 # 14 pairs * PAIR H3: 2,9 BLK 3 G3: 2,9,3 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 594278613632194785781536924145963278379852146268741359926415837417389562853627491 G3: 3 => CTR * ..427..1..3.19478.7.15.63.41...63..8379852.4...8.41..3..641.837.1738..6...3627... * PAIR H3: 2,9 ROW 3 B3: 2,9,8 # reduction candidate for 2,9 B3: 2,9 => CTR * ..427..1..3.19478.7.15863.41...63..8379852.4...8..1.....6.1.837.173...6...3627... B3: 8 => SOLVED * 594278613632194785781536924145963278379852146268741359926415837417389562853627491 * PAIR H3: 2,9 COL H H4: 2,9,5,7 # reduction candidate for 2,9 H4: 2,9 # 17 pairs H6: 2,9,5,7 # reduction candidate for 2,9 H6: 2,9 # 16 pairs * PAIR C4: 2,5 BLK 4 B4: 2,5,4 # reduction candidate for 2,5 B4: 2,5 => CTR * ..4273.1..3.19478.7.15863.41..469.78379852146..8731.....6915837.17348.6...36274.1 B4: 4 # 14 pairs A6: 2,5,4,6 # reduction candidate for 2,5 A6: 2,5 # 15 pairs B6: 2,5,4,6 # reduction candidate for 2,5 B6: 2,5 => CTR * 864273.1..3.194786791586..414..6...83798526416.8..1.....6.1.837.173..4624836271.. B6: 4,6 # 14 pairs * PAIR C4: 2,5 ROW 4 G4: 2,5,3,9 # reduction candidate for 2,5 G4: 2,5 => SOLVED * 594278613632194785781536924145963278379852146268741359926415837417389562853627491 G4: 3,9 # 15 pairs H4: 2,5,7,9 # reduction candidate for 2,5 H4: 2,5 # 16 pairs * PAIR F4: 3,9 ROW 4 G4: 3,9,2,5 # reduction candidate for 3,9 G4: 2,5 => SOLVED * 594278613632194785781536924145963278379852146268741359926415837417389562853627491 G4: 3,9 # 15 pairs * PAIR D7: 4,9 ROW 7 A7: 4,9,2,5 # reduction candidate for 4,9 A7: 4,9 # 17 pairs B7: 4,9,2,5 # reduction candidate for 4,9 B7: 4,9 # 15 pairs * PAIR D7: 4,9 COL D D4: 4,9,7 # reduction candidate for 4,9 D4: 4,9 # 14 pairs D6: 4,9,7 # reduction candidate for 4,9 D6: 4,9 # 14 pairs * PAIR F7: 5,9 BLK 8 F8: 5,9,8 # reduction candidate for 5,9 F8: 5,9 => SOLVED * 594278613632194785781536924145963278379852146268741359926415837417389562853627491 F8: 8 => CTR * ..4273.1..3.19478.7.15863.41...69..8379852.4...8.31.....6915837.17348.6...36274.1 * PAIR F7: 5,9 ROW 7 A7: 5,9,2,4 # reduction candidate for 5,9 A7: 5,9 => SOLVED * 594278613632194785781536924145963278379852146268741359926415837417389562853627491 A7: 2,4 # 14 pairs B7: 5,9,2,4 # reduction candidate for 5,9 B7: 5,9 => CTR * .64278.1.532194786781536..414..63..8379852.4..28.41...2.641.837.1738..6.8.36274.1 B7: 2,4 # 14 pairs * PAIR H9: 5,9 BLK 9 G8: 5,9,2,4 # reduction candidate for 5,9 G8: 5,9 # 16 pairs I8: 5,9,2 # reduction candidate for 5,9 I8: 5,9 # 20 pairs G9: 5,9,1,4 # reduction candidate for 5,9 G9: 5,9 => CTR * ..427.61.6321947857.15.6..41.5.6...8379852146.68.41.....641.837.1738.462483627..1 G9: 1,4 # 14 pairs I9: 5,9,1 # reduction candidate for 5,9 I9: 5,9 => CTR * ..427..1..3.19478.7.15.6..41...6...8379852641..8.41.....641.837.1738.4624836271.. I9: 1 # 13 pairs * PAIR H9: 5,9 ROW 9 A9: 5,9,4,8 # reduction candidate for 5,9 A9: 5,9 => CTR * 8.4273.1..3.19478.7.15863.41...69..8379852.4...8.31.....6915837.17348.6..836274.1 A9: 4,8 # 14 pairs B9: 5,9,4,8 # reduction candidate for 5,9 B9: 5,9 # 15 pairs * PAIR H9: 5,9 COL H H4: 5,9,2,7 # reduction candidate for 5,9 H4: 5,9 # 17 pairs H6: 5,9,2,7 # reduction candidate for 5,9 H6: 5,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190318-absurd-base-pr-000.dot * REASONING * DIS # A2: 2,5 => CTR => A2: 6 * DIS # I2: 6 => CTR => I2: 2,5 * PRF # G3: 2,9 => SOL * DIS # G3: 3 => CTR => G3: 2,9 * DIS # B3: 2,9 => CTR => B3: 8 * PRF # B3: 8 => SOL * DIS # B4: 2,5 => CTR => B4: 4 * DIS # B6: 2,5 => CTR => B6: 4,6 * PRF # G4: 2,5 => SOL * PRF # G4: 2,5 => SOL * PRF # F8: 5,9 => SOL * DIS # F8: 8 => CTR => F8: 5,9 * PRF # A7: 5,9 => SOL * DIS # B7: 5,9 => CTR => B7: 2,4 * DIS # G9: 5,9 => CTR => G9: 1,4 * DIS # I9: 5,9 => CTR => I9: 1 * DIS # A9: 5,9 => CTR => A9: 4,8 * CNT 17 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C4,D7,E3,E6,E8,F1,F4,F7,G5,H3,H9,I5) * ..427..1..3.19478.7.15.6..41...6...8379852.4...8..1.....6.1.837.173...6...3627... * PAIR C2: 2,5 BLK 1 A2: 2,5,6 # reduction candidate for 2,5 A2: 2,5 => CTR * ..427..1..3.1947867.15.6..41...6...8379852641..8.41.....641.837.1738.4624836271.. * PAIR H3: 2,9 BLK 3 G3: 2,9,3 # reduction candidate for 2,9 G3: 2,9 => SOLVED * 594278613632194785781536924145963278379852146268741359926415837417389562853627491 * DURATION: 0:00:02.938940 START: 04:38:14.747154 END: 04:38:17.686094 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190318-absurd-base-pr-001.dot * REASONING * DIS # A2: 2,5 => CTR => A2: 6 * PRF A2: 6 # G3: 2,9 => SOL * STA A2: 6 + G3: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190318, absurd
Solution
position: 594278613632194785781536924145963278379852146268741359926415837417389562853627491 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 # A2: 2,5 => CTR => A2: 6 * INC # A2: 6 => UNS * INC # I2: 2,5 => UNS * DIS # I2: 6 => CTR => I2: 2,5 * PRF # G3: 2,9 => SOL * DIS # G3: 3 => CTR => G3: 2,9 * DIS # B3: 2,9 => CTR => B3: 8 * PRF # B3: 8 => SOL * INC # H4: 2,9 => UNS * INC # H6: 2,9 => UNS * DIS # B4: 2,5 => CTR => B4: 4 * INC # B4: 4 => UNS * INC # A6: 2,5 => UNS * DIS # B6: 2,5 => CTR => B6: 4,6 * INC # B6: 4,6 => UNS * PRF # G4: 2,5 => SOL * INC # G4: 3,9 => UNS * INC # H4: 2,5 => UNS * INC # G4: 3,9 => UNS * PRF # G4: 2,5 => SOL * INC # A7: 4,9 => UNS * INC # B7: 4,9 => UNS * INC # D4: 4,9 => UNS * INC # D6: 4,9 => UNS * PRF # F8: 5,9 => SOL * DIS # F8: 8 => CTR => F8: 5,9 * PRF # A7: 5,9 => SOL * INC # A7: 2,4 => UNS * DIS # B7: 5,9 => CTR => B7: 2,4 * INC # B7: 2,4 => UNS * INC # G8: 5,9 => UNS * INC # I8: 5,9 => UNS * DIS # G9: 5,9 => CTR => G9: 1,4 * INC # G9: 1,4 => UNS * DIS # I9: 5,9 => CTR => I9: 1 * INC # I9: 1 => UNS * DIS # A9: 5,9 => CTR => A9: 4,8 * INC # A9: 4,8 => UNS * INC # B9: 5,9 => UNS * INC # H4: 5,9 => UNS * INC # H6: 5,9 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 2,5 => CTR => A2: 6 * PRF A2: 6 # G3: 2,9 => SOL * STA A2: 6 + G3: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED