Analysis of zz-www.sudokuoftheday.co.uk-20060402-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: 4.8.2...75.7...4...1.4.76.....2.8....96...1.....61...8.59.......7.9..2.6...7....4 initial
Autosolve
position: 4.8.2...75.78..4..91.4.768....2.8.6.896.7.1.....61...8.59...87..7498.2.6.8.7....4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 2 => CTR => B2: 3,6 * DIS # I3: 2,3 => CTR => I3: 5 * DIS # F1: 3,5 => CTR => F1: 1,6,9 * DIS # I3: 2 => CTR => I3: 3,5 * DIS # B6: 3,4 => CTR => B6: 2 * DIS # E4: 3,4 => CTR => E4: 5,9 * DIS # F5: 3,5 => CTR => F5: 4 * DIS # F6: 3,5 => CTR => F6: 4,9 * DIS # A9: 1,3 => CTR => A9: 2,6 * DIS # F7: 4 => CTR => F7: 2,6 * DIS # A9: 1,3 => CTR => A9: 2,6 * PRF # D1: 5 => SOL * CNT 12 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 2 => CTR => B2: 3,6 * PRF B2: 3,6 # D1: 3,5 => SOL * STA B2: 3,6 + D1: 3,5 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.8.2...75.7...4...1.4.76.....2.8....96...1.....61...8.59.......7.9..2.6...7....4 | initial |
| 4.8.2...75.78..4..91.4.768....2.8.6.896.7.1.....61...8.59...87..7498.2.6.8.7....4 | autosolve |
| 468521937537896421912437685143258769896374152725619348659142873374985216281763594 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 3,6 C3: 2,3 E3: 3,5 B4: 3,4 D5: 3,5 A7: 2,6 A8: 1,3 D7: 1,3 E7: 4,6 I7: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,C4: 1.. / A4 = 1 => 13 pairs (_) / C4 = 1 => 12 pairs (_) D7,I7: 1.. / D7 = 1 => 16 pairs (_) / I7 = 1 => 16 pairs (_) C4,C9: 1.. / C4 = 1 => 12 pairs (_) / C9 = 1 => 13 pairs (_) D1,D7: 1.. / D1 = 1 => 16 pairs (_) / D7 = 1 => 16 pairs (_) I2,I7: 1.. / I2 = 1 => 16 pairs (_) / I7 = 1 => 16 pairs (_) B2,C3: 2.. / B2 = 2 => 0 pairs (X) / C3 = 2 => 14 pairs (_) H5,I5: 2.. / H5 = 2 => 11 pairs (_) / I5 = 2 => 14 pairs (_) F7,F9: 2.. / F7 = 2 => 8 pairs (_) / F9 = 2 => 15 pairs (_) C3,I3: 2.. / C3 = 2 => 14 pairs (_) / I3 = 2 => 0 pairs (X) A7,F7: 2.. / A7 = 2 => 15 pairs (_) / F7 = 2 => 8 pairs (_) B2,B6: 2.. / B2 = 2 => 0 pairs (X) / B6 = 2 => 14 pairs (_) H2,H5: 2.. / H2 = 2 => 14 pairs (_) / H5 = 2 => 11 pairs (_) D7,I7: 3.. / D7 = 3 => 16 pairs (_) / I7 = 3 => 16 pairs (_) B4,B6: 4.. / B4 = 4 => 10 pairs (_) / B6 = 4 => 0 pairs (X) H5,H6: 4.. / H5 = 4 => 0 pairs (X) / H6 = 4 => 10 pairs (_) E7,F7: 4.. / E7 = 4 => 10 pairs (_) / F7 = 4 => 0 pairs (X) B4,E4: 4.. / B4 = 4 => 10 pairs (_) / E4 = 4 => 0 pairs (X) F5,H5: 4.. / F5 = 4 => 10 pairs (_) / H5 = 4 => 0 pairs (X) E4,E7: 4.. / E4 = 4 => 0 pairs (X) / E7 = 4 => 10 pairs (_) C4,C6: 5.. / C4 = 5 => 14 pairs (_) / C6 = 5 => 11 pairs (_) E3,I3: 5.. / E3 = 5 => 0 pairs (X) / I3 = 5 => 19 pairs (_) F8,H8: 5.. / F8 = 5 => 15 pairs (_) / H8 = 5 => 13 pairs (_) D1,D5: 5.. / D1 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) B1,B2: 6.. / B1 = 6 => 10 pairs (_) / B2 = 6 => 13 pairs (_) A7,A9: 6.. / A7 = 6 => 8 pairs (_) / A9 = 6 => 15 pairs (_) B1,F1: 6.. / B1 = 6 => 10 pairs (_) / F1 = 6 => 13 pairs (_) A4,A6: 7.. / A4 = 7 => 12 pairs (_) / A6 = 7 => 13 pairs (_) G4,G6: 7.. / G4 = 7 => 13 pairs (_) / G6 = 7 => 12 pairs (_) A4,G4: 7.. / A4 = 7 => 12 pairs (_) / G4 = 7 => 13 pairs (_) A6,G6: 7.. / A6 = 7 => 13 pairs (_) / G6 = 7 => 12 pairs (_) E4,F6: 9.. / E4 = 9 => 0 pairs (X) / F6 = 9 => 11 pairs (_) G9,H9: 9.. / G9 = 9 => 11 pairs (_) / H9 = 9 => 11 pairs (_) E2,E4: 9.. / E2 = 9 => 11 pairs (_) / E4 = 9 => 0 pairs (X) I2,I4: 9.. / I2 = 9 => 0 pairs (X) / I4 = 9 => 11 pairs (_) * DURATION: 0:00:35.025597 START: 22:05:45.536004 END: 22:06:20.561601 2019-04-30 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B1,B4,C3,D5,D7,E3,E7,I7) * 4.8.2...75.78..4..91.4.768....2.8.6.896.7.1.....61...8.59...87..7498.2.6.8.7....4 * PAIR B1: 3,6 BLK 1 B2: 3,6,2 # reduction candidate for 3,6 B2: 2 => CTR * 46812...75278.6419913457682.4.298.65896574123.3.61..48.593..871.7498.2.6.8.76...4 B2: 3,6 # 14 pairs * PAIR B1: 3,6 ROW 1 F1: 3,6,1,5,9 # reduction candidate for 3,6 F1: 3,6 # 14 pairs F1: 1,5,9 # 10 pairs * PAIR C3: 2,3 BLK 1 B2: 2,3,6 # reduction candidate for 2,3 B2: 6 # 13 pairs B2: 2,3 # 10 pairs * PAIR C3: 2,3 ROW 3 I3: 2,3,5 # reduction candidate for 2,3 I3: 2,3 => CTR * 468129..75.78..41991.457682.4.298.6589657.123..5613.48.5934.871.7498.2.6.8276..94 I3: 5 # 19 pairs * PAIR C3: 2,3 COL C C6: 2,3,5 # reduction candidate for 2,3 C6: 2,3 # 14 pairs C9: 2,3,1 # reduction candidate for 2,3 C9: 2,3 # 12 pairs * PAIR E3: 3,5 BLK 2 D1: 3,5,1 # reduction candidate for 3,5 D1: 3,5 # 16 pairs F1: 3,5,1,6,9 # reduction candidate for 3,5 F1: 3,5 => CTR * 46812...75.789641.91.4.7685...2.8.6989657.123...619.48.593..871.7498.2.6.8.75...4 F1: 1,6,9 # 10 pairs * PAIR E3: 3,5 ROW 3 I3: 3,5,2 # reduction candidate for 3,5 I3: 2 => CTR * 4.812...75278.6419913457682.4.298.65896574123.3.61..48.593..871.7498.2.6.8.76...4 I3: 3,5 # 14 pairs * PAIR E3: 3,5 COL E E4: 3,5,4,9 # reduction candidate for 3,5 E4: 3,5 # 9 pairs E9: 3,5,6 # reduction candidate for 3,5 E9: 3,5 # 14 pairs * PAIR B4: 3,4 BLK 4 B6: 3,4,2 # reduction candidate for 3,4 B6: 3,4 => CTR * 46812...75278.6419913457682.4.298.65896574123.3.61..48.593..871.7498.2.6.8.76...4 B6: 2 # 14 pairs * PAIR B4: 3,4 ROW 4 E4: 3,4,5,9 # reduction candidate for 3,4 E4: 3,4 => CTR * 4.8.2...75.789.4..912437685...248.69896.7.142...619..8.59...87..7498.2.6.8.75...4 E4: 5,9 # 11 pairs * PAIR D5: 3,5 BLK 5 E4: 3,5,4,9 # reduction candidate for 3,5 E4: 3,5 # 9 pairs F5: 3,5,4 # reduction candidate for 3,5 F5: 3,5 => CTR * 4.8129..75.78..429912457683.4.298.65896573142.25614..8.5934.871.7498.2.6.8.76...4 F5: 4 # 10 pairs F6: 3,5,4,9 # reduction candidate for 3,5 F6: 3,5 => CTR * 4.8129..75.78..41991.457682.4.29876.8965741237.5613948.5934.871.7498.2.6.8276..94 F6: 4,9 # 11 pairs * PAIR D5: 3,5 ROW 5 H5: 3,5,2,4 # reduction candidate for 3,5 H5: 3,5 # 15 pairs I5: 3,5,2 # reduction candidate for 3,5 I5: 3,5 # 11 pairs * PAIR D5: 3,5 COL D D1: 3,5,1 # reduction candidate for 3,5 D1: 3,5 # 16 pairs D1: 1 # 16 pairs * PAIR A7: 2,6 BLK 7 A9: 2,6,1,3 # reduction candidate for 2,6 A9: 1,3 => CTR * 46812...75278.64199134576827412.8.6.89657.12323561.748659342871.7498.2.6.8276...4 A9: 2,6 # 13 pairs * PAIR A7: 2,6 ROW 7 F7: 2,6,4 # reduction candidate for 2,6 F7: 4 => CTR * 4.8.2...75.78..4..91.4.768....248.6.896.7.142.42619..8259.6487..7498.2.668.7.2..4 F7: 2,6 # 10 pairs * PAIR A8: 1,3 BLK 7 A9: 1,3,2,6 # reduction candidate for 1,3 A9: 1,3 => CTR * 46812...75278.64199134576827412.8.6.89657.12323561.748659342871.7498.2.6.8276...4 A9: 2,6 # 13 pairs C9: 1,3,2 # reduction candidate for 1,3 C9: 1,3 # 13 pairs * PAIR A8: 1,3 ROW 8 F8: 1,3,5 # reduction candidate for 1,3 F8: 1,3 # 13 pairs H8: 1,3,5 # reduction candidate for 1,3 H8: 1,3 # 15 pairs * PAIR A8: 1,3 COL A A4: 1,3,7 # reduction candidate for 1,3 A4: 1,3 # 13 pairs A4: 7 # 12 pairs * PAIR D7: 1,3 BLK 8 F8: 1,3,5 # reduction candidate for 1,3 F8: 1,3 # 13 pairs F9: 1,3,2,5,6 # reduction candidate for 1,3 F9: 1,3 # 14 pairs * PAIR D7: 1,3 COL D D1: 1,3,5 # reduction candidate for 1,3 D1: 5 => SOLVED * 468521937537896421912437685143258769896374152725619348659142873374985216281763594 D1: 1,3 # 12 pairs * PAIR E7: 4,6 BLK 8 F7: 4,6,2 # reduction candidate for 4,6 F7: 4,6 # 15 pairs F7: 2 # 8 pairs * PAIR I7: 1,3 BLK 9 H8: 1,3,5 # reduction candidate for 1,3 H8: 1,3 # 15 pairs H9: 1,3,5,9 # reduction candidate for 1,3 H9: 1,3 # 14 pairs * PAIR I7: 1,3 COL I I2: 1,3,2,9 # reduction candidate for 1,3 I2: 2,9 # 16 pairs I2: 1,3 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060402-absurd-base-pr-000.dot * REASONING * DIS # B2: 2 => CTR => B2: 3,6 * DIS # I3: 2,3 => CTR => I3: 5 * DIS # F1: 3,5 => CTR => F1: 1,6,9 * DIS # I3: 2 => CTR => I3: 3,5 * DIS # B6: 3,4 => CTR => B6: 2 * DIS # E4: 3,4 => CTR => E4: 5,9 * DIS # F5: 3,5 => CTR => F5: 4 * DIS # F6: 3,5 => CTR => F6: 4,9 * DIS # A9: 1,3 => CTR => A9: 2,6 * DIS # F7: 4 => CTR => F7: 2,6 * DIS # A9: 1,3 => CTR => A9: 2,6 * PRF # D1: 5 => SOL * CNT 12 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B1,B4,C3,D5,D7,E3,E7,I7) * 4.8.2...75.78..4..91.4.768....2.8.6.896.7.1.....61...8.59...87..7498.2.6.8.7....4 * PAIR B1: 3,6 BLK 1 B2: 3,6,2 # reduction candidate for 3,6 B2: 2 => CTR * 46812...75278.6419913457682.4.298.65896574123.3.61..48.593..871.7498.2.6.8.76...4 * PAIR B1: 3,6 ROW 1 F1: 3,6,1,5,9 # reduction candidate for 3,6 F1: 3,6 # 15 pairs F1: 1,5,9 # 13 pairs * PAIR E3: 3,5 BLK 2 D1: 3,5,1 # reduction candidate for 3,5 D1: 3,5 => SOLVED * 468521937537896421912437685143258769896374152725619348659142873374985216281763594 * DURATION: 0:00:04.239838 START: 22:06:49.845378 END: 22:06:54.085216 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060402-absurd-base-pr-001.dot * REASONING * DIS # B2: 2 => CTR => B2: 3,6 * PRF B2: 3,6 # D1: 3,5 => SOL * STA B2: 3,6 + D1: 3,5 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060402, absurd
Solution
position: 468521937537896421912437685143258769896374152725619348659142873374985216281763594 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:
* INC # B2: 3,6 => UNS * DIS # B2: 2 => CTR => B2: 3,6 * INC # F1: 3,6 => UNS * INC # F1: 1,5,9 => UNS * INC # B2: 2,3 => UNS * INC # B2: 6 => UNS * DIS # I3: 2,3 => CTR => I3: 5 * INC # I3: 5 => UNS * INC # C6: 2,3 => UNS * INC # C9: 2,3 => UNS * INC # D1: 3,5 => UNS * DIS # F1: 3,5 => CTR => F1: 1,6,9 * INC # F1: 1,6,9 => UNS * INC # I3: 3,5 => UNS * DIS # I3: 2 => CTR => I3: 3,5 * INC # E4: 3,5 => UNS * INC # E9: 3,5 => UNS * DIS # B6: 3,4 => CTR => B6: 2 * INC # B6: 2 => UNS * DIS # E4: 3,4 => CTR => E4: 5,9 * INC # E4: 5,9 => UNS * INC # E4: 3,5 => UNS * DIS # F5: 3,5 => CTR => F5: 4 * INC # F5: 4 => UNS * DIS # F6: 3,5 => CTR => F6: 4,9 * INC # F6: 4,9 => UNS * INC # H5: 3,5 => UNS * INC # I5: 3,5 => UNS * INC # D1: 3,5 => UNS * INC # D1: 1 => UNS * INC # A9: 2,6 => UNS * DIS # A9: 1,3 => CTR => A9: 2,6 * INC # F7: 2,6 => UNS * DIS # F7: 4 => CTR => F7: 2,6 * DIS # A9: 1,3 => CTR => A9: 2,6 * INC # A9: 2,6 => UNS * INC # C9: 1,3 => UNS * INC # F8: 1,3 => UNS * INC # H8: 1,3 => UNS * INC # A4: 1,3 => UNS * INC # A4: 7 => UNS * INC # F8: 1,3 => UNS * INC # F9: 1,3 => UNS * INC # D1: 1,3 => UNS * PRF # D1: 5 => SOL * INC # F7: 4,6 => UNS * INC # F7: 2 => UNS * INC # H8: 1,3 => UNS * INC # H9: 1,3 => UNS * INC # I2: 1,3 => UNS * INC # I2: 2,9 => UNS * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 3,6 => UNS * DIS # B2: 2 => CTR => B2: 3,6 * INC B2: 3,6 # F1: 3,6 => UNS * INC B2: 3,6 # F1: 1,5,9 => UNS * PRF B2: 3,6 # D1: 3,5 => SOL * STA B2: 3,6 + D1: 3,5 * CNT 5 HDP CHAINS / 5 HYP OPENED