Analysis of zz-www.sudokuoftheday.co.uk-20060521-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: ...973.48.83..4...7...2.....7...15.......9.....9.38.2........5.8.1.....6.52.1...3 initial
Autosolve
position: ...973.48.831.4...7..82.....7...15.......9.....9.38.2...7.8..5.8.1.9..76.52.17..3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 4,6 => CTR => B3: 1,9 * PRF # C4: 4,6 => SOL * DIS # G2: 6,9 => CTR => G2: 2,7 * PRF # G3: 6,9 => SOL * DIS # A2: 2 => CTR => A2: 6,9 * DIS # D5: 2,6 => CTR => D5: 5,7 * DIS # E5: 5 => CTR => E5: 4,6 * PRF # C4: 4,6 => SOL * DIS # I7: 4,9 => CTR => I7: 1,2 * DIS # B7: 3,4 => CTR => B7: 6,9 * DIS # D8: 5 => CTR => D8: 3,4 * DIS # A9: 9 => CTR => A9: 4,6 * DIS # G9: 4 => CTR => G9: 8,9 * PRF # H4: 8,9 => SOL * CNT 14 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 4,6 => CTR => B3: 1,9 * DIS B3: 1,9 # G2: 6,9 => CTR => G2: 2,7 * PRF B3: 1,9 + G2: 2,7 # G3: 6,9 => SOL * STA B3: 1,9 + G2: 2,7 + G3: 6,9 * CNT 3 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...973.48.83..4...7...2.....7...15.......9.....9.38.2........5.8.1.....6.52.1...3 | initial |
| ...973.48.831.4...7..82.....7...15.......9.....9.38.2...7.8..5.8.1.9..76.52.17..3 | autosolve |
| 265973148983154762714826935376241589528769314149538627697382451831495276452617893 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) C1: 5,6 C3: 4,6 E2: 5,6 F3: 5,6 H2: 6,9 D4: 2,6 E4: 4,6 I4: 4,9 B8: 3,4 F7: 2,6 F8: 2,5 D9: 4,6 G8: 2,4 H9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G7,I7: 1.. / G7 = 1 => 15 pairs (_) / I7 = 1 => 21 pairs (_) H3,H5: 1.. / H3 = 1 => 16 pairs (_) / H5 = 1 => 25 pairs (_) D4,D5: 2.. / D4 = 2 => 13 pairs (_) / D5 = 2 => 0 pairs (X) F7,F8: 2.. / F7 = 2 => 16 pairs (_) / F8 = 2 => 0 pairs (X) A4,D4: 2.. / A4 = 2 => 0 pairs (X) / D4 = 2 => 13 pairs (_) F8,G8: 2.. / F8 = 2 => 0 pairs (X) / G8 = 2 => 16 pairs (_) B1,B5: 2.. / B1 = 2 => 17 pairs (_) / B5 = 2 => 14 pairs (_) I2,I7: 2.. / I2 = 2 => 16 pairs (_) / I7 = 2 => 0 pairs (X) G3,H3: 3.. / G3 = 3 => 14 pairs (_) / H3 = 3 => 0 pairs (*) D7,D8: 3.. / D7 = 3 => 14 pairs (_) / D8 = 3 => 22 pairs (_) A4,H4: 3.. / A4 = 3 => 15 pairs (_) / H4 = 3 => 14 pairs (_) B8,D8: 3.. / B8 = 3 => 14 pairs (_) / D8 = 3 => 22 pairs (_) G3,G5: 3.. / G3 = 3 => 14 pairs (_) / G5 = 3 => 0 pairs (*) B3,C3: 4.. / B3 = 4 => 0 pairs (X) / C3 = 4 => 14 pairs (_) E4,E5: 4.. / E4 = 4 => 15 pairs (_) / E5 = 4 => 17 pairs (_) A1,C1: 5.. / A1 = 5 => 0 pairs (X) / C1 = 5 => 13 pairs (_) E2,F3: 5.. / E2 = 5 => 16 pairs (_) / F3 = 5 => 0 pairs (X) I2,I3: 5.. / I2 = 5 => 0 pairs (X) / I3 = 5 => 16 pairs (_) D8,F8: 5.. / D8 = 5 => 0 pairs (X) / F8 = 5 => 16 pairs (_) E2,I2: 5.. / E2 = 5 => 16 pairs (_) / I2 = 5 => 0 pairs (X) F3,I3: 5.. / F3 = 5 => 0 pairs (X) / I3 = 5 => 16 pairs (_) A6,D6: 5.. / A6 = 5 => 14 pairs (_) / D6 = 5 => 18 pairs (_) C1,C5: 5.. / C1 = 5 => 13 pairs (_) / C5 = 5 => 0 pairs (X) E2,E5: 5.. / E2 = 5 => 16 pairs (_) / E5 = 5 => 0 pairs (X) F3,F8: 5.. / F3 = 5 => 0 pairs (X) / F8 = 5 => 16 pairs (_) E2,F3: 6.. / E2 = 6 => 0 pairs (X) / F3 = 6 => 16 pairs (_) A9,D9: 6.. / A9 = 6 => 17 pairs (_) / D9 = 6 => 17 pairs (_) F3,F7: 6.. / F3 = 6 => 16 pairs (_) / F7 = 6 => 0 pairs (X) G2,I2: 7.. / G2 = 7 => 14 pairs (_) / I2 = 7 => 0 pairs (X) D5,D6: 7.. / D5 = 7 => 15 pairs (_) / D6 = 7 => 14 pairs (_) C4,C5: 8.. / C4 = 8 => 14 pairs (_) / C5 = 8 => 0 pairs (*) G9,H9: 8.. / G9 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) C4,H4: 8.. / C4 = 8 => 14 pairs (_) / H4 = 8 => 0 pairs (*) G5,G9: 8.. / G5 = 8 => 14 pairs (_) / G9 = 8 => 0 pairs (*) A2,B3: 9.. / A2 = 9 => 0 pairs (*) / B3 = 9 => 0 pairs (X) H4,I4: 9.. / H4 = 9 => 0 pairs (X) / I4 = 9 => 14 pairs (_) B3,B7: 9.. / B3 = 9 => 17 pairs (_) / B7 = 9 => 0 pairs (*) * DURATION: 0:00:42.230726 START: 23:18:28.134267 END: 23:19:10.364993 2019-04-30 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C1,C3,D4,D9,E2,E4,F3,F7,F8,G8,H2,H9,I4) * ...973.48.831.4...7..82.....7...15.......9.....9.38.2...7.8..5.8.1.9..76.52.17..3 * PAIR C1: 5,6 BLK 1 A1: 5,6,1,2 # reduction candidate for 5,6 A1: 5,6 # 20 pairs A1: 1,2 # 14 pairs * PAIR C1: 5,6 COL C C5: 5,6,4,8 # reduction candidate for 5,6 C5: 5,6 # 14 pairs C5: 4,8 # 14 pairs * PAIR C3: 4,6 BLK 1 B3: 4,6,1,9 # reduction candidate for 4,6 B3: 4,6 => CTR * ...973.489831.4.6.7..826..5.7...15.......9.....9.38.2..97.82.5.8.1.95276.52.17..3 B3: 1,9 # 15 pairs * PAIR C3: 4,6 COL C C4: 4,6,8 # reduction candidate for 4,6 C4: 4,6 => SOLVED * 265973148983154762714826935376241589528769314149538627697382451831495276452617893 C4: 8 # 14 pairs C5: 4,6,5,8 # reduction candidate for 4,6 C5: 4,6 # 14 pairs * PAIR E2: 5,6 COL E E5: 5,6,4 # reduction candidate for 5,6 E5: 4 # 17 pairs E5: 5,6 # 15 pairs * PAIR H2: 6,9 BLK 3 G2: 6,9,2,7 # reduction candidate for 6,9 G2: 6,9 => CTR * ...973.48.831.4..77..82...5.7...15.......9.....9.38.2...7.8..528.1.9..76.52.17..3 G2: 2,7 # 15 pairs G3: 6,9,1,3 # reduction candidate for 6,9 G3: 6,9 => SOLVED * 265973148983154762714826935376241589528769314149538627697382451831495276452617893 G3: 1,3 # 15 pairs H3: 6,9,1,3 # reduction candidate for 6,9 H3: 6,9 # 24 pairs * PAIR H2: 6,9 ROW 2 A2: 6,9,2 # reduction candidate for 6,9 A2: 2 => CTR * 165973248283164.95794825..1.7.2415.942..59317519738624.47.86152831592476652417..3 A2: 6,9 # 16 pairs * PAIR H2: 6,9 COL H H4: 6,9,3,8 # reduction candidate for 6,9 H4: 6,9 # 16 pairs H4: 3,8 # 15 pairs * PAIR D4: 2,6 BLK 5 D5: 2,6,5,7 # reduction candidate for 2,6 D5: 2,6 => CTR * 16597324828316479579482536137..415.9....59.17519738624947386152831592476652417983 D5: 5,7 # 14 pairs * PAIR D4: 2,6 ROW 4 A4: 2,6,3,4 # reduction candidate for 2,6 A4: 2,6 # 15 pairs A4: 3,4 # 14 pairs * PAIR E4: 4,6 BLK 5 E5: 4,6,5 # reduction candidate for 4,6 E5: 5 => CTR * 165973248283164795794825..1378241569....59.1.519.38.24..7386152831592476652417983 E5: 4,6 # 16 pairs * PAIR E4: 4,6 ROW 4 A4: 4,6,2,3 # reduction candidate for 4,6 A4: 4,6 # 19 pairs C4: 4,6,8 # reduction candidate for 4,6 C4: 4,6 => SOLVED * 265973148983154762714826935376241589528769314149538627697382451831495276452617893 C4: 8 # 14 pairs * PAIR I4: 4,9 COL I I7: 4,9,1,2 # reduction candidate for 4,9 I7: 4,9 => CTR * ..5973648683154792794826315.78..15.9..6.4983..19.3842.9.7.821548.1.95276.52.17983 I7: 1,2 # 15 pairs * PAIR B8: 3,4 BLK 7 A7: 3,4,6,9 # reduction candidate for 3,4 A7: 3,4 # 17 pairs B7: 3,4,6,9 # reduction candidate for 3,4 B7: 3,4 => CTR * 165973248283164.95794825..1.7.2415.942..59317519738624.47.86152831592476652417..3 B7: 6,9 # 15 pairs * PAIR B8: 3,4 ROW 8 D8: 3,4,5 # reduction candidate for 3,4 D8: 5 => CTR * 165973248283164795794825..1378241569....59.1.519.38.24947386152831592476652417983 D8: 3,4 # 16 pairs * PAIR B8: 3,4 COL B B5: 3,4,1,2,6 # reduction candidate for 3,4 B5: 3,4 # 24 pairs B5: 1,2,6 # 14 pairs * PAIR D9: 4,6 BLK 8 D7: 4,6,3 # reduction candidate for 4,6 D7: 4,6 # 22 pairs D7: 3 # 14 pairs * PAIR D9: 4,6 ROW 9 A9: 4,6,9 # reduction candidate for 4,6 A9: 9 => CTR * ...973648683154792794826315.782.15.9..6.4983...9.38124..7.82.5.8.1.95276952617483 A9: 4,6 # 16 pairs * PAIR G8: 2,4 BLK 9 G7: 2,4,1,9 # reduction candidate for 2,4 G7: 2,4 # 23 pairs I7: 2,4,1,9 # reduction candidate for 2,4 I7: 2,4 # 18 pairs * PAIR H9: 8,9 BLK 9 G9: 8,9,4 # reduction candidate for 8,9 G9: 4 => CTR * ...973648683154792794826315.782.15.9..6.4983...9.38124..7.82.5.8.1.95276952617483 G9: 8,9 # 16 pairs * PAIR H9: 8,9 COL H H4: 8,9,3,6 # reduction candidate for 8,9 H4: 8,9 => SOLVED * 265973148983154762714826935376241589528769314149538627697382451831495276452617893 H4: 3,6 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060521-absurd-base-pr-000.dot * REASONING * DIS # B3: 4,6 => CTR => B3: 1,9 * PRF # C4: 4,6 => SOL * DIS # G2: 6,9 => CTR => G2: 2,7 * PRF # G3: 6,9 => SOL * DIS # A2: 2 => CTR => A2: 6,9 * DIS # D5: 2,6 => CTR => D5: 5,7 * DIS # E5: 5 => CTR => E5: 4,6 * PRF # C4: 4,6 => SOL * DIS # I7: 4,9 => CTR => I7: 1,2 * DIS # B7: 3,4 => CTR => B7: 6,9 * DIS # D8: 5 => CTR => D8: 3,4 * DIS # A9: 9 => CTR => A9: 4,6 * DIS # G9: 4 => CTR => G9: 8,9 * PRF # H4: 8,9 => SOL * CNT 14 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C1,C3,D4,D9,E2,E4,F3,F7,F8,G8,H2,H9,I4) * ...973.48.831.4...7..82.....7...15.......9.....9.38.2...7.8..5.8.1.9..76.52.17..3 * PAIR C1: 5,6 BLK 1 A1: 5,6,1,2 # reduction candidate for 5,6 A1: 5,6 # 20 pairs A1: 1,2 # 14 pairs * PAIR C1: 5,6 COL C C5: 5,6,4,8 # reduction candidate for 5,6 C5: 5,6 # 14 pairs C5: 4,8 # 14 pairs * PAIR C3: 4,6 BLK 1 B3: 4,6,1,9 # reduction candidate for 4,6 B3: 4,6 => CTR * ...973.489831.4.6.7..826..5.7...15.......9.....9.38.2..97.82.5.8.1.95276.52.17..3 * PAIR E2: 5,6 COL E E5: 5,6,4 # reduction candidate for 5,6 E5: 4 # 17 pairs E5: 5,6 # 15 pairs * PAIR H2: 6,9 BLK 3 G2: 6,9,2,7 # reduction candidate for 6,9 G2: 6,9 => CTR * ...973.48.831.4..77.482...5.7...15.......9.....9.38.2...7.8..528.1.9..76.52.17..3 G3: 6,9,1,3 # reduction candidate for 6,9 G3: 6,9 => SOLVED * 265973148983154762714826935376241589528769314149538627697382451831495276452617893 * DURATION: 0:00:06.283609 START: 23:19:39.028462 END: 23:19:45.312071 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060521-absurd-base-pr-001.dot * REASONING * DIS # B3: 4,6 => CTR => B3: 1,9 * DIS B3: 1,9 # G2: 6,9 => CTR => G2: 2,7 * PRF B3: 1,9 + G2: 2,7 # G3: 6,9 => SOL * STA B3: 1,9 + G2: 2,7 + G3: 6,9 * CNT 3 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060521, absurd
Solution
position: 265973148983154762714826935376241589528769314149538627697382451831495276452617893 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 # A1: 5,6 => UNS * INC # A1: 1,2 => UNS * INC # C5: 5,6 => UNS * INC # C5: 4,8 => UNS * DIS # B3: 4,6 => CTR => B3: 1,9 * INC # B3: 1,9 => UNS * PRF # C4: 4,6 => SOL * INC # C4: 8 => UNS * INC # C5: 4,6 => UNS * INC # E5: 5,6 => UNS * INC # E5: 4 => UNS * DIS # G2: 6,9 => CTR => G2: 2,7 * INC # G2: 2,7 => UNS * PRF # G3: 6,9 => SOL * INC # G3: 1,3 => UNS * INC # H3: 6,9 => UNS * INC # A2: 6,9 => UNS * DIS # A2: 2 => CTR => A2: 6,9 * INC # H4: 6,9 => UNS * INC # H4: 3,8 => UNS * DIS # D5: 2,6 => CTR => D5: 5,7 * INC # D5: 5,7 => UNS * INC # A4: 2,6 => UNS * INC # A4: 3,4 => UNS * INC # E5: 4,6 => UNS * DIS # E5: 5 => CTR => E5: 4,6 * INC # A4: 4,6 => UNS * PRF # C4: 4,6 => SOL * INC # C4: 8 => UNS * DIS # I7: 4,9 => CTR => I7: 1,2 * INC # I7: 1,2 => UNS * INC # A7: 3,4 => UNS * DIS # B7: 3,4 => CTR => B7: 6,9 * INC # B7: 6,9 => UNS * INC # D8: 3,4 => UNS * DIS # D8: 5 => CTR => D8: 3,4 * INC # B5: 3,4 => UNS * INC # B5: 1,2,6 => UNS * INC # D7: 4,6 => UNS * INC # D7: 3 => UNS * INC # A9: 4,6 => UNS * DIS # A9: 9 => CTR => A9: 4,6 * INC # G7: 2,4 => UNS * INC # I7: 2,4 => UNS * INC # G9: 8,9 => UNS * DIS # G9: 4 => CTR => G9: 8,9 * PRF # H4: 8,9 => SOL * INC # H4: 3,6 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 5,6 => UNS * INC # A1: 1,2 => UNS * INC # C5: 5,6 => UNS * INC # C5: 4,8 => UNS * DIS # B3: 4,6 => CTR => B3: 1,9 * INC B3: 1,9 # E5: 5,6 => UNS * INC B3: 1,9 # E5: 4 => UNS * DIS B3: 1,9 # G2: 6,9 => CTR => G2: 2,7 * PRF B3: 1,9 + G2: 2,7 # G3: 6,9 => SOL * STA B3: 1,9 + G2: 2,7 + G3: 6,9 * CNT 9 HDP CHAINS / 9 HYP OPENED