Analysis of zz-www.sudokuoftheday.co.uk-20060605-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: ..82....7..6..4...1.38...4...4.9.8..8....3..52...8.....613...8......6.2.9..1...3. initial
Autosolve
position: ..82....7..6..4..81.38...4.6.4.9.8..8....3..52...8.....613...8.38...6.2.9.21.8.3. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 4,5 => CTR => B1: 9 * DIS # A7: 7 => CTR => A7: 4,5 * DIS # B2: 5,7 => CTR => B2: 2,9 * DIS # D2: 5,7 => CTR => D2: 9 * DIS # E2: 5,7 => CTR => E2: 1,3 * DIS # A7: 4 => CTR => A7: 5,7 * DIS # B4: 1,7 => CTR => B4: 3,5 * PRF # B6: 1,7 => SOL * DIS # H5: 1,7 => CTR => H5: 6,9 * DIS # C6: 7,9 => CTR => C6: 5 * PRF # C6: 5 => SOL * DIS # H5: 7,9 => CTR => H5: 1,6 * DIS # F4: 5,7 => CTR => F4: 1,2 * DIS # D6: 5,7 => CTR => D6: 4,6 * DIS # B4: 5,7 => CTR => B4: 1,3 * DIS # D2: 5,7 => CTR => D2: 9 * DIS # H5: 1,7 => CTR => H5: 6,9 * DIS # B4: 1,7 => CTR => B4: 3,5 * DIS # F4: 1,7 => CTR => F4: 2,5 * DIS # B9: 5,7 => CTR => B9: 4 * DIS # G8: 5,7 => CTR => G8: 1,4,9 * DIS # C6: 9 => CTR => C6: 5,7 * DIS # G7: 4,9 => CTR => G7: 5,7 * DIS # G9: 4,6 => CTR => G9: 5,7 * DIS # I6: 4,6 => CTR => I6: 1,3,9 * CNT 25 HDP CHAINS / 60 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 4,5 => CTR => B1: 9 * DIS B1: 9 # B2: 5,7 => CTR => B2: 2 * DIS B1: 9 + B2: 2 # D2: 5,7 => CTR => D2: 9 * PRF B1: 9 + B2: 2 + D2: 9 # B6: 1,7 => SOL * STA B1: 9 + B2: 2 + D2: 9 + B6: 1,7 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..82....7..6..4...1.38...4...4.9.8..8....3..52...8.....613...8......6.2.9..1...3. | initial |
| ..82....7..6..4..81.38...4.6.4.9.8..8....3..52...8.....613...8.38...6.2.9.21.8.3. | autosolve |
| 498235617726914358153867942634592871819743265275681493561329784387456129942178536 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A1: 4,5 A2: 5,7 B5: 1,7 C5: 7,9 D4: 5,7 H4: 1,7 C8: 5,7 I7: 4,9 I9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G8,I8: 1.. / G8 = 1 => 23 pairs (_) / I8 = 1 => 10 pairs (_) B2,B3: 2.. / B2 = 2 => 9 pairs (_) / B3 = 2 => 0 pairs (X) F4,E5: 2.. / F4 = 2 => 11 pairs (_) / E5 = 2 => 0 pairs (X) I4,G5: 2.. / I4 = 2 => 0 pairs (X) / G5 = 2 => 11 pairs (_) E7,F7: 2.. / E7 = 2 => 11 pairs (_) / F7 = 2 => 0 pairs (X) B2,G2: 2.. / B2 = 2 => 9 pairs (_) / G2 = 2 => 0 pairs (X) F4,I4: 2.. / F4 = 2 => 11 pairs (_) / I4 = 2 => 0 pairs (X) E5,G5: 2.. / E5 = 2 => 0 pairs (X) / G5 = 2 => 11 pairs (_) E5,E7: 2.. / E5 = 2 => 0 pairs (X) / E7 = 2 => 11 pairs (_) F4,F7: 2.. / F4 = 2 => 11 pairs (_) / F7 = 2 => 0 pairs (X) I3,I4: 2.. / I3 = 2 => 11 pairs (_) / I4 = 2 => 0 pairs (X) E1,E2: 3.. / E1 = 3 => 22 pairs (_) / E2 = 3 => 9 pairs (_) G1,G2: 3.. / G1 = 3 => 9 pairs (_) / G2 = 3 => 22 pairs (_) B4,B6: 3.. / B4 = 3 => 11 pairs (_) / B6 = 3 => 10 pairs (_) I4,I6: 3.. / I4 = 3 => 10 pairs (_) / I6 = 3 => 11 pairs (_) E1,G1: 3.. / E1 = 3 => 22 pairs (_) / G1 = 3 => 9 pairs (_) E2,G2: 3.. / E2 = 3 => 9 pairs (_) / G2 = 3 => 22 pairs (_) B4,I4: 3.. / B4 = 3 => 11 pairs (_) / I4 = 3 => 10 pairs (_) B6,I6: 3.. / B6 = 3 => 10 pairs (_) / I6 = 3 => 11 pairs (_) A1,B1: 4.. / A1 = 4 => 12 pairs (_) / B1 = 4 => 0 pairs (X) A7,B9: 4.. / A7 = 4 => 0 pairs (X) / B9 = 4 => 12 pairs (_) A1,A7: 4.. / A1 = 4 => 12 pairs (_) / A7 = 4 => 0 pairs (X) B1,B9: 4.. / B1 = 4 => 0 pairs (X) / B9 = 4 => 12 pairs (_) H1,H2: 5.. / H1 = 5 => 0 pairs (X) / H2 = 5 => 0 pairs (_) C6,C8: 5.. / C6 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) E1,E3: 6.. / E1 = 6 => 0 pairs (X) / E3 = 6 => 22 pairs (_) D5,D6: 6.. / D5 = 6 => 0 pairs (X) / D6 = 6 => 10 pairs (_) G9,I9: 6.. / G9 = 6 => 0 pairs (X) / I9 = 6 => 9 pairs (_) A2,A7: 7.. / A2 = 7 => 10 pairs (_) / A7 = 7 => 0 pairs (X) C5,C6: 9.. / C5 = 9 => 9 pairs (_) / C6 = 9 => 0 pairs (X) F7,D8: 9.. / F7 = 9 => 21 pairs (_) / D8 = 9 => 0 pairs (X) D2,D8: 9.. / D2 = 9 => 21 pairs (_) / D8 = 9 => 0 pairs (X) * DURATION: 0:00:33.581075 START: 23:38:38.872849 END: 23:39:12.453924 2019-04-30 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B5,C5,C8,D4,H4,I7,I9) * ..82....7..6..4..81.38...4.6.4.9.8..8....3..52...8.....613...8.38...6.2.9.21.8.3. * PAIR A1: 4,5 BLK 1 B1: 4,5,9 # reduction candidate for 4,5 B1: 4,5 => CTR * ..82613977269341581938..6426.4.928..8794132652.5687.1..613297843875.6.2.9.21.8.3. B1: 9 # 12 pairs * PAIR A1: 4,5 COL A A7: 4,5,7 # reduction candidate for 4,5 A7: 7 => CTR * 4982.1.57526..4..81738...4.6.4.9.8..8...132.52...8....76132..8.385.46.2.9421.8.36 A7: 4,5 # 10 pairs * PAIR A2: 5,7 BLK 1 B2: 5,7,2,9 # reduction candidate for 5,7 B2: 5,7 => CTR * .982..3.7..6.342.81238...4.6.4.9.8.28...23..52...8...3.613.2.8.38.9.6.219.21.8.3. B2: 2,9 # 10 pairs B3: 5,7,2,9 # reduction candidate for 5,7 B3: 5,7 # 13 pairs * PAIR A2: 5,7 ROW 2 D2: 5,7,9 # reduction candidate for 5,7 D2: 5,7 => CTR * 498261357.26.34..81.38.96426.4.928..8794132652.5687...56132..8.38.9.6.2.9421.8.36 D2: 9 # 21 pairs E2: 5,7,1,3 # reduction candidate for 5,7 E2: 5,7 => CTR * ..8231.57.269.43181.386.9426.459287.8794132652.5687.9..61329.84387..6.2.9.21.8.3. E2: 1,3 # 10 pairs * PAIR A2: 5,7 COL A A7: 5,7,4 # reduction candidate for 5,7 A7: 4 => CTR * 5482....77.65.4..81.38...4.6.479.81.8....3..52...8....4613...8938.9.6.219.21.8.3. A7: 5,7 # 12 pairs * PAIR B5: 1,7 BLK 4 B4: 1,7,3,5 # reduction candidate for 1,7 B4: 1,7 => CTR * 4.82....77269.4.581.38679426.45928.38.9.432.5235.8149..61329784387456.2.942178536 B4: 3,5 # 10 pairs B6: 1,7,3,5 # reduction candidate for 1,7 B6: 1,7 => SOLVED * 498235617726914358153867942634592871819743265275681493561329784387456129942178536 B6: 3,5 # 10 pairs * PAIR B5: 1,7 ROW 5 E5: 1,7,2,4 # reduction candidate for 1,7 E5: 1,7 # 13 pairs H5: 1,7,6,9 # reduction candidate for 1,7 H5: 1,7 => CTR * 4982.5.677269.4.581538672496.459.8..8.9..3..52...8..9..613.9.8438.4.69219421.8.36 H5: 6,9 # 10 pairs * PAIR C5: 7,9 BLK 4 C6: 7,9,5 # reduction candidate for 7,9 C6: 7,9 => CTR * ..82.9..7..67.4..81738.5.4.6.459.8..81...3..525..8.....613...8.385..6.2.9.21.8.3. C6: 5 => SOLVED * 498235617726914358153867942634592871819743265275681493561329784387456129942178536 * PAIR C5: 7,9 ROW 5 H5: 7,9,1,6 # reduction candidate for 7,9 H5: 7,9 => CTR * 4982.5..77269.4.58153867.4.6.45928..81.6432.52.578146956132978438745692.9421.8.36 H5: 1,6 # 10 pairs * PAIR D4: 5,7 BLK 5 F4: 5,7,1,2 # reduction candidate for 5,7 F4: 5,7 => CTR * 4.82.9..7.96..42.81.386..49634.9.81281..23..52...81..3.613.298438.946.219421.8.36 F4: 1,2 # 10 pairs D6: 5,7,4,6 # reduction candidate for 5,7 D6: 5,7 => CTR * 4.82.5..7.269.4.581538.79426.45928..8..6432.52.578146956132978438745612.9421.8.36 D6: 4,6 # 10 pairs F6: 5,7,1 # reduction candidate for 5,7 F6: 5,7 # 14 pairs * PAIR D4: 5,7 ROW 4 B4: 5,7,1,3 # reduction candidate for 5,7 B4: 5,7 => CTR * .982.5.67.269.4.58153867942674592813819643275235781.9.561329784387456.219.21.8.3. B4: 1,3 # 11 pairs * PAIR D4: 5,7 COL D D2: 5,7,9 # reduction candidate for 5,7 D2: 5,7 => CTR * 498261357.26.34..81.38.96426.4.928..8794132652.5687...56132..8.38.9.6.2.9421.8.36 D2: 9 # 21 pairs D8: 5,7,4,9 # reduction candidate for 5,7 D8: 5,7 # 23 pairs * PAIR H4: 1,7 BLK 6 H5: 1,7,6,9 # reduction candidate for 1,7 H5: 1,7 => CTR * 4982.5.677269.4.581538672496.459.8..8.9..3..52...8..9..613.9.8438.4.69219421.8.36 H5: 6,9 # 10 pairs H6: 1,7,6,9 # reduction candidate for 1,7 H6: 1,7 # 16 pairs * PAIR H4: 1,7 ROW 4 B4: 1,7,3,5 # reduction candidate for 1,7 B4: 1,7 => CTR * 4.82....77269.4.581.38679426.45928.38.9.432.5235.8149..61329784387456.2.942178536 B4: 3,5 # 10 pairs F4: 1,7,2,5 # reduction candidate for 1,7 F4: 1,7 => CTR * 4982....75267.4..817386.24.63459.8.281..23..525..8...37613.2.8.3859.6.219421.8.36 F4: 2,5 # 10 pairs * PAIR C8: 5,7 BLK 7 A7: 5,7,4 # reduction candidate for 5,7 A7: 5,7 # 12 pairs B9: 5,7,4 # reduction candidate for 5,7 B9: 5,7 => CTR * 5482....77.65.4..81.38...4.6.479.81.8....3..52...8....4613...8938.9.6.219.21.8.3. B9: 4 # 12 pairs * PAIR C8: 5,7 ROW 8 D8: 5,7,4,9 # reduction candidate for 5,7 D8: 5,7 # 23 pairs E8: 5,7,4 # reduction candidate for 5,7 E8: 5,7 # 13 pairs G8: 5,7,1,4,9 # reduction candidate for 5,7 G8: 5,7 => CTR * 498261357.26.34..81.38.96426.4.928.3879413265235687...56132..8.38.946.219421.8.36 G8: 1,4,9 # 11 pairs * PAIR C8: 5,7 COL C C6: 5,7,9 # reduction candidate for 5,7 C6: 9 => CTR * ..82.9..7..67.4..81738.5.4.6.459.8..817..3..5259.8.....613...8.385..6.2.9.21.8.3. C6: 5,7 # 9 pairs * PAIR I7: 4,9 BLK 9 G7: 4,9,5,7 # reduction candidate for 4,9 G7: 4,9 => CTR * 498261357.26.34..81.38.9642614592873879413265235687....6132..8.38.946.219421.8.36 G7: 5,7 # 10 pairs G8: 4,9,1,5,7 # reduction candidate for 4,9 G8: 4,9 # 13 pairs I8: 4,9,1 # reduction candidate for 4,9 I8: 4,9 # 23 pairs * PAIR I7: 4,9 COL I I6: 4,9,1,3,6 # reduction candidate for 4,9 I6: 4,9 # 10 pairs I6: 1,3,6 # 9 pairs * PAIR I9: 4,6 BLK 9 G9: 4,6,5,7 # reduction candidate for 4,6 G9: 4,6 => CTR * 5482....77.65.4..81.38...4.6.479.81.8....3..52...8....4613...8938.946.219.21.8.3. G9: 5,7 # 10 pairs * PAIR I9: 4,6 COL I I6: 4,6,1,3,9 # reduction candidate for 4,6 I6: 4,6 => CTR * ..8261357.26.34..81.38.9642614592873879413265235687..4.61325.89387946.219.21.8.36 I6: 1,3,9 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060605-absurd-base-pr-000.dot * REASONING * DIS # B1: 4,5 => CTR => B1: 9 * DIS # A7: 7 => CTR => A7: 4,5 * DIS # B2: 5,7 => CTR => B2: 2,9 * DIS # D2: 5,7 => CTR => D2: 9 * DIS # E2: 5,7 => CTR => E2: 1,3 * DIS # A7: 4 => CTR => A7: 5,7 * DIS # B4: 1,7 => CTR => B4: 3,5 * PRF # B6: 1,7 => SOL * DIS # H5: 1,7 => CTR => H5: 6,9 * DIS # C6: 7,9 => CTR => C6: 5 * PRF # C6: 5 => SOL * DIS # H5: 7,9 => CTR => H5: 1,6 * DIS # F4: 5,7 => CTR => F4: 1,2 * DIS # D6: 5,7 => CTR => D6: 4,6 * DIS # B4: 5,7 => CTR => B4: 1,3 * DIS # D2: 5,7 => CTR => D2: 9 * DIS # H5: 1,7 => CTR => H5: 6,9 * DIS # B4: 1,7 => CTR => B4: 3,5 * DIS # F4: 1,7 => CTR => F4: 2,5 * DIS # B9: 5,7 => CTR => B9: 4 * DIS # G8: 5,7 => CTR => G8: 1,4,9 * DIS # C6: 9 => CTR => C6: 5,7 * DIS # G7: 4,9 => CTR => G7: 5,7 * DIS # G9: 4,6 => CTR => G9: 5,7 * DIS # I6: 4,6 => CTR => I6: 1,3,9 * CNT 25 HDP CHAINS / 60 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B5,C5,C8,D4,H4,I7,I9) * ..82....7..6..4..81.38...4.6.4.9.8..8....3..52...8.....613...8.38...6.2.9.21.8.3. * PAIR A1: 4,5 BLK 1 B1: 4,5,9 # reduction candidate for 4,5 B1: 4,5 => CTR * ..82613977269341581938..6426.4.928..8794132652.5687.1..613297843875.6.2.9.21.8.3. * PAIR A2: 5,7 BLK 1 B2: 5,7,2 # reduction candidate for 5,7 B2: 5,7 => CTR * 4982....7..6..42.81238...496.4.9.8.28...23..52...8...3.613...8.38...6.2.9421.8.36 * RESTART * PAIR A2: 5,7 ROW 2 D2: 5,7,9 # reduction candidate for 5,7 D2: 5,7 => CTR * 498261357.26.34..81.38.9642614592873879413265235687...56132..8.38.946.219421.8.36 * RESTART * PAIR RESTART * PAIR B5: 1,7 BLK 4 B6: 1,7,3,5 # reduction candidate for 1,7 B6: 1,7 => SOLVED * 498235617726914358153867942634592871819743265275681493561329784387456129942178536 * DURATION: 0:00:04.572693 START: 23:39:46.848749 END: 23:39:51.421442 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060605-absurd-base-pr-001.dot * REASONING * DIS # B1: 4,5 => CTR => B1: 9 * DIS B1: 9 # B2: 5,7 => CTR => B2: 2 * DIS B1: 9 + B2: 2 # D2: 5,7 => CTR => D2: 9 * PRF B1: 9 + B2: 2 + D2: 9 # B6: 1,7 => SOL * STA B1: 9 + B2: 2 + D2: 9 + B6: 1,7 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060605, absurd
Solution
position: 498235617726914358153867942634592871819743265275681493561329784387456129942178536 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 # B1: 4,5 => CTR => B1: 9 * INC # B1: 9 => UNS * INC # A7: 4,5 => UNS * DIS # A7: 7 => CTR => A7: 4,5 * DIS # B2: 5,7 => CTR => B2: 2,9 * INC # B2: 2,9 => UNS * INC # B3: 5,7 => UNS * DIS # D2: 5,7 => CTR => D2: 9 * INC # D2: 9 => UNS * DIS # E2: 5,7 => CTR => E2: 1,3 * INC # E2: 1,3 => UNS * INC # A7: 5,7 => UNS * DIS # A7: 4 => CTR => A7: 5,7 * DIS # B4: 1,7 => CTR => B4: 3,5 * INC # B4: 3,5 => UNS * PRF # B6: 1,7 => SOL * INC # B6: 3,5 => UNS * INC # E5: 1,7 => UNS * DIS # H5: 1,7 => CTR => H5: 6,9 * INC # H5: 6,9 => UNS * DIS # C6: 7,9 => CTR => C6: 5 * PRF # C6: 5 => SOL * DIS # H5: 7,9 => CTR => H5: 1,6 * INC # H5: 1,6 => UNS * DIS # F4: 5,7 => CTR => F4: 1,2 * INC # F4: 1,2 => UNS * DIS # D6: 5,7 => CTR => D6: 4,6 * INC # D6: 4,6 => UNS * INC # F6: 5,7 => UNS * DIS # B4: 5,7 => CTR => B4: 1,3 * INC # B4: 1,3 => UNS * DIS # D2: 5,7 => CTR => D2: 9 * INC # D2: 9 => UNS * INC # D8: 5,7 => UNS * DIS # H5: 1,7 => CTR => H5: 6,9 * INC # H5: 6,9 => UNS * INC # H6: 1,7 => UNS * DIS # B4: 1,7 => CTR => B4: 3,5 * INC # B4: 3,5 => UNS * DIS # F4: 1,7 => CTR => F4: 2,5 * INC # F4: 2,5 => UNS * INC # A7: 5,7 => UNS * DIS # B9: 5,7 => CTR => B9: 4 * INC # B9: 4 => UNS * INC # D8: 5,7 => UNS * INC # E8: 5,7 => UNS * DIS # G8: 5,7 => CTR => G8: 1,4,9 * INC # G8: 1,4,9 => UNS * INC # C6: 5,7 => UNS * DIS # C6: 9 => CTR => C6: 5,7 * DIS # G7: 4,9 => CTR => G7: 5,7 * INC # G7: 5,7 => UNS * INC # G8: 4,9 => UNS * INC # I8: 4,9 => UNS * INC # I6: 4,9 => UNS * INC # I6: 1,3,6 => UNS * DIS # G9: 4,6 => CTR => G9: 5,7 * INC # G9: 5,7 => UNS * DIS # I6: 4,6 => CTR => I6: 1,3,9 * INC # I6: 1,3,9 => UNS * CNT 60 HDP CHAINS / 60 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 4,5 => CTR => B1: 9 * DIS B1: 9 # B2: 5,7 => CTR => B2: 2 * DIS B1: 9 + B2: 2 # D2: 5,7 => CTR => D2: 9 * PRF B1: 9 + B2: 2 + D2: 9 # B6: 1,7 => SOL * STA B1: 9 + B2: 2 + D2: 9 + B6: 1,7 * CNT 4 HDP CHAINS / 4 HYP OPENED