Analysis of zz-www.sudokuoftheday.co.uk-20060319-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: .....6...27...3..6..3...8.1.8...1.5....3.74.2....2.....6.4....89.......3.21....7. initial
Autosolve
position: ...2.673.27...3..66.3...821.82..135....3.74.2.3..2.....6.4....89.......3.21....7. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 4,5 => CTR => A1: 1,8 * DIS # B1: 4,5 => CTR => B1: 1,9 * DIS # A7: 5,7 => CTR => A7: 3 * DIS # C6: 5,7 => CTR => C6: 4,6,9 * DIS # B1: 4,5 => CTR => B1: 1,9 * CNT 5 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 4,5 => CTR => A1: 1,8 * DIS A1: 1,8 # B1: 4,5 => CTR => B1: 1,9 * DIS A1: 1,8 + B1: 1,9 # A7: 5,7 => CTR => A7: 3 * PRF A1: 1,8 + B1: 1,9 + A7: 3 # C8: 5,7 => SOL * STA A1: 1,8 + B1: 1,9 + A7: 3 + C8: 5,7 * CNT 4 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....6...27...3..6..3...8.1.8...1.5....3.74.2....2.....6.4....89.......3.21....7. | initial |
| ...2.673.27...3..66.3...821.82..135....3.74.2.3..2.....6.4....89.......3.21....7. | autosolve |
| 194286735278153946653974821782641359516397482439825167367412598945768213821539674 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) I1: 4,5 G2: 5,9 H2: 4,9 A4: 4,7 A5: 1,5 D4: 6,9 I4: 7,9 G6: 1,6 I6: 7,9 C7: 5,7 B8: 4,5 H7: 1,9 I9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 19 pairs (_) / B1 = 1 => 14 pairs (_) D2,E2: 1.. / D2 = 1 => 15 pairs (_) / E2 = 1 => 15 pairs (_) B1,B5: 1.. / B1 = 1 => 14 pairs (_) / B5 = 1 => 19 pairs (_) D2,D8: 1.. / D2 = 1 => 15 pairs (_) / D8 = 1 => 15 pairs (_) F7,F8: 2.. / F7 = 2 => 14 pairs (_) / F8 = 2 => 14 pairs (_) G7,G8: 2.. / G7 = 2 => 14 pairs (_) / G8 = 2 => 14 pairs (_) F7,G7: 2.. / F7 = 2 => 14 pairs (_) / G7 = 2 => 14 pairs (_) F8,G8: 2.. / F8 = 2 => 14 pairs (_) / G8 = 2 => 14 pairs (_) A7,A9: 3.. / A7 = 3 => 13 pairs (_) / A9 = 3 => 0 pairs (X) E7,E9: 3.. / E7 = 3 => 0 pairs (X) / E9 = 3 => 13 pairs (_) A7,E7: 3.. / A7 = 3 => 13 pairs (_) / E7 = 3 => 0 pairs (X) A9,E9: 3.. / A9 = 3 => 0 pairs (X) / E9 = 3 => 13 pairs (_) I1,H2: 4.. / I1 = 4 => 0 pairs (X) / H2 = 4 => 12 pairs (_) E4,F6: 4.. / E4 = 4 => 13 pairs (_) / F6 = 4 => 14 pairs (_) H8,I9: 4.. / H8 = 4 => 0 pairs (X) / I9 = 4 => 12 pairs (_) A4,E4: 4.. / A4 = 4 => 14 pairs (_) / E4 = 4 => 13 pairs (_) A9,I9: 4.. / A9 = 4 => 0 pairs (X) / I9 = 4 => 12 pairs (_) F3,F6: 4.. / F3 = 4 => 13 pairs (_) / F6 = 4 => 14 pairs (_) H2,H8: 4.. / H2 = 4 => 12 pairs (_) / H8 = 4 => 0 pairs (X) I1,I9: 4.. / I1 = 4 => 0 pairs (X) / I9 = 4 => 12 pairs (_) I1,G2: 5.. / I1 = 5 => 12 pairs (_) / G2 = 5 => 0 pairs (X) I1,I9: 5.. / I1 = 5 => 12 pairs (_) / I9 = 5 => 0 pairs (X) C5,C6: 6.. / C5 = 6 => 14 pairs (_) / C6 = 6 => 0 pairs (X) D4,E4: 6.. / D4 = 6 => 15 pairs (_) / E4 = 6 => 17 pairs (_) C5,H5: 6.. / C5 = 6 => 14 pairs (_) / H5 = 6 => 0 pairs (X) D3,E3: 7.. / D3 = 7 => 13 pairs (_) / E3 = 7 => 16 pairs (_) I4,I6: 7.. / I4 = 7 => 14 pairs (_) / I6 = 7 => 13 pairs (_) A4,I4: 7.. / A4 = 7 => 13 pairs (_) / I4 = 7 => 14 pairs (_) D3,D8: 7.. / D3 = 7 => 13 pairs (_) / D8 = 7 => 16 pairs (_) H5,H6: 8.. / H5 = 8 => 15 pairs (_) / H6 = 8 => 17 pairs (_) C8,A9: 8.. / C8 = 8 => 18 pairs (_) / A9 = 8 => 16 pairs (_) E5,H5: 8.. / E5 = 8 => 17 pairs (_) / H5 = 8 => 15 pairs (_) A1,A9: 8.. / A1 = 8 => 18 pairs (_) / A9 = 8 => 16 pairs (_) G2,H2: 9.. / G2 = 9 => 12 pairs (_) / H2 = 9 => 0 pairs (X) I4,I6: 9.. / I4 = 9 => 13 pairs (_) / I6 = 9 => 14 pairs (_) H2,H7: 9.. / H2 = 9 => 0 pairs (X) / H7 = 9 => 12 pairs (_) * DURATION: 0:00:38.398651 START: 20:00:04.280139 END: 20:00:42.678790 2019-04-30 * CP COUNT: (36) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B8,C7,D4,G2,G6,H2,H7,I1,I4,I6,I9) * ...2.673.27...3..66.3...821.82..135....3.74.2.3..2.....6.4....89.......3.21....7. * PAIR I1: 4,5 ROW 1 A1: 4,5,1,8 # reduction candidate for 4,5 A1: 4,5 => CTR * 4192867352781539466539748217826413591963.7482534.2.16736.41..9894.768213821.3.674 A1: 1,8 # 14 pairs B1: 4,5,1,9 # reduction candidate for 4,5 B1: 4,5 => CTR * 148296735275..3946693...821.82..135.519387462.36.2.18.36741..98954.....3821.3..74 B1: 1,9 # 14 pairs C1: 4,5,8,9 # reduction candidate for 4,5 C1: 4,5 # 24 pairs E1: 4,5,8,9 # reduction candidate for 4,5 E1: 4,5 # 22 pairs * PAIR G2: 5,9 COL G G7: 5,9,1,2 # reduction candidate for 5,9 G7: 5,9 # 18 pairs G9: 5,9,6 # reduction candidate for 5,9 G9: 5,9 # 16 pairs * PAIR A4: 4,7 BLK 4 A6: 4,7,1,5 # reduction candidate for 4,7 A6: 4,7 # 16 pairs C6: 4,7,5,6,9 # reduction candidate for 4,7 C6: 4,7 # 20 pairs * PAIR A5: 1,5 BLK 4 B5: 1,5,9 # reduction candidate for 1,5 B5: 1,5 # 21 pairs A6: 1,5,4,7 # reduction candidate for 1,5 A6: 1,5 # 20 pairs * PAIR A5: 1,5 COL A A1: 1,5,4,8 # reduction candidate for 1,5 A1: 1,5 # 19 pairs A1: 4,8 # 15 pairs * PAIR D4: 6,9 BLK 5 E4: 6,9,4 # reduction candidate for 6,9 E4: 6,9 # 14 pairs E4: 4 # 13 pairs * PAIR D4: 6,9 COL D D9: 6,9,5,8 # reduction candidate for 6,9 D9: 6,9 # 16 pairs D9: 5,8 # 16 pairs * PAIR G6: 1,6 BLK 6 H5: 1,6,8 # reduction candidate for 1,6 H5: 1,6 # 17 pairs H6: 1,6,8 # reduction candidate for 1,6 H6: 1,6 # 15 pairs * PAIR G6: 1,6 COL G G8: 1,6,2,5 # reduction candidate for 1,6 G8: 1,6 # 17 pairs G8: 2,5 # 14 pairs * PAIR I6: 7,9 ROW 6 C6: 7,9,4,5,6 # reduction candidate for 7,9 C6: 7,9 # 16 pairs C6: 4,5,6 # 15 pairs * PAIR C7: 5,7 BLK 7 A7: 5,7,3 # reduction candidate for 5,7 A7: 5,7 => CTR * 814296735275..3946693...821.82..135..5.3.74.2.3..2.....6743.198948...263321...574 A7: 3 # 13 pairs C8: 5,7,4,8 # reduction candidate for 5,7 C8: 5,7 # 23 pairs * PAIR C7: 5,7 ROW 7 E7: 5,7,1,3,9 # reduction candidate for 5,7 E7: 5,7 # 16 pairs E7: 1,3,9 # 13 pairs * PAIR C7: 5,7 COL C C6: 5,7,4,6,9 # reduction candidate for 5,7 C6: 5,7 => CTR * .1924673527...3946643...821482..1357.963.74.2.3..24..9.6.4...98954.....3821....74 C6: 4,6,9 # 14 pairs * PAIR B8: 4,5 BLK 7 C8: 4,5,7,8 # reduction candidate for 4,5 C8: 4,5 # 18 pairs A9: 4,5,3,8 # reduction candidate for 4,5 A9: 4,5 # 20 pairs * PAIR B8: 4,5 COL B B1: 4,5,1,9 # reduction candidate for 4,5 B1: 4,5 => CTR * 148296735275..3946693...821.82..135.519387462.36.2.18.36741..98954.....3821.3..74 B1: 1,9 # 14 pairs B3: 4,5,9 # reduction candidate for 4,5 B3: 4,5 # 16 pairs * PAIR H7: 1,9 BLK 9 G7: 1,9,2,5 # reduction candidate for 1,9 G7: 1,9 # 18 pairs G7: 2,5 # 14 pairs * PAIR H7: 1,9 ROW 7 E7: 1,9,3,5,7 # reduction candidate for 1,9 E7: 3,5,7 # 15 pairs E7: 1,9 # 15 pairs * PAIR I9: 4,5 ROW 9 A9: 4,5,3,8 # reduction candidate for 4,5 A9: 4,5 # 20 pairs A9: 3,8 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060319-absurd-base-pr-000.dot * REASONING * DIS # A1: 4,5 => CTR => A1: 1,8 * DIS # B1: 4,5 => CTR => B1: 1,9 * DIS # A7: 5,7 => CTR => A7: 3 * DIS # C6: 5,7 => CTR => C6: 4,6,9 * DIS # B1: 4,5 => CTR => B1: 1,9 * CNT 5 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B8,C7,D4,G2,G6,H2,H7,I1,I4,I6,I9) * ...2.673.27...3..66.3...821.82..135....3.74.2.3..2.....6.4....89.......3.21....7. * PAIR I1: 4,5 ROW 1 A1: 4,5,1,8 # reduction candidate for 4,5 A1: 4,5 => CTR * 4192867352781539466539748217826413591963.7482534.2.16736.41..9894.768213821.3.674 B1: 4,5,1,9 # reduction candidate for 4,5 B1: 4,5 => CTR * 148296735275..3946693...821.82..135.519387462.36.2.18.36741..98954.....3821.3..74 C1: 4,5,8,9 # reduction candidate for 4,5 C1: 4,5 # 24 pairs E1: 4,5,8,9 # reduction candidate for 4,5 E1: 4,5 # 22 pairs * PAIR RESTART * PAIR I1: 4,5 ROW 1 C1: 4,5,8,9 # reduction candidate for 4,5 C1: 4,5 # 24 pairs E1: 4,5,8,9 # reduction candidate for 4,5 E1: 4,5 # 22 pairs * PAIR G2: 5,9 COL G G7: 5,9,1,2 # reduction candidate for 5,9 G7: 5,9 # 20 pairs G9: 5,9,6 # reduction candidate for 5,9 G9: 5,9 # 18 pairs * PAIR A4: 4,7 BLK 4 A6: 4,7,1,5 # reduction candidate for 4,7 A6: 4,7 # 17 pairs C6: 4,7,5,6,9 # reduction candidate for 4,7 C6: 4,7 # 25 pairs * PAIR A5: 1,5 BLK 4 B5: 1,5,9 # reduction candidate for 1,5 B5: 1,5 # 22 pairs A6: 1,5,4,7 # reduction candidate for 1,5 A6: 1,5 # 25 pairs * PAIR D4: 6,9 BLK 5 E4: 6,9,4 # reduction candidate for 6,9 E4: 4 # 25 pairs E4: 6,9 # 15 pairs * PAIR D4: 6,9 COL D D9: 6,9,5,8 # reduction candidate for 6,9 D9: 6,9 # 18 pairs D9: 5,8 # 18 pairs * PAIR G6: 1,6 BLK 6 H5: 1,6,8 # reduction candidate for 1,6 H5: 1,6 # 19 pairs H6: 1,6,8 # reduction candidate for 1,6 H6: 1,6 # 17 pairs * PAIR G6: 1,6 COL G G8: 1,6,2,5 # reduction candidate for 1,6 G8: 1,6 # 19 pairs G8: 2,5 # 16 pairs * PAIR I6: 7,9 ROW 6 C6: 7,9,4,5,6 # reduction candidate for 7,9 C6: 7,9 # 17 pairs C6: 4,5,6 # 17 pairs * PAIR C7: 5,7 BLK 7 A7: 5,7,3 # reduction candidate for 5,7 A7: 5,7 => CTR * 814296735275..3946693...821.82..135..5.3.74.2.3..2.....6743.198948...263321...574 C8: 5,7,4,8 # reduction candidate for 5,7 C8: 5,7 => SOLVED * 194286735278153946653974821782641359516397482439825167367412598945768213821539674 * DURATION: 0:00:16.421918 START: 20:01:07.536465 END: 20:01:23.958383 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060319-absurd-base-pr-001.dot * REASONING * DIS # A1: 4,5 => CTR => A1: 1,8 * DIS A1: 1,8 # B1: 4,5 => CTR => B1: 1,9 * DIS A1: 1,8 + B1: 1,9 # A7: 5,7 => CTR => A7: 3 * PRF A1: 1,8 + B1: 1,9 + A7: 3 # C8: 5,7 => SOL * STA A1: 1,8 + B1: 1,9 + A7: 3 + C8: 5,7 * CNT 4 HDP CHAINS / 24 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060319, absurd
Solution
position: 194286735278153946653974821782641359516397482439825167367412598945768213821539674 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 # A1: 4,5 => CTR => A1: 1,8 * INC # A1: 1,8 => UNS * DIS # B1: 4,5 => CTR => B1: 1,9 * INC # B1: 1,9 => UNS * INC # C1: 4,5 => UNS * INC # E1: 4,5 => UNS * INC # G7: 5,9 => UNS * INC # G9: 5,9 => UNS * INC # A6: 4,7 => UNS * INC # C6: 4,7 => UNS * INC # B5: 1,5 => UNS * INC # A6: 1,5 => UNS * INC # A1: 1,5 => UNS * INC # A1: 4,8 => UNS * INC # E4: 6,9 => UNS * INC # E4: 4 => UNS * INC # D9: 6,9 => UNS * INC # D9: 5,8 => UNS * INC # H5: 1,6 => UNS * INC # H6: 1,6 => UNS * INC # G8: 1,6 => UNS * INC # G8: 2,5 => UNS * INC # C6: 7,9 => UNS * INC # C6: 4,5,6 => UNS * DIS # A7: 5,7 => CTR => A7: 3 * INC # A7: 3 => UNS * INC # C8: 5,7 => UNS * INC # E7: 5,7 => UNS * INC # E7: 1,3,9 => UNS * DIS # C6: 5,7 => CTR => C6: 4,6,9 * INC # C6: 4,6,9 => UNS * INC # C8: 4,5 => UNS * INC # A9: 4,5 => UNS * DIS # B1: 4,5 => CTR => B1: 1,9 * INC # B1: 1,9 => UNS * INC # B3: 4,5 => UNS * INC # G7: 1,9 => UNS * INC # G7: 2,5 => UNS * INC # E7: 1,9 => UNS * INC # E7: 3,5,7 => UNS * INC # A9: 4,5 => UNS * INC # A9: 3,8 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 4,5 => CTR => A1: 1,8 * DIS A1: 1,8 # B1: 4,5 => CTR => B1: 1,9 * INC A1: 1,8 + B1: 1,9 # C1: 4,5 => UNS * INC A1: 1,8 + B1: 1,9 # E1: 4,5 => UNS * INC A1: 1,8 + B1: 1,9 # C1: 4,5 => UNS * INC A1: 1,8 + B1: 1,9 # E1: 4,5 => UNS * INC A1: 1,8 + B1: 1,9 # G7: 5,9 => UNS * INC A1: 1,8 + B1: 1,9 # G9: 5,9 => UNS * INC A1: 1,8 + B1: 1,9 # A6: 4,7 => UNS * INC A1: 1,8 + B1: 1,9 # C6: 4,7 => UNS * INC A1: 1,8 + B1: 1,9 # B5: 1,5 => UNS * INC A1: 1,8 + B1: 1,9 # A6: 1,5 => UNS * INC A1: 1,8 + B1: 1,9 # E4: 6,9 => UNS * INC A1: 1,8 + B1: 1,9 # E4: 4 => UNS * INC A1: 1,8 + B1: 1,9 # D9: 6,9 => UNS * INC A1: 1,8 + B1: 1,9 # D9: 5,8 => UNS * INC A1: 1,8 + B1: 1,9 # H5: 1,6 => UNS * INC A1: 1,8 + B1: 1,9 # H6: 1,6 => UNS * INC A1: 1,8 + B1: 1,9 # G8: 1,6 => UNS * INC A1: 1,8 + B1: 1,9 # G8: 2,5 => UNS * INC A1: 1,8 + B1: 1,9 # C6: 7,9 => UNS * INC A1: 1,8 + B1: 1,9 # C6: 4,5,6 => UNS * DIS A1: 1,8 + B1: 1,9 # A7: 5,7 => CTR => A7: 3 * PRF A1: 1,8 + B1: 1,9 + A7: 3 # C8: 5,7 => SOL * STA A1: 1,8 + B1: 1,9 + A7: 3 + C8: 5,7 * CNT 24 HDP CHAINS / 24 HYP OPENED