Analysis of zz-www.sudokuoftheday.co.uk-20060720-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: 57..194...9......82.4.3.....1..8.3...27....8....6..1..............7..543...425..7 initial
Autosolve
position: 57..194...9......82.4.3....41698.3...27.5..8..5.6..1..745........27..543.3.425..7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A2: 1,3 => SOL * DIS # A2: 6 => CTR => A2: 1,3 * PRF # H2: 2,5 => SOL * DIS # H2: 3 => CTR => H2: 2,5 * DIS # F2: 4,7 => CTR => F2: 6 * PRF # F2: 6 => SOL * DIS # F2: 4 => CTR => F2: 6,7 * DIS # H1: 2,6 => CTR => H1: 3 * PRF # H1: 3 => SOL * DIS # A6: 3,9 => CTR => A6: 8 * DIS # F6: 2,7 => CTR => F6: 3,4 * DIS # H4: 5 => CTR => H4: 2,7 * DIS # H4: 2,5 => CTR => H4: 7 * DIS # G7: 6,9 => CTR => G7: 2,8 * DIS # G9: 6,9 => CTR => G9: 8 * DIS # F7: 1,3 => CTR => F7: 8 * DIS # G7: 6,9 => CTR => G7: 2,8 * PRF # A8: 6,9 => SOL * DIS # A8: 1,8 => CTR => A8: 6,9 * DIS # F7: 3 => CTR => F7: 1,8 * DIS # A8: 1,8 => CTR => A8: 6,9 * PRF # A8: 6,9 => SOL * CNT 22 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A2: 1,3 => SOL * STA A2: 1,3 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 57..194...9......82.4.3.....1..8.3...27....8....6..1..............7..543...425..7 | initial |
| 57..194...9......82.4.3....41698.3...27.5..8..5.6..1..745........27..543.3.425..7 | autosolve |
| 578219436391546728264837951416982375927153684853674192745368219682791543139425867 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) C1: 3,8 C2: 1,3 B3: 6,8 D1: 2,8 D2: 2,5 E2: 4,7 D3: 5,8 F3: 6,7 I1: 2,6 G2: 2,7 G3: 7,9 A5: 3,9 F4: 2,7 D5: 1,3 E6: 4,7 I4: 2,5 G5: 6,9 B8: 6,8 D7: 1,3 E7: 6,9 E8: 6,9 F8: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,C2: 1.. / A2 = 1 => 0 pairs (X) / C2 = 1 => 23 pairs (_) H3,I3: 1.. / H3 = 1 => 23 pairs (_) / I3 = 1 => 23 pairs (_) D5,F5: 1.. / D5 = 1 => 22 pairs (_) / F5 = 1 => 0 pairs (X) A8,F8: 1.. / A8 = 1 => 0 pairs (X) / F8 = 1 => 22 pairs (_) C2,C9: 1.. / C2 = 1 => 23 pairs (_) / C9 = 1 => 0 pairs (X) D5,D7: 1.. / D5 = 1 => 22 pairs (_) / D7 = 1 => 0 pairs (X) I3,I7: 1.. / I3 = 1 => 23 pairs (_) / I7 = 1 => 23 pairs (_) D1,D2: 2.. / D1 = 2 => 0 pairs (*) / D2 = 2 => 0 pairs (X) F4,F6: 2.. / F4 = 2 => 22 pairs (_) / F6 = 2 => 0 pairs (X) G2,G7: 2.. / G2 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) H1,H2: 3.. / H1 = 3 => 0 pairs (*) / H2 = 3 => 0 pairs (X) D7,F7: 3.. / D7 = 3 => 22 pairs (_) / F7 = 3 => 0 pairs (X) C1,H1: 3.. / C1 = 3 => 0 pairs (X) / H1 = 3 => 0 pairs (_) D5,D7: 3.. / D5 = 3 => 0 pairs (X) / D7 = 3 => 22 pairs (_) E2,F2: 4.. / E2 = 4 => 22 pairs (_) / F2 = 4 => 0 pairs (X) I5,I6: 4.. / I5 = 4 => 20 pairs (_) / I6 = 4 => 24 pairs (_) F5,I5: 4.. / F5 = 4 => 24 pairs (_) / I5 = 4 => 20 pairs (_) E2,E6: 4.. / E2 = 4 => 22 pairs (_) / E6 = 4 => 0 pairs (X) D2,D3: 5.. / D2 = 5 => 0 pairs (*) / D3 = 5 => 0 pairs (X) H4,I4: 5.. / H4 = 5 => 0 pairs (X) / I4 = 5 => 23 pairs (_) D2,H2: 5.. / D2 = 5 => 0 pairs (*) / H2 = 5 => 0 pairs (X) I3,I4: 5.. / I3 = 5 => 0 pairs (X) / I4 = 5 => 23 pairs (_) A2,B3: 6.. / A2 = 6 => 0 pairs (X) / B3 = 6 => 0 pairs (_) F2,F3: 6.. / F2 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) H1,I1: 6.. / H1 = 6 => 0 pairs (X) / I1 = 6 => 23 pairs (_) G5,I5: 6.. / G5 = 6 => 23 pairs (_) / I5 = 6 => 0 pairs (X) E7,E8: 6.. / E7 = 6 => 22 pairs (_) / E8 = 6 => 0 pairs (X) A2,F2: 6.. / A2 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) B3,F3: 6.. / B3 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) B3,B8: 6.. / B3 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) G2,G3: 7.. / G2 = 7 => 0 pairs (*) / G3 = 7 => 0 pairs (X) H4,H6: 7.. / H4 = 7 => 22 pairs (_) / H6 = 7 => 0 pairs (X) F3,G3: 7.. / F3 = 7 => 0 pairs (*) / G3 = 7 => 0 pairs (X) F4,H4: 7.. / F4 = 7 => 0 pairs (X) / H4 = 7 => 22 pairs (_) E2,E6: 7.. / E2 = 7 => 0 pairs (X) / E6 = 7 => 22 pairs (_) C1,B3: 8.. / C1 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) D1,D3: 8.. / D1 = 8 => 0 pairs (X) / D3 = 8 => 0 pairs (_) A6,C6: 8.. / A6 = 8 => 23 pairs (_) / C6 = 8 => 0 pairs (X) F7,F8: 8.. / F7 = 8 => 22 pairs (_) / F8 = 8 => 0 pairs (X) G7,G9: 8.. / G7 = 8 => 0 pairs (X) / G9 = 8 => 22 pairs (_) C1,D1: 8.. / C1 = 8 => 0 pairs (*) / D1 = 8 => 0 pairs (X) B3,D3: 8.. / B3 = 8 => 0 pairs (X) / D3 = 8 => 0 pairs (_) F7,G7: 8.. / F7 = 8 => 22 pairs (_) / G7 = 8 => 0 pairs (X) B3,B8: 8.. / B3 = 8 => 0 pairs (X) / B8 = 8 => 0 pairs (_) E7,E8: 9.. / E7 = 9 => 0 pairs (X) / E8 = 9 => 22 pairs (_) A8,E8: 9.. / A8 = 9 => 0 pairs (X) / E8 = 9 => 22 pairs (_) C6,C9: 9.. / C6 = 9 => 23 pairs (_) / C9 = 9 => 24 pairs (_) * DURATION: 0:00:58.078274 START: 00:50:03.827069 END: 00:51:01.905343 2019-05-01 * CP COUNT: (47) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B3,B8,C1,C2,D1,D2,D3,D5,D7,E2,E6,E7,E8,F3,F4,F8,G2,G3,G5,I1,I4) * 57..194...9......82.4.3....41698.3...27.5..8..5.6..1..745........27..543.3.425..7 * PAIR C1: 3,8 COL C C6: 3,8,9 # reduction candidate for 3,8 C6: 3,8 # 24 pairs C6: 9 # 23 pairs * PAIR C2: 1,3 BLK 1 A2: 1,3,6 # reduction candidate for 1,3 A2: 1,3 => SOLVED * 578219436391546728264837951416982375927153684853674192745368219682791543139425867 A2: 6 => CTR * 57..194..691....382845367..41698.352.27.5..8..5.6.217.745.......6279.543.3.425..7 * PAIR D2: 2,5 ROW 2 H2: 2,5,3 # reduction candidate for 2,5 H2: 2,5 => SOLVED * 578219436391546728264837951416982375927153684853674192745368219682791543139425867 H2: 3 => CTR * 57..194...9.5..2382.483.7..41698.3...27.5..8..5.6..1..745.......827.1543.3.4258.7 * PAIR E2: 4,7 BLK 2 F2: 4,7,6 # reduction candidate for 4,7 F2: 4,7 => CTR * 57..194..691....382845367..41698.352.27.5..8..5.6.217.745.......6279.543.3.425..7 F2: 6 => SOLVED * 578219436391546728264837951416982375927153684853674192745368219682791543139425867 * PAIR F3: 6,7 BLK 2 F2: 6,7,4 # reduction candidate for 6,7 F2: 4 => CTR * 57..194..691..4.382845367..41698.352.27.5..84.5.642179745.......6279.543.39425..7 F2: 6,7 # 22 pairs * PAIR I1: 2,6 BLK 3 H1: 2,6,3 # reduction candidate for 2,6 H1: 2,6 => CTR * 5738194...912..7.82.4.3....41698.3...27.5..8..5.6..1..745........27..543.3.425..7 H1: 3 => SOLVED * 578219436391546728264837951416982375927153684853674192745368219682791543139425867 * PAIR I1: 2,6 COL I I7: 2,6,1,9 # reduction candidate for 2,6 I7: 2,6 # 29 pairs I7: 1,9 # 23 pairs * PAIR A5: 3,9 BLK 4 A6: 3,9,8 # reduction candidate for 3,9 A6: 3,9 => CTR * 5738194...912..7.82.4.3....41698.3...27.5..8..586..1..745........27..543.39425..7 A6: 8 # 23 pairs C6: 3,9,8 # reduction candidate for 3,9 C6: 3,9 # 23 pairs * PAIR F4: 2,7 BLK 5 F6: 2,7,3,4 # reduction candidate for 2,7 F6: 2,7 => CTR * 57.219436.91.742.82.4.367..41698.3..927.5.684.5.64.1..745.689...62791543139425867 F6: 3,4 # 22 pairs * PAIR F4: 2,7 ROW 4 H4: 2,7,5 # reduction candidate for 2,7 H4: 5 => CTR * 57..194.6.915742382.4.3....416987352.27.5..8..5.642179745........27..543.39425..7 H4: 2,7 # 23 pairs * PAIR D5: 1,3 BLK 5 F5: 1,3,4 # reduction candidate for 1,3 F5: 4 # 24 pairs F5: 1,3 # 20 pairs * PAIR E6: 4,7 BLK 5 F6: 4,7,2,3 # reduction candidate for 4,7 F6: 2,3 # 23 pairs F6: 4,7 # 21 pairs * PAIR I4: 2,5 BLK 6 H4: 2,5,7 # reduction candidate for 2,5 H4: 2,5 => CTR * 57.219436.91.742.82.4.367914169873.5927.5.684.5.642179745...9.2.6279.543.39425867 H4: 7 # 22 pairs * PAIR G5: 6,9 BLK 6 I5: 6,9,4 # reduction candidate for 6,9 I5: 6,9 # 24 pairs I5: 4 # 20 pairs * PAIR G5: 6,9 COL G G7: 6,9,2,8 # reduction candidate for 6,9 G7: 6,9 => CTR * 57.2194.6.9.5..2382.4.3.7..41698.3...27.5..8..5.6..1..745..8.....27.1543.3.4258.7 G7: 2,8 # 23 pairs G9: 6,9,8 # reduction candidate for 6,9 G9: 6,9 => CTR * 57..194...9....2.828453....41698.3...27.5..8..5.6..1..745...8....27.8543.3.425..7 G9: 8 # 22 pairs * PAIR B8: 6,8 BLK 7 A8: 6,8,1,9 # reduction candidate for 6,8 A8: 6,8 # 22 pairs A9: 6,8,1,9 # reduction candidate for 6,8 A9: 6,8 # 25 pairs * PAIR D7: 1,3 BLK 8 F7: 1,3,8 # reduction candidate for 1,3 F7: 1,3 => CTR * 57..194...9....2.828453....41698.3...27.5..8..5.6..1..745...8....27.8543.3.425..7 F7: 8 # 22 pairs * PAIR E7: 6,9 ROW 7 G7: 6,9,2,8 # reduction candidate for 6,9 G7: 6,9 => CTR * 57.2194.6.9.5..2382.4.3.7..41698.3...27.5..8..5.6..1..745..8.....27.1543.3.4258.7 G7: 2,8 # 23 pairs H7: 6,9,1,2 # reduction candidate for 6,9 H7: 6,9 # 25 pairs I7: 6,9,1,2 # reduction candidate for 6,9 I7: 6,9 # 26 pairs * PAIR E8: 6,9 ROW 8 A8: 6,9,1,8 # reduction candidate for 6,9 A8: 6,9 => SOLVED * 578219436391546728264837951416982375927153684853674192745368219682791543139425867 A8: 1,8 => CTR * 57..194..691....382845367..41698.352.27.5..8..5.6.217.745.6.....6279.543.3.425..7 * PAIR F8: 1,8 BLK 8 F7: 1,8,3 # reduction candidate for 1,8 F7: 3 => CTR * 57..194...9....2.828453....41698.3...27.5..8..5.6..1..745..38....27.8543.3.425..7 F7: 1,8 # 22 pairs * PAIR F8: 1,8 ROW 8 A8: 1,8,6,9 # reduction candidate for 1,8 A8: 1,8 => CTR * 57..194..691....382845367..41698.352.27.5..8..5.6.217.745.6.....6279.543.3.425..7 A8: 6,9 => SOLVED * 578219436391546728264837951416982375927153684853674192745368219682791543139425867 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060720-absurd-base-pr-000.dot * REASONING * PRF # A2: 1,3 => SOL * DIS # A2: 6 => CTR => A2: 1,3 * PRF # H2: 2,5 => SOL * DIS # H2: 3 => CTR => H2: 2,5 * DIS # F2: 4,7 => CTR => F2: 6 * PRF # F2: 6 => SOL * DIS # F2: 4 => CTR => F2: 6,7 * DIS # H1: 2,6 => CTR => H1: 3 * PRF # H1: 3 => SOL * DIS # A6: 3,9 => CTR => A6: 8 * DIS # F6: 2,7 => CTR => F6: 3,4 * DIS # H4: 5 => CTR => H4: 2,7 * DIS # H4: 2,5 => CTR => H4: 7 * DIS # G7: 6,9 => CTR => G7: 2,8 * DIS # G9: 6,9 => CTR => G9: 8 * DIS # F7: 1,3 => CTR => F7: 8 * DIS # G7: 6,9 => CTR => G7: 2,8 * PRF # A8: 6,9 => SOL * DIS # A8: 1,8 => CTR => A8: 6,9 * DIS # F7: 3 => CTR => F7: 1,8 * DIS # A8: 1,8 => CTR => A8: 6,9 * PRF # A8: 6,9 => SOL * CNT 22 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B3,B8,C1,C2,D1,D2,D3,D5,D7,E2,E6,E7,E8,F3,F4,F8,G2,G3,G5,I1,I4) * 57..194...9......82.4.3....41698.3...27.5..8..5.6..1..745........27..543.3.425..7 * PAIR C1: 3,8 COL C C6: 3,8,9 # reduction candidate for 3,8 C6: 3,8 # 24 pairs C6: 9 # 23 pairs * PAIR C2: 1,3 BLK 1 A2: 1,3,6 # reduction candidate for 1,3 A2: 1,3 => SOLVED * 578219436391546728264837951416982375927153684853674192745368219682791543139425867 * DURATION: 0:00:03.224190 START: 00:51:35.542598 END: 00:51:38.766788 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060720-absurd-base-pr-001.dot * REASONING * PRF # A2: 1,3 => SOL * STA A2: 1,3 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060720, absurd
Solution
position: 578219436391546728264837951416982375927153684853674192745368219682791543139425867 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 # C6: 3,8 => UNS * INC # C6: 9 => UNS * PRF # A2: 1,3 => SOL * DIS # A2: 6 => CTR => A2: 1,3 * PRF # H2: 2,5 => SOL * DIS # H2: 3 => CTR => H2: 2,5 * DIS # F2: 4,7 => CTR => F2: 6 * PRF # F2: 6 => SOL * INC # F2: 6,7 => UNS * DIS # F2: 4 => CTR => F2: 6,7 * DIS # H1: 2,6 => CTR => H1: 3 * PRF # H1: 3 => SOL * INC # I7: 2,6 => UNS * INC # I7: 1,9 => UNS * DIS # A6: 3,9 => CTR => A6: 8 * INC # A6: 8 => UNS * INC # C6: 3,9 => UNS * DIS # F6: 2,7 => CTR => F6: 3,4 * INC # F6: 3,4 => UNS * INC # H4: 2,7 => UNS * DIS # H4: 5 => CTR => H4: 2,7 * INC # F5: 1,3 => UNS * INC # F5: 4 => UNS * INC # F6: 4,7 => UNS * INC # F6: 2,3 => UNS * DIS # H4: 2,5 => CTR => H4: 7 * INC # H4: 7 => UNS * INC # I5: 6,9 => UNS * INC # I5: 4 => UNS * DIS # G7: 6,9 => CTR => G7: 2,8 * INC # G7: 2,8 => UNS * DIS # G9: 6,9 => CTR => G9: 8 * INC # G9: 8 => UNS * INC # A8: 6,8 => UNS * INC # A9: 6,8 => UNS * DIS # F7: 1,3 => CTR => F7: 8 * INC # F7: 8 => UNS * DIS # G7: 6,9 => CTR => G7: 2,8 * INC # G7: 2,8 => UNS * INC # H7: 6,9 => UNS * INC # I7: 6,9 => UNS * PRF # A8: 6,9 => SOL * DIS # A8: 1,8 => CTR => A8: 6,9 * INC # F7: 1,8 => UNS * DIS # F7: 3 => CTR => F7: 1,8 * DIS # A8: 1,8 => CTR => A8: 6,9 * PRF # A8: 6,9 => SOL * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C6: 3,8 => UNS * INC # C6: 9 => UNS * PRF # A2: 1,3 => SOL * STA A2: 1,3 * CNT 3 HDP CHAINS / 3 HYP OPENED