Analysis of zz-www.sudokuoftheday.co.uk-20190308-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: .7.259...9...74.3...8.........9..5.4......2....4..3.7.1.......764..1..2.....68.1. initial
Autosolve
position: 37.259...9..874.3.4.8.3.7.....9..5.4....4.2.3..4..3.7.18..92..764..1..28....68.1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I3: 2,5 => CTR => I3: 9 * PRF # I3: 9 => SOL * DIS # B6: 2,5 => CTR => B6: 6,9 * PRF # F5: 1,6 => SOL * DIS # G6: 1,6 => CTR => G6: 8,9 * DIS # I3: 2,5 => CTR => I3: 9 * PRF # I3: 9 => SOL * DIS # I3: 2 => CTR => I3: 5,9 * DIS # B6: 5,6 => CTR => B6: 2,9 * DIS # H5: 6,8 => CTR => H5: 9 * PRF # H5: 9 => SOL * PRF # G6: 6,8 => SOL * DIS # G6: 1,6 => CTR => G6: 8,9 * DIS # C8: 3,5 => CTR => C8: 7,9 * PRF # D7: 3,5 => SOL * DIS # D9: 5,7 => CTR => D9: 3,4 * DIS # C8: 5,7 => CTR => C8: 3,9 * PRF # F5: 1,6 => SOL * PRF # G9: 3,9 => SOL * DIS # C8: 5,7 => CTR => C8: 3,9 * DIS # I3: 2 => CTR => I3: 5,9 * CNT 21 HDP CHAINS / 61 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I3: 2,5 => CTR => I3: 9 * PRF I3: 9 => SOL * STA I3: 9 * CNT 2 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.259...9...74.3...8.........9..5.4......2....4..3.7.1.......764..1..2.....68.1. | initial |
| 37.259...9..874.3.4.8.3.7.....9..5.4....4.2.3..4..3.7.18..92..764..1..28....68.1. | autosolve |
| 371259486956874132428136759213987564867541293594623871185392647649715328732468915 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) C1: 1,6 B3: 2,5 D3: 1,6 F3: 1,6 G1: 4,8 H1: 4,8 I1: 1,6 G2: 1,6 I2: 2,5 H3: 5,9 E4: 2,8 D6: 5,6 E6: 2,8 H4: 6,8 I6: 1,6 C7: 3,5 F8: 5,7 G8: 3,9 I9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,F3: 1.. / D3 = 1 => 18 pairs (_) / F3 = 1 => 23 pairs (_) I1,G2: 1.. / I1 = 1 => 0 pairs (X) / G2 = 1 => 15 pairs (_) G6,I6: 1.. / G6 = 1 => 0 pairs (X) / I6 = 1 => 15 pairs (_) C1,I1: 1.. / C1 = 1 => 15 pairs (_) / I1 = 1 => 0 pairs (X) D3,D5: 1.. / D3 = 1 => 18 pairs (_) / D5 = 1 => 23 pairs (_) G2,G6: 1.. / G2 = 1 => 15 pairs (_) / G6 = 1 => 0 pairs (X) I1,I6: 1.. / I1 = 1 => 0 pairs (X) / I6 = 1 => 15 pairs (_) I2,I3: 2.. / I2 = 2 => 18 pairs (_) / I3 = 2 => 0 pairs (X) E4,E6: 2.. / E4 = 2 => 18 pairs (_) / E6 = 2 => 18 pairs (_) B3,I3: 2.. / B3 = 2 => 18 pairs (_) / I3 = 2 => 0 pairs (X) B4,C4: 3.. / B4 = 3 => 19 pairs (_) / C4 = 3 => 0 pairs (*) B4,B9: 3.. / B4 = 3 => 19 pairs (_) / B9 = 3 => 0 pairs (*) G1,H1: 4.. / G1 = 4 => 0 pairs (*) / H1 = 4 => 0 pairs (X) D7,D9: 4.. / D7 = 4 => 19 pairs (_) / D9 = 4 => 0 pairs (*) D9,G9: 4.. / D9 = 4 => 0 pairs (*) / G9 = 4 => 0 pairs (X) H1,H7: 4.. / H1 = 4 => 18 pairs (_) / H7 = 4 => 0 pairs (*) H7,I9: 5.. / H7 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) F5,F8: 5.. / F5 = 5 => 18 pairs (_) / F8 = 5 => 20 pairs (_) H3,H7: 5.. / H3 = 5 => 0 pairs (*) / H7 = 5 => 0 pairs (X) D3,F3: 6.. / D3 = 6 => 23 pairs (_) / F3 = 6 => 18 pairs (_) I1,G2: 6.. / I1 = 6 => 15 pairs (_) / G2 = 6 => 0 pairs (X) G7,H7: 6.. / G7 = 6 => 17 pairs (_) / H7 = 6 => 0 pairs (X) C1,I1: 6.. / C1 = 6 => 0 pairs (X) / I1 = 6 => 15 pairs (_) I1,I6: 6.. / I1 = 6 => 15 pairs (_) / I6 = 6 => 0 pairs (X) G1,H1: 8.. / G1 = 8 => 18 pairs (_) / H1 = 8 => 0 pairs (*) E4,E6: 8.. / E4 = 8 => 18 pairs (_) / E6 = 8 => 18 pairs (_) A5,H5: 8.. / A5 = 8 => 22 pairs (_) / H5 = 8 => 0 pairs (X) G1,G6: 8.. / G1 = 8 => 18 pairs (_) / G6 = 8 => 0 pairs (*) H3,I3: 9.. / H3 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) H5,G6: 9.. / H5 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) B6,G6: 9.. / B6 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) C8,G8: 9.. / C8 = 9 => 23 pairs (_) / G8 = 9 => 0 pairs (X) H3,H5: 9.. / H3 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) I3,I9: 9.. / I3 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) * DURATION: 0:00:53.569473 START: 04:20:19.107046 END: 04:21:12.676519 2019-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,C1,C7,D3,D6,E4,E6,F3,F8,G1,G2,G8,H1,H3,H4,I1,I2,I6,I9) * 37.259...9..874.3.4.8.3.7.....9..5.4....4.2.3..4..3.7.18..92..764..1..28....68.1. * PAIR C1: 1,6 BLK 1 B2: 1,6,2,5 # reduction candidate for 1,6 B2: 1,6 # 21 pairs C2: 1,6,2,5 # reduction candidate for 1,6 C2: 1,6 # 23 pairs * PAIR C1: 1,6 COL C C4: 1,6,2,3,7 # reduction candidate for 1,6 C4: 1,6 # 22 pairs C5: 1,6,5,7,9 # reduction candidate for 1,6 C5: 1,6 # 22 pairs * PAIR B3: 2,5 BLK 1 B2: 2,5,1,6 # reduction candidate for 2,5 B2: 2,5 # 23 pairs C2: 2,5,1,6 # reduction candidate for 2,5 C2: 2,5 # 21 pairs * PAIR B3: 2,5 ROW 3 I3: 2,5,9 # reduction candidate for 2,5 I3: 2,5 => CTR * 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..4..3971183492657649.1.328...368419 I3: 9 => SOLVED * 371259486956874132428136759213987564867541293594623871185392647649715328732468915 * PAIR B3: 2,5 COL B B6: 2,5,6,9 # reduction candidate for 2,5 B6: 2,5 => CTR * 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..46.397118.492657649.1.328...368419 B6: 6,9 # 20 pairs B9: 2,5,3,9 # reduction candidate for 2,5 B9: 2,5 # 23 pairs * PAIR D3: 1,6 COL D D5: 1,6,5,7 # reduction candidate for 1,6 D5: 1,6 # 21 pairs D5: 5,7 # 17 pairs * PAIR F3: 1,6 COL F F4: 1,6,7 # reduction candidate for 1,6 F4: 1,6 # 22 pairs F5: 1,6,5,7 # reduction candidate for 1,6 F5: 1,6 => SOLVED * 371259486956874132428136759213987564867541293594623871185392647649715328732468915 F5: 5,7 # 22 pairs * PAIR G2: 1,6 ROW 2 B2: 1,6,2,5 # reduction candidate for 1,6 B2: 1,6 # 21 pairs C2: 1,6,2,5 # reduction candidate for 1,6 C2: 1,6 # 23 pairs * PAIR G2: 1,6 COL G G6: 1,6,8,9 # reduction candidate for 1,6 G6: 1,6 => CTR * 37.25984.9..874.3.4.8.3.759...9..5848...4.293.94.83.7.18..92.6764..1..28....68.15 G6: 8,9 # 17 pairs * PAIR I2: 2,5 BLK 3 I3: 2,5,9 # reduction candidate for 2,5 I3: 2,5 => CTR * 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..4..3971183492657649.1.328...368419 I3: 9 => SOLVED * 371259486956874132428136759213987564867541293594623871185392647649715328732468915 * PAIR I2: 2,5 ROW 2 B2: 2,5,1,6 # reduction candidate for 2,5 B2: 2,5 # 23 pairs C2: 2,5,1,6 # reduction candidate for 2,5 C2: 2,5 # 21 pairs * PAIR H3: 5,9 BLK 3 I3: 5,9,2 # reduction candidate for 5,9 I3: 2 => CTR * 3712598469..874135458.3.792...9..5.4.9..4.2.3..4..3971183492657649.1.328.2..68419 I3: 5,9 # 18 pairs * PAIR E4: 2,8 ROW 4 A4: 2,8,7 # reduction candidate for 2,8 A4: 7 # 23 pairs A4: 2,8 # 21 pairs * PAIR D6: 5,6 BLK 5 D5: 5,6,1,7 # reduction candidate for 5,6 D5: 5,6 # 21 pairs F5: 5,6,1,7 # reduction candidate for 5,6 F5: 5,6 # 22 pairs * PAIR D6: 5,6 ROW 6 B6: 5,6,2,9 # reduction candidate for 5,6 B6: 5,6 => CTR * 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..4..397118.492657649.1.328...368419 B6: 2,9 # 20 pairs * PAIR E6: 2,8 ROW 6 A6: 2,8,5 # reduction candidate for 2,8 A6: 5 # 19 pairs A6: 2,8 # 19 pairs * PAIR H4: 6,8 BLK 6 H5: 6,8,9 # reduction candidate for 6,8 H5: 6,8 => CTR * 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..4..3971183492657649.1.328...368419 H5: 9 => SOLVED * 371259486956874132428136759213987564867541293594623871185392647649715328732468915 G6: 6,8,1,9 # reduction candidate for 6,8 G6: 6,8 => SOLVED * 371259486956874132428136759213987564867541293594623871185392647649715328732468915 G6: 1,9 # 19 pairs * PAIR I6: 1,6 BLK 6 G6: 1,6,8,9 # reduction candidate for 1,6 G6: 1,6 => CTR * 37.25984.9..874.3.4.8.3.759...9..5848...4.293.94.83.7.18..92.6764..1..28....68.15 G6: 8,9 # 17 pairs * PAIR C7: 3,5 BLK 7 C8: 3,5,7,9 # reduction candidate for 3,5 C8: 3,5 => CTR * 37.259...9..874.32428.3.759...9..5.4....4.293.94..3.7.18..92..764..1.928.39.68415 C8: 7,9 # 21 pairs B9: 3,5,2,9 # reduction candidate for 3,5 B9: 3,5 # 23 pairs C9: 3,5,2,7,9 # reduction candidate for 3,5 C9: 3,5 # 24 pairs * PAIR C7: 3,5 ROW 7 D7: 3,5,4 # reduction candidate for 3,5 D7: 3,5 => SOLVED * 371259486956874132428136759213987564867541293594623871185392647649715328732468915 D7: 4 # 19 pairs * PAIR F8: 5,7 BLK 8 D8: 5,7,3 # reduction candidate for 5,7 D8: 5,7 # 23 pairs D9: 5,7,3,4 # reduction candidate for 5,7 D9: 5,7 => CTR * 37.25984.9..874.32428.3.759...9..5.4....4.293.94..3.7.185492367647315928239.68415 D9: 3,4 # 20 pairs * PAIR F8: 5,7 ROW 8 C8: 5,7,3,9 # reduction candidate for 5,7 C8: 5,7 => CTR * 37.259...9..874.32428.3.759...9..5.4....4.293.94..3.7.18..92..764.31.928.39.68415 C8: 3,9 # 23 pairs * PAIR F8: 5,7 COL F F5: 5,7,1,6 # reduction candidate for 5,7 F5: 1,6 => SOLVED * 371259486956874132428136759213987564867541293594623871185392647649715328732468915 F5: 5,7 # 22 pairs * PAIR G8: 3,9 BLK 9 G9: 3,9,4 # reduction candidate for 3,9 G9: 3,9 => SOLVED * 371259486956874132428136759213987564867541293594623871185392647649715328732468915 G9: 4 # 19 pairs * PAIR G8: 3,9 ROW 8 C8: 3,9,5,7 # reduction candidate for 3,9 C8: 5,7 => CTR * 37.259...9..874.32428.3.759...9..5.4....4.293.94..3.7.18..92..764.31.928.39.68415 C8: 3,9 # 23 pairs * PAIR I9: 5,9 ROW 9 B9: 5,9,2,3 # reduction candidate for 5,9 B9: 5,9 # 22 pairs C9: 5,9,2,3,7 # reduction candidate for 5,9 C9: 5,9 # 23 pairs * PAIR I9: 5,9 COL I I3: 5,9,2 # reduction candidate for 5,9 I3: 2 => CTR * 3712598469..874135458.3.792...9..5.4.9..4.2.3..4..3971183492657649.1.328.2..68419 I3: 5,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190308-absurd-base-pr-000.dot * REASONING * DIS # I3: 2,5 => CTR => I3: 9 * PRF # I3: 9 => SOL * DIS # B6: 2,5 => CTR => B6: 6,9 * PRF # F5: 1,6 => SOL * DIS # G6: 1,6 => CTR => G6: 8,9 * DIS # I3: 2,5 => CTR => I3: 9 * PRF # I3: 9 => SOL * DIS # I3: 2 => CTR => I3: 5,9 * DIS # B6: 5,6 => CTR => B6: 2,9 * DIS # H5: 6,8 => CTR => H5: 9 * PRF # H5: 9 => SOL * PRF # G6: 6,8 => SOL * DIS # G6: 1,6 => CTR => G6: 8,9 * DIS # C8: 3,5 => CTR => C8: 7,9 * PRF # D7: 3,5 => SOL * DIS # D9: 5,7 => CTR => D9: 3,4 * DIS # C8: 5,7 => CTR => C8: 3,9 * PRF # F5: 1,6 => SOL * PRF # G9: 3,9 => SOL * DIS # C8: 5,7 => CTR => C8: 3,9 * DIS # I3: 2 => CTR => I3: 5,9 * CNT 21 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,C1,C7,D3,D6,E4,E6,F3,F8,G1,G2,G8,H1,H3,H4,I1,I2,I6,I9) * 37.259...9..874.3.4.8.3.7.....9..5.4....4.2.3..4..3.7.18..92..764..1..28....68.1. * PAIR C1: 1,6 BLK 1 B2: 1,6,2,5 # reduction candidate for 1,6 B2: 1,6 # 21 pairs C2: 1,6,2,5 # reduction candidate for 1,6 C2: 1,6 # 23 pairs * PAIR C1: 1,6 COL C C4: 1,6,2,3,7 # reduction candidate for 1,6 C4: 1,6 # 22 pairs C5: 1,6,5,7,9 # reduction candidate for 1,6 C5: 1,6 # 22 pairs * PAIR B3: 2,5 BLK 1 B2: 2,5,1,6 # reduction candidate for 2,5 B2: 2,5 # 23 pairs C2: 2,5,1,6 # reduction candidate for 2,5 C2: 2,5 # 21 pairs * PAIR B3: 2,5 ROW 3 I3: 2,5,9 # reduction candidate for 2,5 I3: 2,5 => CTR * 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..4..3971183492657649.1.328...368419 I3: 9 => SOLVED * 371259486956874132428136759213987564867541293594623871185392647649715328732468915 * DURATION: 0:00:07.443123 START: 04:22:02.484899 END: 04:22:09.928022 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190308-absurd-base-pr-001.dot * REASONING * DIS # I3: 2,5 => CTR => I3: 9 * PRF I3: 9 => SOL * STA I3: 9 * CNT 2 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190308, absurd
Solution
position: 371259486956874132428136759213987564867541293594623871185392647649715328732468915 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: 1,6 => UNS * INC # C2: 1,6 => UNS * INC # C4: 1,6 => UNS * INC # C5: 1,6 => UNS * INC # B2: 2,5 => UNS * INC # C2: 2,5 => UNS * DIS # I3: 2,5 => CTR => I3: 9 * PRF # I3: 9 => SOL * DIS # B6: 2,5 => CTR => B6: 6,9 * INC # B6: 6,9 => UNS * INC # B9: 2,5 => UNS * INC # D5: 1,6 => UNS * INC # D5: 5,7 => UNS * INC # F4: 1,6 => UNS * PRF # F5: 1,6 => SOL * INC # F5: 5,7 => UNS * INC # B2: 1,6 => UNS * INC # C2: 1,6 => UNS * DIS # G6: 1,6 => CTR => G6: 8,9 * INC # G6: 8,9 => UNS * DIS # I3: 2,5 => CTR => I3: 9 * PRF # I3: 9 => SOL * INC # B2: 2,5 => UNS * INC # C2: 2,5 => UNS * INC # I3: 5,9 => UNS * DIS # I3: 2 => CTR => I3: 5,9 * INC # A4: 2,8 => UNS * INC # A4: 7 => UNS * INC # D5: 5,6 => UNS * INC # F5: 5,6 => UNS * DIS # B6: 5,6 => CTR => B6: 2,9 * INC # B6: 2,9 => UNS * INC # A6: 2,8 => UNS * INC # A6: 5 => UNS * DIS # H5: 6,8 => CTR => H5: 9 * PRF # H5: 9 => SOL * PRF # G6: 6,8 => SOL * INC # G6: 1,9 => UNS * DIS # G6: 1,6 => CTR => G6: 8,9 * INC # G6: 8,9 => UNS * DIS # C8: 3,5 => CTR => C8: 7,9 * INC # C8: 7,9 => UNS * INC # B9: 3,5 => UNS * INC # C9: 3,5 => UNS * PRF # D7: 3,5 => SOL * INC # D7: 4 => UNS * INC # D8: 5,7 => UNS * DIS # D9: 5,7 => CTR => D9: 3,4 * INC # D9: 3,4 => UNS * DIS # C8: 5,7 => CTR => C8: 3,9 * INC # C8: 3,9 => UNS * INC # F5: 5,7 => UNS * PRF # F5: 1,6 => SOL * PRF # G9: 3,9 => SOL * INC # G9: 4 => UNS * INC # C8: 3,9 => UNS * DIS # C8: 5,7 => CTR => C8: 3,9 * INC # B9: 5,9 => UNS * INC # C9: 5,9 => UNS * INC # I3: 5,9 => UNS * DIS # I3: 2 => CTR => I3: 5,9 * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 1,6 => UNS * INC # C2: 1,6 => UNS * INC # C4: 1,6 => UNS * INC # C5: 1,6 => UNS * INC # B2: 2,5 => UNS * INC # C2: 2,5 => UNS * DIS # I3: 2,5 => CTR => I3: 9 * PRF I3: 9 => SOL * STA I3: 9 * CNT 8 HDP CHAINS / 7 HYP OPENED