Analysis of zz-www.sudokuoftheday.co.uk-20190309-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: .........8.6....237....51.61......9..2..3...1..792...4...5..7..9..6......34.....8 initial
Autosolve
position: ....6....8.6....237....51.61...5..9..29.3...1..7921..4...5..7..97.6......34.....8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 4,9 => CTR => B2: 1,5 * PRF # E3: 8 => SOL * DIS # C1: 2,3 => CTR => C1: 1,5 * DIS # H1: 4,8 => CTR => H1: 5,7 * DIS # G4: 3,8 => CTR => G4: 2,6 * DIS # A9: 5 => CTR => A9: 2,6 * DIS # G9: 2,9 => CTR => G9: 5,6 * DIS # F7: 2,9 => CTR => F7: 3,4,8 * DIS # G8: 2,5 => CTR => G8: 3,4 * DIS # C8: 1,8 => CTR => C8: 2,5 * CNT 10 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 4,9 => CTR => B2: 1,5 * DIS B2: 1,5 # B1: 1,5 => CTR => B1: 4,9 * DIS B2: 1,5 + B1: 4,9 # E3: 4,9 => CTR => E3: 8 * PRF B2: 1,5 + B1: 4,9 + E3: 8 => SOL * STA B2: 1,5 + B1: 4,9 + E3: 8 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .........8.6....237....51.61......9..2..3...1..792...4...5..7..9..6......34.....8 | initial |
| ....6....8.6....237....51.61...5..9..29.3...1..7921..4...5..7..97.6......34.....8 | autosolve |
| 341269875856174923792385146183456297429837651567921384218543769975618432634792518 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B3: 4,9 C3: 2,3 D3: 2,3 H3: 4,8 C4: 3,8 I4: 2,7 A7: 2,6 I7: 2,9 I8: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,I4: 2.. / G4 = 2 => 13 pairs (_) / I4 = 2 => 0 pairs (X) C3,D3: 2.. / C3 = 2 => 8 pairs (_) / D3 = 2 => 0 pairs (X) D1,D3: 3.. / D1 = 3 => 0 pairs (X) / D3 = 3 => 8 pairs (_) C4,A6: 3.. / C4 = 3 => 12 pairs (_) / A6 = 3 => 0 pairs (X) F7,F8: 3.. / F7 = 3 => 9 pairs (_) / F8 = 3 => 11 pairs (_) C3,D3: 3.. / C3 = 3 => 0 pairs (X) / D3 = 3 => 8 pairs (_) C4,G4: 3.. / C4 = 3 => 12 pairs (_) / G4 = 3 => 0 pairs (X) F7,H7: 3.. / F7 = 3 => 9 pairs (_) / H7 = 3 => 11 pairs (_) A1,A6: 3.. / A1 = 3 => 12 pairs (_) / A6 = 3 => 0 pairs (X) B4,A5: 4.. / B4 = 4 => 0 pairs (X) / A5 = 4 => 11 pairs (_) A1,A5: 4.. / A1 = 4 => 0 pairs (X) / A5 = 4 => 11 pairs (_) C8,A9: 5.. / C8 = 5 => 17 pairs (_) / A9 = 5 => 0 pairs (X) B2,G2: 5.. / B2 = 5 => 17 pairs (_) / G2 = 5 => 0 pairs (X) C1,C8: 5.. / C1 = 5 => 0 pairs (X) / C8 = 5 => 17 pairs (_) I1,I8: 5.. / I1 = 5 => 17 pairs (_) / I8 = 5 => 0 pairs (X) F4,F5: 6.. / F4 = 6 => 10 pairs (_) / F5 = 6 => 11 pairs (_) H1,I1: 7.. / H1 = 7 => 13 pairs (_) / I1 = 7 => 0 pairs (X) I4,H5: 7.. / I4 = 7 => 13 pairs (_) / H5 = 7 => 0 pairs (X) E2,E9: 7.. / E2 = 7 => 13 pairs (_) / E9 = 7 => 11 pairs (_) H1,H5: 7.. / H1 = 7 => 13 pairs (_) / H5 = 7 => 0 pairs (X) I1,I4: 7.. / I1 = 7 => 0 pairs (X) / I4 = 7 => 13 pairs (_) E3,H3: 8.. / E3 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) I7,G9: 9.. / I7 = 9 => 9 pairs (_) / G9 = 9 => 0 pairs (X) B3,E3: 9.. / B3 = 9 => 9 pairs (_) / E3 = 9 => 15 pairs (_) I1,I7: 9.. / I1 = 9 => 0 pairs (X) / I7 = 9 => 9 pairs (_) * DURATION: 0:00:26.212300 START: 04:22:20.208717 END: 04:22:46.421017 2019-05-01 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,C3,C4,D3,H3,I4,I7,I8) * ....6....8.6....237....51.61...5..9..29.3...1..7921..4...5..7..97.6......34.....8 * PAIR B3: 4,9 BLK 1 B1: 4,9,1,5 # reduction candidate for 4,9 B1: 4,9 # 13 pairs B2: 4,9,1,5 # reduction candidate for 4,9 B2: 4,9 => CTR * 21536..798.6...5237.32.51.61.8.5..97.29.3..51.57921..4...5..7.29726....5534...968 B2: 1,5 # 10 pairs * PAIR B3: 4,9 ROW 3 E3: 4,9,8 # reduction candidate for 4,9 E3: 8 => SOLVED * 341269875856174923792385146183456297429837651567921384218543769975618432634792518 E3: 4,9 # 10 pairs * PAIR C3: 2,3 BLK 1 A1: 2,3,4,5 # reduction candidate for 2,3 A1: 2,3 # 13 pairs C1: 2,3,1,5 # reduction candidate for 2,3 C1: 2,3 => CTR * ....6...5856....237....51.61...5.297.29.3...1..7921..4..15..7.99756....2.34.....8 C1: 1,5 # 13 pairs * PAIR D3: 2,3 BLK 2 D1: 2,3,1,4,8 # reduction candidate for 2,3 D1: 2,3 # 11 pairs D1: 1,4,8 # 11 pairs * PAIR H3: 4,8 BLK 3 G1: 4,8,5,9 # reduction candidate for 4,8 G1: 4,8 # 12 pairs H1: 4,8,5,7 # reduction candidate for 4,8 H1: 4,8 => CTR * ..5.6...78.6...5237....51.61...5..92.29.3..71.57921..4...5..7.997.6....5534.....8 H1: 5,7 # 10 pairs * PAIR H3: 4,8 ROW 3 E3: 4,8,9 # reduction candidate for 4,8 E3: 9 # 15 pairs E3: 4,8 # 9 pairs * PAIR C4: 3,8 ROW 4 G4: 3,8,2,6 # reduction candidate for 3,8 G4: 3,8 => CTR * ..5.6...78.6...5237....51.61...5..92.29.3..71.57921..4...5..7.997.6....5534.....8 G4: 2,6 # 13 pairs * PAIR A7: 2,6 BLK 7 A9: 2,6,5 # reduction candidate for 2,6 A9: 5 => CTR * 2.536..798.6...5237.32.51.61.8.5..97.29.3..51.57921..4...5..7.29726....5534...968 A9: 2,6 # 17 pairs * PAIR I7: 2,9 BLK 9 G9: 2,9,5,6 # reduction candidate for 2,9 G9: 2,9 => CTR * 2.536..798.6...5237.32.51.61.8.5..97.29.3..51.57921..4...5..7.29726....5534...968 G9: 5,6 # 10 pairs * PAIR I7: 2,9 ROW 7 F7: 2,9,3,4,8 # reduction candidate for 2,9 F7: 2,9 => CTR * ....6..4.8.6....2374..951861...5..9.429.3...1..7921.646..54.73.97.683.1..34...658 F7: 3,4,8 # 9 pairs * PAIR I8: 2,5 BLK 9 G8: 2,5,3,4 # reduction candidate for 2,5 G8: 2,5 => CTR * ..5.6..798.6....237....51861...5..9..29.3...1..7921..4...5..7..97.6......34.....8 G8: 3,4 # 10 pairs G9: 2,5,6,9 # reduction candidate for 2,5 G9: 2,5 # 12 pairs * PAIR I8: 2,5 ROW 8 C8: 2,5,1,8 # reduction candidate for 2,5 C8: 1,8 => CTR * ..5.6..798.6...5237....51.61...5..97.29.3..51.57921..4...5..7.297.6.2..5534...968 C8: 2,5 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190309-absurd-base-pr-000.dot * REASONING * DIS # B2: 4,9 => CTR => B2: 1,5 * PRF # E3: 8 => SOL * DIS # C1: 2,3 => CTR => C1: 1,5 * DIS # H1: 4,8 => CTR => H1: 5,7 * DIS # G4: 3,8 => CTR => G4: 2,6 * DIS # A9: 5 => CTR => A9: 2,6 * DIS # G9: 2,9 => CTR => G9: 5,6 * DIS # F7: 2,9 => CTR => F7: 3,4,8 * DIS # G8: 2,5 => CTR => G8: 3,4 * DIS # C8: 1,8 => CTR => C8: 2,5 * CNT 10 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,C3,C4,D3,H3,I4,I7,I8) * ....6....8.6....237....51.61...5..9..29.3...1..7921..4...5..7..97.6......34.....8 * PAIR B3: 4,9 BLK 1 B1: 4,9,1,5 # reduction candidate for 4,9 B1: 4,9 # 13 pairs B2: 4,9,1,5 # reduction candidate for 4,9 B2: 4,9 => CTR * 21536..798.6...5237.32.51.61.8.5..97.29.3..51.57921..4...5..7.29726....5534...968 * RESTART * PAIR B3: 4,9 BLK 1 B1: 4,9,1,5 # reduction candidate for 4,9 B1: 1,5 => CTR * 4...6....8.6....2379...51.6148756392.29.3..713.7921..4.8.5..7.997.6....5534.....8 * PAIR B3: 4,9 ROW 3 E3: 4,9,8 # reduction candidate for 4,9 E3: 4,9 => CTR * 3.1.6..75856....237.23.51861.3.5.297429.3...15.7921..4.1854.7.9975683412.34.....8 E3: 8 => SOLVED * 341269875856174923792385146183456297429837651567921384218543769975618432634792518 * DURATION: 0:00:05.556324 START: 04:23:03.805258 END: 04:23:09.361582 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190309-absurd-base-pr-001.dot * REASONING * DIS # B2: 4,9 => CTR => B2: 1,5 * DIS B2: 1,5 # B1: 1,5 => CTR => B1: 4,9 * DIS B2: 1,5 + B1: 4,9 # E3: 4,9 => CTR => E3: 8 * PRF B2: 1,5 + B1: 4,9 + E3: 8 => SOL * STA B2: 1,5 + B1: 4,9 + E3: 8 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190309, absurd
Solution
position: 341269875856174923792385146183456297429837651567921384218543769975618432634792518 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 # B1: 4,9 => UNS * DIS # B2: 4,9 => CTR => B2: 1,5 * INC # B2: 1,5 => UNS * INC # E3: 4,9 => UNS * PRF # E3: 8 => SOL * INC # A1: 2,3 => UNS * DIS # C1: 2,3 => CTR => C1: 1,5 * INC # C1: 1,5 => UNS * INC # D1: 2,3 => UNS * INC # D1: 1,4,8 => UNS * INC # G1: 4,8 => UNS * DIS # H1: 4,8 => CTR => H1: 5,7 * INC # H1: 5,7 => UNS * INC # E3: 4,8 => UNS * INC # E3: 9 => UNS * DIS # G4: 3,8 => CTR => G4: 2,6 * INC # G4: 2,6 => UNS * INC # A9: 2,6 => UNS * DIS # A9: 5 => CTR => A9: 2,6 * DIS # G9: 2,9 => CTR => G9: 5,6 * INC # G9: 5,6 => UNS * DIS # F7: 2,9 => CTR => F7: 3,4,8 * INC # F7: 3,4,8 => UNS * DIS # G8: 2,5 => CTR => G8: 3,4 * INC # G8: 3,4 => UNS * INC # G9: 2,5 => UNS * INC # C8: 2,5 => UNS * DIS # C8: 1,8 => CTR => C8: 2,5 * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 4,9 => UNS * DIS # B2: 4,9 => CTR => B2: 1,5 * INC B2: 1,5 # B1: 4,9 => UNS * DIS B2: 1,5 # B1: 1,5 => CTR => B1: 4,9 * DIS B2: 1,5 + B1: 4,9 # E3: 4,9 => CTR => E3: 8 * PRF B2: 1,5 + B1: 4,9 + E3: 8 => SOL * STA B2: 1,5 + B1: 4,9 + E3: 8 * CNT 6 HDP CHAINS / 5 HYP OPENED