Analysis of zz-www.sudokuoftheday.co.uk-20190316-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: 3.5....16..7.....9....854..8....3....1....73.9..5.......2..41..4....8.......9.26. initial
Autosolve
position: 3459..816.87..6..9....854..8....3....1.8.973.9.35..6....2..41..4....8.....8.9.264 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A3: 1,2 => SOL * DIS # E6: 2,7 => CTR => E6: 1,4 * DIS # D2: 1,3 => CTR => D2: 4 * DIS # D8: 1,3 => CTR => D8: 2,6,7 * DIS # G8: 9 => CTR => G8: 3,5 * DIS # I3: 2,7 => CTR => I3: 3 * PRF # B4: 7 => SOL * PRF # B4: 2,7 => SOL * DIS # B4: 5 => CTR => B4: 2,7 * DIS # E6: 2,7 => CTR => E6: 1,4 * DIS # H4: 5,9 => CTR => H4: 2,4 * DIS # G8: 5,9 => CTR => G8: 3 * DIS # E7: 6,7 => CTR => E7: 3,5 * DIS # D8: 1,7 => CTR => D8: 2,3,6 * DIS # E8: 1,7 => CTR => E8: 2,3,5,6 * DIS # D9: 1,7 => CTR => D9: 3 * PRF # D9: 3 => SOL * PRF # A9: 1,7 => SOL * DIS # A9: 5 => CTR => A9: 1,7 * CNT 19 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A3: 1,2 => SOL * STA A3: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.5....16..7.....9....854..8....3....1....73.9..5.......2..41..4....8.......9.26. | initial |
| 3459..816.87..6..9....854..8....3....1.8.973.9.35..6....2..41..4....8.....8.9.264 | autosolve |
| 345972816187436529269185473876213945514869732923547681632754198491628357758391264 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A2: 1,2 C3: 1,9 E1: 2,7 F1: 2,7 D3: 1,3 G2: 3,5 H2: 2,5 H3: 2,7 C4: 4,6 A5: 2,5 C5: 4,6 B6: 2,7 E5: 4,6 G4: 5,9 I5: 2,5 A7: 6,7 C8: 1,9 B9: 3,5 F9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I4,I6: 1.. / I4 = 1 => 20 pairs (_) / I6 = 1 => 22 pairs (_) C8,A9: 1.. / C8 = 1 => 19 pairs (_) / A9 = 1 => 0 pairs (X) C3,C8: 1.. / C3 = 1 => 0 pairs (X) / C8 = 1 => 19 pairs (_) F6,F9: 1.. / F6 = 1 => 23 pairs (_) / F9 = 1 => 23 pairs (_) E1,F1: 2.. / E1 = 2 => 20 pairs (_) / F1 = 2 => 18 pairs (_) D8,E8: 2.. / D8 = 2 => 19 pairs (_) / E8 = 2 => 0 pairs (*) A2,H2: 2.. / A2 = 2 => 0 pairs (X) / H2 = 2 => 24 pairs (_) A5,I5: 2.. / A5 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) D4,D8: 2.. / D4 = 2 => 0 pairs (*) / D8 = 2 => 0 pairs (X) F1,F6: 2.. / F1 = 2 => 18 pairs (_) / F6 = 2 => 20 pairs (_) G2,I3: 3.. / G2 = 3 => 0 pairs (X) / I3 = 3 => 24 pairs (_) D3,I3: 3.. / D3 = 3 => 0 pairs (X) / I3 = 3 => 24 pairs (_) B9,D9: 3.. / B9 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) G2,G8: 3.. / G2 = 3 => 0 pairs (X) / G8 = 3 => 24 pairs (_) D2,E2: 4.. / D2 = 4 => 20 pairs (_) / E2 = 4 => 0 pairs (X) C4,C5: 4.. / C4 = 4 => 18 pairs (_) / C5 = 4 => 16 pairs (_) H4,H6: 4.. / H4 = 4 => 19 pairs (_) / H6 = 4 => 20 pairs (_) C5,E5: 4.. / C5 = 4 => 16 pairs (_) / E5 = 4 => 18 pairs (_) E6,H6: 4.. / E6 = 4 => 19 pairs (_) / H6 = 4 => 20 pairs (_) D2,D4: 4.. / D2 = 4 => 20 pairs (_) / D4 = 4 => 0 pairs (X) G2,H2: 5.. / G2 = 5 => 24 pairs (_) / H2 = 5 => 0 pairs (X) B4,A5: 5.. / B4 = 5 => 0 pairs (X) / A5 = 5 => 0 pairs (_) A9,B9: 5.. / A9 = 5 => 0 pairs (X) / B9 = 5 => 0 pairs (_) E7,E8: 5.. / E7 = 5 => 19 pairs (_) / E8 = 5 => 0 pairs (X) A5,I5: 5.. / A5 = 5 => 0 pairs (*) / I5 = 5 => 0 pairs (X) A5,A9: 5.. / A5 = 5 => 0 pairs (*) / A9 = 5 => 0 pairs (X) B4,B9: 5.. / B4 = 5 => 0 pairs (X) / B9 = 5 => 0 pairs (_) A3,B3: 6.. / A3 = 6 => 21 pairs (_) / B3 = 6 => 0 pairs (*) C4,C5: 6.. / C4 = 6 => 16 pairs (_) / C5 = 6 => 18 pairs (_) C5,E5: 6.. / C5 = 6 => 18 pairs (_) / E5 = 6 => 16 pairs (_) A3,A7: 6.. / A3 = 6 => 21 pairs (_) / A7 = 6 => 0 pairs (*) E1,F1: 7.. / E1 = 7 => 18 pairs (_) / F1 = 7 => 20 pairs (_) H3,I3: 7.. / H3 = 7 => 20 pairs (_) / I3 = 7 => 0 pairs (X) B4,B6: 7.. / B4 = 7 => 0 pairs (*) / B6 = 7 => 0 pairs (X) A7,A9: 7.. / A7 = 7 => 21 pairs (_) / A9 = 7 => 0 pairs (*) H6,I6: 8.. / H6 = 8 => 21 pairs (_) / I6 = 8 => 21 pairs (_) H7,I7: 8.. / H7 = 8 => 21 pairs (_) / I7 = 8 => 21 pairs (_) H6,H7: 8.. / H6 = 8 => 21 pairs (_) / H7 = 8 => 21 pairs (_) I6,I7: 8.. / I6 = 8 => 21 pairs (_) / I7 = 8 => 21 pairs (_) B3,C3: 9.. / B3 = 9 => 0 pairs (X) / C3 = 9 => 19 pairs (_) G4,H4: 9.. / G4 = 9 => 19 pairs (_) / H4 = 9 => 0 pairs (X) B7,H7: 9.. / B7 = 9 => 20 pairs (_) / H7 = 9 => 0 pairs (*) C3,C8: 9.. / C3 = 9 => 19 pairs (_) / C8 = 9 => 0 pairs (X) G4,G8: 9.. / G4 = 9 => 19 pairs (_) / G8 = 9 => 0 pairs (X) * DURATION: 0:00:54.672916 START: 04:34:02.205980 END: 04:34:56.878896 2019-05-01 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A7,B6,B9,C3,C4,C5,C8,D3,E1,E5,F1,F9,G2,G4,H2,H3,I5) * 3459..816.87..6..9....854..8....3....1.8.973.9.35..6....2..41..4....8.....8.9.264 * PAIR A2: 1,2 BLK 1 A3: 1,2,6 # reduction candidate for 1,2 A3: 1,2 => SOLVED * 345972816187436529269185473876213945514869732923547681632754198491628357758391264 A3: 6 # 21 pairs * PAIR E1: 2,7 COL E E4: 2,7,1,4,6 # reduction candidate for 2,7 E4: 2,7 # 21 pairs E6: 2,7,1,4 # reduction candidate for 2,7 E6: 2,7 => CTR * 345972816.87.16..91693854..8..7.3..1.1.8.973.973521648.92..418.4.1..8.....8197264 E6: 1,4 # 20 pairs E8: 2,7,1,3,5,6 # reduction candidate for 2,7 E8: 2,7 # 26 pairs * PAIR F1: 2,7 COL F F6: 2,7,1 # reduction candidate for 2,7 F6: 2,7 # 23 pairs F6: 1 # 23 pairs * PAIR D3: 1,3 BLK 2 D2: 1,3,4 # reduction candidate for 1,3 D2: 1,3 => CTR * 3459..816.87.46..96291854738564739.1.1486973.9.35..648.926.418.4612.8....38791264 D2: 4 # 20 pairs E2: 1,3,4 # reduction candidate for 1,3 E2: 1,3 # 20 pairs * PAIR D3: 1,3 COL D D8: 1,3,2,6,7 # reduction candidate for 1,3 D8: 1,3 => CTR * 345972816.874.6..96..1854.387.2.3...51.8.973.9.35..6....26.41..46..28.....8791264 D8: 2,6,7 # 19 pairs D9: 1,3,7 # reduction candidate for 1,3 D9: 1,3 # 25 pairs * PAIR G2: 3,5 COL G G8: 3,5,9 # reduction candidate for 3,5 G8: 9 => CTR * 3459..816.87..6359...3854..8....359.51.8.97329.35..648.92..41..4....8.....8.9.264 G8: 3,5 # 19 pairs * PAIR H2: 2,5 COL H H4: 2,5,4,9 # reduction candidate for 2,5 H4: 2,5 # 21 pairs H4: 4,9 # 20 pairs * PAIR H3: 2,7 BLK 3 I3: 2,7,3 # reduction candidate for 2,7 I3: 2,7 => CTR * 3459..816287..6359...3854..85...3....1.8.973.9.35..6....2..41..4....8....38.9.264 I3: 3 # 24 pairs * PAIR C4: 4,6 ROW 4 D4: 4,6,1,2,7 # reduction candidate for 4,6 D4: 4,6 # 25 pairs E4: 4,6,1,2,7 # reduction candidate for 4,6 E4: 4,6 # 23 pairs * PAIR A5: 2,5 BLK 4 B4: 2,5,7 # reduction candidate for 2,5 B4: 7 => SOLVED * 345972816187436529269185473876213945514869732923547681632754198491628357758391264 B4: 2,5 # 20 pairs * PAIR B6: 2,7 BLK 4 B4: 2,7,5 # reduction candidate for 2,7 B4: 2,7 => SOLVED * 345972816187436529269185473876213945514869732923547681632754198491628357758391264 B4: 5 => CTR * 3459..816187..6.2962918547385...394.21486973597354.68.7.2..41.84.1..83.7538791264 * PAIR B6: 2,7 ROW 6 E6: 2,7,1,4 # reduction candidate for 2,7 E6: 2,7 => CTR * 345972816.87.16..91693854..8..7.3..1.1.8.973.973521648.92..418.4.1..8.....8197264 E6: 1,4 # 20 pairs F6: 2,7,1 # reduction candidate for 2,7 F6: 2,7 # 23 pairs * PAIR E5: 4,6 BLK 5 D4: 4,6,1,2,7 # reduction candidate for 4,6 D4: 4,6 # 25 pairs E4: 4,6,1,2,7 # reduction candidate for 4,6 E4: 4,6 # 23 pairs * PAIR G4: 5,9 BLK 6 H4: 5,9,2,4 # reduction candidate for 5,9 H4: 5,9 => CTR * 3459..816.87.365292691854738....395151.8.97329.351.64869275418.4.1..8...758391264 H4: 2,4 # 21 pairs * PAIR G4: 5,9 COL G G8: 5,9,3 # reduction candidate for 5,9 G8: 5,9 => CTR * 3459..816287..6359...3854..85...3....1.8.973.9.35..6....2..41..4....8....38.9.264 G8: 3 # 24 pairs * PAIR I5: 2,5 BLK 6 H4: 2,5,4,9 # reduction candidate for 2,5 H4: 2,5 # 21 pairs I4: 2,5,1 # reduction candidate for 2,5 I4: 2,5 # 22 pairs * PAIR A7: 6,7 ROW 7 D7: 6,7,3 # reduction candidate for 6,7 D7: 6,7 # 22 pairs E7: 6,7,3,5 # reduction candidate for 6,7 E7: 6,7 => CTR * 3459..81618743652962918547385.67394..1.8.973.9.35..6...923641..461258397.38791264 E7: 3,5 # 20 pairs * PAIR F9: 1,7 BLK 8 D8: 1,7,2,3,6 # reduction candidate for 1,7 D8: 1,7 => CTR * 345972816.874.6..96...854..87.2.3...51.8.97329235.76..7.26541..46..28...1.8.9.264 D8: 2,3,6 # 19 pairs E8: 1,7,2,3,5,6 # reduction candidate for 1,7 E8: 1,7 => CTR * 3459..816.87.36529...1854738....39...1.8.973.9.35..6....26541..4612783957.8.9.264 E8: 2,3,5,6 # 19 pairs D9: 1,7,3 # reduction candidate for 1,7 D9: 1,7 => CTR * 3459..816187..6.2962918547385...394.21486973597354.68.7.2..41.84.1..83.7538791264 D9: 3 => SOLVED * 345972816187436529269185473876213945514869732923547681632754198491628357758391264 * PAIR F9: 1,7 ROW 9 A9: 1,7,5 # reduction candidate for 1,7 A9: 1,7 => SOLVED * 345972816187436529269185473876213945514869732923547681632754198491628357758391264 A9: 5 => CTR * 3459.7816187..652962918547385..739412148697359735..6..7.2..41.84.1..83.7538791264 * PAIR F9: 1,7 COL F F6: 1,7,2 # reduction candidate for 1,7 F6: 2 # 20 pairs F6: 1,7 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190316-absurd-base-pr-000.dot * REASONING * PRF # A3: 1,2 => SOL * DIS # E6: 2,7 => CTR => E6: 1,4 * DIS # D2: 1,3 => CTR => D2: 4 * DIS # D8: 1,3 => CTR => D8: 2,6,7 * DIS # G8: 9 => CTR => G8: 3,5 * DIS # I3: 2,7 => CTR => I3: 3 * PRF # B4: 7 => SOL * PRF # B4: 2,7 => SOL * DIS # B4: 5 => CTR => B4: 2,7 * DIS # E6: 2,7 => CTR => E6: 1,4 * DIS # H4: 5,9 => CTR => H4: 2,4 * DIS # G8: 5,9 => CTR => G8: 3 * DIS # E7: 6,7 => CTR => E7: 3,5 * DIS # D8: 1,7 => CTR => D8: 2,3,6 * DIS # E8: 1,7 => CTR => E8: 2,3,5,6 * DIS # D9: 1,7 => CTR => D9: 3 * PRF # D9: 3 => SOL * PRF # A9: 1,7 => SOL * DIS # A9: 5 => CTR => A9: 1,7 * CNT 19 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A7,B6,B9,C3,C4,C5,C8,D3,E1,E5,F1,F9,G2,G4,H2,H3,I5) * 3459..816.87..6..9....854..8....3....1.8.973.9.35..6....2..41..4....8.....8.9.264 * PAIR A2: 1,2 BLK 1 A3: 1,2,6 # reduction candidate for 1,2 A3: 1,2 => SOLVED * 345972816187436529269185473876213945514869732923547681632754198491628357758391264 * DURATION: 0:00:02.034185 START: 04:35:30.933095 END: 04:35:32.967280 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190316-absurd-base-pr-001.dot * REASONING * PRF # A3: 1,2 => SOL * STA A3: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190316, absurd
Solution
position: 345972816187436529269185473876213945514869732923547681632754198491628357758391264 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:
* PRF # A3: 1,2 => SOL * INC # A3: 6 => UNS * INC # E4: 2,7 => UNS * DIS # E6: 2,7 => CTR => E6: 1,4 * INC # E6: 1,4 => UNS * INC # E8: 2,7 => UNS * INC # F6: 2,7 => UNS * INC # F6: 1 => UNS * DIS # D2: 1,3 => CTR => D2: 4 * INC # D2: 4 => UNS * INC # E2: 1,3 => UNS * DIS # D8: 1,3 => CTR => D8: 2,6,7 * INC # D8: 2,6,7 => UNS * INC # D9: 1,3 => UNS * INC # G8: 3,5 => UNS * DIS # G8: 9 => CTR => G8: 3,5 * INC # H4: 2,5 => UNS * INC # H4: 4,9 => UNS * DIS # I3: 2,7 => CTR => I3: 3 * INC # I3: 3 => UNS * INC # D4: 4,6 => UNS * INC # E4: 4,6 => UNS * INC # B4: 2,5 => UNS * PRF # B4: 7 => SOL * PRF # B4: 2,7 => SOL * DIS # B4: 5 => CTR => B4: 2,7 * DIS # E6: 2,7 => CTR => E6: 1,4 * INC # E6: 1,4 => UNS * INC # F6: 2,7 => UNS * INC # D4: 4,6 => UNS * INC # E4: 4,6 => UNS * DIS # H4: 5,9 => CTR => H4: 2,4 * INC # H4: 2,4 => UNS * DIS # G8: 5,9 => CTR => G8: 3 * INC # G8: 3 => UNS * INC # H4: 2,5 => UNS * INC # I4: 2,5 => UNS * INC # D7: 6,7 => UNS * DIS # E7: 6,7 => CTR => E7: 3,5 * INC # E7: 3,5 => UNS * DIS # D8: 1,7 => CTR => D8: 2,3,6 * INC # D8: 2,3,6 => UNS * DIS # E8: 1,7 => CTR => E8: 2,3,5,6 * INC # E8: 2,3,5,6 => UNS * DIS # D9: 1,7 => CTR => D9: 3 * PRF # D9: 3 => SOL * PRF # A9: 1,7 => SOL * DIS # A9: 5 => CTR => A9: 1,7 * INC # F6: 1,7 => UNS * INC # F6: 2 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A3: 1,2 => SOL * STA A3: 1,2 * CNT 1 HDP CHAINS / 1 HYP OPENED