Analysis of zz-www.sudokuoftheday.co.uk-20190323-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: .49....1.8..........6.....4..1....95..56..8..7....962...872..5....38.2..3...5..8. initial
Autosolve
position: 54926..188......62..6.....4..1....95..56..8..78.5.962...872..5..5.38.2..3.295..8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 3,7 => CTR => B2: 1 * DIS # F2: 3,7 => CTR => F2: 5 * DIS # B3: 1,2 => CTR => B3: 3,7 * DIS # F2: 3,7 => CTR => F2: 5 * DIS # E3: 3,7 => CTR => E3: 9 * DIS # F3: 3,7 => CTR => F3: 5,8 * DIS # G4: 3,7 => CTR => G4: 4 * PRF # G4: 4 => SOL * DIS # E3: 3,7 => CTR => E3: 9 * DIS # F3: 3,7 => CTR => F3: 5,8 * PRF # H5: 3,7 => SOL * DIS # H5: 4 => CTR => H5: 3,7 * PRF # E6: 1 => SOL * PRF # I5: 1,3 => SOL * PRF # E6: 1,3 => SOL * DIS # E6: 4 => CTR => E6: 1,3 * DIS # F9: 1,6 => CTR => F9: 4 * DIS # A8: 9 => CTR => A8: 1,6 * DIS # H5: 3 => CTR => H5: 4,7 * PRF # I7: 6,9 => SOL * DIS # B9: 1 => CTR => B9: 6,7 * CNT 21 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:
* DIS # B2: 3,7 => CTR => B2: 1 * DIS B2: 1 # G4: 3,7 => CTR => G4: 4 * PRF B2: 1 + G4: 4 => SOL * STA B2: 1 + G4: 4 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .49....1.8..........6.....4..1....95..56..8..7....962...872..5....38.2..3...5..8. | initial |
| 54926..188......62..6.....4..1....95..56..8..78.5.962...872..5..5.38.2..3.295..8. | autosolve |
| 549263718813475962276198534621837495935642871784519623498721356157386249362954187 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C2: 3,7 A3: 1,2 F1: 3,7 D2: 1,4 D3: 1,8 G1: 3,7 G2: 5,9 G3: 5,9 H3: 3,7 C6: 3,4 D4: 4,8 I6: 1,3 C8: 4,7 F8: 1,6 H8: 4,7 I8: 6,9 I9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 0 pairs (X) / D3 = 1 => 19 pairs (_) E5,E6: 1.. / E5 = 1 => 18 pairs (_) / E6 = 1 => 0 pairs (*) I5,I6: 1.. / I5 = 1 => 0 pairs (*) / I6 = 1 => 0 pairs (X) G7,G9: 1.. / G7 = 1 => 24 pairs (_) / G9 = 1 => 20 pairs (_) B2,D2: 1.. / B2 = 1 => 19 pairs (_) / D2 = 1 => 0 pairs (X) E5,I5: 1.. / E5 = 1 => 18 pairs (_) / I5 = 1 => 0 pairs (*) E6,I6: 1.. / E6 = 1 => 0 pairs (*) / I6 = 1 => 0 pairs (X) A8,F8: 1.. / A8 = 1 => 22 pairs (_) / F8 = 1 => 19 pairs (_) A3,B3: 2.. / A3 = 2 => 22 pairs (_) / B3 = 2 => 0 pairs (X) F4,F5: 2.. / F4 = 2 => 20 pairs (_) / F5 = 2 => 21 pairs (_) G1,H3: 3.. / G1 = 3 => 0 pairs (X) / H3 = 3 => 24 pairs (_) G7,I7: 3.. / G7 = 3 => 0 pairs (*) / I7 = 3 => 0 pairs (X) F1,G1: 3.. / F1 = 3 => 24 pairs (_) / G1 = 3 => 0 pairs (X) C2,C6: 3.. / C2 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) H3,H5: 3.. / H3 = 3 => 24 pairs (_) / H5 = 3 => 0 pairs (X) D2,E2: 4.. / D2 = 4 => 19 pairs (_) / E2 = 4 => 0 pairs (X) G4,H5: 4.. / G4 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) A7,C8: 4.. / A7 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) F7,F9: 4.. / F7 = 4 => 0 pairs (X) / F9 = 4 => 19 pairs (_) C6,E6: 4.. / C6 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) C8,H8: 4.. / C8 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) F9,G9: 4.. / F9 = 4 => 19 pairs (_) / G9 = 4 => 0 pairs (X) C6,C8: 4.. / C6 = 4 => 0 pairs (*) / C8 = 4 => 0 pairs (X) D2,D4: 4.. / D2 = 4 => 19 pairs (_) / D4 = 4 => 0 pairs (X) H5,H8: 4.. / H5 = 4 => 0 pairs (X) / H8 = 4 => 0 pairs (_) F2,F3: 5.. / F2 = 5 => 15 pairs (_) / F3 = 5 => 0 pairs (X) G2,G3: 5.. / G2 = 5 => 0 pairs (X) / G3 = 5 => 15 pairs (_) F2,G2: 5.. / F2 = 5 => 15 pairs (_) / G2 = 5 => 0 pairs (X) F3,G3: 5.. / F3 = 5 => 0 pairs (X) / G3 = 5 => 15 pairs (_) A4,B4: 6.. / A4 = 6 => 19 pairs (_) / B4 = 6 => 20 pairs (_) G1,H3: 7.. / G1 = 7 => 24 pairs (_) / H3 = 7 => 0 pairs (X) C8,B9: 7.. / C8 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) F1,G1: 7.. / F1 = 7 => 0 pairs (X) / G1 = 7 => 24 pairs (_) C8,H8: 7.. / C8 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) C2,C8: 7.. / C2 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) I5,I9: 7.. / I5 = 7 => 22 pairs (_) / I9 = 7 => 0 pairs (*) D3,F3: 8.. / D3 = 8 => 0 pairs (X) / F3 = 8 => 19 pairs (_) D4,F4: 8.. / D4 = 8 => 19 pairs (_) / F4 = 8 => 0 pairs (X) D3,D4: 8.. / D3 = 8 => 0 pairs (X) / D4 = 8 => 19 pairs (_) F3,F4: 8.. / F3 = 8 => 19 pairs (_) / F4 = 8 => 0 pairs (X) E2,E3: 9.. / E2 = 9 => 0 pairs (X) / E3 = 9 => 15 pairs (_) G2,G3: 9.. / G2 = 9 => 15 pairs (_) / G3 = 9 => 0 pairs (X) A5,B5: 9.. / A5 = 9 => 19 pairs (_) / B5 = 9 => 19 pairs (_) I7,I8: 9.. / I7 = 9 => 0 pairs (X) / I8 = 9 => 18 pairs (_) E2,G2: 9.. / E2 = 9 => 0 pairs (X) / G2 = 9 => 15 pairs (_) E3,G3: 9.. / E3 = 9 => 15 pairs (_) / G3 = 9 => 0 pairs (X) A8,I8: 9.. / A8 = 9 => 0 pairs (X) / I8 = 9 => 18 pairs (_) B5,B7: 9.. / B5 = 9 => 19 pairs (_) / B7 = 9 => 19 pairs (_) * DURATION: 0:00:58.596454 START: 04:44:14.260810 END: 04:45:12.857264 2019-05-01 * CP COUNT: (48) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C2,C6,C8,D2,D3,D4,F1,F8,G1,G2,G3,H3,H8,I6,I8,I9) * 54926..188......62..6.....4..1....95..56..8..78.5.962...872..5..5.38.2..3.295..8. * PAIR C2: 3,7 BLK 1 B2: 3,7,1 # reduction candidate for 3,7 B2: 3,7 => CTR * 54926..188..14.962..689.5.4..14.8.95..56.284.7845.962.4.872..5..5738.2..3.295..8. B2: 1 # 19 pairs B3: 3,7,1,2 # reduction candidate for 3,7 B3: 3,7 # 19 pairs * PAIR C2: 3,7 ROW 2 E2: 3,7,4,9 # reduction candidate for 3,7 E2: 3,7 # 19 pairs F2: 3,7,5 # reduction candidate for 3,7 F2: 3,7 => CTR * 54926..188...9.562..68.59.4..14.8.95..56.28..78.5.962...872..5..5.38.2..3.295..8. F2: 5 # 15 pairs * PAIR A3: 1,2 BLK 1 B3: 1,2,3,7 # reduction candidate for 1,2 B3: 1,2 => CTR * 54926..188...45962..6.9.5.4..14.8.95..56.284.7845.962.4.872..5..5738.2..3.295..8. B3: 3,7 # 19 pairs * PAIR F1: 3,7 BLK 2 E2: 3,7,4,9 # reduction candidate for 3,7 E2: 3,7 # 19 pairs F2: 3,7,5 # reduction candidate for 3,7 F2: 3,7 => CTR * 54926..188...9.562..68.59.4..14.8.95..56.28..78.5.962...872..5..5.38.2..3.295..8. F2: 5 # 15 pairs E3: 3,7,9 # reduction candidate for 3,7 E3: 3,7 => CTR * 54926..188..49.562..6..59.4..1..8.95..56.28..78.5.962...872..5..5.38.2..3.295..8. E3: 9 # 15 pairs F3: 3,7,5,8 # reduction candidate for 3,7 F3: 3,7 => CTR * 54926..188....5962..689.5.4..14.8.95..56.284.7845.962.4.872..5..5738.2..3.295..8. F3: 5,8 # 18 pairs * PAIR F1: 3,7 COL F F4: 3,7,2,8 # reduction candidate for 3,7 F4: 3,7 # 21 pairs F5: 3,7,2 # reduction candidate for 3,7 F5: 3,7 # 20 pairs * PAIR G1: 3,7 COL G G4: 3,7,4 # reduction candidate for 3,7 G4: 3,7 => CTR * 54926.7188.7....62..6....344618.2395..56..847783549621..872..53.5438.27937295..86 G4: 4 => SOLVED * 549263718813475962276198534621837495935642871784519623498721356157386249362954187 * PAIR H3: 3,7 ROW 3 B3: 3,7,1,2 # reduction candidate for 3,7 B3: 3,7 # 19 pairs E3: 3,7,9 # reduction candidate for 3,7 E3: 3,7 => CTR * 54926..188..49.562..6..59.4..1..8.95..56.28..78.5.962...872..5..5.38.2..3.295..8. E3: 9 # 15 pairs F3: 3,7,5,8 # reduction candidate for 3,7 F3: 3,7 => CTR * 54926..188....5962..689.5.4..14.8.95..56.284.7845.962.4.872..5..5738.2..3.295..8. F3: 5,8 # 18 pairs * PAIR H3: 3,7 COL H H5: 3,7,4 # reduction candidate for 3,7 H5: 3,7 => SOLVED * 549263718813475962276198534621837495935642871784519623498721356157386249362954187 H5: 4 => CTR * 5492637188.7..5962..6.975344618...95..56..84.78.5.962...872..5..5438.27.37295..86 * PAIR C6: 3,4 ROW 6 E6: 3,4,1 # reduction candidate for 3,4 E6: 1 => SOLVED * 549263718813475962276198534621837495935642871784519623498721356157386249362954187 E6: 3,4 # 18 pairs * PAIR I6: 1,3 BLK 6 I5: 1,3,7 # reduction candidate for 1,3 I5: 1,3 => SOLVED * 549263718813475962276198534621837495935642871784519623498721356157386249362954187 I5: 7 # 22 pairs * PAIR I6: 1,3 ROW 6 E6: 1,3,4 # reduction candidate for 1,3 E6: 1,3 => SOLVED * 549263718813475962276198534621837495935642871784519623498721356157386249362954187 E6: 4 => CTR * 54926.7188.74...62..61.8534..1....95..561.8..78.549621..872..5..5438.27.37295..86 * PAIR F8: 1,6 BLK 8 F7: 1,6,4 # reduction candidate for 1,6 F7: 1,6 # 19 pairs F9: 1,6,4 # reduction candidate for 1,6 F9: 1,6 => CTR * 549263718837....62..6....34..1...395..56..847783549621..8724153154386279372951486 F9: 4 # 19 pairs * PAIR F8: 1,6 ROW 8 A8: 1,6,9 # reduction candidate for 1,6 A8: 9 => CTR * 54926..188.3....62..6.....4.31...495.956..87.7845.962.418726359957381246362954187 A8: 1,6 # 18 pairs * PAIR H8: 4,7 BLK 9 G9: 4,7,1 # reduction candidate for 4,7 G9: 4,7 # 24 pairs G9: 1 # 20 pairs * PAIR H8: 4,7 COL H H5: 4,7,3 # reduction candidate for 4,7 H5: 3 => CTR * 5492673188..4...62..61.8574..187.495..5612837784539621..872..53.5.38.2493.2954786 H5: 4,7 # 24 pairs * PAIR I8: 6,9 BLK 9 I7: 6,9,3 # reduction candidate for 6,9 I7: 6,9 => SOLVED * 549263718813475962276198534621837495935642871784519623498721356157386249362954187 I7: 3 # 22 pairs * PAIR I8: 6,9 ROW 8 A8: 6,9,1 # reduction candidate for 6,9 A8: 1 # 22 pairs A8: 6,9 # 19 pairs * PAIR I9: 6,7 ROW 9 B9: 6,7,1 # reduction candidate for 6,7 B9: 1 => CTR * 549267318873145962126893574..14...95..56..8..78.5.962...872..5..5738.24.312954786 B9: 6,7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190323-absurd-base-pr-000.dot * REASONING * DIS # B2: 3,7 => CTR => B2: 1 * DIS # F2: 3,7 => CTR => F2: 5 * DIS # B3: 1,2 => CTR => B3: 3,7 * DIS # F2: 3,7 => CTR => F2: 5 * DIS # E3: 3,7 => CTR => E3: 9 * DIS # F3: 3,7 => CTR => F3: 5,8 * DIS # G4: 3,7 => CTR => G4: 4 * PRF # G4: 4 => SOL * DIS # E3: 3,7 => CTR => E3: 9 * DIS # F3: 3,7 => CTR => F3: 5,8 * PRF # H5: 3,7 => SOL * DIS # H5: 4 => CTR => H5: 3,7 * PRF # E6: 1 => SOL * PRF # I5: 1,3 => SOL * PRF # E6: 1,3 => SOL * DIS # E6: 4 => CTR => E6: 1,3 * DIS # F9: 1,6 => CTR => F9: 4 * DIS # A8: 9 => CTR => A8: 1,6 * DIS # H5: 3 => CTR => H5: 4,7 * PRF # I7: 6,9 => SOL * DIS # B9: 1 => CTR => B9: 6,7 * CNT 21 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C2,C6,C8,D2,D3,D4,F1,F8,G1,G2,G3,H3,H8,I6,I8,I9) * 54926..188......62..6.....4..1....95..56..8..78.5.962...872..5..5.38.2..3.295..8. * PAIR C2: 3,7 BLK 1 B2: 3,7,1 # reduction candidate for 3,7 B2: 3,7 => CTR * 54926..188..14.962..689.5.4..14.8.95..56.284.7845.962.4.872..5..5738.2..3.295..8. * RESTART * PAIR F1: 3,7 COL F F4: 3,7,2 # reduction candidate for 3,7 F4: 3,7 # 21 pairs F5: 3,7,2 # reduction candidate for 3,7 F5: 3,7 # 20 pairs * PAIR G1: 3,7 COL G G4: 3,7,4 # reduction candidate for 3,7 G4: 3,7 => CTR * 54926..1881.4.59622.61985.4..18...95..56..84.78.5.962...872..5..5438.27.37295..86 G4: 4 => SOLVED * 549263718813475962276198534621837495935642871784519623498721356157386249362954187 * DURATION: 0:00:05.427743 START: 04:45:48.166728 END: 04:45:53.594471 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190323-absurd-base-pr-001.dot * REASONING * DIS # B2: 3,7 => CTR => B2: 1 * DIS B2: 1 # G4: 3,7 => CTR => G4: 4 * PRF B2: 1 + G4: 4 => SOL * STA B2: 1 + G4: 4 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190323, absurd
Solution
position: 549263718813475962276198534621837495935642871784519623498721356157386249362954187 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 # B2: 3,7 => CTR => B2: 1 * INC # B2: 1 => UNS * INC # B3: 3,7 => UNS * INC # E2: 3,7 => UNS * DIS # F2: 3,7 => CTR => F2: 5 * INC # F2: 5 => UNS * DIS # B3: 1,2 => CTR => B3: 3,7 * INC # B3: 3,7 => UNS * INC # E2: 3,7 => UNS * DIS # F2: 3,7 => CTR => F2: 5 * INC # F2: 5 => UNS * DIS # E3: 3,7 => CTR => E3: 9 * INC # E3: 9 => UNS * DIS # F3: 3,7 => CTR => F3: 5,8 * INC # F3: 5,8 => UNS * INC # F4: 3,7 => UNS * INC # F5: 3,7 => UNS * DIS # G4: 3,7 => CTR => G4: 4 * PRF # G4: 4 => SOL * INC # B3: 3,7 => UNS * DIS # E3: 3,7 => CTR => E3: 9 * INC # E3: 9 => UNS * DIS # F3: 3,7 => CTR => F3: 5,8 * INC # F3: 5,8 => UNS * PRF # H5: 3,7 => SOL * DIS # H5: 4 => CTR => H5: 3,7 * INC # E6: 3,4 => UNS * PRF # E6: 1 => SOL * PRF # I5: 1,3 => SOL * INC # I5: 7 => UNS * PRF # E6: 1,3 => SOL * DIS # E6: 4 => CTR => E6: 1,3 * INC # F7: 1,6 => UNS * DIS # F9: 1,6 => CTR => F9: 4 * INC # F9: 4 => UNS * INC # A8: 1,6 => UNS * DIS # A8: 9 => CTR => A8: 1,6 * INC # G9: 4,7 => UNS * INC # G9: 1 => UNS * INC # H5: 4,7 => UNS * DIS # H5: 3 => CTR => H5: 4,7 * PRF # I7: 6,9 => SOL * INC # I7: 3 => UNS * INC # A8: 6,9 => UNS * INC # A8: 1 => UNS * INC # B9: 6,7 => UNS * DIS # B9: 1 => CTR => B9: 6,7 * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 3,7 => CTR => B2: 1 * INC B2: 1 # F4: 3,7 => UNS * INC B2: 1 # F5: 3,7 => UNS * DIS B2: 1 # G4: 3,7 => CTR => G4: 4 * PRF B2: 1 + G4: 4 => SOL * STA B2: 1 + G4: 4 * CNT 5 HDP CHAINS / 4 HYP OPENED