Analysis of zz-www.sudokuoftheday.co.uk-20060418-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: .....1...9..4.31.7....9.24..41.........3.8...3.9....5....6....38......2..5..8479. initial
Autosolve
position: .....1...9..4.31.713..9.24..41.........3.8...389....5....6....38...3..2..53.8479. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 2,6 => CTR => A1: 4,5,7 * DIS # C2: 2,6 => CTR => C2: 5,8 * DIS # E2: 2,6 => CTR => E2: 5 * DIS # H1: 6,8 => CTR => H1: 3 * DIS # I1: 6,8 => CTR => I1: 5,9 * DIS # I3: 6,8 => CTR => I3: 5 * DIS # C2: 2,5 => CTR => C2: 6,8 * DIS # H4: 6,8 => CTR => H4: 3,7 * DIS # G5: 4,6 => CTR => G5: 9 * DIS # A1: 2,6 => CTR => A1: 4,5,7 * PRF # I8: 1,6 => SOL * CNT 11 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 2,6 => CTR => A1: 4,5,7 * DIS A1: 4,5,7 # C2: 2,6 => CTR => C2: 5,8 * DIS A1: 4,5,7 + C2: 5,8 # E2: 2,6 => CTR => E2: 5 * DIS A1: 4,5,7 + C2: 5,8 + E2: 5 # G5: 4,6 => CTR => G5: 9 * PRF A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 # G8: 5 => SOL * STA A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 + G8: 5 * CNT 5 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....1...9..4.31.7....9.24..41.........3.8...3.9....5....6....38......2..5..8479. | initial |
| .....1...9..4.31.713..9.24..41.........3.8...389....5....6....38...3..2..53.8479. | autosolve |
| 465721839928453167137896245241569378576348912389172654792615483814937526653284791 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B2: 2,6 H2: 6,8 G6: 4,6 B7: 1,9 B8: 1,9 A9: 2,6 D9: 1,2 H7: 1,8 I9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B7,B8: 1.. / B7 = 1 => 0 pairs (X) / B8 = 1 => 7 pairs (_) D9,I9: 1.. / D9 = 1 => 0 pairs (X) / I9 = 1 => 0 pairs (_) H5,H7: 1.. / H5 = 1 => 21 pairs (_) / H7 = 1 => 0 pairs (X) A9,D9: 2.. / A9 = 2 => 0 pairs (X) / D9 = 2 => 0 pairs (_) G1,H1: 3.. / G1 = 3 => 0 pairs (X) / H1 = 3 => 9 pairs (_) G4,H4: 3.. / G4 = 3 => 9 pairs (_) / H4 = 3 => 0 pairs (X) G1,G4: 3.. / G1 = 3 => 0 pairs (X) / G4 = 3 => 9 pairs (_) H1,H4: 3.. / H1 = 3 => 9 pairs (_) / H4 = 3 => 0 pairs (X) A1,C1: 4.. / A1 = 4 => 10 pairs (_) / C1 = 4 => 14 pairs (_) E5,E6: 4.. / E5 = 4 => 10 pairs (_) / E6 = 4 => 17 pairs (_) A1,A7: 4.. / A1 = 4 => 10 pairs (_) / A7 = 4 => 14 pairs (_) C2,E2: 5.. / C2 = 5 => 0 pairs (X) / E2 = 5 => 16 pairs (_) C8,A9: 6.. / C8 = 6 => 0 pairs (X) / A9 = 6 => 0 pairs (_) A9,I9: 6.. / A9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) H4,H5: 7.. / H4 = 7 => 11 pairs (_) / H5 = 7 => 0 pairs (X) A4,H4: 7.. / A4 = 7 => 0 pairs (X) / H4 = 7 => 11 pairs (_) B1,B5: 7.. / B1 = 7 => 12 pairs (_) / B5 = 7 => 16 pairs (_) D1,D3: 8.. / D1 = 8 => 12 pairs (_) / D3 = 8 => 10 pairs (_) G7,H7: 8.. / G7 = 8 => 0 pairs (X) / H7 = 8 => 21 pairs (_) C2,H2: 8.. / C2 = 8 => 18 pairs (_) / H2 = 8 => 0 pairs (X) G1,I1: 9.. / G1 = 9 => 0 pairs (X) / I1 = 9 => 9 pairs (_) D4,F4: 9.. / D4 = 9 => 9 pairs (_) / F4 = 9 => 9 pairs (_) G5,I5: 9.. / G5 = 9 => 9 pairs (_) / I5 = 9 => 0 pairs (X) B7,B8: 9.. / B7 = 9 => 7 pairs (_) / B8 = 9 => 0 pairs (X) B7,F7: 9.. / B7 = 9 => 7 pairs (_) / F7 = 9 => 0 pairs (X) D4,D8: 9.. / D4 = 9 => 9 pairs (_) / D8 = 9 => 9 pairs (_) G1,G5: 9.. / G1 = 9 => 0 pairs (X) / G5 = 9 => 9 pairs (_) I1,I5: 9.. / I1 = 9 => 9 pairs (_) / I5 = 9 => 0 pairs (X) * DURATION: 0:00:29.896342 START: 22:28:50.113470 END: 22:29:20.009812 2019-04-30 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B2,B7,B8,D9,G6,H2,H7,I9) * .....1...9..4.31.713..9.24..41.........3.8...389....5....6....38...3..2..53.8479. * PAIR B2: 2,6 BLK 1 A1: 2,6,4,5,7 # reduction candidate for 2,6 A1: 2,6 => CTR * 674..1...92.4.316713..9624.741.6....5623.8.7.389...65.4976...1381..3..2..53184796 A1: 4,5,7 # 9 pairs B1: 2,6,7 # reduction candidate for 2,6 B1: 2,6 # 16 pairs C1: 2,6,4,5,7,8 # reduction candidate for 2,6 C1: 2,6 # 16 pairs C2: 2,6,5,8 # reduction candidate for 2,6 C2: 2,6 => CTR * .....1..996245318713..96245.415.9..8.2.3.89.1389.12.5..9.6.5813816.3.524253184796 C2: 5,8 # 10 pairs * PAIR B2: 2,6 ROW 2 E2: 2,6,5 # reduction candidate for 2,6 E2: 2,6 => CTR * .....1..996542318713..96245.41.....8...3489.1389...45..9.6..813816.3.524253184796 E2: 5 # 16 pairs * PAIR B2: 2,6 COL B B5: 2,6,7 # reduction candidate for 2,6 B5: 7 # 16 pairs B5: 2,6 # 12 pairs * PAIR H2: 6,8 BLK 3 G1: 6,8,3,5,9 # reduction candidate for 6,8 G1: 6,8 # 13 pairs H1: 6,8,3 # reduction candidate for 6,8 H1: 6,8 => CTR * .7...13.99..4.31.713..9.245741...638...348971389.16452.9.67.81381..3.524.53184796 H1: 3 # 9 pairs I1: 6,8,5,9 # reduction candidate for 6,8 I1: 6,8 => CTR * .7...19389.845316713.89.245.415.9382...318479389.4.651.9.6.5813816937524253184796 I1: 5,9 # 10 pairs I3: 6,8,5 # reduction candidate for 6,8 I3: 6,8 => CTR * .7.8.1.3.928453167135796248741.6.3825623.8.7.3892.7.5..9.6..813816.3..2.253184796 I3: 5 # 11 pairs * PAIR H2: 6,8 ROW 2 C2: 6,8,2,5 # reduction candidate for 6,8 C2: 2,5 => CTR * .....1..996.4.318713..96245.41.....8...3489.1389...45..9.6..813816.3.524253184796 C2: 6,8 # 17 pairs * PAIR H2: 6,8 COL H H4: 6,8,3,7 # reduction candidate for 6,8 H4: 6,8 => CTR * .74..1.3.9..4.31.713.79624.741...3.....3.8.7.38927..5.4976..813816.3..2.253184796 H4: 3,7 # 10 pairs * PAIR G6: 4,6 BLK 6 G5: 4,6,9 # reduction candidate for 4,6 G5: 4,6 => CTR * .7...193.928453167135.96248741569382562318479389.4.65149762.813816.3.524253184796 G5: 9 # 9 pairs I5: 4,6,1,2,9 # reduction candidate for 4,6 I5: 4,6 # 15 pairs I6: 4,6,1,2 # reduction candidate for 4,6 I6: 4,6 # 19 pairs * PAIR G6: 4,6 ROW 6 E6: 4,6,1,2,7 # reduction candidate for 4,6 E6: 4,6 # 12 pairs E6: 1,2,7 # 10 pairs * PAIR G6: 4,6 COL G G8: 4,6,5 # reduction candidate for 4,6 G8: 5 # 15 pairs G8: 4,6 # 13 pairs * PAIR B8: 1,9 ROW 8 D8: 1,9,5,7 # reduction candidate for 1,9 D8: 1,9 # 11 pairs D8: 5,7 # 10 pairs * PAIR A9: 2,6 COL A A1: 2,6,4,5,7 # reduction candidate for 2,6 A1: 2,6 => CTR * 674..1...92.4.316713..9624.741.6....5623.8.7.389...65.4976...1381..3..2..53184796 A1: 4,5,7 # 9 pairs A4: 2,6,5,7 # reduction candidate for 2,6 A4: 2,6 # 14 pairs A5: 2,6,5,7 # reduction candidate for 2,6 A5: 2,6 # 14 pairs * PAIR D9: 1,2 BLK 8 E7: 1,2,5,7 # reduction candidate for 1,2 E7: 5,7 # 13 pairs E7: 1,2 # 13 pairs * PAIR D9: 1,2 COL D D6: 1,2,7 # reduction candidate for 1,2 D6: 7 # 13 pairs D6: 1,2 # 12 pairs * PAIR I9: 1,6 BLK 9 I8: 1,6,4,5 # reduction candidate for 1,6 I8: 1,6 => SOLVED * 465721839928453167137896245241569378576348912389172654792615483814937526653284791 I8: 4,5 # 10 pairs * PAIR I9: 1,6 COL I I5: 1,6,2,4,9 # reduction candidate for 1,6 I5: 1,6 # 15 pairs I6: 1,6,2,4 # reduction candidate for 1,6 I6: 1,6 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060418-absurd-base-pr-000.dot * REASONING * DIS # A1: 2,6 => CTR => A1: 4,5,7 * DIS # C2: 2,6 => CTR => C2: 5,8 * DIS # E2: 2,6 => CTR => E2: 5 * DIS # H1: 6,8 => CTR => H1: 3 * DIS # I1: 6,8 => CTR => I1: 5,9 * DIS # I3: 6,8 => CTR => I3: 5 * DIS # C2: 2,5 => CTR => C2: 6,8 * DIS # H4: 6,8 => CTR => H4: 3,7 * DIS # G5: 4,6 => CTR => G5: 9 * DIS # A1: 2,6 => CTR => A1: 4,5,7 * PRF # I8: 1,6 => SOL * CNT 11 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B2,B7,B8,D9,G6,H2,H7,I9) * .....1...9..4.31.713..9.24..41.........3.8...389....5....6....38...3..2..53.8479. * PAIR B2: 2,6 BLK 1 A1: 2,6,4,5,7 # reduction candidate for 2,6 A1: 2,6 => CTR * 674..1...92.4.316713..9624.741.6....5623.8.7.389...65.4976...1381..3..2..53184796 B1: 2,6,7 # reduction candidate for 2,6 B1: 2,6 # 16 pairs C1: 2,6,4,5,7,8 # reduction candidate for 2,6 C1: 2,6 # 16 pairs C2: 2,6,5,8 # reduction candidate for 2,6 C2: 2,6 => CTR * .....1..996245318713..96245.415.9..8.2.3.89.1389.12.5..9.6.5813816.3.524253184796 * PAIR B2: 2,6 ROW 2 E2: 2,6,5 # reduction candidate for 2,6 E2: 2,6 => CTR * .....1..996542318713..96245.41.....8...3489.1389...45..9.6..813816.3.524253184796 * PAIR RESTART * PAIR G6: 4,6 BLK 6 G5: 4,6,9 # reduction candidate for 4,6 G5: 4,6 => CTR * .....193.92845316713..9.24..415.9382...318479389.4.651.9.6.5813816937524253184796 I5: 4,6,1,2 # reduction candidate for 4,6 I5: 4,6 # 22 pairs I6: 4,6,1,2 # reduction candidate for 4,6 I6: 4,6 # 24 pairs * PAIR G6: 4,6 ROW 6 E6: 4,6,1,2,7 # reduction candidate for 4,6 E6: 4,6 # 22 pairs E6: 1,2,7 # 18 pairs * PAIR G6: 4,6 COL G G8: 4,6,5 # reduction candidate for 4,6 G8: 5 => SOLVED * 465721839928453167137896245241569378576348912389172654792615483814937526653284791 * DURATION: 0:00:09.777348 START: 22:29:43.550257 END: 22:29:53.327605 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060418-absurd-base-pr-001.dot * REASONING * DIS # A1: 2,6 => CTR => A1: 4,5,7 * DIS A1: 4,5,7 # C2: 2,6 => CTR => C2: 5,8 * DIS A1: 4,5,7 + C2: 5,8 # E2: 2,6 => CTR => E2: 5 * DIS A1: 4,5,7 + C2: 5,8 + E2: 5 # G5: 4,6 => CTR => G5: 9 * PRF A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 # G8: 5 => SOL * STA A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 + G8: 5 * CNT 5 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060418, absurd
Solution
position: 465721839928453167137896245241569378576348912389172654792615483814937526653284791 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 # A1: 2,6 => CTR => A1: 4,5,7 * INC # A1: 4,5,7 => UNS * INC # B1: 2,6 => UNS * INC # C1: 2,6 => UNS * DIS # C2: 2,6 => CTR => C2: 5,8 * INC # C2: 5,8 => UNS * DIS # E2: 2,6 => CTR => E2: 5 * INC # E2: 5 => UNS * INC # B5: 2,6 => UNS * INC # B5: 7 => UNS * INC # G1: 6,8 => UNS * DIS # H1: 6,8 => CTR => H1: 3 * INC # H1: 3 => UNS * DIS # I1: 6,8 => CTR => I1: 5,9 * INC # I1: 5,9 => UNS * DIS # I3: 6,8 => CTR => I3: 5 * INC # I3: 5 => UNS * INC # C2: 6,8 => UNS * DIS # C2: 2,5 => CTR => C2: 6,8 * DIS # H4: 6,8 => CTR => H4: 3,7 * INC # H4: 3,7 => UNS * DIS # G5: 4,6 => CTR => G5: 9 * INC # G5: 9 => UNS * INC # I5: 4,6 => UNS * INC # I6: 4,6 => UNS * INC # E6: 4,6 => UNS * INC # E6: 1,2,7 => UNS * INC # G8: 4,6 => UNS * INC # G8: 5 => UNS * INC # D8: 1,9 => UNS * INC # D8: 5,7 => UNS * DIS # A1: 2,6 => CTR => A1: 4,5,7 * INC # A1: 4,5,7 => UNS * INC # A4: 2,6 => UNS * INC # A5: 2,6 => UNS * INC # E7: 1,2 => UNS * INC # E7: 5,7 => UNS * INC # D6: 1,2 => UNS * INC # D6: 7 => UNS * PRF # I8: 1,6 => SOL * INC # I8: 4,5 => UNS * INC # I5: 1,6 => UNS * INC # I6: 1,6 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 2,6 => CTR => A1: 4,5,7 * INC A1: 4,5,7 # B1: 2,6 => UNS * INC A1: 4,5,7 # C1: 2,6 => UNS * DIS A1: 4,5,7 # C2: 2,6 => CTR => C2: 5,8 * DIS A1: 4,5,7 + C2: 5,8 # E2: 2,6 => CTR => E2: 5 * DIS A1: 4,5,7 + C2: 5,8 + E2: 5 # G5: 4,6 => CTR => G5: 9 * INC A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 # I5: 4,6 => UNS * INC A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 # I6: 4,6 => UNS * INC A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 # E6: 4,6 => UNS * INC A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 # E6: 1,2,7 => UNS * INC A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 # G8: 4,6 => UNS * PRF A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 # G8: 5 => SOL * STA A1: 4,5,7 + C2: 5,8 + E2: 5 + G5: 9 + G8: 5 * CNT 12 HDP CHAINS / 12 HYP OPENED