Analysis of zz-www.sudokuoftheday.co.uk-20060321-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: .4.....8.1...........2...7...27...39....938..5..8.276.729.5164......8.....1.4..9. initial
Autosolve
position: 24.1...8.1........9..2...7...276..39....938..593812764729351648...928..7..1647.9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 8 => CTR => E2: 3,7 * DIS # E2: 7 => CTR => E2: 3,8 * DIS # G2: 2,5 => CTR => G2: 3,4,9 * DIS # I2: 2,5 => CTR => I2: 3,6 * DIS # H5: 1 => CTR => H5: 2,5 * DIS # C5: 4,6 => CTR => C5: 7 * DIS # A8: 4,6 => CTR => A8: 3 * PRF # A8: 3 => SOL * DIS # I5: 1,5 => CTR => I5: 2 * DIS # G3: 1,5 => CTR => G3: 3,4 * PRF # G8: 1,5 => SOL * DIS # G8: 3 => CTR => G8: 1,5 * DIS # C8: 5,6 => CTR => C8: 4 * DIS # B2: 5,6 => CTR => B2: 3,7 * DIS # B3: 5,6 => CTR => B3: 3 * PRF # G8: 1,5 => SOL * DIS # G8: 3 => CTR => G8: 1,5 * DIS # H5: 2 => CTR => H5: 1,5 * CNT 18 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 8 => CTR => E2: 3,7 * DIS E2: 3,7 # G2: 2,5 => CTR => G2: 3,4,9 * DIS E2: 3,7 + G2: 3,4,9 # I2: 2,5 => CTR => I2: 3,6 * DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 # C5: 4,6 => CTR => C5: 7 * DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 # F2: 9 => CTR => F2: 4,5 * PRF E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 # G8: 1,5 => SOL * STA E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 + G8: 1,5 * CNT 6 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4.....8.1...........2...7...27...39....938..5..8.276.729.5164......8.....1.4..9. | initial |
| 24.1...8.1........9..2...7...276..39....938..593812764729351648...928..7..1647.9. | autosolve |
| 246179385178534926935286471482765139617493852593812764729351648364928517851647293 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) E1: 3,7 D2: 4,5 E3: 3,8 H2: 2,5 A4: 4,8 B4: 1,8 A5: 4,6 F4: 4,5 D5: 4,5 G4: 1,5 B8: 5,6 A9: 3,8 B9: 5,8 H8: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,I3: 1.. / G3 = 1 => 0 pairs (X) / I3 = 1 => 15 pairs (_) B4,B5: 1.. / B4 = 1 => 0 pairs (X) / B5 = 1 => 0 pairs (_) G8,H8: 1.. / G8 = 1 => 0 pairs (X) / H8 = 1 => 15 pairs (_) B4,G4: 1.. / B4 = 1 => 0 pairs (X) / G4 = 1 => 0 pairs (_) H5,H8: 1.. / H5 = 1 => 0 pairs (X) / H8 = 1 => 15 pairs (_) I3,I5: 1.. / I3 = 1 => 15 pairs (_) / I5 = 1 => 0 pairs (X) H5,I5: 2.. / H5 = 2 => 0 pairs (X) / I5 = 2 => 15 pairs (_) G9,I9: 2.. / G9 = 2 => 15 pairs (_) / I9 = 2 => 0 pairs (X) G2,G9: 2.. / G2 = 2 => 0 pairs (X) / G9 = 2 => 15 pairs (_) H2,H5: 2.. / H2 = 2 => 15 pairs (_) / H5 = 2 => 0 pairs (X) B2,B3: 3.. / B2 = 3 => 0 pairs (X) / B3 = 3 => 15 pairs (_) A8,A9: 3.. / A8 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) A8,G8: 3.. / A8 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) G2,G3: 4.. / G2 = 4 => 0 pairs (X) / G3 = 4 => 16 pairs (_) F4,D5: 4.. / F4 = 4 => 0 pairs (X) / D5 = 4 => 0 pairs (_) A8,C8: 4.. / A8 = 4 => 0 pairs (X) / C8 = 4 => 17 pairs (_) F3,G3: 4.. / F3 = 4 => 0 pairs (X) / G3 = 4 => 16 pairs (_) A4,F4: 4.. / A4 = 4 => 0 pairs (*) / F4 = 4 => 0 pairs (X) C5,C8: 4.. / C5 = 4 => 0 pairs (X) / C8 = 4 => 17 pairs (_) D2,D5: 4.. / D2 = 4 => 0 pairs (X) / D5 = 4 => 0 pairs (_) F4,D5: 5.. / F4 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) F4,G4: 5.. / F4 = 5 => 0 pairs (*) / G4 = 5 => 0 pairs (X) D2,D5: 5.. / D2 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) A5,A8: 6.. / A5 = 6 => 16 pairs (_) / A8 = 6 => 0 pairs (X) E1,E2: 7.. / E1 = 7 => 17 pairs (_) / E2 = 7 => 0 pairs (X) B5,C5: 7.. / B5 = 7 => 0 pairs (X) / C5 = 7 => 16 pairs (_) C1,E1: 7.. / C1 = 7 => 0 pairs (X) / E1 = 7 => 17 pairs (_) B2,B5: 7.. / B2 = 7 => 16 pairs (_) / B5 = 7 => 0 pairs (X) C2,C3: 8.. / C2 = 8 => 15 pairs (_) / C3 = 8 => 0 pairs (X) E2,E3: 8.. / E2 = 8 => 0 pairs (X) / E3 = 8 => 15 pairs (_) A4,B4: 8.. / A4 = 8 => 0 pairs (X) / B4 = 8 => 0 pairs (_) A9,B9: 8.. / A9 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) C2,E2: 8.. / C2 = 8 => 15 pairs (_) / E2 = 8 => 0 pairs (X) C3,E3: 8.. / C3 = 8 => 0 pairs (X) / E3 = 8 => 15 pairs (_) A4,A9: 8.. / A4 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) B4,B9: 8.. / B4 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) F1,F2: 9.. / F1 = 9 => 18 pairs (_) / F2 = 9 => 15 pairs (_) G1,G2: 9.. / G1 = 9 => 15 pairs (_) / G2 = 9 => 18 pairs (_) F1,G1: 9.. / F1 = 9 => 18 pairs (_) / G1 = 9 => 15 pairs (_) F2,G2: 9.. / F2 = 9 => 15 pairs (_) / G2 = 9 => 18 pairs (_) * DURATION: 0:00:43.333080 START: 20:14:47.792622 END: 20:15:31.125702 2019-04-30 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A9,B4,B8,B9,D2,D5,E1,E3,F4,G4,H2,H8) * 24.1...8.1........9..2...7...276..39....938..593812764729351648...928..7..1647.9. * PAIR E1: 3,7 BLK 2 E2: 3,7,8 # reduction candidate for 3,7 E2: 8 => CTR * 24.17..8313748..5.9.823.471812764539.7.5938..593812764729351648...928..7.81647.95 E2: 3,7 # 15 pairs * PAIR D2: 4,5 BLK 2 F2: 4,5,6,9 # reduction candidate for 4,5 F2: 4,5 # 21 pairs F3: 4,5,6 # reduction candidate for 4,5 F3: 4,5 # 17 pairs * PAIR D2: 4,5 ROW 2 G2: 4,5,2,3,9 # reduction candidate for 4,5 G2: 4,5 # 18 pairs G2: 2,3,9 # 16 pairs * PAIR E3: 3,8 BLK 2 E2: 3,8,7 # reduction candidate for 3,8 E2: 7 => CTR * 2471359861.8479.5.9..286471812764539.7.5938..593812764729351648...928..7.81647.95 E2: 3,8 # 17 pairs * PAIR H2: 2,5 BLK 3 G2: 2,5,3,4,9 # reduction candidate for 2,5 G2: 2,5 => CTR * 24.1..98.1....9...9..2..471..2764539...593812593812764729351648...928157..1647.9. G2: 3,4,9 # 15 pairs I2: 2,5,3,6 # reduction candidate for 2,5 I2: 2,5 => CTR * 24.1...8.1..4.....9..2..471..2764539...593812593812764729351648...928157.51647293 I2: 3,6 # 15 pairs * PAIR H2: 2,5 COL H H5: 2,5,1 # reduction candidate for 2,5 H5: 1 => CTR * 24.1...8.1......2.9..2...7...276..39....93812593812764729351648...928157.51647293 H5: 2,5 # 15 pairs * PAIR A5: 4,6 BLK 4 C5: 4,6,7 # reduction candidate for 4,6 C5: 4,6 => CTR * 24.1...8.1..4...5.9..2..471812764539.7.5938..593812764729351648...928..7.81647.95 C5: 7 # 16 pairs * PAIR A5: 4,6 COL A A8: 4,6,3 # reduction candidate for 4,6 A8: 4,6 => CTR * 24.1...8.1........9..2...7.812764539....938..593812764729351648...928317381647.9. A8: 3 => SOLVED * 246179385178534926935286471482765139617493852593812764729351648364928517851647293 * PAIR F4: 4,5 COL F F2: 4,5,6,9 # reduction candidate for 4,5 F2: 4,5 # 21 pairs F3: 4,5,6 # reduction candidate for 4,5 F3: 4,5 # 17 pairs * PAIR G4: 1,5 BLK 6 H5: 1,5,2 # reduction candidate for 1,5 H5: 1,5 # 15 pairs I5: 1,5,2 # reduction candidate for 1,5 I5: 1,5 => CTR * 24.1...8.1..4...529..2...7...276..39...593821593812764729351648...928.17..1647.95 I5: 2 # 15 pairs * PAIR G4: 1,5 COL G G3: 1,5,3,4 # reduction candidate for 1,5 G3: 1,5 => CTR * 24.1...8.1.....4..9..2.4.7.4827651396174938..5938127647293516483.49285.7..1647.9. G3: 3,4 # 16 pairs G8: 1,5,3 # reduction candidate for 1,5 G8: 1,5 => SOLVED * 246179385178534926935286471482765139617493852593812764729351648364928517851647293 G8: 3 => CTR * 24.1...8.1........9..2...7.812764539....938..593812764729351648...928317381647.9. * PAIR B8: 5,6 BLK 7 C8: 5,6,4 # reduction candidate for 5,6 C8: 5,6 => CTR * 24.1...8.1..4...5.9..2..4718.276..39..45938..5938127647293516484..928317381647.9. C8: 4 # 17 pairs * PAIR B8: 5,6 COL B B2: 5,6,3,7 # reduction candidate for 5,6 B2: 5,6 => CTR * 2471359861.8479.53935286471812764539.7.5938..593812764729351648...928..7.81647.95 B2: 3,7 # 15 pairs B3: 5,6,3 # reduction candidate for 5,6 B3: 5,6 => CTR * 24.1...8.13.4...5.9..2..471812764539.7.5938..593812764729351648...928..7.81647.95 B3: 3 # 15 pairs * PAIR H8: 1,5 BLK 9 G8: 1,5,3 # reduction candidate for 1,5 G8: 1,5 => SOLVED * 246179385178534926935286471482765139617493852593812764729351648364928517851647293 G8: 3 => CTR * 24.1...8.1........9..2...7.812764539....938..593812764729351648...928317381647.9. * PAIR H8: 1,5 COL H H5: 1,5,2 # reduction candidate for 1,5 H5: 2 => CTR * 24.1...8.1..4...529..2...7...276..39...593821593812764729351648...928.17..1647.95 H5: 1,5 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060321-absurd-base-pr-000.dot * REASONING * DIS # E2: 8 => CTR => E2: 3,7 * DIS # E2: 7 => CTR => E2: 3,8 * DIS # G2: 2,5 => CTR => G2: 3,4,9 * DIS # I2: 2,5 => CTR => I2: 3,6 * DIS # H5: 1 => CTR => H5: 2,5 * DIS # C5: 4,6 => CTR => C5: 7 * DIS # A8: 4,6 => CTR => A8: 3 * PRF # A8: 3 => SOL * DIS # I5: 1,5 => CTR => I5: 2 * DIS # G3: 1,5 => CTR => G3: 3,4 * PRF # G8: 1,5 => SOL * DIS # G8: 3 => CTR => G8: 1,5 * DIS # C8: 5,6 => CTR => C8: 4 * DIS # B2: 5,6 => CTR => B2: 3,7 * DIS # B3: 5,6 => CTR => B3: 3 * PRF # G8: 1,5 => SOL * DIS # G8: 3 => CTR => G8: 1,5 * DIS # H5: 2 => CTR => H5: 1,5 * CNT 18 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A9,B4,B8,B9,D2,D5,E1,E3,F4,G4,H2,H8) * 24.1...8.1........9..2...7...276..39....938..593812764729351648...928..7..1647.9. * PAIR E1: 3,7 BLK 2 E2: 3,7,8 # reduction candidate for 3,7 E2: 8 => CTR * 24.17..8313748..5.9.823.471812764539.7.5938..593812764729351648...928..7.81647.95 * PAIR D2: 4,5 BLK 2 F2: 4,5,6,9 # reduction candidate for 4,5 F2: 4,5 # 21 pairs F3: 4,5,6 # reduction candidate for 4,5 F3: 4,5 # 18 pairs * PAIR D2: 4,5 ROW 2 G2: 4,5,2,3,9 # reduction candidate for 4,5 G2: 4,5 # 19 pairs G2: 2,3,9 # 17 pairs * PAIR H2: 2,5 BLK 3 G2: 2,5,3,4,9 # reduction candidate for 2,5 G2: 2,5 => CTR * 24.1..98.1.8..9...9..28.471..2764539...593812593812764729351648...928157..1647.9. I2: 2,5,3,6 # reduction candidate for 2,5 I2: 2,5 => CTR * 24.1...8.1.84.....9..28.471..2764539...5938125938127647293516483.49281578.164729. * PAIR A5: 4,6 BLK 4 C5: 4,6,7 # reduction candidate for 4,6 C5: 4,6 => CTR * 24713..8.1.8.7..2.9..28..71..276..39.7..93812593812764729351648...928157.51647293 * PAIR F4: 4,5 COL F F2: 4,5,9 # reduction candidate for 4,5 F2: 9 => CTR * 24.17..8.17853942693.2845714827651396174938525938127647293516483.4928..7..164729. * PAIR RESTART * PAIR G4: 1,5 COL G G8: 1,5,3 # reduction candidate for 1,5 G8: 1,5 => SOLVED * 246179385178534926935286471482765139617493852593812764729351648364928517851647293 * DURATION: 0:00:10.033224 START: 20:15:53.758990 END: 20:16:03.792214 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060321-absurd-base-pr-001.dot * REASONING * DIS # E2: 8 => CTR => E2: 3,7 * DIS E2: 3,7 # G2: 2,5 => CTR => G2: 3,4,9 * DIS E2: 3,7 + G2: 3,4,9 # I2: 2,5 => CTR => I2: 3,6 * DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 # C5: 4,6 => CTR => C5: 7 * DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 # F2: 9 => CTR => F2: 4,5 * PRF E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 # G8: 1,5 => SOL * STA E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 + G8: 1,5 * CNT 6 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060321, absurd
Solution
position: 246179385178534926935286471482765139617493852593812764729351648364928517851647293 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 # E2: 3,7 => UNS * DIS # E2: 8 => CTR => E2: 3,7 * INC # F2: 4,5 => UNS * INC # F3: 4,5 => UNS * INC # G2: 4,5 => UNS * INC # G2: 2,3,9 => UNS * INC # E2: 3,8 => UNS * DIS # E2: 7 => CTR => E2: 3,8 * DIS # G2: 2,5 => CTR => G2: 3,4,9 * INC # G2: 3,4,9 => UNS * DIS # I2: 2,5 => CTR => I2: 3,6 * INC # I2: 3,6 => UNS * INC # H5: 2,5 => UNS * DIS # H5: 1 => CTR => H5: 2,5 * DIS # C5: 4,6 => CTR => C5: 7 * INC # C5: 7 => UNS * DIS # A8: 4,6 => CTR => A8: 3 * PRF # A8: 3 => SOL * INC # F2: 4,5 => UNS * INC # F3: 4,5 => UNS * INC # H5: 1,5 => UNS * DIS # I5: 1,5 => CTR => I5: 2 * INC # I5: 2 => UNS * DIS # G3: 1,5 => CTR => G3: 3,4 * INC # G3: 3,4 => UNS * PRF # G8: 1,5 => SOL * DIS # G8: 3 => CTR => G8: 1,5 * DIS # C8: 5,6 => CTR => C8: 4 * INC # C8: 4 => UNS * DIS # B2: 5,6 => CTR => B2: 3,7 * INC # B2: 3,7 => UNS * DIS # B3: 5,6 => CTR => B3: 3 * INC # B3: 3 => UNS * PRF # G8: 1,5 => SOL * DIS # G8: 3 => CTR => G8: 1,5 * INC # H5: 1,5 => UNS * DIS # H5: 2 => CTR => H5: 1,5 * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 3,7 => UNS * DIS # E2: 8 => CTR => E2: 3,7 * INC E2: 3,7 # F2: 4,5 => UNS * INC E2: 3,7 # F3: 4,5 => UNS * INC E2: 3,7 # G2: 4,5 => UNS * INC E2: 3,7 # G2: 2,3,9 => UNS * DIS E2: 3,7 # G2: 2,5 => CTR => G2: 3,4,9 * DIS E2: 3,7 + G2: 3,4,9 # I2: 2,5 => CTR => I2: 3,6 * DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 # C5: 4,6 => CTR => C5: 7 * INC E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 # F2: 4,5 => UNS * DIS E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 # F2: 9 => CTR => F2: 4,5 * PRF E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 # G8: 1,5 => SOL * STA E2: 3,7 + G2: 3,4,9 + I2: 3,6 + C5: 7 + F2: 4,5 + G8: 1,5 * CNT 12 HDP CHAINS / 12 HYP OPENED