Analysis of zz-www.sudokuoftheday.co.uk-20060831-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: 61...8.....5.7.8.....43..51.4.......5.91.738.7.13..46.......7.69.6......1..82.... initial
Autosolve
position: 61...8.....56718.....43.651.4..6....56914738272138.46.......7.69.67....81..826... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 2 => CTR => A2: 3,4 * PRF # C7: 3,4 => SOL * DIS # H2: 3,9 => CTR => H2: 2,4 * PRF # C3: 2,8 => SOL * PRF # A7: 2,8 => SOL * DIS # D1: 5,9 => CTR => D1: 2 * DIS # E7: 1 => CTR => E7: 5,9 * DIS # D1: 5 => CTR => D1: 2,9 * DIS # F4: 5 => CTR => F4: 2,9 * DIS # H2: 3,4 => CTR => H2: 2,9 * DIS # D1: 5 => CTR => D1: 2,9 * DIS # A7: 3,8 => CTR => A7: 2,4 * DIS # C7: 3,8 => CTR => C7: 2,4 * DIS # F4: 5 => CTR => F4: 2,9 * DIS # D1: 5 => CTR => D1: 2,9 * DIS # F4: 5,9 => CTR => F4: 2 * DIS # G4: 5,9 => CTR => G4: 1 * DIS # B7: 3,5 => CTR => B7: 8 * PRF # B9: 3,5 => SOL * DIS # E7: 1 => CTR => E7: 5,9 * DIS # D1: 5,9 => CTR => D1: 2 * PRF # C7: 3,4 => SOL * DIS # H7: 3,4 => CTR => H7: 1 * DIS # E7: 1,5 => CTR => E7: 9 * DIS # G8: 1,5 => CTR => G8: 2 * DIS # H8: 1,2 => CTR => H8: 3,4 * DIS # G4: 5,9 => CTR => G4: 1 * CNT 27 HDP CHAINS / 64 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 2 => CTR => A2: 3,4 * PRF A2: 3,4 # C3: 2,8 => SOL * STA A2: 3,4 + C3: 2,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 61...8.....5.7.8.....43..51.4.......5.91.738.7.13..46.......7.69.6......1..82.... | initial |
| 61...8.....56718.....43.651.4..6....56914738272138.46.......7.69.67....81..826... | autosolve |
| 613258947495671823872439651348962175569147382721385469284593716956714238137826594 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 3,4 B2: 3,9 A3: 2,8 E1: 5,9 F3: 2,9 G1: 2,9 A4: 3,8 C4: 3,8 D4: 2,9 F6: 5,9 I6: 5,9 B8: 3,5 D7: 5,9 F7: 3,4 E8: 1,5 F8: 3,4 G9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,H4: 1.. / G4 = 1 => 19 pairs (_) / H4 = 1 => 0 pairs (X) E7,E8: 1.. / E7 = 1 => 0 pairs (X) / E8 = 1 => 20 pairs (_) E7,H7: 1.. / E7 = 1 => 0 pairs (X) / H7 = 1 => 20 pairs (_) G4,G8: 1.. / G4 = 1 => 19 pairs (_) / G8 = 1 => 0 pairs (X) D1,F3: 2.. / D1 = 2 => 15 pairs (_) / F3 = 2 => 0 pairs (X) G1,H2: 2.. / G1 = 2 => 0 pairs (X) / H2 = 2 => 15 pairs (_) D4,F4: 2.. / D4 = 2 => 0 pairs (X) / F4 = 2 => 15 pairs (_) A7,C7: 2.. / A7 = 2 => 0 pairs (*) / C7 = 2 => 0 pairs (X) G8,H8: 2.. / G8 = 2 => 15 pairs (_) / H8 = 2 => 0 pairs (X) D1,G1: 2.. / D1 = 2 => 15 pairs (_) / G1 = 2 => 0 pairs (X) A2,H2: 2.. / A2 = 2 => 0 pairs (X) / H2 = 2 => 15 pairs (_) C3,C7: 2.. / C3 = 2 => 0 pairs (*) / C7 = 2 => 0 pairs (X) D1,D4: 2.. / D1 = 2 => 15 pairs (_) / D4 = 2 => 0 pairs (X) F3,F4: 2.. / F3 = 2 => 0 pairs (X) / F4 = 2 => 15 pairs (_) G1,G8: 2.. / G1 = 2 => 0 pairs (X) / G8 = 2 => 15 pairs (_) H2,H8: 2.. / H2 = 2 => 15 pairs (_) / H8 = 2 => 0 pairs (X) A4,C4: 3.. / A4 = 3 => 17 pairs (_) / C4 = 3 => 0 pairs (X) F7,F8: 3.. / F7 = 3 => 17 pairs (_) / F8 = 3 => 0 pairs (X) C1,A2: 4.. / C1 = 4 => 24 pairs (_) / A2 = 4 => 0 pairs (*) F7,F8: 4.. / F7 = 4 => 0 pairs (X) / F8 = 4 => 17 pairs (_) F8,H8: 4.. / F8 = 4 => 17 pairs (_) / H8 = 4 => 0 pairs (X) A2,A7: 4.. / A2 = 4 => 0 pairs (*) / A7 = 4 => 0 pairs (X) D1,E1: 5.. / D1 = 5 => 0 pairs (X) / E1 = 5 => 18 pairs (_) F4,F6: 5.. / F4 = 5 => 0 pairs (X) / F6 = 5 => 21 pairs (_) F6,I6: 5.. / F6 = 5 => 21 pairs (_) / I6 = 5 => 0 pairs (X) D1,D7: 5.. / D1 = 5 => 0 pairs (X) / D7 = 5 => 18 pairs (_) B3,C3: 7.. / B3 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) H1,I1: 7.. / H1 = 7 => 19 pairs (_) / I1 = 7 => 23 pairs (_) H4,I4: 7.. / H4 = 7 => 23 pairs (_) / I4 = 7 => 19 pairs (_) B9,C9: 7.. / B9 = 7 => 20 pairs (_) / C9 = 7 => 0 pairs (*) B3,B9: 7.. / B3 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) C3,C9: 7.. / C3 = 7 => 20 pairs (_) / C9 = 7 => 0 pairs (*) H1,H4: 7.. / H1 = 7 => 19 pairs (_) / H4 = 7 => 23 pairs (_) I1,I4: 7.. / I1 = 7 => 23 pairs (_) / I4 = 7 => 19 pairs (_) A4,C4: 8.. / A4 = 8 => 0 pairs (X) / C4 = 8 => 17 pairs (_) B3,B7: 8.. / B3 = 8 => 0 pairs (X) / B7 = 8 => 20 pairs (_) B2,B3: 9.. / B2 = 9 => 15 pairs (_) / B3 = 9 => 0 pairs (X) D7,E7: 9.. / D7 = 9 => 0 pairs (X) / E7 = 9 => 18 pairs (_) B3,F3: 9.. / B3 = 9 => 0 pairs (X) / F3 = 9 => 15 pairs (_) F6,I6: 9.. / F6 = 9 => 0 pairs (X) / I6 = 9 => 21 pairs (_) E1,E7: 9.. / E1 = 9 => 0 pairs (X) / E7 = 9 => 18 pairs (_) * DURATION: 0:00:52.041561 START: 02:14:45.523398 END: 02:15:37.564959 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B2,B8,C1,C4,D4,D7,E1,E8,F3,F6,F7,F8,G1,G9,I6) * 61...8.....56718.....43.651.4..6....56914738272138.46.......7.69.67....81..826... * PAIR C1: 3,4 BLK 1 A2: 3,4,2 # reduction candidate for 3,4 A2: 2 => CTR * 614..8...2356718..89743265134826....56914738272138.46.482..37169.67....81..826... A2: 3,4 # 15 pairs * PAIR C1: 3,4 ROW 1 H1: 3,4,7 # reduction candidate for 3,4 H1: 3,4 # 23 pairs I1: 3,4,7 # reduction candidate for 3,4 I1: 3,4 # 19 pairs * PAIR C1: 3,4 COL C C7: 3,4,2,8 # reduction candidate for 3,4 C7: 3,4 => SOLVED * 613258947495671823872439651348962175569147382721385469284593716956714238137826594 C7: 2,8 # 18 pairs C9: 3,4,7 # reduction candidate for 3,4 C9: 3,4 # 20 pairs * PAIR B2: 3,9 ROW 2 H2: 3,9,2,4 # reduction candidate for 3,9 H2: 3,9 => CTR * 61...82..2.56718.48.743265134826....56914738272138.46.482..37169.67145281..826... H2: 2,4 # 18 pairs I2: 3,9,4 # reduction candidate for 3,9 I2: 3,9 # 20 pairs * PAIR A3: 2,8 BLK 1 C3: 2,8,7 # reduction candidate for 2,8 C3: 2,8 => SOLVED * 613258947495671823872439651348962175569147382721385469284593716956714238137826594 C3: 7 # 20 pairs * PAIR A3: 2,8 COL A A7: 2,8,3,4 # reduction candidate for 2,8 A7: 2,8 => SOLVED * 613258947495671823872439651348962175569147382721385469284593716956714238137826594 A7: 3,4 # 22 pairs * PAIR E1: 5,9 BLK 2 D1: 5,9,2 # reduction candidate for 5,9 D1: 5,9 => CTR * 61...82..2.56718..8.743265134826....56914738272138.46.482..37169.67145281..826... D1: 2 # 15 pairs * PAIR E1: 5,9 COL E E7: 5,9,1 # reduction candidate for 5,9 E7: 1 => CTR * 61..982..2.56718..89743265134826....56914738272138.46.482...7.69.67....81..826... E7: 5,9 # 20 pairs * PAIR F3: 2,9 BLK 2 D1: 2,9,5 # reduction candidate for 2,9 D1: 5 => CTR * 61.5982..2.56718..89743265134826....56914738272138.46.4829537169.67145281..826... D1: 2,9 # 18 pairs * PAIR F3: 2,9 COL F F4: 2,9,5 # reduction candidate for 2,9 F4: 5 => CTR * 61...82..2.56718..897432651348265...569147382721389465482..37169.67145281..826... F4: 2,9 # 21 pairs * PAIR G1: 2,9 BLK 3 H2: 2,9,3,4 # reduction candidate for 2,9 H2: 3,4 => CTR * 61...82..2.56718.989743265134826....569147382721389465482..37169.67145281..826... H2: 2,9 # 19 pairs * PAIR G1: 2,9 ROW 1 D1: 2,9,5 # reduction candidate for 2,9 D1: 5 => CTR * 61.5982..2.56718..89743265134826....56914738272138.46.4829537169.67145281..826... D1: 2,9 # 18 pairs * PAIR A4: 3,8 COL A A7: 3,8,2,4 # reduction candidate for 3,8 A7: 3,8 => CTR * 6132589.44956718232.743965134896217.569147382721385469..259.7169.671.2.81.4826.9. A7: 2,4 # 18 pairs * PAIR C4: 3,8 COL C C7: 3,8,2,4 # reduction candidate for 3,8 C7: 3,8 => CTR * 61...8.....56718....2439651.4.962...5691473827213854692..59.7169.671...81..826... C7: 2,4 # 18 pairs * PAIR D4: 2,9 BLK 5 F4: 2,9,5 # reduction candidate for 2,9 F4: 5 => CTR * 61...82..2.56718..897432651348265...569147382721389465482..37169.67145281..826... F4: 2,9 # 21 pairs * PAIR D4: 2,9 COL D D1: 2,9,5 # reduction candidate for 2,9 D1: 5 => CTR * 61.5982..2.56718..89743265134826....56914738272138.46.4829537169.67145281..826... D1: 2,9 # 18 pairs * PAIR F6: 5,9 BLK 5 F4: 5,9,2 # reduction candidate for 5,9 F4: 5,9 => CTR * 61...82..2.56718..89743265134826....56914738272138.46.482..37169.67145281..826... F4: 2 # 15 pairs * PAIR I6: 5,9 BLK 6 G4: 5,9,1 # reduction candidate for 5,9 G4: 5,9 => CTR * 61.59827.2.56718..89.43.651.4..6..1756914738272138.46.....1.7.69.675.1281..826... G4: 1 # 19 pairs I4: 5,9,7 # reduction candidate for 5,9 I4: 5,9 # 23 pairs * PAIR I6: 5,9 COL I I9: 5,9,3,4 # reduction candidate for 5,9 I9: 5,9 # 25 pairs I9: 3,4 # 19 pairs * PAIR B8: 3,5 BLK 7 B7: 3,5,8 # reduction candidate for 3,5 B7: 3,5 => CTR * 61.2589...9567182.287439651.48962175569147382721385469832594716956713248174826593 B7: 8 # 20 pairs B9: 3,5,7 # reduction candidate for 3,5 B9: 3,5 => SOLVED * 613258947495671823872439651348962175569147382721385469284593716956714238137826594 B9: 7 # 20 pairs * PAIR D7: 5,9 BLK 8 E7: 5,9,1 # reduction candidate for 5,9 E7: 1 => CTR * 61..982..2.56718..89743265134826....56914738272138.46.482...7.69.67....81..826... E7: 5,9 # 20 pairs * PAIR D7: 5,9 COL D D1: 5,9,2 # reduction candidate for 5,9 D1: 5,9 => CTR * 61...82..2.56718..8.743265134826....56914738272138.46.482..37169.67145281..826... D1: 2 # 15 pairs * PAIR F7: 3,4 ROW 7 A7: 3,4,2,8 # reduction candidate for 3,4 A7: 3,4 # 22 pairs C7: 3,4,2,8 # reduction candidate for 3,4 C7: 3,4 => SOLVED * 613258947495671823872439651348962175569147382721385469284593716956714238137826594 C7: 2,8 # 18 pairs H7: 3,4,1 # reduction candidate for 3,4 H7: 3,4 => CTR * 61.5982..2.56718..89.43.651.4..6....56914738272138.46.....1.7.69.675...81..826... H7: 1 # 20 pairs * PAIR E8: 1,5 BLK 8 E7: 1,5,9 # reduction candidate for 1,5 E7: 1,5 => CTR * 61..982..2.56718..89743265134826....56914738272138.46.4829537169.67145281..826... E7: 9 # 18 pairs * PAIR E8: 1,5 ROW 8 G8: 1,5,2 # reduction candidate for 1,5 G8: 1,5 => CTR * 61...82..2.56718..8.743265134826....56914738272138.46.482..37169.67145281..826... G8: 2 # 15 pairs * PAIR F8: 3,4 ROW 8 H8: 3,4,1,2 # reduction candidate for 3,4 H8: 1,2 => CTR * 61...8....956718.....439651.4.962...569147382721385469...5937169367145281578269.. H8: 3,4 # 15 pairs * PAIR G9: 5,9 BLK 9 I9: 5,9,3,4 # reduction candidate for 5,9 I9: 5,9 # 25 pairs I9: 3,4 # 19 pairs * PAIR G9: 5,9 COL G G4: 5,9,1 # reduction candidate for 5,9 G4: 5,9 => CTR * 61.59827.2.56718..89.43.651.4..6..1756914738272138.46.....1.7.69.675.1281..826... G4: 1 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060831-absurd-base-pr-000.dot * REASONING * DIS # A2: 2 => CTR => A2: 3,4 * PRF # C7: 3,4 => SOL * DIS # H2: 3,9 => CTR => H2: 2,4 * PRF # C3: 2,8 => SOL * PRF # A7: 2,8 => SOL * DIS # D1: 5,9 => CTR => D1: 2 * DIS # E7: 1 => CTR => E7: 5,9 * DIS # D1: 5 => CTR => D1: 2,9 * DIS # F4: 5 => CTR => F4: 2,9 * DIS # H2: 3,4 => CTR => H2: 2,9 * DIS # D1: 5 => CTR => D1: 2,9 * DIS # A7: 3,8 => CTR => A7: 2,4 * DIS # C7: 3,8 => CTR => C7: 2,4 * DIS # F4: 5 => CTR => F4: 2,9 * DIS # D1: 5 => CTR => D1: 2,9 * DIS # F4: 5,9 => CTR => F4: 2 * DIS # G4: 5,9 => CTR => G4: 1 * DIS # B7: 3,5 => CTR => B7: 8 * PRF # B9: 3,5 => SOL * DIS # E7: 1 => CTR => E7: 5,9 * DIS # D1: 5,9 => CTR => D1: 2 * PRF # C7: 3,4 => SOL * DIS # H7: 3,4 => CTR => H7: 1 * DIS # E7: 1,5 => CTR => E7: 9 * DIS # G8: 1,5 => CTR => G8: 2 * DIS # H8: 1,2 => CTR => H8: 3,4 * DIS # G4: 5,9 => CTR => G4: 1 * CNT 27 HDP CHAINS / 64 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B2,B8,C1,C4,D4,D7,E1,E8,F3,F6,F7,F8,G1,G9,I6) * 61...8.....56718.....43.651.4..6....56914738272138.46.......7.69.67....81..826... * PAIR C1: 3,4 BLK 1 A2: 3,4,2 # reduction candidate for 3,4 A2: 2 => CTR * 614..8...2356718..89743265134826....56914738272138.46.482..37169.67....81..826... * PAIR A3: 2,8 BLK 1 C3: 2,8,7 # reduction candidate for 2,8 C3: 2,8 => SOLVED * 613258947495671823872439651348962175569147382721385469284593716956714238137826594 * DURATION: 0:00:03.347206 START: 02:16:21.906447 END: 02:16:25.253653 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060831-absurd-base-pr-001.dot * REASONING * DIS # A2: 2 => CTR => A2: 3,4 * PRF A2: 3,4 # C3: 2,8 => SOL * STA A2: 3,4 + C3: 2,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060831, absurd
Solution
position: 613258947495671823872439651348962175569147382721385469284593716956714238137826594 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 # A2: 3,4 => UNS * DIS # A2: 2 => CTR => A2: 3,4 * INC # H1: 3,4 => UNS * INC # I1: 3,4 => UNS * PRF # C7: 3,4 => SOL * INC # C7: 2,8 => UNS * INC # C9: 3,4 => UNS * DIS # H2: 3,9 => CTR => H2: 2,4 * INC # H2: 2,4 => UNS * INC # I2: 3,9 => UNS * PRF # C3: 2,8 => SOL * INC # C3: 7 => UNS * PRF # A7: 2,8 => SOL * INC # A7: 3,4 => UNS * DIS # D1: 5,9 => CTR => D1: 2 * INC # D1: 2 => UNS * INC # E7: 5,9 => UNS * DIS # E7: 1 => CTR => E7: 5,9 * INC # D1: 2,9 => UNS * DIS # D1: 5 => CTR => D1: 2,9 * INC # F4: 2,9 => UNS * DIS # F4: 5 => CTR => F4: 2,9 * INC # H2: 2,9 => UNS * DIS # H2: 3,4 => CTR => H2: 2,9 * INC # D1: 2,9 => UNS * DIS # D1: 5 => CTR => D1: 2,9 * DIS # A7: 3,8 => CTR => A7: 2,4 * INC # A7: 2,4 => UNS * DIS # C7: 3,8 => CTR => C7: 2,4 * INC # C7: 2,4 => UNS * INC # F4: 2,9 => UNS * DIS # F4: 5 => CTR => F4: 2,9 * INC # D1: 2,9 => UNS * DIS # D1: 5 => CTR => D1: 2,9 * DIS # F4: 5,9 => CTR => F4: 2 * INC # F4: 2 => UNS * DIS # G4: 5,9 => CTR => G4: 1 * INC # G4: 1 => UNS * INC # I4: 5,9 => UNS * INC # I9: 5,9 => UNS * INC # I9: 3,4 => UNS * DIS # B7: 3,5 => CTR => B7: 8 * INC # B7: 8 => UNS * PRF # B9: 3,5 => SOL * INC # B9: 7 => UNS * INC # E7: 5,9 => UNS * DIS # E7: 1 => CTR => E7: 5,9 * DIS # D1: 5,9 => CTR => D1: 2 * INC # D1: 2 => UNS * INC # A7: 3,4 => UNS * PRF # C7: 3,4 => SOL * INC # C7: 2,8 => UNS * DIS # H7: 3,4 => CTR => H7: 1 * INC # H7: 1 => UNS * DIS # E7: 1,5 => CTR => E7: 9 * INC # E7: 9 => UNS * DIS # G8: 1,5 => CTR => G8: 2 * INC # G8: 2 => UNS * INC # H8: 3,4 => UNS * DIS # H8: 1,2 => CTR => H8: 3,4 * INC # I9: 5,9 => UNS * INC # I9: 3,4 => UNS * DIS # G4: 5,9 => CTR => G4: 1 * INC # G4: 1 => UNS * CNT 64 HDP CHAINS / 64 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 3,4 => UNS * DIS # A2: 2 => CTR => A2: 3,4 * PRF A2: 3,4 # C3: 2,8 => SOL * STA A2: 3,4 + C3: 2,8 * CNT 3 HDP CHAINS / 3 HYP OPENED