A General Logic for Sudoku

Golden Nugget

Elimination 10

Although it is not difficult to trace the logic and prove the elimination, set logic provides an easier way.  If 286 = 1 then r2c3<>6. If 6r2c8 is true then both 7r2c6 and 7r4c7 are true and both are linkset triplets. When they are occupied the global rank must be 1 and the candidate is eliminated by the overlap of linksets 6r2 and 2n3. The set logic is:

rank 3: S10={7r3 247r4 24c3 2n8 7b179},

L13={6r2 7r8 7c1678 1n3 2n3 4n78 7b3 24b4}

=> (6r2*2n3) => r2c3<>6

Logic Diagram

Below is a logic diagram for elimination 10. Triplets appear horizontally in two vertical linkset columns along with a unique letter designation, e.g., A, B, C. If 6r2c8 is occupied then 6r2c3 candidate is eliminated, otherwise triplets 7r2c8 and 7r4c7 (red) will both be occupied, which also leads to the elimination of the candidate by a rank 1 structure.

p412==p472==p482                                                              rank -1

 |     |     |                                                                R2

 |    p474==p484==p424                                                       

 |     |     |     |                                                          R2

p632===|=====|=====|====p132==p232                                            

       |     |     |     |     |                                              R3

       |     |    p534==p134==p234                                           

       |     |           |     |                                              R2

       |     |          p137==p237==p117                                     

       |     |                 .     |                                        R2

       |     |                 .    p817E=p817E                               

       |     |                 .    p717  p837                               

       |     |                 .           |                                  R1

       |     |                 .          p887F=======p777==p887F            

       |     |                 .          p897         |     |               

       |     |                 .                       |     |                R2

      p477C=p487D===============================p467==p477C=p487D            

                               .                 |           |                R3

                               .                p367========p387B=p387B      

                               .                             |    p397       

                               .                             |     |          R2

                            (6r2c3)- - - - - - - - - -p286=p287A=p287A 

                                                                              R3