Let us take a look at box 1 in the above example. We have pencil marks of 1,2 at R1C1. 1,2,3 at R1C2 and 1,2,3 at R3C2. In a Non-Consecutive sudoku, whenever we have consecutive numbers as pencil marks in a cell, then we can simply remove them from the adjacent cells. For example, if R1C2 was 1, then R1C1 would become 2, and if R1C2 was 2 then R1C1 would be 1. Since either scenario is not allowed in a Non-Consecutive sudoku, we can safely eliminate 1 and 2 from R1C2.
Since we have 3 in R1C2, we can again eliminate 2 from R1C1. so we have 1 at R1C1 and 2 at R3C2.
Now let us look at box 6. We have options of 1,2,7 at R4C7,R5C7 and R6C7. since 1 and 2 are consecutive numbers they will always be separated by the third number. So 7 will always be in R5C7.
