Today we will look at a solving technique for tackling the Anti-Knight Sudoku. To demonstrate that, I am using the Antiknight-Non-consecutive puzzle that I had displayed earlier on my blog.
I have updated the pencil marks for the grid. Now let us look at the possibilities for number 8 in Box 5. When we look at it, we see that the possibilities for number 8 forms an L shape, marked by the orange lines.
Now, let us draw a reverse L shape extending to 2 cells on either side from the junction point of the original L shape. This new reverse L shape is marked by green lines in the next image.
Since the number 8 has to be in one of the 3 cells in the original orange colored L, it can NEVER exist at the ends of the green L (R2C4 and R4C2 ). Hence the possibility of number 8 can be removed from these 2 cells.
Now you may wonder why this holds true, so let me go further and explain. Let us take R4C2 for example. now if 8 was in R4C4 or R4C5, then it is in the same row and automatically 8 gets eliminated from R4C2. And if 8 was in R5C4 then it is eliminated again from R4C2 since it is at a knights step. so irrespective of where 8 comes in the original orange L shape, it cannot be at R4C2. similarly it also holds true for R2C4. So we can safely remove 8 from R4C2 and place a 9 there.
This is always true for any L shape, however please remember that this L shape rule is true only and only if the other cells in that box (box 5 in this example ) do not contain a possibility of the number 8.