**The question:**

> 
> A *rectangular fence* is a set of 4 cells on a solved sudoku grid with
>  co-ordinates $(i,j)$, $(m,j)$, $(m,n)$ and $(i,n)$. You can visualize
>  this as the 4 corners of a rectangle.
> 
> 
> A *symmetric rectangular fence* is a rectangular fence where opposite
>  corners hold the same value. Meaning $grid(i,j)=grid(m,n)$ and
>  $grid(m,j)=grid(i,n)$
> 
> 
> Make a 9x9 completely-filled sudoku that has a minimum number of symmetric rectangular fences.
> 
> 
> 

**Why I asked?**

I have been trying to prove that there exists no 16-hint solvable sudoku. I realized that if there exists a symmetric rectangular fence (as I have termed it), then it becomes necessary to give at least one of the 4 cells as a hint. So, minimizing the number of such occurences would make it possible to create lesser-hint sudoku's and maybe throw some light on why 17 hints are still required.

For puzzlers, the question in section 1 is complete by itself; you need not bother about the rest. You may use a program to find the answer, but there are many, many possibilities, so you will still have to use some logical approach to it.