Daily Archives: April 19, 2016

Cross Diagonal Cover – II

Standard

I will continue the previous post. Now the question to  be answered is that:

What percentage (or how many) of given m\times n grid can be covered by following Cross Diagonal Cover Algorithm?

I did some calculations, for example:

 

New Doc 16_1

As per my calculations, I have following conjecture:

The following 3 cases are possible:

  1. If m = n, then m squares will be covered.
  2. If m>n and both m,n are odd, then m squares will be covered.
  3. If at least one of m,n is even then \frac{mn}{2} squares will be covered.

As you can see that Case – 1 is quite trivial. I tried to prove other two cases for one week, but failed, so decided to post it as conjecture.