I want to explain the exact cover problem to my colleagues who don't have any mathematical background as such. I want to explain them where it can be used and how? So my question goes like this: How can I explain the exact cover problem to someone who don't have a mathematical background or rather to children and make it more interesting and intuitive? With this I also want to explain the concept of P-NP (in general) as well.
I think a good analogy here is a puzzle.
Let's say there is a square on the floor you want to cover, but instead of having the regular setup where you have the exact amount and shapes to cover it once and they all fit in a certain way, you have enough pieces to cover it many times.
The problem is to find a bunch of pieces that:
A. They all fit together (no overlaps, no gaps).
B. They cover the right surface area (the square you have).