Sorry, I don't know how to search this.
I hope it is not a double post. Also, I didn't know where to put it. I think this is the best place.

I saw this in TV once. Back then TiVo didn't exist. So, I taped it. I saw it over and figured it out. But, I don't remember how the trick goes any more.

Ok, enough mystery, this is what I need help on:

There is a set of squares (could be pictures, or round bottle-caps, whatever)

[] [] [] [] [] []
[] [] [] [] [] []
[] [] [] [] [] []
[] [] [] [] [] []
[] [] [] [] [] []
[] [] [] [] [] []

The audience is asked to choose any square. Now, move in either direction so many spaces. Then, a set of squares are removed:

[] [] [] [] [] []
[] [] [] [] []
[] [] [] [] []
[] [] [] [] [] []
[] [] [] [] [] []
[] [] [] [] []

This pattern continues until there is only one:

[]

What is the pattern?

I'm not sure this is exactly what you're looking for since it uses a 3 X 3 matrix and your diagram shows a 6 X 6. Actually your description wouldn't work with your diagram since there 36 squares in your matrix- if you remove the squares in sets of 2 then you'll either be left with 2 squares or zero squares- never just one.

But it's been published (and sold) in many versions. The first one I ever saw was sold by Tannen's in the 1970's under the name Room For Doubt. Copperfield used it to have a train car selected in one of his specials. The Magic Hands in Germany used to sell one using coins and a gambling theme.

Simon Aronson covers it in Simply Simon (Moves and Removes). While he refers you to Martin Gardner Presents for a more extensive description and history, he does give a brief explanation of the principle which you could apply to other matrices (although I'm not sure it would work with 6 X 6).