Reason at the bottom
Short version: Is it possible, to tile a rectangle with rectangles in a way to keep a non-moveable hole?
Long version: Considering two (fat) rectangles $R_{1}$ ($A\,\times\,B$) and $R_2$ ($C\,\times\,D$), which may or may not be of similar shape;
Is it possible, to tile the larger $R_{1}$, with an integer number $n$ tiles of shape $R_{2}$, in such way, as to leave a hole, which either
A) can not be moved through the tiling at all, or
B) only allowing movement of a single stone a time, and only lengthwhise
?
Additional Data:
The Hole Your pattern may have a single or multiple holes, but should in general be massive (mostly hole-free). (Simply stacking the excluded solution 1. is not intended.) If you use multiple holes they may not be combined to break the rules. Size and shape of the hole are free to choose, but between half the width and two times the length of $R_2$, and square, rectangular or $L$-shaped is probably a good starting point.
Rectangles Both rectangles are fat, meaning their length is at most two times their width (If you find solutions for higher ratios, still feel free to post them) Their sides are not given. They, as well as the (or a) pattern are searched for parts of a solution.
the main goal is to find a pattern with $n$ being at most $200$ less than $50$ would be nice. (If you find solutions for higher numbers, still feel free to post them.)
Excluded Solutions: The following simplex cases are closed. However feel free to use them in a larger solution of your own:
$R_1$ is square and sized $C+k*D$ (thanks to @quarague) (The solution here is a ring with the hole being $D-C$)
The hole can be moved or combined to stretch over a complete side of $R_1$
EDITs:
The question is not if there is any solution, or if there allways is a solution, but to find a non-trivial solution.
The rectangles are ment to be non-square. (Thanks to @Andrei for pointing it out.)
Reason: (Added as sort of explanation) Consider filling a box with packages. You want to fill the box to the brim. However you want to be able to retrieve each package, one after another. During the ransport, it should not rattle: There is to be no space left. A tight packing, spare for one hole, where to start pulling the packages out. If possible, there should be no way of moving the hole, as to not allow rattling. However, as there might be fairly few solutions for this, there are two loopholes provided:
there might be more than one hole, provided it is still a rather tight packing
a single package may slide, in one direction to fill the hole and open it somewhere else. Just one though, and only along its length, as otherwhise the packing could start to loosen and rattle again.
I know of tiling rectangles with $2\times 1$-rectangles with a single, or fairly few holes, the question is can one do this with fat rectangles too, and could one achieve non-moveable holes with it.