Well, this is a bit of a mess!
Your bathroom has a rectangular floorspace of size $xn$ by $yn$, where $x, y, n$ are all positive integers, and now that you've removed those ghastly yellow and purple tiles, you need to redo the entire floorspace.
You love thin rectangles, so you've ordered a huge batch of 1 by $n$ rectangular tiles, and you're going to use these to tile the entire floorspace (in this highly unrealistic bathroom, apparently toilets, drains, baths and showers don't affect the area you need to tile).
Can you tile your bathroom floor completely without any overla - of course you can, that wouldn't be puzzling at all, would it? In fact, you made quick work of the tiling and have already tiled your bathroom floor.
But you've noticed, that in your tiling, somewhere in your room there is an $n * n$ square which completely contains exactly $n$ tiles of the same orientation.
(Here's an example visual, with $n = 6$.)
You don't like squares, so you try to tile it again without making an $n*n$ square. But you fail. Again and again. You feel like this is a personal attack. From squares.
Now, is it possible to tile your bathroom floor completely, with no overlaps, and no partial tiles, such that there exists no $n*n$ square?