There is a centipede residing in one of our litter boxes (thankfully one that sees little use). It has been there for a couple of days so far. Is there a reason it might be drawn to our cat litter and not our ant infestation? 
The walls of the litter box are probably slick. It may be stuck in there after incautiously exploring. I get these stuck in my bathtub and sinks that way.
needs a centipede ladder. A twig hooked over the edge would be fine.
Loved the thread title, but it raised a rather different expectation than the ensuing content 
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Arthropods in general tend to have difficulty with smooth-sided human artifacts such as sinks and bathtubs.