'splain this one

I was emptying out the dishwasher this morning and pulled out half a plate. Yep, broken right down the middle. I'm thinking, okay, the plate crashed against another one in the washer or broke when someone was putting it in, I can deal. But, when I went to take the other half out of the dishwasher so it could join its twin in the garbage, I discovered there was none. The half plate was the only half there, and I couldn't find it any place else either. Of course, the inhabitants of this household all plead ignorance and claim they have no idea how/where/why there was half a broken plate in the dishwasher. Later this afternoon I stepped on a tiny shard of, what looked like, remnants of a broken plate and did that little jumpy dance you do when pain is shooting through the ball of your foot until I could pull the glass out. This brings me to the hypothesis that the plate was broken in the general area of the kitchen peninsula counter, but no closer to the culprit. Life's full of little mysteries.