I was deliberately arranging apples in an HCP array, not for fun, but because I wanted to fit as many in the box as possible and they were too big for me to use a cubic packing and get three wide. Moreover, I realized that some of the apples were larger than others, and I thought that, if the size difference were great enough, and I had the proper ratio that maybe a BCC would work out better. Of course this lead to a web search on close packing while eating one of the apples. Suffice to say that either HCP or FCC (or CCP) would pack the best, but since I only have enough apples for 1 layer plus a bit, there is no way to distinguish the two.
I think I need more apples.