The Packing Problem
Whether it’s spheres in a cylinder, presents in a stocking, cars in a parking lot, or potatoes in a pot, the packing problem is a classic mathematical idea rich in application and complexity. Here is a nice little article on it, and just in time for Christmas!
The seminal result in packing is that spheres, packed cannon-ball style, can occupy around 74% of the available space when you pack them in, say, a cylinder. The article summarizes some other interesting experiments involving the packing of other solids (including M&Ms!), but none of them can be packed as efficiently as spheres.
Unfortunately, this probably won’t help you get everything in your sleigh for the trip to Grandma’s house, unless of course every gift you are giving happens to be a platonic solid.