You have an old-fashioned refrigerator with a small freezer compartment capable of holding seven ice cube trays stacked vertically. But there are no shelves to separate the trays, and if you stack one tray on top of another before the ice cubes in the bottom tray are fully frozen, the top tray will nestle into it, and you won't get full cubes in the bottom tray. You have an unlimited supply of trays, each of which can make a dozen cubes.
What's the fastest way to make full-sized ice cubes?
I think you need to stack them like a pyramid, that way you'd be able to put 28 trays in there (if I did my math right), giving you 336 ice cubes.