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 will make the non implicit assumption that each tray is of indentical n x 2 rectangular dimension and n > 1. Begin by filling four of the trays with water and seperating them using three upsidedown trays, 8n cubes will be produced. This much is obvious but there is a trick to now producing additional cubes. Now empty the trays, By my assumption you will then have enough cubes now to stick 2 in alternating diagonal corners of each of six empty trays. Do this, fill up all the remaining holes of these 6 trays with water and put it back in the freezer with a seventh tray entirely filled with water at the top. This will produce 14n-12 cubes. Utilizing this process is your most efficient method of cube production under the current scenario. So after c freezing cycles you will have 8n +(c-1)*(14n-12) cubes.
Right Answer
