Balanced Eggs (in an Egg Box / Egg Carton)

Warning: Utterly pointless. Possibly fun. My favourite egg carton (egg box) is the one which has a capacity of fifteen eggs (3 eggs by 5 eggs). If you take eggs from one side of an egg box, then the weight in the egg box is not distributed equally across the whole box, meaning it is unstable when you pick it up. An added problem is that if it's a cardboard egg box, then you can't see the egg distribution to know whether it's centre of gravity is in the central. We of course need balanced eggs! With a 2 x 3 egg box, you can't distribute the eggs evenly for all possible numbers of eggs (i.e. you can have 1, 2, 3, 4, 5 or 6 eggs in such a box, but only 2, 4 and 6 can be distributed evenly. The reason I like a 3 x 5 egg box, is that for every total number of eggs (from 1 to...
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