Friday Puzzle #5

29 09 2011

A bottle has diameter of 1 unit.  A box having size 2*2 units can contain four bottles at most.  A box having size 2*3 units can contain six bottles at most. A box having size 2*4 units can contain eight bottles at most. Et cetera…

Is there a box having size 2*N units that can contain more than 2*N bottles? Can you suggest an upper limit for N? Can you compute and prove (or at least justify) a minimum value for N?

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