Superficiality: solution
Is it better for you to stay in one group or to split up into two or more smaller groups? This was a problem faced by naval convoys trying to avoid being found by enemy submarines during World War II, and it was also the problem posed in last issue's Outer Space.
It is better to stay in a big convoy rather than to divide. Suppose that a
big convoy covers an area A and the ships are as close together as
they can be, so that if we divide the convoy into two smaller ones of area
A/2 the spacings between ships are the same. The single convoy has
a perimeter equal to 
but the total perimeter of the two smaller convoys equals 
which is
bigger. So, the total perimeter distance that has to be patrolled by
destroyers to protect the two smaller convoys from being penetrated by
submarines is greater than that to be patrolled if it stays as a single
convoy. Also, when the submarine searches for convoys to attack, its chance
of seeing them is proportional to their diameter, because this is what you
see in the periscope. The diameter of the single circular convoy of area
A is just 
whereas the sum of the two diameters
of the convoys of area A/2 that don't overlap in the field of view
is bigger by a factor of 
and so the divided convoy is more likely to be detected by the attacking submarine than is the single one.
So, a single convoy is harder to detect and easier to defend than a divided one.
