5. Six children are evenly spaced around a circular table. Initially, one has a pile
of n > 0 sweets in front of them, and the others have nothing. If a child has
at least four sweets in front of them, they may perform the following move:
eat one sweet and give one sweet to each of their immediate neighbours and
to the child directly opposite them. An arrangement is called perfect if there
is a sequence of moves which results in each child having the same number
of sweets in front of them. For which values of n is the initial arrangement
perfect?
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