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The problem can be easily solved if you take three educated guesses*:
the solution f(p,q,r) is a polynom in p,q,r (the side lengths)
the polynom is symmetric in p,q,r
the polynom has order 2
then the solution can be expressed for instance as
By inserting some examples, it is elementary to resolve for k,l,m,n.
(*) the guesses are motivated by:
(1,2): the 2-dimensional case has a simple solution of this kind and there is some similarity to Ehrhart polynoms.
(3) intuitivly the growth rate is area-like i.e. of order 2
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Ichigo and Cubes
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The problem can be easily solved if you take three educated guesses*:
then the solution can be expressed for instance as
By inserting some examples, it is elementary to resolve for k,l,m,n.
(*) the guesses are motivated by:
(1,2): the 2-dimensional case has a simple solution of this kind and there is some similarity to Ehrhart polynoms. (3) intuitivly the growth rate is area-like i.e. of order 2