It looks like no one spotted the mistake in the formulation of this problem, which makes the problem incorrectly posed.
"P cm of wire" makes perfect sense, but "S cm²" doesn't. This is because the solution depends on the shape of the piece of paper to be used. Even the shape of the piece of paper is not specified; for example, it's never said that this is a rectangle. It, for example, the input condition was a statement that there the piece of paper was a square, the problem would be correctly formulated. But nothing like that is formulated.
Another way to formulate the problem correctly would be this: suppose that one could buy a piece of paper of unlimited size and shape in a paper shop. A person is supposed to first calculate the "optimal" box size, assuming that the total paper surface should be S cm² and only then order the piece of paper of the required shape in the shop. Maybe this is what was implied, but I could not be sure. The failure to formulate what a shape should be is just the bad logical mistake.
Another little problem is: it is not specified of the wire should remain in one piece or can be cut. Strictly speaking, this is also not obvious. It would just make two different problems; each can be solved separately.
(By the way, there is no such term as "rectangular box". It probably should assume that this is "
cuboid", but only because it's hard to interpret it in any different way. This is a minor problem though.)
The only correct solution would be to dismiss the problem as incorrectly formulated.
Finally, I would like to note that the proof of that some solution is the extremum is not mentioned. Without such proof, such problems have little value. By the way, the problem has nothing to do with programming at all. Some mathematical problems could be considered also algorithmic ones and hence relevant, but not this one.
—SA