Summary:  We consider the problem of finding a position of a <i>d</i>dimensional box with given edge lengths that maximizes the number of enclosed points of the given finite set <inlineformula> <math display="inline"> <semantics> <mrow> <mi>P</mi> <mo>⊂</mo> <msup> <mi mathvariant="doublestruck">R</mi> <mi>d</mi> </msup> </mrow> </semantics> </math> </inlineformula>, i.e., the problem of optimal box positioning. We prove that while this problem is polynomial for fixed values of <i>d</i>, it is NPhard in the general case. The proof is based on a polynomial reduction technique applied to the considered problem and the 3CNF satisfiability problem.
