The View-Obstruction Problem forn-Dimensional Cubes Original Research Article

The view-obstruction problem for then-dimensional cube is equivalent to the conjecture that for anynpositive integersv1, …, vnthere is a real numberxsuch that each double vertical barvixdouble vertical bargreater-or-equal, slanted(n+1)−1(here double vertical barydouble vertical bar denotes the distance fromyto the nearest integer). This conjecture has been previously solved fornless-than-or-equals, slant4. In this paper we prove that when 2n−3 is a prime andngreater-or-equal, slanted4 we can find a real numberxwhich gives each double vertical barvixdouble vertical bargreater-or-equal, slanted1/(2n−3). In fact more than this is proved.