The view-obstruction problem for 5-dimensional cubes

The view-obstruction problem for the n-dimensional cube is equivalent to the conjecture that for any n positive integers v_l.....v_n there is a real number x such that each ∥v_ix∥≥(n + 1)^-1 (here ∥y∥ denotes the distance from y to the nearest integer). This conjecture has been previously solved for n≤4. In this paper we prove that when n = 5 we can find x which gives each ∥v_ix∥≥1/7; this is the first improvement over the easy result ∥v_ix∥≥1/10.