RU-ALLRUSSIAN 1965 Problem 10

Given n real numbers $\mathrm{a_1,a_2,\ldots,a_n}$ , prove that you can find n integers $\mathrm{b_1,b_2,\ldots,b_n}$ , such that $\mathrm{|a_i - b_i| < 1}$ and the sum of any subset of the original numbers differs from the sum of the corresponding $\mathrm{b_i}$ by at most $(\mathrm{n} + 1) / 4$ .