Problem selection hub.

Find integer $n$ with the following property : for all real numbers $a_1, a_2, . . . , a_n$ and $b_1, b_2, . . . , b_n$ satisfying $\left| { a }_{ k } \right| + \left| { b }_{ k } \right| = 1$ for $1 \le k \le n$ there exist $x_1, x_2, . . . , x_n$ , each of which is either $-1$ or $1$ , such that

$\large\ \left| \sum _{ k=1 }^{ n }{ { x }_{ k }{ a }_{ k } } \right| + \left| \sum _{ k=1 }^{ n }{ { x }_{ k }{ b }_{ k } } \right| \le 1$ .