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## IMC 2013 Problem 8

Problem 8. Suppose that ${v_1,..,v_d}$ are unit vectors in ${\Bbb{R}^d}$. Prove that there exists a unit vector ${u}$ such that

$\displaystyle |u\cdot v_i|\leq 1/\sqrt{d}$

for ${i=1,2,..,d}$.